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Eureka / EngageNY Math (Free) Squared ($300k)

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Eureka / EngageNY Math (Free) Squared ($300k)

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EngageNY provides opportunities for students to explain and justify their work, and that it addresses conceptual understanding, procedural skills, and application to real-life contexts with equal time and intensity.
Eureka stole or bought EngageNY Resources and now sells it as Math Squared.  Original EngageNY Resources can be found at: http://www.nysed.gov/curriculum-instruction/engageny.
Gary Rubenstein reviewed Eureka as flawed and boring: https://garyrubinstein.wordpress.com/2015/05/19/you-reeka-math/ (e.g. Mistakes in Exponents raises negative numbers to exponents without parenthesis, Boring Pythagorean proof uses algebraic proof.)
EdWeek reviewed Eureka as the most CCSS aligned.

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Thoughtfully constructed and designed like a story, Eureka Math is meticulously coherent, with an intense focus on key concepts that layer over time, creating enduring knowledge. Students gain a complete body of math knowledge, not just a discrete set of skills. They use the same models and problem-solving methods from grade to grade, so math concepts stay with them, year after year.

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Eureka Math® - Elementary and Middle School Math Curriculum

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Learn about Eureka Math®, an elementary and middle school math curriculum from Great Minds® sequencing mathematical progressions into expertly crafted modules.

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OERCommons - Source of OER Mathematics Curriculum

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OERCommons - Source of OER Mathematics Curriculum

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Create a standalone learning module, lesson, assignment, assessment or activity

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An Introduction to US Standard Units

Also known as "English Units" or "US Customary Units"

Wow, I just flew in from planet Micron. It was a long flight, but well worth it to get to spend time with you!

My name is Maggie in your language (but you couldn't pronounce my real name!)

When I first arrived I couldn't understand how you measure things, but my friend Tom taught me all about measurement, and I am going to share with you everything he taught me.

The first thing Tom told me was that you can measure things using two different systems: US Standard Units and Metric.

Today is my day to learn US Standard Units !

Liquids

The first thing I need to know when asking for a drink is the types of units used to measure liquids, which are:

Fluid Ounces (oz) are small.

Then Tom showed me a small carton, and told me it held 8 fluid ounces, which is also called 1 cup. But I wanted more!

(Tom also told me that I can measure things using measuring cups)

So now I know that 1 ounce is too small for me, but 1 gallon is too much. I think I will ask for a pint of juice!

Final thoughts about measuring liquids:
1 Gallon = 4 quarts = 8 pints = 16 cups= 128 fluid ounces
Mass (Weight)

Next I wanted to eat some chocolate ... so I should learn about mass. You often call it "weight", but it is only because of the gravity on your planet that items have weight!

Tom says I need to know:

Tom says:

If you mean an ounce of fluid say "fluid ounce" ("fl oz")
Otherwise ounce usually means mass.

So we are not talking about fluids! I already had a drink. I need to know about mass.

But when you add up the ounces you get a new label for mass:

1 pound = 16 ounces

But if something weighs many pounds we use yet another label

1 ton = 2,000 pounds

So now I know that 1 ounce of chocolate is too small for me, but 1 ton is way too much. I think I will ask for a pound of chocolate!

Final thoughts about mass:

1 Ton = 2,000 pounds = 32,000 ounces

Length

The last kind of measurement we will explore is length. This is important for lots of different reasons. Measurement of length helps you to know how far you have traveled, how far you have left to travel, how tall you are and many other things.

I need to know about:

Lots of things are measured in inches from rainfall to paper length.

Measuring in inches gives us a way for everyone to understand the size of something.

When we have 12 inches together, it is known as a foot.

1 foot = 12 inches

A long time ago, people used their feet to measure things. But everyone has different sized feet so it did not work very well.

Using 12 inches put together to make one foot lets everyone have an accurate picture of what exactly a "foot" of length is.

When 3 feet are together, this is called a yard. (This isn't the same thing as a lawn, though they are both referred to as a "yard"!)

1 yard = 3 feet

The length of this guitar is about 1 yard.

When you put together 1,760 yards, you have a mile.

1 mile = 1,760 yards = 5,280 feet

Miles are long distances and are mostly used to measure the distance between places which are far away from each other. Most people refer to miles when they are driving, biking or jogging.

Final thoughts about measuring length:

1 foot = 12 inches
1 yard = 3 feet = 36 inches 1 mile = 1,760 yards = 5,280 feet = 63,360 inches
Temperature

I was feeling a bit hot, so I asked Tom how to measure temperature.

So he showed me a thermometer. But I saw 2 sets of numbers!

Tom explained that a thermometer measures in degrees (°) of either Celsius or Fahrenheit.
"Why two scales?", I asked. Tom said that some people like one scale and some like the other, and that I should learn both!
He then gave me an example: when water freezes the thermometer shows:

0 degrees Celsius on the left side,

but on the right side it shows 32 degrees Fahrenheit.

Two numbers for the same thing!

He gave me more examples.

A hot sunny day with a temperature of 30 degrees Celsius is 86 degrees in Fahrenheit.

Water boils at 100 degrees Celsius or 212 degrees Fahrenheit.

And you can bake cookies in your oven at a temperature of 180 degrees Celsius, which is 356 degrees Fahrenheit.

I decided to get my own thermometer, so I can learn all about this.

Bye for Now!

Now I must return home.

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Wow, I just flew in from planet Micron. It was a long flight, but well worth it to get to spend time with you! My name is Maggie in your language (but you couldn't pronounce my real name!)

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What is Mathematics and Why does it Matter?

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What is Mathematics and Why does it Matter?

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1.1 Day 1 AO - What is Mathematics and Why Does It Matter

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1 Experience - What is Middle School Mathematics

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Use teacher account or click on student or family.

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Two Pathways to Foster Deep, Conceptual Understanding

The high school math curriculum, authored by Mathematics Vision Project (MVP), is a complete three-year high school curriculum available in a traditional and integrated pathway. Each pathway includes an intentional lesson design that gives students ownership of their learning and connects math to real-world contexts.

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High School Math Curriculum | Online Math Curriculum

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The high school math curriculum, authored by Mathematics Vision Project (MVP), is a complete three-year high school curriculum available in a traditional and integrated pathway. Each pathway includes an intentional lesson design that gives students ownership of their learning and connects math to real-world contexts.

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i-Ready Learning Materials and Assessments

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i-Ready Learning Materials and Assessments

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From Curriculum Associates

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i-Ready Learning is a collection of high-quality instructional resources that help students learn and grow by accessing grade-level materials. Grounded in best-practice instructional design, these tools provide rigorous and motivating reading and mathematics instruction that:

Engages students of all levels and backgrounds

Motivates students to persist in skill building

Provides scaffolded support that meets the needs of all students

Creates personal learning pathways for each student in i-Ready Personalized Instruction

Connects to i-Ready Diagnostic data so teachers can make informed teaching decisions

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i-Ready Learning | Instructional Resources for K-8

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i-Ready Learning's instructional resources help educators engage students and accelerate growth.

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OpenStax | Free Textbooks Online with No Catch

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OpenStax offers free college textbooks for all types of students, making education accessible & affordable for everyone. Browse our list of available subjects!

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A series of mathematics workbooks that enables learners to explore at their own pace subjects through their variations and outliers.

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The 7-book Algebra 1 Series is designed for self-paced learning. Subscribe to videos to access step-by-step guidance through scenarios in each of the 7 books in the series.

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About BSMART - The Brooklyn School for Math and Research

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On September 7, 2011, the Brooklyn School for Math and Research opened its door for the first time in the Bushwick neighborhood of Brooklyn, NY. On that day, 42 students and their families took a leap of faith on nothing more than a vision. The vision of Dr. Perry C. Rainey, the founding Principal o…

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Kinda dated - most are better offered through DESMOS or Nearpod, but still a good place to check for simulations.

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By converting our sims to HTML5, we make them seamlessly available across platforms and devices. Whether you have laptops, iPads, chromebooks, or BYOD, your favorite PhET sims are always right at your fingertips.Become part of our mission today, and transform the learning experiences of students everywhere!

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The Mathematicians Project - Source of Mathematicians Listings

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The Mathematicians Project - Source of Mathematicians Listings

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This was the original blog post. I'm no longer updating this page, but absolutely still updating the list. The most up to date list is here. Resource list here.

The Short Version:

We as math teachers tend to only talk about white male mathematicians.

Most of my students don't look like that, and thus, they have few mathematical role models they can identify with.

Take 10-15 minutes a week to research (read Wikipedia, that's all you need) a not-old-dead-white-dude mathematician, and then take 5 minutes in class to tell your students about them. Include a picture. It's worth it, I swear.

Here is the presentation from NCTM Regionals in Chicago
Here is a SEARCHABLE SPREADSHEET LIST of mathematicians
Explanatory Blogs

I've blogged at MTMS about this project in far more detail than I have here. Check out those four posts below.
Post #1 The Mathematician Project Post #2 How to Enact the Mathematician Project Post #3 What I Learned About My Students Post #4 Extensions of the Mathematician Project
For the super excited, you can read the paper I wrote about the project below.
Mathematicians Paper
List of Mathematicians (Or use this spreadsheet)
Men (alphabetical by last name) Women (alphabetical by last name)
This book is a great resource for many of these women.
Trans Mathematicians FYI, I should say that I cringed to use the labels "Men" and "Women" because of a former student who has graciously educated me more about transgender and non-binary people, but I recognize that those labels are still helpful as categories.
General Resources for Researching Mathematicians
Lego NASA Women Women of NASA to be Immortilized in Lego Form Biographies of Women Mathematicians Black Heroes of Mathematics Black Mathematical Excellence Grandma Got STEM Intersections - Poetry and Mathematics Math Mentoring Project Mathematically Gifted and Black
Mathematicians of the African Diaspora (h/t Keith Devlin)
Macarthur Fellows
Mathematicians Born/Died on this Day This has a huge number of mathematicians. You'll have to seek a bit for the non-white-male ones, but you can look at the Birthplace Index to help out. (h/t Andrew Thomas)

Math History Course Notes courtesy of commenter below. Includes Sophie Germain.
"On Being a Black Female Math Whiz During the Space Race" NYTimes
Beyond Banneker: Black Mathematicians and the Paths to Excellence by Erica N Walker
African American Registry Mathematicians of the African Diaspora Special Articles
I have no good visuals for this project. The best I've got is this map that 1) Is scaled to accurately represent area 2) Gets pins for the location of each mathematician we introduce to class.

I also have added a Hidden Figures poster with tags on each of the women.

Each of which I like and students enjoy. But Brian (on twitter @_b_p and blogging at https://lazyocho.com/) has made some excellent printable posters to put up and he's been kind enough to share them here! What a nice guy!
Beyond_White_Dudes_Mathematicians

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The Mathematicians Project: Mathematicians Are Not Just White Dudes

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This was the original blog post. I'm no longer updating this page, but absolutely still updating the list. The most up to date list is here. Resource list here. What is the Mathematicians Project? The Short Version: We as math teachers tend to only talk about white male mathematicians.

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Wow - a wonderful resource for elementary mathematics. I have not had the chance to peruse for high school, but used these resources extensively for my elementary and middle school math club.

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Sixth Math Worksheets | Teachers Pay Teachers

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Browse resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources.

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Algebra 1 Curriculum.  https://im.kendallhunt.com/HS/teachers/1/index.html

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Dr. Hung-Hsi Wu, Professor Emeritus, Berkeley Math

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All Resources | Expert Interview

Sign in to share, email, rate, comment or favorite.

Dr. Hung-Hsi Wu discusses the topics of school algebra and their importance for student learning. He explains each of these foundational topics and provides examples, describes the connections across topics, and talks about some common difficulties that teachers have in learning and teaching algebra.

Dr. Wu served as a member of the National Mathematics Advisory Panel and was part of the Conceptual Knowledge and Skills and Teachers and Teacher Education Task Groups.

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All Resources | Expert Interview Sign in to share, email, rate, comment or favorite. Dr. Hung-Hsi Wu discusses the topics of school algebra and their importance for student learning. He explains each of these foundational topics and provides examples, describes the connections across topics, and talks about some common difficulties that teachers have in learning and teaching algebra.

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A coherent framework of the mathematics that I learned in elementary and middle school.

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Building Upon It - My Mathematics Reference Framework

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Building Upon It - My Mathematics Reference Framework

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Applications of Universal Design in Primary and Secondary Education | DO-IT

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scald=2850:sdl_editor_representation {"link":""}] Applying universal design within the precollege setting ensures that all students and teachers, including those with disabilities, can fully participate in all educational offerings.

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Peter Liljedahl

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Building Thinking ClassroomsÂ [pptx]

Virginia Commonwealth University (Sept 18, 2020)

Building Thinking ClassroomsÂ [pptx]

ERLC, Edmonton (March 6, 2020)

Building Thinking ClassroomsÂ [pptx]

Video of Thinking Class [Twitter]

SD#74 + SD#58, Merritt (Feb 21, 2020)

Blank Rubric [docx]

Outcomes-based Assessment [pptx]

4Â Purposes of Assessment - article [pdf]

TIE-BC Conference, Richmond (Feb 20, 2020)

Building Thinking ClassroomsÂ [pptx]

Video of Thinking Class [Twitter]

Alberta Conference Teacher Convention, Lacombe (Feb 19, 2020)

Building Thinking ClassroomsÂ [pptx]

Video of Thinking Class [Twitter]

NRLC, Grande Prairie (Jan 23, 2020)

ISOMA Conference, Toronto (Jan 16, 2020)

Building Thinking ClassroomsÂ [pptx]

Video of Thinking Class [Twitter]

Winnipeg School Board (Jan 8-10, 2020)

Archived Presentations

NRLC, Grande Prairie (Dec 11, 2019)

SAPDC, Medicine Hat (Dec 10, 2019)

SAPDC, Lethbridge (Dec 9, 2019)

Novemberkonferansen, Trondheim, Norway (Nov 26-27, 2019)

Sudbury Catholic School Board (Nov 15-16, 2019)

South Surrey Math Teachers Association (Nov 6, 2019)

SD#74 + SD#58, Ashcroft (Nov 5, 2019)

Prairie Spirit School Division, Warman, Sask. (Oct 31-Nov 1, 2019)

Living Sky School Division, North Battleford, Sask. (Oct 30, 2019)

Prairie South School Division, Moose Jaw, Sask. (Oct 29, 2019)

BCAMT Conference, Surrey (Oct 25, 2019)

Pembina Trails School Division, Winnipeg (Oct 23-24, 2019)

Halton Catholic District School Board, OakvilleÂ (Oct 18, 2019)

Sudbury Catholic School Board (Oct 16-17, 2019)

Numeracy Performance Tasks, Victoria (Oct 10, 2019)

SD#74 + SD#58, Ashcroft (Oct 8, 2019)

Prairie South School Division, Moose Jaw, Saskatchewan (Oct 4, 2019)

Prairie Spirit School Division, Warman, Saskatchewan (Oct 3, 2019)

Living Sky School Division, North Battleford, Saskatchewan (Oct 2, 2019)

Warman, Saskatchewan (Oct 1, 2019)

Warman, Saskatchewan (Sept 30, 2019)

Kootenay Lake School District, Nelson (Sept 20, 2019)

Kootenay-Columbia School District, Trail (Sept 19, 2019)

Winnipeg School Board (Sept 11-13, 2019)

Manitoba Rural Learning Consortium, (mRLC), Portage la Prairie (Sept 10, 2019)

Matematikvejlederkonference, Odense, Denmark (Sept 5, 2019)

Kootenay-Columbia School District, Trail (Aug 29, 2019)

Boundary School District, Grand Forks (Aug 28, 2019)

Comox Valley School District, Comox (Aug 27, 2019)

The International Group for the Psychology of Mathematics Education (PME), Pretoria, South Africa (July 6-12, 2019)

SzkoÅ‚a Edukacji, Uniwersytetu Warszawskiego, Warsaw, Poland (June 26-27, 2019)

University of Iceland, Reykjavik (June 19-20, 2019)

Thames ValleyÂ District School Board, London (June 10-13, 2019)

Halton Catholic District School Board, Oakville (June 7-11, 2019)

SzkoÅ‚a Edukacji, Uniwersytetu Warszawskiego, Warsaw, Poland (April 13-15, 2019)

Technion - Israel Institute of Technology, Haifa (April 17, 2019)

Levinski College, Tel Aviv, Israel (April 15, 2019)

SzkoÅ‚a Edukacji, Uniwersytetu Warszawskiego, Warsaw, Poland (March 25-27, 2019)

UniversitÃ degli Studi di Salerno, Italy (March 19, 2019)

University of Naples Federico II, Italy (March 15, 22, 29, 2019)

Greater EdmontonÂ Teachers' Convention, Edmonton (March 1, 2019)

Margaret Sinclair Talk, Fields Institute, Toronto (Feb 23, 2019)

Thinking about Thinking Classrooms [pptx]

Vernon School District, Vernon (Feb 22, 2019)

Jenny's Assessment [pptx]

Lynden School Districts (Feb 19-20, 2019)

Problems Worth Solving - grade 8 (with links to Ontario curriculum) [docx]

Pruner's Math tasks [pdf]

Good Problems

Jenny's Assessment [pptx]

Prairie Spirit School Division + Friends, Martensville,Â SaskatchewanÂ (Feb 15, 2019)

NRLC, Grande Prairie (Feb 12-14, 2019)

Congress of the European Researchers of Mathematics Education, Utrecht, Netherlands (Feb 6-10, 2019)

Work done by TWG 8 in the previous CERME: The past, the present
and the future [pptx]

Beliefs about Becoming Researchers [pptx]

Surrey Association of Mathematics Teachers (Jan 30, 2019)

Prairie Spirit School Division + Friends, Warman, Saskatchewan (Jan 18, 2019)

NRLC, Grande Prairie (Jan 15-17, 2019)

St. Albert Public School District (Jan 14, 2019)

ASCD Mannitoba, Winnipeg (Jan 10, 2019)

Winnipeg School District (Jan 9-11, 2019)

Bellingham-Lynden-Sedro Woolley School Districts, Bellingham (Jan 8, 2019)

Problems Worth Solving - grade 8 (with links to Ontario curriculum) [docx]

Pruner's Math tasks [pdf]

Good Problems

Langley School District (Jan 7, 2019)

UBC Faculty of Education (Jan 7, 2019)

Instytut Matematyki,Â Uniwersytet Pedagogiczny w Krakowie, KrakÃ³w, Poland (Dec 13-14, 2018)

Building Thinking ClassroomsÂ [pdf |Â pptx]

Mathematicians on Creativity [book | pptx]

SzkoÅ‚a Edukacji, Uniwersytetu Warszawskiego, Warsaw, Poland (Dec 10-11, 2018)

Sudbury Catholic School Board (Dec 6-7, 2018)

Conseil des Ã©coles publiques de l'Est de l'Ontario, Ottawa (Dec 3-5, 2018)

NCTM Regional Conference, Seattle (Nov 28-30, 2018)

Langley School District (Nov 26, 2018)

St. Benedict Catholic Secondary School, Waterloo (Nov 23, 2018)

Building Thinking Classrooms [pptx]

Noticing Thinking Classroom Practices [pptx]

Problems Worth Solving - grade 8 (with links to Ontario curriculum) [docx]

York Regional District School Board, Toronto (Nov 19-22, 2018)

Jenny's Assessment [pptx]

Myth of Objectivity [pdf]

Problems Worth Solving - grade 8 (with links to Ontario curriculum) [docx]

Waterloo Catholic District School Board (Nov 16, 2018)

Building Thinking Classrooms [pptx]

Hastings and Prince Edward District School Board, Belleville (Nov 13-15, 2018)

Building Thinking Classrooms [pptx]

Problems Worth Solving - grade 8 (with links to Ontario curriculum) [docx]

Jenny's Assessment [pptx]

QSLMA Mini Connect 2018, Kingston (Nov 12, 2018)

Building Thinking Classrooms - system theory [pptx]

Limestone District School Board, Kingston (Nov 12, 2018)

Building Thinking Classrooms [pptx]

Vernon School District, Vernon (Nov 8, 2018)

Building Thinking Classrooms [pptx]

NRLC, Grande Prairie (Nov 5-7, 2018)

NCTM Regional Conference, Kansas City (Nov 3, 2018)

Thames Valley District School Board, London (Oct 31, 2018)

Sudbury Catholic School Board (Oct 29-30, 2018)

Jenny's Assessment [pptx]

York Regional District School Board, Toronto (Oct 23-27, 2018)

Conseil des Ã©coles publiques de l'Est de l'Ontario, Ottawa (Oct 22, 2018)

Building Thinking ClassroomsÂ [pptx]

St. James-Assiniboia School Division,Â Winnipeg (Oct 15-17, 2018)

Bellingham-Lynden-Sedro Woolley school Districts, Bellingham (Oct 4-5, 2018)

Kamloops School District (Oct 2, 2018)Â

Jenny's Assessment [pptx]

Langley School District (Oct 1, 2018)

Renfrew County District School Board, Pembroke (Sept 24+28, 2018)

Conseil des Ã©coles publiques de l'Est de l'Ontario, Ottawa (Sept 25-27, 2018)

Peel District School Board, Mississauga (Sept 20, 2018)

Building Thinking ClassroomsÂ [pptx]

Halton Catholic District School Board, Oakville (Sept 20-21, 2018)

Sudbury Catholic School Board (Sept 18-19, 2018)

Building Thinking ClassroomsÂ [pptx]

Thames Valley District School Board, London (Sept 17, 2018)

Prairie Spirit School Division, Warman (Sept 12-13, 2018)

Winnipeg School District (Sept 10-11, 2018)

Kootenay School District, Nelson (Sept 7, 2018)

Halton District School Board, Burlington (Aug 30, 2018)

King's Christian Collegiate, Oakville (Aug 28-29, 2018)

BC School Superintendents Association (BCSSA), Kelowna (Aug 15-16, 2018)

York Regional District School Board, Toronto (Aug 13-14, 2018)

PCMI, Park City, USA (July 17, 2018)

Halton Catholic District School Board, Oakville (June 19, 2018)

Sudbury Catholic School Board (June 18, 2018)

Southeast Kootenay and Rocky Mountain School Districts, St. Eugene Mission (June 14, 2018)

Collingwood School, West Vancouver (June 11, 2018)

Jenny's Assessment [pptx]

York Regional District School Board, Toronto (May 23-24, 2018)

Thames Valley District School Board, London (May 22, 2018)

Vernon Teachersâ€™ Association Professional Day (May 18, 2018)

Mission School District (May 14, 2018)

Learning Together Conference, SFU (May 12, 2018)

Writing for Publication [pptx]

Innovation in Education: Cmolik Engagement Series, Kelowna (May 10, 2018)

Building Thinking Classrooms [pptx]

Ontario Association of Mathematics Educators (OAME), Toronto (May 3-4, 2018)

York Regional District School Board, Toronto (May 1-2, 2018)

Thames Valley District School Board, London (April 30, 2018)

Hanover School District, Steinbach (April 25, 2018)

Mission School District (April 23, 2018)

Building Thinking Classrooms [pptx]

NRLC, Grande Prairie (April 17-20, 2018)

Conseil des Ã©coles publiques de l'Est de l'Ontario, Ottawa (March 20-22, 2018)

West Point Gray Academy, Vancouver (March 12, 2018)

Lynden and Bellingham School Districts (March 7, 2018)

Building Thinking Classrooms [pptx]

Winnipeg School District (March 1-2, 2018)

Building Thinking Classrooms [pptx]

CentralÂ OkanaganÂ Teachers Association Conference, Kelowna (Feb 23, 2018)

Building Thinking Classrooms [pptx]

Vernon School District, Vernon (Feb 22, 2018)

Building Thinking Classrooms [pptx]

Norma Rose Point School, Vancouver (Feb 19, 2018)

Ontario Mathematics Coordinators Association, Hockley Valley (Feb 15-16, 2018)

Maple Ridge School District (Feb 13, 2018)

Quesnel School District Curriculum Day (Feb 9, 2018)

West Point Grey Academy (Feb 5, 2018)

Southeast Kootenay and Rocky Mountain School Districts, Kimberley (Feb 1, 2018)

Vernon School District, Vernon (Jan 29, 2018)

Matematikbiennalen 2018, Karlstad, Sweden (Jan 25-26, 2018)

Building Thinking Classrooms [pptx]

MADIF-11, Karlstad, Sweden (Jan 24, 2018)

What Teachers WantÂ from Professional Development [pptx]

Lynden and Bellingham School Districts (Jan 10, 2018)

West Point Grey Academy (Jan 8, 2018)

Brentwood College (Jan 3, 2018)

NRLC, Grande Prairie (Dec 5-7, 2017)

Problem Solving in Patagonia, Chile (Nov 28-Dec 1, 2017)

Student Problem Solving Behaviour in a Thinking Classroom [pptx]

Punta Arenas, Chile (Nov 27, 2017)

OAME Leadership Conference, Ottawa (Nov 10, 2017)

University of Ottawa (Nov 8, 2017)

Flow in the Classroom: Looking at Teacher Moves and Students' Autonomous Actions [pptx]

Hastings and Prince Edward District School Board, Belleville, Ontario (Nov 6-7, 2017)

York Regional District School Board, Toronto (Oct 24-26, 2017)

Conseil des Ã©coles publiques de l'Est de l'Ontario, Ottawa (Oct 23 & 27, 2017)

Montana Council for Mathematics Teachers, Missoula (Oct 19, 2017)

University of Montana, Missoula (Oct 18, 2017)

What is the Nature of Illumination? [pptx]

Milano Teachers, Italy (Oct 11, 2017)

MAVI 23 -Â Essen, Germany (Oct 4-6, 2017)

Affect as a System: The Case of Sara [pptx]

Thames Valley District School Board, London (Sept 28, 2017)

York Regional District School Board, Toronto (Sept 26, 27, 29, 2017)

St. John Paul II School, Grande Prairie (Sept 22, 2017)

Building Thinking Classrooms (day 2) [pptx]

NRLC, Grande Prairie (Sept 20-21, 2017)

Building Thinking Classrooms [pptx]

Winnipeg School District (Sept 13-15, 2017)

Building Thinking Classrooms (Sept 13-14) [pptx]

Building Thinking Classrooms (Sept 15) [pptx]

Vertical Surfaces [docxÂ from Rob Cop]

St. John Paul II School, Grande Prairie (Aug 31, 2017)

Building Thinking Classrooms [pptx]

CirConference, Calgary Board of Education (Aug 29, 2017)

NIMS & KSME, Daejeon, Korea (July 26-28, 2017)

PME 41, Singapore (July 17-22, 2017)

Mathematical Transgressions Conference, Krakow, Poland (June 18-23, 2017)

Eagle Mountain Middle School, Port Moody (May 19, 2017)

Edmonton Public School Board, Edmonton (May 15, 2017)

myPITA Conference, Whistler (May 12, 2017)

Delta School District, Delta (May 9, 2017)

West Point Grey Academy, Vancouver (May 8, 2017)

Building Thinking Classrooms [pptx]

York Regional District School Board, Toronto (May 5, 2017)

Kamloops/Thompson School District - Kamloops (April 19-20, 2017)

Regional Specialist Associations, Kimberley (April 10, 2017)

Building Thinking Classrooms [pptx]

Lynden School District, Washington (March 17, 2017)

Global Math Department (March 14, 2017)

Southeast Kootenay and Rocky Mountain School Districts, Cranbrook (March 10, 2017)

NRLC, Grande Prairie (March 8, 2017)

Building Thinking Classrooms [pdf]

St. James-Assiniboia School Division,Â Winnipeg (March 1, 2017)

Ottawa-Carleton District School Board, Ottawa (Feb 17, 2017)

Building Thinking Classrooms [pptx]

York House, Vancouver (Feb 10, 2017)

NRLC, Grande Prairie (Feb 9, 2017)

CERME 10 - Dublin, Ireland (Feb 2, 2017)

On the Edges of Flow [pptx]

Delta School District (Jan 30, 2017)

PDP Fine Arts Module, SFU (Jan 26, 2017)

Okanagan Similkameen and Okanagan Skaha School District, Oliver (Jan 25, 2017)

Burnaby School District (Jan 24, 2017)

Vertical Surfaces [docx from Rob Cop]

York House, Vancouver (Dec 15, 2016)

North Vancouver School District (Dec 5, 2016)

Beijing Normal University, China (Nov 18, 2016)

Building Thinking Classrooms: A Story of Teacher Professional Development [pptx]

Vernon School District, Vernon (Nov 14-15, 2016)

BuildingÂ Thinking Classroom [pptx]

International Forum for the Professional Development of Teachers - Seoul, Korea (Nov 3, 2016)

Building Thinking Classrooms: A Story of Teacher Professional Development [pptx]

Korean Society for Mathematics Education (KSME) Forum - Seoul, Korea (Nov 2, 2016)

Flow: A Framework for Discussion Teaching [pptx]

Seoul National University Graduate Seminar - Seoul, Korea (Oct 31, 2016)

In the Words of the Creators [pptx]

Mathematics Council of the Alberta Teachers' Association Conference (MCATA), Canmore, Alberta (Oct 21-22, 2016)

Building Thinking Classrooms [pdfÂ | pptx]

Visibly Random GroupsÂ [pdf]

Flow: A Framework for Discussing Teaching [pdf]

Flow: Student Autonomous Action [pdf]

Vertical Surfaces [docx from Rob Cop]

Centro de InvestigaciÃ³n Avanzada en EducaciÃ³n,Â Universidad de Chile - Santiago, Chile (Oct 13, 2016)

Detroit Area Council of Mathematics Teachers - DACMT (Oct 8, 2016)

Building Thinking Classrooms [pdfÂ |Â pptx]

Visibly Random GroupsÂ [pdf]

Vertical Surfaces [docx from Rob Cop]

North Vancouver School District (Oct 4, 2016)

Ottawa Catholic School District, Ottawa (Sept 27-30, 2016)

Burnaby South Secondary, Burnaby (Sept 23, 2016)

Okanagan Similkameen and Okanagan Skaha School District, Oliver (Sept 20, 2016)

BCAMT Leadership Summit, North Vancouver (Sept 19, 2016)

Assessment in the New Curriculum [pptx]

MAVI 22 - VÃ¤xjÃ¶,Â Sweden (Sept 13-15, 2016)

Relationship between Proxies for Learning and Mathematically Related Beliefs [pptx]

PME 40, Szeged, Hungary (July 3-7)

Flow: A Framework for Discussing Teaching [pptx]

ICME 13, Hamburg, Germany (July 24-31)

Park City Math Institute (July 18, 2016)

York House, Vancouver (June 14, 2016)

Vernon School District, Vernon (May 19, 2016)

Assessment for a Thinking Classroom [pptx]

York House, Vancouver (May 16, 2016)

Building Thinking Classrooms [pptx]

Health and Physical Education Council (HPEC), Alberta Conference, Grande Prairie (May 14, 2016)

St. Joseph Catholic High School, Grande Prairie (May 13, 2016)

Building Thinking Classrooms [pptx]

Static Cling White Boards [Amazon.ca]

Peace River School District, Dawson Creek (May 9, 2016)

Okanagan Similkameen School District, Oliver (May 4, 2016)

Assessment for a Thinking Classroom [pptx]

Hanover School Division - Steinbach, Manitoba (April 27-29, 2016)

St. James-Assiniboia School Division,Â Winnipeg (April 26, 2016)

Moscrop Secondary School, Burnaby (April 25, 2016)

Vernon School District, Vernon (April 21, 2016)

Building Thinking Classrooms [pptx]

Static Cling White Boards [Amazon.ca]

Flow [pptx]

Kamloops/Thompson School District - Kamloops (April 18, 2016)

Peace River School District, Dawson Creek (April 11, 2016)

University of Helsinki, Finland (March 17, 2016)

Building Thinking Classrooms [pptx]

St. James-Assiniboia School Division,Â Winnipeg (March 10-11, 2016)

Building Thinking Classrooms [pptx]

Static Cling White Boards [Amazon.ca]

Ottawa Catholic School Board, Ottawa (March 2-4, 2016)

Building Thinking Classrooms - teachers [pptx]

Building Thinking Classrooms - administrators [pptx]

Assessment for a Thinking Classroom [pptx]

Static Cling White Boards [Amazon.ca]

Frank Ryan Catholic Intermediate School SuccessÂ [video link]

Peace River School District, Dawson Creek (Feb 29, 2016)

University of Wollongong, Australia (Feb 23-24, 2016)

Building Thinking Classrooms (workshop) [pptx]

Static Cling White Boards [Amazon.ca]

Building Thinking Classrooms (seminar) [pptx]

SD41 Home Ec. Teachers, Burnaby (Feb 19, 2016)

Hanover School Division - Steinbach, Manitoba (Feb 10-12, 2016)

Fields Institute MathEd Forum - Skype (Jan 30, 2016)

Building Thinking Classrooms [pptx]

Collingwood School - West Vancouver (Jan 25, 2016)

Assessment for the 21st Century [pptx]

Gulf Island School District - Ganges (Jan 15, 2016)

Building Thinking Classrooms [pptx]

Static Cling White Boards [Amazon.ca]

MISA/PNC Celebration of Thinking Through Collaboration - Kingston (Jan 7-8, 2016)

Kamloops/Thompson School District - Kamloops (Jan 6, 2016)

Assessment for aÂ Thinking Classrooms [pptx]

Okanagan Similkameen School District (Dec 9, 2015)

Building Thinking Classrooms [pptx]

Kamloops/Thompson School District - Kamloops (Dec 7, 2015)

Building Thinking Classrooms [pptx]

Cariboo High School (Nov 27, 2015)

Conceptualizing and Actualizing the New Curriculum [pptx]

MAVI 21 - Milan, Italy (Nov 17-19, 2015)

Numeracy Task Design: A Case of Teacher Change [pptx]

Burnaby Learning Team (Nov 13, 2015)

Okanagan Similkameen School District (Nov 9, 2015)

Queen's University - Kingston (Nov 5, 2015)

Mother Theresa High School - Ottawa (Nov 4, 2015)

Professional Development Seminar - Richmond (Nov 3, 2015)

Aiming for Excellence - Dawson Creek (Oct 26-27, 2015)

Northwest Mathematics Conference - Whistler (Oct 22-24, 2015)

North Vancouver School District (October 22, 2015)

Building Thinking Classrooms - part II [pptx]

Hanover School Division - Steinbach, Manitoba (Oct 15-17, 2015)

North Vancouver School District (October 7, 2015)

Building Thinking Classrooms - part I [pptx]

Chinese University of Hong Kong, Hong Kong (Sept 30, 2015)

Action Research in Action [pptx]

Moscrop Secondary School, Burnaby (Sept 25, 2015)

Kamloops/Thompson School District - Kamloops (Sept 23, 2015)

Okanagan Similkameen School District (Sept 2, 2015)

Learning or Studenting [pptx]

PME 39 - Hobart, Australia (July 13-18, 2015)

Centro de InvestigaciÃ³n Avanzada en EducaciÃ³n,Â Universidad de Chile - Santiago, Chile (July 9, 2015)

Centro de Modelamiento MatemÃ¡tico, Universidad de Chile - Santiago, Chile (July 7, 2015)Â

PÃ³lya, Cards, and CsÃkszentmihÃ¡lyi: The Phenomenon of Flow [pptx]

CMESG 2015 -Â UniversitÃ© de Moncton (June 5-9, 2015)

Building Thinking Classrooms [pptx]

Kamloops/Thompson School District - Kamloops (May 11, 2015)

Changing the Culture - Vancouver (May 8, 2015)

Building Thinking Classrooms [pptx]

OECTA - Toronto (May 2, 2015)

Building Thinking Classrooms [pptx]

Hanover School Division - Steinbach, Manitoba (April 29-30, 2015)

Professional Development Seminar - Richmond (April 10, 2015)

Berkshire Park Elementary - Surrey (April 1, 2015)

Adult Basic Mathematics Education - Vancouver (March 6, 2015)

Thinking, Learning, or Studenting - The View from the Back of the Classroom [pptx]

Interior Mathematics Conference - Kamloops (Feb 20, 2015)

Building a Thinking Classroom [pptx]

Flow [pdf]

Studenting: The Case of Homework [pdf]

Studenting: The case of "now you try one" [pdf]

The affordances of using visually random groups in a mathematics classroom [pdf]

Building thinking classrooms: Conditions for Problem Solving [pdf]

CERME 9 - Prague, Czech Republic (Feb 2-4, 2015)

Emotions as an Orienting Experience [pptx]

Symposium - Politecnico di Milano, Milan, Italy (Feb 2, 2015)Â

MAVI 20 - Falun, Sweden (Sept 29 - Oct 1, 2014)

Emotions as Orienting Experiences [pptx]

Seeing Studentâ€™s Interactions Through Teachersâ€™ Eyes [pptx]

Changing the Culture - Vancouver (May 16, 2014)

Panel - Motivating Students [pptx]

Symposium on Teaching and Learning - SFU (May 14, 2014)

Canadian Mathematics Education Forum - Ottawa (May 1-4, 2014)

Workshop in Mathematics Problem Solving - Santiago, Chile (Dec 11, 2013)

Environments to Occasion Problem Solving [pptx]

UniversitÃ© du QuÃ©bec Ã MontrÃ©al Colloquim - Montreal (Nov 5, 2013)

Studenting: What Really Happens in a Mathematics Classroom [pptx]

National Taiwan Normal University Colloquium -Â Taipei, Taiwan (Oct 24, 2013)

New Frameworks for Looking at Student Interactions [pptx]

MAVI 19 - Freiburg, Germany (Sept 27-29, 2013)

Studentsâ€™ Gazes: New Insights into Student Interactions [pptx]

PME 37 - Kiel, Germany (July 28-Aug 2, 2013)

Studenting: The case of "Now you Try one" [pptx]

Instituto de MatemÃ¡ticas, Pontificia Universidad CatÃ³lica de ValparaÃso - Valparaiso, Chile (June 21, 2013)

The Affordances of Using Visibly Random Groups in the Mathematics Classroom [pptx]

The Affordances of Using Visibly Random Groups in the Mathematics Classroom - article [pdf]

Centro de InvestigaciÃ³n Avanzada en EducaciÃ³n,Â Universidad de Chile - Santiago, Chile (June 20, 2013)

Centro de Modelamiento MatemÃ¡tico, Universidad de Chile - Santiago, Chile (June 18, 2013)Â

Lectures in Mathematics Education - VaxjÃ¶, Sweden (May 15, 2013)

The Hidden Classroom: A Look Behind the FaÃ§ade of Learning [pptx]

BCAMT New Teacher Conference - Surrey (Feb 16, 2013)

Teaching and Studenting: Observations from the Back of the Classroom [pptx]

Delta District Day (Feb 15, 2013)

Studenting in the Mathematics Classroom: Gaming vs. Learning [pptx]

CERME 8 - Antalya, Turkey (Feb 6, 2013)

Approaching Professional Learning: Teachers' GoalsÂ [pptx]

Burnaby North Pro-D - Burnaby (Nov 19, 2012)Â

Rethinking Student Thinking [pptx]

MAVI 18 - Helsinki, Finland (Sept 10-16, 2012)

Illumination: Cognitive or affective? Â [pptx]

PME 36 - Taipei, Taiwan (July 18-22, 2012)

Lillian Osborne High School - Edmonton (June 26, 2012)

Alberta Webinar #3 (April 23, 2012)

Alberta Webinar #2 (March 19, 2012)

Sherwood Park (March 2, 2012)

Alberta Webinar #1 (Feb 27, 2012)

Initiating Thinking [pptx]

SD 36 District Day - Surrey (Feb 10, 2012)

Math Institute - Edmonton, Alberta (Jan 26, 2012)

Edmonton Pro-D (Nov 30 - Dec 1, 2011)

for numeracy tasks click here

Blank Rubrick [doc]

Producibles [doc]

Re-Writes [doc]

Evaluate What We Value [pdf]

Four Purposes of Assessment - article [pdf]

BCAMT Conference - Burnaby (Oct 21, 2011)

Lessons Learned While NOT Teaching [ppt]

Linnaeus University Colloquium - VÃ¤xjÃ¶, Sweden (Sept 21-23, 2011)

MAVI 17 - Bochum, Germany (Sept 17-20, 2011)

The theory of conceptual change as a theory for changing conceptions [ppt]

Calgary Pro-D (March 14-15, 2011)

Grande Prairie Pro-D (March 9-11, 2011)

Grande Prairie Pro-D - grades 6-9 (Jan 21, 2011)

Grande Prairie Pro-D - grades K-5 (Jan 20, 2011)

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MAT246Y1 Offical Webpage for the 2003-2004 Term

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Successful teaching and learning of mathematics play an important role in ensuring that students have the right skills required to compete in a 21st century global economy. When properly implemented and coupled with opportunities for students to engage in mathematical investigation, communication and problem solving, rigorous mathematics standards hold the promise of elevating the mathematical knowledge and skill of every learner to levels competitive with the best in the world, of preparing our college entrants to undertake advanced work in the mathematical sciences, and of readying the next generation for the jobs their world will demand.

Vision for Mathematics Education in New Jersey

A New Jersey education in Mathematics builds quantitatively and analytically literate citizens prepared to meet the demands of college and career, and to engage productively in an information-driven society. All students will have access to a high-quality mathematics education that fosters a population that:

leverages data in decision-making and as a lens for discussing, analyzing, and responding to practical questions.

persists to make sense of and model problems arising in everyday life, society, and the workplace.

thinks critically and strategically to assess quantitative relationships and to solutions to complex problems.

employs precise reasoning and constructs viable arguments to deduce conclusions, recognize false statements and assess peers' reasoning.

interprets, evaluates and critiques the mathematics embedded in social, scientific and commercial systems, as well as the claims made in the private and public sectors.

communicates precisely when conveying, representing, and justifying both qualitative and quantitative perspectives.

An important feature of the New Jersey Student Learning Standards for Mathematics (NJSLS-M) is their organization into groups of related standards. In K-8, these groups are called domains and reflect an area of focus for the grade level. The K-5 domains and associated descriptions appear below.

Counting and Cardinality

The Counting and Cardinality domain begins with early rote counting and moves to counting to find how many in one group of objects. Learners build on this work to develop strategies to compare two concrete quantities, two number words and two numerals. Addition, subtraction, multiplication, and division grow from these early roots. This domain involves important ideas that need to be taught in ways that are interesting and engaging to young students.

Operations and Algebraic Thinking

The Operations and Algebraic Thinking domain deals with the basic operations, the kinds of quantitative relationships they model, and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships. Although most of the standards organized under this heading involve whole numbers, the domain includes concepts, properties, and representations that extend to other number systems, to measures, and to algebra.

Number and Operations in Base Ten

The base-ten system is an efficient and uniform system for representing all numbers. Using only the ten digits 0 through 9, every number can be represented as a string of digits. Learners' work with the base-ten system is intertwined with their work on counting and cardinality, and with the meanings and properties of addition, subtraction, multiplication, and division. Standard algorithms for base-ten computations with the four operations are included in this domain, with the standards distinguishing strategies from algorithms. Work with computation (i.e. addition, subtraction, multiplication, division) begins with the use of strategies and efficient, accurate, generalizable methods. For each operation, the culmination of the work is indicated in the standards by the use of the term "standard algorithm".

Measurement and Data

Geometric measurement connects the two most critical domains of early mathematics, geometry and number, with each providing conceptual support to the other. Measurement, the process of assigning a number to a magnitude of some attribute, is central to mathematics, to other disciplines, especially science, and to activities in everyday life. Before learning to measure attributes, the attribute to be measured has to "stand out" for the student. Children need to recognize them and distinguishing them from other attributes (e.g. distinguish length from area).

Students also work with data in grades K-5, building foundations for the later study of statistics and probability. the K-5 data standards run along two paths. One path involves categorical data and focuses on bar graphs as a way to represent and analyze such data. Categorical data comes from sorting objects into categories. The other path deals with measurement data - data that comes from taking measurements. Other ways to generate measurement data might include measuring liquid volumes with graduated cylinders or measuring room temperatures with a thermometer. In each case, the NJSLS-M call for students to represent measurement data with a line plot.

Number and Operation - Fractions

In the NJSLS-M, the word "fraction" is used to refer to a type of number. That number can be expressed in different ways. It can be written in the form numerator over denominator or in decimal notation. If it is greater than 1, it can be written in the form of a whole number followed by a number less than 1 written as a fraction (i.e., a mixed number). In later grades, each of these forms of fraction are considered rational numbers. Expectations for computing with fractions appear in the domains of Number and Operations-Fractions, Number and Operations in Base Ten, and the Number System.

Geometry

Like core knowledge of number, core geometrical knowledge seems to be a universal capability of the human mind. Geometric and spatial thinking are important in and of themselves, because they connect mathematics with the physical world, and play an important role in modeling phenomena whose origins are not necessarily physical (i.e. networks or graphs). They are also important because they support the development of number and arithmetic concepts and skills. Thus, geometry is essential for all grade levels for many reasons: its mathematical content, its roles in physical sciences, engineering, and many other subjects, and its strong aesthetic connections.

Reference: Common Core Standards Writing Team. (2018). Progressions for the Common Core State Standards in Mathematics (August10 draft). Tucson, AZ: Institute for Mathematics and Education, University of Arizona

An important feature of the New Jersey Student Learning Standards for Mathematics (NJSLS-M) is their organization into groups of related standards. In K-8, these groups are called domains and reflect an area of focus for the grade level. In high school, they are called conceptual categories. The grades 6-12 domains/conceptual categories and associated descriptions appear below.

Ratio and Proportional Relationships (6-7)

The study of ratios and proportional relationships extends students' work in measurement and in multiplication and division in the elementary grades. Ratios and proportional relationships are foundational for further study in mathematics and science and useful in everyday life. Students use ratios in geometry and in algebra when they study similar figures and slopes of lines, and later when they study sine, cosine, tangent, and other trigonometric ratios in high school. Students use ratios when they work with situations involving constant rates of change, and later in calculus when they work with average and instantaneous rates of change of functions. An understanding of ratio is essential in the sciences to make sense of quantities that involve derived attributes such as speed, acceleration, density, surface tension, electric or magnetic field strength, and to understand percentages and ratios used in describing chemical solutions. Ratios and percentages are also useful in many situations in daily life, such as in cooking and in calculating tips, miles per gallon, taxes, and discounts. They also are also involved in a variety of descriptive statistics, including demographic, economic, medical, meteorological, and agricultural statistics.

Expressions and Equations (6-8)

In Grades 6-8, students start to use properties of operations to manipulate algebraic expressions and to produce different but equivalent expressions for different purposes. An expression expresses something. Facial expressions express emotions. Mathematical expressions express calculations with numbers. Some of the numbers might be given explicitly, like $2$ or $.75$. Other numbers in the expression might be represented by letters, such as $x$, $y$, $P$, or $n$. The calculation an expression represents might use only a single operation, as in $4 + 3$ or $3x$. Or it might use a series of nested or parallel operations, as in $3(a + 9)$.

An expression is a phrase in a sentence about a mathematical or real-world situation. As with a facial expression, you can read a lot from an algebraic expression without knowing the story behind it. It is a goal of this domain for students to see expressions as objects, and to read both the general appearance and fine details of algebraic expressions.

The Number System (6-HS)

In Grades 6-8 students began to widen the possible types of number they can conceptualize on the number line. In Grade 8 students glimpse the existence of irrational numbers. In high school, they undertake a systematic study of functions that can take on irrational values, such as exponential, logarithmic, and power functions. The study of such functions brings with it a need for an extended understanding of the meaning of an exponent. The first step in this direction is the understanding of numerical expressions in which the exponent is not a whole number.

Geometry (6-HS)

Geometry has two important streams that begin in elementary grades: understanding properties of geometric figures and the logical connections between them, and developing and using formulas to compute lengths, areas and volumes. A third stream, coordinate geometry, surfaces in Grade 5, gains importance in Grades 6-8, and mingles with algebra to become analytic geometry in high school. Informal understandings of congruence and similarity emerge in middle school with congruence criteria appearing in high school. High school students analyze transformations that include dilations, understanding similarity in terms of rigid motions and dilations. Students prove theorems, using the properties of rigid motions established in Grade 8 and the properties of dilations established in high school.

In Grades 6-8, students apply geometric measurement to real-world and mathematical problems, making use of properties of figures as they dissect and rearrange them in order to calculate or estimate lengths, areas, and volumes. Use of geometric measurement continues in high school. Students examine it more closely, giving informal arguments to explain formulas used in earlier grades. Students leverage analytic geometry as they express geometric properties with equations and use coordinates to prove geometric theorems algebraically.

Statistics and Probability (6-HS)

Students build on the knowledge and experiences in data analysis developed in earlier grades. They develop a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center and spread, and terms such as cluster, peak, gap, symmetry, skew, and outlier. They begin to use histograms and box plots to represent and analyze data distributions. Students then move from concentrating on analysis of data to production of data, understanding that good answers to statistical questions depend upon a good plan for collecting data relevant to the questions of interest. Because statistically sound data production is based on random sampling, a probabilistic concept, students must develop some knowledge of probability before launching into sampling. Their introduction to probability is based on seeing probabilities of chance events as long-run relative frequencies, and many opportunities to develop the connection between theoretical probability models and empirical probability approximations. This connection forms the basis of statistical inference.

In high school, students build on knowledge and experience de-scribed in the 6-8 Statistics and Probability Progression. They develop a more formal and precise understanding of statistical inference, which requires a deeper understanding of probability. Students learn that formal inference procedures are designed for studies in which the sampling or assignment of treatments was random, and these procedures may not be informative when analyzing non-randomized studies, often called observational studies. For example, a random selection of 100 students from your school will allow you to draw some conclusion about all the students in the school, whereas taking your class as a sample will not allow that generalization. Probability is still viewed as long-run relative frequency, but the emphasis now shifts to conditional probability and independence, and basic rules for calculating probabilities of compound events. Probability is presented as an essential tool for decision-making in a world of uncertainty.

Functions (8-HS)

Functions describe situations in which one quantity is determined by another. The area of a circle, for example, is a function of its radius. When describing relationships between quantities, the defining characteristic of a function is that the input value determines the output value. The notion of a function is introduced in Grade 8. Linear functions are a major focus but note that students are also expected to give examples of functions that are not linear. In high school, students deepen their understanding of the notion of function, expanding their repertoire to include quadratic and exponential functions, and increasing their understanding of correspondences between geometric transformations of graphs of functions and algebraic transformations of the associated equations.

Algebra

Two Grades 6-8 domains are important in preparing students for Algebra in high school. The Number System prepares students to see all numbers as part of a unified system and become fluent in finding and using the properties of operations to find the values of numerical expressions that include those numbers. The standards of the Expressions and Equations domain ask students to extend their use of these properties to linear equations and expressions with letters. These extend uses of the properties of operations in earlier grades.

The Algebra category in high school is very closely allied with the Functions category. An expression in one variable can be viewed as defining a function. An equation in two variables can sometimes be viewed as defining a function. The notion of equivalent expressions can be understood in terms of functions. Because of these connections, some curricula take a functions-based approach to teaching algebra, in which functions are introduced early and used as a unifying theme for algebra. Other approaches introduce functions later, after extensive work with expressions and equations.

Reference: Common Core Standards Writing Team. (2018). Progressions for the Common Core State Standards in Mathematics (August10 draft). Tucson, AZ: Institute for Mathematics and Education, University of Arizona

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

1. Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

4. Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see $7 \times 8$ equals the well-remembered $7 \times 5 + 7 \times 3$, in preparation for learning about the distributive property. In the expression ${x^2} + 9x + 14$, older students can see the $14$ as $2 \times 7$ and the $9$ as $2 + 7$. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see $5-3(x-y)^2$ as $5$ minus a positive number times a square and use that to realize that its value cannot be more than $5$ for any real numbers $x$ and $y$.

8. Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through ($1, 2$) with slope $3$, middle school students might abstract the equation $\frac{y-2}{x-1} = 3$. Noticing the regularity in the way terms cancel when expanding $(x-1)(x+1)$, $(x-1)({x^2}+x+1)$, and $(x-1)({x^3}+{x^2}+x+1)$ might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results

Graduation Credit Requirement

N.J.A.C. 6A:8-5.1(a) For a State-endorsed diploma, district boards of education shall develop, adopt, and implement local graduation requirements that prepare students for success in post-secondary degree programs, careers, and civic life in the 21st century, and that include the following:

1. Participation in a local program of study of not fewer than 120 credits in courses designed to meet all of the NJSLS, including, but not limited to, the following credits:

2. At least 15 credits in mathematics, including algebra I or the content equivalent effective with the 2008-2009 grade nine class; geometry or the content equivalent effective with the 2010-2011 grade nine class; and a third year of mathematics that builds on the concepts and skills of algebra and geometry and that prepares students for college and 21st century careers effective with the 2012-2013 grade nine class.

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Mathematics, Math, K to 12, NJSLS, Algebra, Geometry, Standards, NJDOE

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Skills available for New Jersey sixth-grade math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

6.RP Ratios and Proportional Relationships

6.RP.A Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Write a ratio (6-R.1)

Write a ratio: word problems (6-R.3)

Which model represents the ratio? (6-R.4)

6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

Unit rates (6-R.9)

6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6.RP.A.3a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Identify equivalent ratios (6-R.5)

Write an equivalent ratio (6-R.6)

Ratio tables (6-R.7)

Equivalent ratios: word problems (6-R.8)

Ratios and rates: complete a table and make a graph (6-R.11)

6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed.

Compare rates: word problems (6-R.14)

Ratios and rates: word problems (6-R.15)

Unit prices (6-V.2)

6.RP.A.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

What percentage is illustrated? (6-S.1)

Understanding percents: strip models (6-S.2)

Convert fractions to percents using grid models (6-S.3)

Convert between percents, fractions, and decimals (6-S.4)

Convert between percents, fractions, and decimals: word problems (6-S.5)

Solve percent problems using grid models (6-S.8)

Solve percent problems using strip models (6-S.9)

Percents of numbers and money amounts (6-S.10)

Percents of numbers: word problems (6-S.11)

Percents of numbers: fractional and decimal percents (6-S.12)

Find what percent one number is of another (6-S.13)

Find what percent one number is of another: word problems (6-S.14)

Find the total given a part and a percent (6-S.15)

Solve percent problems (6-S.16)

Solve percent word problems (6-S.17)

6.RP.A.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Convert and compare customary units (6-T.3)

Convert, compare, add, and subtract mixed customary units (6-T.4)

Customary unit conversions involving fractions and mixed numbers (6-T.6)

Convert and compare metric units (6-T.7)

Convert between customary and metric systems (6-T.8)

6.NS The Number System

6.NS.A Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Reciprocals (6-L.2)

Divide fractions by whole numbers in recipes (6-L.4)

Divide fractions using models (6-L.)

Divide fractions (6-L.5)

Divide fractions and mixed numbers using models (6-L.)

Divide fractions and mixed numbers (6-L.7)

Divide fractions and mixed numbers: word problems (6-L.8)

6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

Division patterns with zeroes (6-C.2)

Divide numbers ending in zeroes: word problems (6-C.3)

Divide whole numbers - 2-digit divisors (6-C.5)

Divide whole numbers - 3-digit divisors (6-C.6)

6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Add and subtract decimal numbers (6-G.1)

Add and subtract decimals: word problems (6-G.2)

Complete the decimal addition or subtraction sentence (6-G.3)

Maps with decimal distances (6-G.5)

Multiply decimals (6-H.2)

Divide decimals by whole numbers (6-H.4)

Divide decimals by whole numbers: word problems (6-H.5)

Multiply and divide decimals by powers of ten (6-H.6)

Division with decimal quotients (6-H.8)

Add, subtract, multiply, or divide two decimals (6-O.6)

Add, subtract, multiply, or divide two decimals: word problems (6-O.7)

6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Identify factors (6-E.4)

Find all the factor pairs of a number (6-E.5)

Greatest common factor (6-E.8)

Least common multiple (6-E.10)

GCF and LCM: word problems (6-E.12)

Factor numerical expressions using the distributive property (6-Y.)

6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Understanding integers (6-M.1)

6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

Understanding opposite integers (6-M.4)

Opposites of rational numbers (6-P.7)

Rational numbers: find the sign (6-P.11)

6.NS.C.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Quadrants (6-X.3)

Reflect a point over an axis (6-X.4)

6.NS.C.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Decimal number lines (6-F.8)

Integers on number lines (6-M.2)

Graph integers on horizontal and vertical number lines (6-M.3)

Rational numbers on number lines (6-P.1)

Objects on a coordinate plane (6-X.1)

Graph points on a coordinate plane (6-X.2)

6.NS.C.7 Understand ordering and absolute value of rational numbers.

6.NS.C.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Compare integers (6-M.7)

6.NS.C.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Compare and order rational numbers using number lines (6-P.3)

Compare rational numbers (6-P.4)

Put rational numbers in order (6-P.5)

Compare and order rational numbers: word problems (6-P.6)

Compare temperatures above and below zero (6-T.9)

6.NS.C.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real- world situation.

Understanding absolute value (6-M.5)

Absolute value (6-M.6)

Absolute value and integers: word problems (6-M.10)

Absolute value of rational numbers (6-P.8)

6.NS.C.7d Distinguish comparisons of absolute value from statements about order.

Integer inequalities with absolute values (6-M.9)

Put rational numbers in order (6-P.5)

Absolute value of rational numbers (6-P.8)

6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Coordinate planes as maps (6-X.5)

Distance between two points (6-X.6)

Follow directions on a coordinate plane (6-X.7)

6.EE Expressions and Equations

6.EE.A Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.

Write multiplication expressions using exponents (6-D.1)

Evaluate exponents (6-D.2)

Write powers of ten with exponents (6-D.3)

Find the missing exponent or base (6-D.4)

Exponents with decimal bases (6-D.5)

Exponents with fractional bases (6-D.6)

6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers.

Write variable expressions: one operation (6-Y.1)

Write variable expressions: two operations (6-Y.2)

6.EE.A.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

Identify terms and coefficients (6-Y.8)

Sort factors of variable expressions (6-Y.9)

6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Evaluate numerical expressions one step at a time (6-O.3)

Evaluate numerical expressions involving whole numbers (6-O.4)

Identify mistakes involving the order of operations (6-O.5)

Evaluate numerical expressions involving decimals (6-O.8)

Evaluate numerical expressions involving fractions (6-O.11)

Convert between Celsius and Fahrenheit (6-T.10)

Evaluate variable expressions with whole numbers (6-Y.4)

Evaluate multi-variable expressions (6-Y.5)

Evaluate variable expressions with decimals, fractions, and mixed numbers (6-Y.6)

Evaluate variable expressions: word problems (6-Y.7)

6.EE.A.3 Apply the properties of operations to generate equivalent expressions.

Multiply using the distributive property: area models (6-Y.13)

Multiply using the distributive property (6-Y.14)

Factor variable expressions: area models (6-Y.)

Factor variable expressions using the distributive property (6-Y.15)

Write equivalent expressions using properties (6-Y.17)

6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

Identify equivalent expressions using strip models (6-Y.10)

Identify equivalent expressions I (6-Y.19)

Identify equivalent expressions II (6-Y.20)

6.EE.B Reason about and solve one-variable equations and inequalities.

6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Does x satisfy an equation? (6-Z.1)

Which x satisfies an equation? (6-Z.2)

Solutions to inequalities (6-AA.1)

6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Write variable expressions: word problems (6-Y.3)

6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Model and solve equations using algebra tiles (6-Z.5)

Model and solve equations using diagrams (6-Z.)

Write and solve equations that represent diagrams (6-Z.6)

Solve one-step addition and subtraction equations with whole numbers (6-Z.7)

Solve one-step multiplication and division equations with whole numbers (6-Z.8)

Solve one-step equations with whole numbers (6-Z.9)

Solve one-step addition and subtraction equations with decimals and fractions (6-Z.10)

Solve one-step multiplication and division equations with decimals and fractions (6-Z.11)

Solve one-step addition and subtraction equations: word problems (6-Z.12)

Solve one-step multiplication and division equations: word problems (6-Z.13)

Write a one-step equation: word problems (6-Z.14)

Solve one-step equations: word problems (6-Z.15)

6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real- world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Graph inequalities on number lines (6-AA.2)

Write inequalities from number lines (6-AA.3)

Write and graph inequalities: word problems (6-AA.4)

6.EE.C Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Identify independent and dependent variables in tables and graphs (6-BB.2)

Write an equation from a graph using a table (6-BB.3)

Identify independent and dependent variables: word problems (6-BB.4)

Find a value using two-variable equations (6-BB.5)

Find a value using two-variable equations: word problems (6-BB.6)

Solve word problems by finding two-variable equations (6-BB.7)

Complete a table for a two-variable relationship (6-BB.8)

Write a two-variable equation from a table (6-BB.9)

Write a two-variable equation (6-BB.10)

Identify the graph of an equation (6-BB.11)

Complete a table and graph a two-variable equation (6-BB.12)

Graph a two-variable equation (6-BB.13)

Interpret a graph: word problems (6-BB.14)

6.G Geometry

6.G.A Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Understanding area of a parallelogram (6-FF.3)

Area of parallelograms (6-FF.4)

Understanding area of a triangle (6-FF.5)

Area of triangles (6-FF.6)

Understanding area of a trapezoid (6-FF.7)

Area of trapezoids (6-FF.8)

Area of rhombuses (6-FF.9)

Area of quadrilaterals (6-FF.10)

Area of compound figures (6-FF.11)

Area of compound figures with triangles (6-FF.12)

6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Volume of cubes and rectangular prisms (6-FF.18)

Volume of cubes and rectangular prisms with fractional side lengths (6-FF.19)

Volume of cubes and rectangular prisms: word problems (6-FF.20)

6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Area and perimeter of squares and rectangles on the coordinate plane (6-X.8)

Graph triangles and quadrilaterals (6-CC.8)

6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Nets of three-dimensional figures (6-EE.3)

Surface area of cubes and rectangular prisms (6-FF.21)

Surface area of triangular prisms (6-FF.23)

Surface area of pyramids (6-FF.24)

6.SP Statistics and Probability

6.SP.A Develop understanding of statistical variability.

6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Identify statistical questions (6-HH.1)

6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Create line plots (6-GG.4)

Interpret stem-and-leaf plots (6-GG.21)

Create stem-and-leaf plots (6-GG.22)

Box plots (6-GG.23)

Calculate quartiles and interquartile range (6-HH.7)

Describe distributions in line plots (6-HH.10)

6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Mean, median, mode, and range: find the missing number (6-HH.4)

Interpret measures of center and variability (6-HH.)

6.SP.B Summarize and describe distributions.

6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Create line plots (6-GG.4)

Create histograms (6-GG.15)

Box plots (6-GG.23)

6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:

6.SP.B.5a Reporting the number of observations.

Interpret line plots (6-GG.3)

Interpret histograms (6-GG.14)

6.SP.B.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Identify representative, random, and biased samples (6-HH.11)

6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Calculate mean, median, mode, and range (6-HH.2)

Interpret charts and graphs to find mean, median, mode, and range (6-HH.3)

Calculate mean absolute deviation (6-HH.6)

Calculate quartiles and interquartile range (6-HH.7)

Identify an outlier and describe the effect of removing it (6-HH.9)

Describe distributions in line plots (6-HH.10)

6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

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IXL's dynamic math practice skills offer comprehensive coverage of New Jersey sixth-grade standards. Find a skill to start practicing!

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Outbound Learning Initiatives - Probability and Statistics - Annenberg Learner

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Outbound Learning Initiatives - Probability and Statistics - Annenberg Learner

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I had a wonderful experience using the Annenberg Learner materials in the subjects of personal finance and statistics. The quality and engagement of the experiential-based learning materials, supported by videos, lesson plans, instructional materials and more was unsurpassed.

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It's actually illegal to teach Common Core in Texas.

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The Texas mathematics curriculum is wonderful because of its inclusion of number sense, mental math, prime numbers and competition mathematics.  However, according to U.S. News, Texas is the 35th-ranking state for K-12 education. The top-performing state is New Jersey, while New Mexico sits bottom of the pile.  Massachusetts places second, followed by Connecticut, New Hampshire and Vermont. Learn more about the Best States for primary education below.

Yet, worldwide we rank 30th based on PISA scores.  Singapore at 569, Macao at 555, Hong Kong at 551, Taiwan at 531, and Japan at 527. China was not included in this ranking, since only four provinces participated.  In the United States, performance in mathematics was significantly below the OECD average

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The State Board of Education (SBOE) has legislative authority to adopt the Texas Essential Knowledge and Skills (TEKS) for each subject of the required curriculum. SBOE members nominated educators, parents, business and industry representatives, and employers to serve on the review committees. This page provides information regarding the review and revision of the mathematics TEKS.

TEKS for Mathematics, Adopted 2012

The SBOE approved the revised TEKS for adoption in April 2012. The revised TEKS are available on the TEA rules page. The revised TEKS have "Adopted 2012" noted in the title. The revised mathematics TEKS for Kindergarten through grade 8 will be implemented in the 2014-2015 school year. The revised mathematics TEKS for high school are scheduled for implementation in the 2015-2016 school year, depending upon the availability of funding for instructional materials (Texas Administrative Code (TAC), Title 19, Part II, Chapter 111. Texas Essential Knowledge and Skills for Mathematics).

Proposals Approved for Second Reading and Final Adoption in April 2012

The following documents reflect proposed revisions to the mathematics TEKS as approved by the State Board of Education on April 20, 2012, for second reading and final adoption, with technical edits, as authorized by State Board of Education operating rules:

Kindergarten - Grade 5 (PDF, 268KB)

Grade 6 - Grade 8 (PDF, 212KB)

High School (PDF, 348KB)

Proposals Approved for First Reading and Filing Authorization in January 2012

The proposed revisions to the mathematics TEKS were posted for public comment from February through April 2012. Following the official public comment period, the SBOE took action to approve these changes in April 2012.

TEKS Review Committee Recommendations for Revisions to the Mathematics TEKS (October 2011)

The following documents are the review committees final draft recommendations:
Elementary School Color-Coded Recommendations (PDF, 1,531KB) Elementary School Clean Copy Recommendations (PDF, 160KB) Middle School Color-Coded Recommendations (PDF, 1,276KB) Middle School Clean Copy Recommendations (PDF, 143KB) High School Color-Coded Recommendations (PDF, 1,363KB) High School Clean Copy Recommendations (PDF, 481KB)
First Drafts of Recommendations for Revisions to the Mathematics TEKS (July 2011)

The draft recommendations were developed by the mathematics TEKS review committees that were appointed by members of the SBOE. These drafts are based on the Commissioner's Draft of the Mathematics Standards:

In anticipation of the State Board of Education's scheduled 2011-2012 revision of the TEKS for Mathematics, the Commissioner of Education convened a group of advisors to review current research and resources and to offer suggestions regarding the upcoming TEKS revision and future professional development. The Commissioner's Mathematics Advisory Group, established in the fall of 2010, includes mathematics educators and mathematicians from Texas. The recommendations of the Commissioner's Mathematics Advisory Group regarding the next generation of mathematics standards in Texas were compiled and then reviewed by a panel of national advisors in mathematics, known as the National Review Team reviewed the recommendations of the Commissioner's Mathematics Advisory Group regarding the next generation of mathematics standards in Texas.

The result of this work is a document titled, " The Commissioner's Draft of the Texas Mathematics Standards (PDF, 954KB)."

SBOE Mathematics TEKS Review Committees

The following lists include individuals appointed by the SBOE to serve on mathematics TEKS review committees. Mathematics TEKS review committees began work on the mathematics TEKS in May 2011:

Kindergarten through Grade 5 (PDF, 67KB)
Grades 6-8 (PDF, 70KB) High School (PDF, 71KB)
SBOE Members Nominated Mathematics Expert Reviewers in January 2011

The following list includes individuals appointed by the SBOE to serve as content expert reviewers for the revision of the mathematics Texas Essential Knowledge and Skills:

Dr. Richard A. Askey, Professor Emeritus of Mathematics
University of Wisconsin-Madison
Review of The Commissioner's Draft of the Texas Mathematics Standards Review of First Draft Recommendations for Revisions to the Mathematics TEKS
Dr. Robert M. Capraro, Professor of Mathematics Education
Texas A&M University
Review of The Commissioner's Draft of the Texas Mathematics Standards Review of First Draft Recommendations for Revisions to the Mathematics TEKS
Dr. R. James Milgram, Professor Emeritus, Department of Mathematics
Stanford University
Review of The Commissioner's Draft of the Texas Mathematics Standards Review of First Draft Recommendations for Revisions to the Mathematics TEKS
Dr. James M. Rath, Research Consultant
Adverplex, Inc.
Review of The Commissioner's Draft of the Texas Mathematics Standards
Dixie Ross, Lead Teacher, AP Mathematics
Pflugerville Independent School District
Review of The Commissioner's Draft of the Texas Mathematics Standards Review of First Draft Recommendations for Revisions to the Mathematics TEKS
Dr. Wilfried Schmid, Professor of Mathematics
Harvard University
Review of The Commissioner's Draft of the Texas Mathematics Standards Review of First Draft Recommendations for Revisions to the Mathematics TEKS
Jacqueline Weilmuenster, Master Teacher UTeach Arlington
The University of Texas at Arlington
Review of The Commissioner's Draft of the Texas Mathematics Standards Review of First Draft Recommendations for Revisions to the Mathematics TEKS

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Mathematics Texas Essential Knowledge and Skills

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The State Board of Education (SBOE) has legislative authority to adopt the Texas Essential Knowledge and Skills (TEKS) for each subject of the required curriculum. SBOE members nominated educators, parents, business and industry representatives, and employers to serve on the review committees. This page provides information regarding the review and revision of the mathematics TEKS.

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Common Core Resources - University of Texas

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Common Core Resources - University of Texas

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Here you will find all fourth grade resources to guide and support mathematics teaching and learning.

These resources are organized by mathematical strand and refer to specific Common Core math content standards.
Quick reference: What are these tools?
Operations and Algebraic Thinking (OA)

4.OA.3

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Performance Assessment Tasks

4.OA.4

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Performance Assessment Tasks

4.OA.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Performance Assessment Tools

Number and Operations in Base Ten (NBT)

4.NBT.4

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Performance Assessment Tasks

4.NBT.6

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Performance Assessment Tasks

Numbers and Operations - Fractions (NF)

4.NF.1

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Performance Assessment Tasks

Formative Re-Engaging Lessons

Measurement and Data (MD)

4.MD.1

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.

4.MD.2

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

4.MD.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Performance Assessment Tasks

4.MD.5

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

Geometry (G)

4.G.1

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Performance Assessment Tasks

4.G.3

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Performance Assessment Tasks

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4th Grade Common Core Resources | Inside Mathematics

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Here you will find all fourth grade resources to guide and support mathematics teaching and learning. These resources are organized by mathematical strand and refer to specific Common Core math content standards. Quick reference: What are these tools?

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Mathleague.ORG Engaging Integrated Math Problems - Elementary, MS, HS

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Mathleague.ORG Engaging Integrated Math Problems - Elementary, MS, HS

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These are just the best well-thought out problems that integrate all areas of mathematics. I would argue that the elementary series would serve any MS student with a good source of practice problems to maintain their understanding of mathematics. Look at the Number Sense contest as a wonderful, engaging way to constantly improve understanding and speed of everything learned up to sixth grade. You do not need to attend the contests to reap the value - though they are sure alotta fun.

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Please visit the links below for product descriptions and to place an order. All single Contest Problem Sets are $10 each and will be delivered within 24 hours after purchase. If you wish to purchase multiple Contest Problem Sets, you may add each one to your cart and return to this page to add additional items prior to checkout.

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Probability and Statistics - Online Curriculum

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Probability and Statistics - Online Curriculum

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A visual introduction to probability and statistics.

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Table of Contents

Course Contents

Faculty Resources

Module 1: Sampling and Data

Module 2: Descriptive Statistics

Module 3: Probability

Module 4: Discrete Random Variables

Module 5: Continuous Random Variables

Module 6: Normal Distribution

Module 7: The Central Limit Theorem

Module 8: Confidence Intervals

Module 9: Hypothesis Testing With One Sample

Module 10: Hypothesis Testing With Two Samples

Module 11: The Chi Square Distribution

Module 12: Linear Regression and Correlation

Module 13: F-Distribution and One-Way ANOVA

Module 14: Multiple and Logistic Regression

Appendices

Copyright

Lumen Learning

Lumen Learning provides a simple, supported path for faculty members to adopt and teach effectively with open educational resources (OER). Read more about what we do.

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Course Contents Faculty Resources Module 1: Sampling and Data Module 2: Descriptive Statistics Module 3: Probability Module 4: Discrete Random Variables Module 5: Continuous Random Variables Module 6: Normal Distribution Module 7: The Central Limit Theorem Module 8: Confidence Intervals Module 9: Hypothesis Testing With One Sample Module 10: Hypothesis Testing With Two Samples Module 11: The Chi Square Distribution Module 12: Linear Regression and Correlation Module 13: F-Distribution and One-Way ANOVA Module 14: Multiple and Logistic Regression Appendices Lumen Learning provides a simple, supported path for faculty members to adopt and teach effectively with open educational resources (OER).

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Education Technology | Calculators | Texas Instruments

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Explore the #1 recommended brand of graphing calculators in the U.S. Get free math and science lessons—Download STEM projects—Sign up for professional learning.

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Math Olympiads for Elementary and Middle Schools – MOEMS

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A must-have digital textbook for pre-calculus.  It takes the long way around, providing a deep understanding built upon real-world problems.

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Contemporary Precalculus Through Applications Third Edition
Print and open access digital edition available now! The first edition of Contemporary Precalculus through Applications was published in 1993, well before the widespread use of computers in the classroom. Collaborating with students and

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https://secureservercdn.net/198.71.189.51/j23.312.myftpupload.com/wp-content/uploads/2022/07/Roller-Coaster-Calculus.pdf

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Promoting the Concepts of Calculus | Roller Coaster Calculus

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Calculus was developed in the seventeenth century to study four types of math problems of that time: Find the slope of a line that just touches a curve at a point Find the area of a region below a curve Find the maximum or minimum value of a quantity Knowing

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https://im.kendallhunt.com/MS/students/3/8/index.html

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Algebra, Precalculus, Probability & Statistics

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Algebra, Precalculus, Probability & Statistics

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OpenStax | Free Textbooks Online with No Catch

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OpenStax offers free college textbooks for all types of students, making education accessible & affordable for everyone. Browse our list of available subjects!

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Algebra 1, 2, Pre; Geometry; Pre-calculus under development

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Algebra 1, 2, Pre; Geometry; Pre-calculus under development

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The Math Bits Notebook is free, covering Algebra 1&2, something they call junior math and geometry. Pre-calc under development. Not comprehensive, but a good source for ideas and problems.

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Mathematics Resources
MathBits.com is devoted to offering fun, yet challenging, lessons and activities in secondary (and college level) mathematics and computer programming for students and teachers. Created by two mathematics teachers.
* Please read the Terms of Use.

"Mathematics seems to endow one with something like a new sense." Charles Darwin

Materials are compatible with state standards for mathematics education.

MathBits' free activities Math
Caching
(A MathBits' creation.)

"MathCaching Topic Series" (for specific topic areas) can be found in all subscription areas.

Includes topics aimed at mathematics standards and assessments, including, but not limited to, MathBits.com presents: MathBitsNotebook.com FREE!
Sections: JrMath, Algebra 1, Geometry, Algebra 2, PreCalc under development
Material is presented in a lesson format with follow-up interactive practice problems.

the New York State Next Generation Mathematics Standards.

Over 28 states allow computer science to be used toward meeting high school mathematics graduation requirements.
Live long and Program!!

Our older Java materials, developed for JBuilder with Breezy GUI, can be found at: Beginning Java

MathBits' Newsletter

What's new at MathBits?

Find out about updates for all MathBits' areas.
Subscription areas
are included.

Find out what new materials have been posted, and more!

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MathBits' Graph Paper

31 Styles of
Downloadable Graph Paper

Free downloadable forms of graph paper, number lines and grid papers.

More MathBits Resources

Topic areas for students and teachers.
All materials are iPad compatible!

MathBits: Math and the Movies

MathBits' Programming C++

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Math Bits Math Resources - Intermediate and Secondary

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Creative and engaging activities and resources for junior and senior high school mathematics students and teachers. Compatible with NY Next Generation Math Standards

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We believe in teaching students flexible thinking rather than rote memorization. Through our discovery-based activities and scaffolded questions, students uncover concepts and ideas on their own.

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At Maneuvering the Middle, we are all reading Project Based Teaching by Suzie Boss and John Larmers. Throughout the next few months, we will be discussing what we are learning as we read the book. There are 7 best practices for Project Best Teaching, and today we are covering building a strong classroom culture. If you are interested in incorporating more projects in your ...

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At Maneuvering the Middle, we are all reading Project Based Teaching by Suzie Boss and John Larmers. Throughout the next few months, we will be discussing what we are learning as we read the book. There are 7 best practices for Project Best Teaching, and today we are covering building a strong classroom culture.

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My 8 Principles for Teaching Mathematics

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My 8 Principles for Teaching Mathematics

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Disheartened I am that major publishers, like McGraw and Kendall are moving in on Illustrative Mathematics.  The latter publisher has already made it more difficult to access the content by adding a wall where you must be a verified teacher associated with a school.

Illustrative Mathematics is a problem-based core curriculum for 21st century learners designed to address content and practice standards to foster learning for all, preparing students to solve problems, reason, communicate, and think critically in the classroom and beyond.

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A coherent sequence of mathematical ideas is critical in the foundational development of students' mathematical understanding. The upcoming IM K-5 curriculum will provide teachers with coherently sequenced materials based on the standards and research-based learning trajectories to support students' learning in these early years. Coming in 2021.

Stay in the loop

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A coherent sequence of mathematical ideas is critical in the foundational development of students' mathematical understanding. The upcoming IM K-5 curriculum will provide teachers with coherently sequenced materials based on the standards and research-based learning trajectories to support students' learning in these early years. Coming in 2021.

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Australian based, highly rated and used world wide for mathematics online curriculum.

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Mathletics United States | Online Learning Math Program

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Mathletics is the award-winning online math program to help students learn math. Engaging, fun, and aligned to curricula across the United States.

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Table of Contents

This article was most recently revised and updated by

astrolabe, any of a type of early scientific instrument used for reckoning time and for observational purposes. One widely employed variety, the planispheric astrolabe, enabled astronomers to calculate the position of the Sun and prominent stars with respect to both the horizon and the meridian. It provided them with a plane image of the celestial sphere and the principal circles-namely, those representing the ecliptic, celestial equator, and tropics of Cancer and Capricorn. Because of such features, the planispheric astrolabe can be regarded as a kind of rudimentary analog computer.

Astrolabes have been traced to the 6th century, and they appear to have come into wide use from the early Middle Ages in Europe and the Islamic world. By about the mid-15th century, astrolabes were adopted by mariners and used in celestial navigation. The so-called mariner's astrolabe was later supplanted by sextants.

The typical planispheric astrolabe employed by medieval astronomers measured from 8 to 46 cm (3 to 18 inches) and was made of metal-usually brass or iron. It had several principal parts: a base plate (the mater) with a network of lines representing celestial coordinates; an open-pattern disk (the rete) with a "map" of the stars, including the aforementioned circles, that rotated on the mater around a centre pin corresponding to the north celestial pole; and a straight rule (the alidade), used for sighting objects in the sky. The alidade made it possible to use the astrolabe for surveying applications-e.g., determining the height of a mountain. Most astrolabes also had one or more plates (called climates) that were engraved with coordinate lines for different latitudes and were placed between the mater and the rete.

Alicja Zelazko.

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Astrolabe | Definition, History, & Facts

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Astrolabe, a type of early scientific instrument used for reckoning time and for observational purposes.

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Are there any good documentaries on history of mathematics?

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556 votes, 64 comments. 2.0m members in the math community.

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The Three Stages of Learning Mathematics

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Teachers assign concepts to students and track their performance in CK-12 classes. Students can join their classes and receive assignments from their teacher.

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E = mc². It's the world's most famous equation, but what does it really mean? "Energy equals mass times the speed of light squared." On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing. Under the right conditions, energy can become mass, and vice versa. We humans don't see them that way-how can a beam of light and a walnut, say, be different forms of the same thing?-but Nature does.

So why would you have to multiply the mass of that walnut by the speed of light to determine how much energy is bound up inside it? The reason is that whenever you convert part of a walnut or any other piece of matter to pure energy, the resulting energy is by definition moving at the speed of light. Pure energy is electromagnetic radiation-whether light or X-rays or whatever-and electromagnetic radiation travels at a constant speed of 300,000 km/sec (186,000 miles/sec).

Why, then, do you have to square the speed of light? It has to do with the nature of energy. When something is moving four times as fast as something else, it doesn't have four times the energy but rather 16 times the energy-in other words, that figure is squared. So the speed of light squared is the conversion factor that decides just how much energy lies within a walnut or any other chunk of matter. And because the speed of light squared is a huge number-90,000,000,000 (km/sec) ² -the amount of energy bound up into even the smallest mass is truly mind-boggling.

Here's an example. If you could turn every one of the atoms in a paper clip into pure energy-leaving no mass whatsoever-the paper clip would yield 18 kilotons of TNT. That's roughly the size of the bomb that destroyed Hiroshima in 1945. On Earth, however, there is no practical way to convert a paper clip or any other object entirely to energy. It would require temperatures and pressures greater than those at the core of our sun.

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E = mc2 . It's the world's most famous equation, but what does it really mean? "Energy equals mass times the speed of light squared." On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.

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history biology literature learning education science humanities school "world history" ap tests smart fun chemistry psychology apush whap study "crash cours...

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At Crash Course, we believe that high-quality educational videos should be available to everyone for free! Subscribe for weekly videos from our current courses! The Crash Course team has produced more than 45 courses on a wide variety of subjects, including organic chemistry, literature, world history, biology, philosophy, theater, ecology, and many more!

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Common Sense Education provides educators and students with the resources they need to harness the power of technology for learning and life. Find a free K-12 Digital Citizenship curriculum, reviews of popular EdTech apps, and resources for protecting student privacy.

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Peter Liljedahl.  Building Thinking Classrooms.  https://www.bigmarker.com/GlobalMathDept/Building-Thinking-Classrooms

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I have great respect for the past. If you don't know where you've come from, you don't know where you're going. I have respect for the past, but I'm a person of the moment. I'm here, and I do my best to be completely centered at the place I'm at, then I go forward to the next place.

Maya Angelou

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"I have great respect for the past. If you don't know where you've come from, you don't know where you're going. I have respect for the past, but I'm a person of the moment. I'm here, and I do my best to be completely centered at the place I'm at,..."

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The Polya problem solving process serves not only to develop a mathematical skill but also teaches constructive reasoning.

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Anders Ericsson - Deliberate practice makes perfect

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+ Larry King's interview of Ericcson @ https://www.youtube.com/watch?v=7gn3f8sEb8Y

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Anders Ericsson - Deliberate practice makes perfect - Insights for Entrepreneurs - Amazon

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Supplement your child’s learning path with these easy-to-facilitate activities at home.

Redbird Mathematics

Redbird keeps your child's math momentum going with personalized practice, math games, and hands-on projects for grades K–7.

Moments for MySELf

An interactive worksheet program promoting a growth mindset, high self-esteem and social and emotional learning for kids in grade levels PreK–6.

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Home Learning Products for Family Use | Supplemental Learning

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Find ways to supplement your child’s education with these interactive home learning products and activities.

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Edmentum - Formative Assessment and Practice

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Edmentum - Formative Assessment and Practice

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Outsourcing Curriculum for Success in Poverty Areas

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Outsourcing Curriculum for Success in Poverty Areas

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https://www.nytimes.com/2022/06/13/opinion/newglobe-education-test-scores.html?referringSource=articleShare

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Visionary governments invest in the transformation of public education. They know that doing so unlocks enormous potential, empowering populations to create economic growth, deliver security and drive development.

NewGlobe supports national and state governments by creating powerful technology-enabled education systems. An education expert and leader in learning, NewGlobe has unequalled experience in dramatically transforming educational outcomes at speed and at scale. Education is a science. NewGlobe has an unprecedented ability to gather and apply data-driven learning improvements across every aspect of the education system, providing a strong foundation for today’s youth and tomorrow’s future.

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NewGlobe brings ECD, primary and secondary school education for students living in underserved communities. Learn how NewGlobe supports students education worldwide.

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The Australian Mathematics Project - Support for Years 11 - 12

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The Australian Mathematics Project - Support for Years 11 - 12

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The modules are written for teachers. Each module contains a discussion of a component of the mathematics curriculum for years 11 and 12. The emphasis is on the content of the Australian Curriculum subject Mathematical Methods. However some extra topics in Specialist Mathematics are also covered. These modules contain material that is suitable for similar state-based courses. There are exercises that teachers may wish to undertake - answers are given at the end of the module and sometimes screencasts giving a solution. There are a number of animations in the modules.

There are also four videos and additional material which exemplify the wide use of mathematics in the world today. They are listed on the Maths delivers menu which can be accessed from the icon below.

The modules are organised through the following topic groupings.

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Modules for the senior curriculum - Home

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The modules are written for teachers. Each module contains a discussion of a component of the mathematics curriculum for years 11 and 12. The emphasis is on the content of the Australian Curriculum subject Mathematical Methods. However some extra topics in Specialist Mathematics are also covered.

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My go-to text for MS and HS mathematics. Excellent zero chapter on Prealgebra and continues through Algebra II and into PreCalculus.

Includes technology, applications, processes, common misconceptions and plenty of opportunities to practice, both scaffolded and independently.

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0.1 REAL NUMBERS 4

0.2 INTEGER EXPONENTS AND SCIENTIFIC NOTATION 17

0.3 POLYNOMIALS: BASIC OPERATIONS 27

0.4 FACTORING POLYNOMIALS 36

0.5 RATIONAL EXPRESSIONS 46

0.6 RATIONAL EXPONENTS AND RADICALS 60

0.7 COMPLEX NUMBERS 70

Review 77

Review Exercises 79

Practice Test 81
[1] Equations and Inequalities 82
1.1 LINEAR EQUATIONS 84

1.2 APPLICATIONS INVOLVING LINEAR EQUATIONS 93

1.3 QUADRATIC EQUATIONS 107

1.4 OTHER TYPES OF EQUATIONS 121

1.5 LINEAR INEQUALITIES 129

1.6 POLYNOMIAL AND RATIONAL INEQUALITIES 139

1.7 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 149

Review 157

Review Exercises 158

Practice Test 162

Cumulative Test 163
[2] Graphs 164
2.1 BASIC TOOLS: CARTESIAN PLANE, DISTANCE, AND MIDPOINT 166

2.2 GRAPHING EQUATIONS, POINT-PLOTTING, INTERCEPTS, AND SYMMETRY 173

2.3 LINES 186

2.4 CIRCLES 202

2.5 LINEAR REGRESSION: BEST FIT 209

Review 231

Review Exercises 232

Practice Test 234

Cumulative Test 235
[3] Functions and Their Graphs 236
3.1 FUNCTIONS 238

3.2 GRAPHS OF FUNCTIONS; PIECEWISE-DEFINED FUNCTIONS; INCREASING AND DECREASING FUNCTIONS; AVERAGE RATE OF CHANGE 255

3.3 GRAPHING TECHNIQUES: TRANSFORMATIONS 274

3.4 OPERATIONS ON FUNCTIONS AND COMPOSITION OF FUNCTIONS 287

3.5 ONE-TO-ONE FUNCTIONS AND INVERSE FUNCTIONS 298

3.6 MODELING FUNCTIONS USING VARIATION 312

Review 322

Review Exercises 324

Practice Test 328

Cumulative Test 329
[4] Polynomial and Rational Functions 330
4.1 QUADRATIC FUNCTIONS 332

4.2 POLYNOMIAL FUNCTIONS OF HIGHER DEGREE 349

4.3 DIVIDING POLYNOMIALS: LONG DIVISION AND SYNTHETIC DIVISION 363

4.4 THE REAL ZEROS OF A POLYNOMIAL FUNCTION 372

4.5 COMPLEX ZEROS: THE FUNDAMENTAL THEOREM OF ALGEBRA 388

4.6 RATIONAL FUNCTIONS 396

Review 416

Review Exercises 418

Practice Test 422

Cumulative Test 423
[5] Exponential and Logarithmic Functions 424
5.1 EXPONENTIAL FUNCTIONS AND THEIR GRAPHS 426

5.2 LOGARITHMIC FUNCTIONS AND THEIR GRAPHS 440

5.3 PROPERTIES OF LOGARITHMS 456

5.4 EXPONENTIAL AND LOGARITHMIC EQUATIONS 464

5.5 EXPONENTIAL AND LOGARITHMIC MODELS 474

Review 485

Review Exercises 487

Practice Test 490

Cumulative Test 491
[6] Trigonometric Functions 492
6.1 ANGLES, DEGREES, AND TRIANGLES 494

6.2 DEFINITION 1 OF TRIGONOMETRIC FUNCTIONS:RIGHT TRIANGLE RATIOS 511

6.3 APPLICATIONS OF RIGHT TRIANGLE TRIGONOMETRY:SOLVING RIGHT TRIANGLES 525

6.4 DEFINITION 2 OF TRIGONOMETRIC FUNCTIONS: CARTESIAN PLANE 538

6.5 TRIGONOMETRIC FUNCTIONS OF NONACUTE ANGLES 552

6.6 RADIAN MEASURE AND APPLICATIONS 567

6.7 DEFINITION 3 OF TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH 584

6.8 GRAPHS OF SINE AND COSINE FUNCTIONS 594

6.9 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS 623

Review 641

Review Exercises 647

Practice Test 650

Cumulative Test 651
[7] Analytic Trigonometry 652
7.1 BASIC TRIGONOMETRIC IDENTITIES 654

7.2 VERIFYING TRIGONOMETRIC IDENTITIES 665

7.3 SUM AND DIFFERENCE IDENTITIES 675

7.4 DOUBLE-ANGLE IDENTITIES 689

7.5 HALF-ANGLE IDENTITIES 697

7.6 PRODUCT-TO-SUM AND SUM-TO-PRODUCT IDENTITIES 708

7.7 INVERSE TRIGONOMETRIC FUNCTIONS 716

7.8 TRIGONOMETRIC EQUATIONS 737

Review 754

Review Exercises 757

Practice Test 762

Cumulative Test 763
[8] Additional Topics in Trigonometry 764
8.1 OBLIQUE TRIANGLES AND THE LAW OF SINES 766

8.2 THE LAW OF COSINES 780

8.3 THE AREA OF A TRIANGLE 791

8.4 VECTORS 798

8.5 THE DOT PRODUCT 813

8.6 POLAR (TRIGONOMETRIC) FORM OF COMPLEX NUMBERS 821

8.7 PRODUCTS, QUOTIENTS, POWERS, AND ROOTS OF COMPLEX NUMBERS;DE MOIVRE'S THEOREM 829

8.8 POLAR EQUATIONS AND GRAPHS 841

Review 856

Review Exercises 859

Practice Test 862

Cumulative Test 863
[9] Systems of Linear Equations and Inequalities 864
9.1 SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES 866

9.2 SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES 881

9.3 PARTIAL FRACTIONS 892

9.4 SYSTEMS OF LINEAR INEQUALITIES IN TWO VARIABLES 903

9.5 THE LINEAR PROGRAMMING MODEL 914

Review 921

Review Exercises 922

Practice Test 924

Cumulative Test 925
[10] Matrices 926
10.1 MATRICES AND SYSTEMS OF LINEAR EQUATIONS 928

10.2 MATRIX ALGEBRA 950

10.3 MATRIX EQUATIONS; THE INVERSE OF A SQUARE MATRIX 964

10.4 THE DETERMINANT OF A SQUARE MATRIX AND CRAMER'S RULE 976

Review 990

Review Exercises 993

Practice Test 996

Cumulative Test 997
[11] Analytic Geometry and Systems of Nonlinear Equations and Inequalities 998
11.1 CONIC BASICS 1000

11.2 THE PARABOLA 1003

11.3 THE ELLIPSE 1015

11.4 THE HYPERBOLA 1028

11.5 SYSTEMS OF NONLINEAR EQUATIONS 1039

11.6 SYSTEMS OF NONLINEAR INEQUALITIES 1049

11.7 ROTATION OF AXES 1057

11.8 POLAR EQUATIONS OF CONICS 1067

11.9 PARAMETRIC EQUATIONS AND GRAPHS 1078

Review 1086

Review Exercises 1089

Practice Test 1093

Cumulative Test 1095
[12] Sequences, Series, and Probability 1096
12.1 SEQUENCES AND SERIES 1098

12.2 ARITHMETIC SEQUENCES AND SERIES 1109

12.3 GEOMETRIC SEQUENCES AND SERIES 1117

12.4 MATHEMATICAL INDUCTION 1128

12.5 THE BINOMIAL THEOREM 1133

12.6 COUNTING, PERMUTATIONS, AND COMBINATIONS 1141

12.7 PROBABILITY 1151

Review 1160

Review Exercises 1162

Practice Test 1166

Cumulative Test 1167

Answers to Odd-Numbered Exercises 1169

Applications Index 1261

Subject Index 1265

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Cynthis Youngs Algebra Trigonometry, Fourth Edition will allow students to take the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right, while seamlessly integrating to Youngs learning content.

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Savvas Realize ® - Savvas Learning Company

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The links below will take you to individual articles or to index pages for articles on these topics.

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The links below will take you to individual articles or to index pages for articles on these topics.

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https://www.youtube.com/watch?v=xSi0lfl-31U
http://www.whyu.org/

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A humorous look at early attempts at creating number systems, leading up to our modern base-10 decimal number system which uses "positional notation". The story takes place on the fictitious island of Cocoloco.

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We must be consistently revisiting the foundational skills to ensure that everything that builds upon it exists on a strong foundation.  These skills include:

* number: number types, representations, estimation strategies, the importance of place value, expanded notation, series and sequences, number systems other than our own (Roman and Binary), prime numbers, composites, ratios and percents, square and cube roots, absolute value, triangular numbers

* equation: adding in our heads, multiplication strategies, divisibility and remainder rules, even and odd number rules, substitution, order of operations,

* geometry: spatial awareness, what shape is this, perimeter, area and volume, triangles and circles, line segments, rays, angles.

* data: basic probability, measurements, lists, tables, chart types.

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Graphic organizers may be one of the most accessible, adaptable, and underrated tools for promoting critical thinking.

Think about it. They can be used for just about any purpose in the classroom, from note-taking, brainstorming, and making connections, to delegating responsibilities and reflecting upon one's own thinking.

Evidence-Based Support for Using Graphic Organizers as Instructional Tools

The power of graphic organizers stems from dual coding theory, developed by psychology professor Allan Paivio in 1971. Essentially, Paivio suggests that our minds operate with two classes of 'codes' - mental images and verbal representations - and that our memory has two 'storage facilities' for these codes. While they are housed independently, they do interact with one another. Paivio's central claim is that we are more likely to retain new information in our memory (and consistently retrieve it later), if it is stored in both the verbal and visual locations of the brain.

While there are certainly limitations to dual coding theory, countless studies have provided evidence to back Paivio's claim, and dual coding is taught in teacher education programs across the globe.

So what does dual coding have to do with graphic organizers? Simply put, graphic organizers allow students to visualize, order, and categorize concepts using text (verbal representations) and drawings (images). Graphic organizers are also beneficial for breaking down complex or abstract concepts into more 'bite-size,' digestible ideas. Graphic organizers provide students with both structure and autonomy - they are given (or can create) a basic template, but they have the flexibility to be creative within that template. This balance of structure and autonomy is ideal for promoting self-directed, differentiated learning.

How are Graphic Organizers Useful?

Research shows that graphic organizers are a useful strategy for GT and SPED populations, but really, all students can benefit from the multimodal learning that graphic organizers support. Graphic organizers are highly versatile. Students can draw them, digitize them, or adapt a teacher-designed template. They are useful at any grade level and within any subject area for tasks like:

Comparing and contrasting

Narrating a sequence of events

Exploring solutions to a problem

Identifying relationships (like cause-and-effect)

Brainstorming ideas

Connecting previous knowledge to new information

We've searched the web for the most common types of graphic organizers and used our own categorizing system for how to present the best templates to you in the way that is most useful for your everyday instruction. Below, we've listed the 6 most common types of graphic organizers. With each type, we've shared an overall purpose and specific examples that you can adapt for your own lessons. We conclude by offering several important tips for using graphic organizers in the classroom, and providing links to some of the best online tools for creating and sharing graphic organizers online.

The 6 Most Common Types of Graphic Organizers

Venn diagrams are probably one of the first graphic organizers that students are introduced to. Easy to create and easy to navigate, Venn diagrams are best used for comparing and contrasting. Typically, Venn diagrams appear in the form of two to three overlapping circles, where the overlapping segments provide space for students to take note of similarities, and the non-overlapping segments are dedicated for unique differences.

Venn diagrams might be used to compare historical events, monarch 'ruling' styles, nutritional value of foods, or important facts about planets in the solar system. Students can use words, phrases, bulleted items, complete sentences, and quotes as verbal representations, along with drawings, symbols, signs, photographs, GIFs, and videos as images.

Concept Maps
Put simply, concept maps allow a creator to fully flesh out an idea. They typically start out with a center 'bubble,' then use lines or arrows to show relationships to surrounding bubbles. More complex concept maps may have more than one central bubble, and make more than one connection from any one bubble to another.

Concept maps are ideal for brainstorming or showing relationships between concepts. For example, a student might perform a 'topic blast' to generate ideas for a personal narrative, in which they are assigned the task of retelling a childhood story through their adolescent point-of-view. In the center bubble, they might write "adventures," and then branch out to surrounding bubbles, where they might write (or draw) the names of specific adventures they've been on, like hiking in a national park, ice fishing on a frozen lake, or going on a safari with their family. They can continue branching out to even more specific bubbles. For example, they could extend additional arrows out from the safari bubble to brainstorm the parts of that adventure that were especially thrilling, such as getting up close to a hippopotamus, having to survive several days without electricity, or watching a cheetah devour its prey.

We've also seen a cool iteration of a concept map called a lotus grid. In this type of graphic organizer, there is a 3 x 3 grid with a main topic in the center-most square (the eight surrounding squares are sub-topics). Then, there are eight similar 3 x 3 grids surrounding the center 3 x 3 grid, with each one designated for exploring subtopics via facts, information, ideas, visuals, examples, etc.

Flow Charts
Flow charts, timelines, storyboards...these are all different names for graphic organizers that perform a similar task: depicting a sequence of events or ideas. Flow charts can move from left to right, down to up, in an S-shape, or in a wheel - there are few limitations here.

In teaching writing, we've seen flow charts used to help students organize paragraphs or entire essays. Freytag's pyramid - a form of a flow chart - helps students diagram dramatic structure, starting with the exposition of a story, building suspense with rising action, reaching a turning point with the conflict at the climax, moving towards resolution with falling action, and ending with a conclusion. Using bubbles or extending lines, students can cite textual evidence that represents each plot point, draw images to represent a storyboard, or create symbols to depict historical events in a timeline.

Flower Grids
A flower grid is similar to a concept map graphic organizer, except it isn't meant for showing relationships. In a flower grid, there is a center bubble, or 'pistil,' which is embedded among a group of outer bubbles, or 'petals' - like a flower! Instead of making connections to other concepts, a flower grid is best used to perform a 'deep dive' into a singular concept.

The most common use for flower grids is to explore a vocabulary word. The user might write a term in the pistil, and in the four surrounding petals, provide a definition, example of the word in a complete sentence, synonyms, and a visual representation.

We've also seen flower grids used as STEAL charts for characterization. STEAL is an acronym for what a character says, what a character thinks, the effects a character has on other characters, how the character acts, and how the character l ooks. In a STEAL chart, the character's name and/or picture is drawn in the pistil - it is surrounded by an oval divided into five segments, which is then surrounded by an additional oval divided into five segments. In the innermost oval, each segment is dedicated to a letter - S, T, E, A, and L. In each segment, the student can write textual evidence of each element of characterization. Next, in the outermost oval, the student writes their own interpretations for what the textual evidence means.

Columned Charts
Ah, old reliable. The 2-column chart (also known as the T-chart) and its second cousins, the 3-column chart, 4-column chart, and so on. What purpose do columned charts not fulfill? They can be used for examining pros vs. cons, similarities vs. differences, causes and effects, claims vs. evidence (vs. significance), and what a character says vs. what they actually mean. They're ideal for crafting analogies, taking notes, giving peer feedback, and making connections to prior learning.

The KWL chart is one particularly useful 3-column chart that students can return to before, during, and after instruction. When being introduced to a new topic, students write down what they already know about the topic under the K column. In the W column, they jot down what they may want to know about a topic. Finally, in the L column, they reflect upon what they actually l earned during instruction.

Taxonomies
Best suited for categorization and identifying relationships, taxonomies can be used to illustrate hierarchies and designate responsibilities. Typically, the most important (or central) role is at the top, and subsequent bubbles stem downward, indicating a possible chain of command or biological taxonomy (i.e., domain, kingdom, phylum, class, order, family, genus, species) or political taxonomy (i.e., making connections between the executive, legislative, and judicial branches, then listing each of their responsibilities). Taxonomies are excellent tools for group collaboration, where students can record responsibilities under each student's name.

Teachers might use taxonomies to promote critical thinking. For example, they might give a small group of students a pack of 30 index cards with different terms or descriptors written on each one, then give the groups a certain amount of time to create a taxonomy or hierarchy.

Make The Most of Graphic Organizers With These Important Tips

While some students may be able to take any form of graphic organizer and run with it, teachers should model how to use a graphic organizer for any given assignment, or at least suggest different graphic organizers that might be conducive for an assigned task. The teacher can use a document camera to model his/her own thinking, or call upon a student to model the graphic organizer while the teacher adds commentary.

The great thing about graphic organizers is that they are flexible vs. rigid. Best used in the beginning stages of guided or independent practice, they can serve as effective formative assessments or checks for understanding; however, there are rare cases where they should be graded as summative assessments.

If you do decide to grade a graphic organizer, strongly consider relaxing expectations on structure and conventions. It usually does not make sense for a student to fill bubbles with complete sentences. For one, there just isn't that much room. Second, graphic organizers are meant to be a little 'messy.' They're essentially a visual representation of a student's thinking, which is not always linear or obvious to an observer's view. Now is not the time to worry about spelling, capitalization, and punctuation. The ideas are the important piece.

Finally, graphic organizers can be differentiated for various student populations. One group might receive a blank graphic organizer, while another group might get a graphic organizer with one example, and yet another group may receive a graphic organizer that is mostly done and acts as 'guided notes.' Consider having students share their thinking from graphic organizers with one another, and encourage them to synthesize insights from others into their own graphic organizers.

The Best Tools for Creating, Sharing, and Adapting Graphic Organizers Online

There are a variety of digital tools geared toward designing graphic organizers. We've included several of the most popular ones below:

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What Are The Best Graphic Organizers For Promoting Critical Thinking?

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Graphic organizers allow students to visualize, order, and categorize concepts using verbal representations & visuals.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Steve Wyborney's Blog: I'm on a Learning Mission. - Sharing Thoughts About Education

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Exploding Dots, Quadratics, Fractions, Area and Probability

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Explore mathematics with our comprehensive courses. Lesson content that reveals new approaches to learning will help you understand rather than just memorize solutions.

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The beginnings of heuristics - a list of how we solve it?

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Cognition - How We Teach Problem Solving - Heuristics

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Cognition - How We Teach Problem Solving - Heuristics

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How We Manage Resources?

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Number Sense - My Six Strategies for Adding In Our Heads

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Number Sense - My Six Strategies for Adding In Our Heads

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GO Math! Program | K-8 Curriculum | Houghton Mifflin Harcourt

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Pros - Strong at providing teaching directives, provides learner questions to promote mathematical reasoning, covered outliers, provided plenty of practice opportunities.

Cons - No support for anchor charts or advanced organizers (note: learner workbooks are cluttered with information) and problems are not always engaging and are never multi-step nor integrated.  Teachers are expected to teach directly from the workbook and this model does not support constructive teaching (learner building ideas, parking lots), the stages of learning (concrete, iconic and symbolic), support for cognitive growth (deliberate practice, spaced learning (learners were throwing out each completed workbook), building on ideas (it hops across skills; we should be building up), nor a multimodal approach to vocabulary.

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HMH GO Math! Program | K-6 Math Curriculum | Houghton Mifflin Harcourt

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Go Math! for grades K–6 emphasizes ease of use, bringing together assessment, personalized practice, and on-demand professional learning in one place.

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Khan Academy | Free Online Courses, Lessons & Practice

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Khan Academy Online and Supplemental Curriculum

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Khan Academy Online and Supplemental Curriculum

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A comprehensive curriculum to students in kindergarten through college. Run by a team of over 150 people who continue to enhance the available course catalog.

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Why Singapore Math Works Best for Us in our Homeschool

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Singapore Mathematics as a Home School Curriculum

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Singapore Mathematics as a Home School Curriculum

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Why Singapore Math Works Best for Us in our Homeschool

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This guide tells you everything you ever wanted to know about Singapore Math: is it spiral or mastery? Do I need the Home Instructor’s Guide? What makes Singapore Math different from other ho…

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https://www.bbc.co.uk/bitesize/subjects/zqhs34j

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KS3 Maths learning resources for adults, children, parents and teachers.

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KEY FEATURES
1. CPA (Concrete Pictorial Abstract) Approach: Introduces concepts in a tangible way and progresses to increasing levels of abstraction.
2. Number Bonds: Shows the part-whole relationship between numbers.
3. Bar Modeling: Helps students visualize a range of math concepts, such as fractions, ratios, and percentages. Allows students to determine the knowns and unknowns in a given situation.
4. Mental Math: Helps students develop number sense and flexibility in thinking about numbers.

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6 Reasons Why Singapore Math Might Just Be the Better Way

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“When is Cheryl’s birthday?” When the ambiguous high school math problem went viral in April, complete with a handful of seemingly arbitrary answers, it sent many older Americans into a tailspin of confusion. Given the relatively cryptic clues provided, so many wondered, how could you possibly arriv…

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Start Using DeltaMath.com Today (and what DeltaMath can and cannot yet do)

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DeltaMath describes itself as "an online math practice and learning site." If you want your students to practice math concepts from grade 6 through AP Calculus BC, and you want students to get instant feedback, and you want to spend less time answering "is this right?" or "how do I do this?", and you want to spend less time grading homework, then you should start using DeltaMath today.

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"DeltaMath is the bomb dot com." That is what I said to a former colleague when he admitted to having never used DeltaMath.com. He and I have been teaching high school math for over 20 years (which you could probably guess by my use of the very trendy "dot com" joke).

Check out my related posts: How to Use DeltaMath and History of DeltaMath

First, a disclaimer: No, I do not work for DeltaMath. I am not affiliated in any way with DeltaMath. I am not getting paid for writing about how much I love DeltaMath. I am just a huge fan.
me in my DeltaMath merchandise October 2020
What is DeltaMath? What can it do?

If you are a middle school or high school math teacher and are not using DeltaMath with your students, you need to start immediately. DeltaMath is the best website for students to practice math online.

Scroll to the bottom to see my infographic about what DeltaMath can and cannot (yet) do.

If you want your students to practice math concepts from grade 6 through AP Calculus BC, and you want students to get instant feedback, and you want to spend less time answering "is this right?" or "how do I do this?", and you want to spend less time grading homework, then you should start using DeltaMath today.

DeltaMath describes itself as " an online math practice and learning site."

Once a teacher sets up an account, she can assign an unlimited number of problems to an unlimited number of students for FREE! Students will get instant feedback and the assignments are graded automatically.
If you would like to learn more about the creator of DeltaMath, check out my blog post, History of DeltaMath.
I stumbled upon DeltaMath in the summer of 2017 while perusing blogs of math teachers. I started using it that Fall with my Precalculus and Calculus students; they loved it and I was hooked. I convinced several of my colleagues to start using it with their students.

My students love instant feedback which makes sense because when you assign a worksheet or textbook problems, they don't always know if they're right or wrong. Even if you provide the answers to the worksheet or they can reference B.O.B. (the Back Of the Book), students may not be able to determine their error. Even if students can determine their error, they may need a few more practice problems to help prevent that error from reoccurring.

DeltaMath is ideal in the math classroom because students can practice as many problems as they need in order to master a skill.

Top 10 Reasons Why You Should Start Using DeltaMath

1. It's free.

2. It's user-friendly. The interface is better than Khan Academy. It's easy to set up a class and gets students to join the class.

3. There are thousands and thousands of skills available.

4. The students get instant feedback.

5. Students can practice a skill repeatedly until they have mastered it.

6. You don't have to grade papers!

7. You don't have to answer as many "how-to" or "is this right" questions from students.

8. You can easily copy assignments from colleagues.

9. Students can work at their own pace

10. The creator and his team are very receptive to suggestions for improvement. The creator is Zach Korzyk - he tweets @MrDeltaMath; he and his team are active in the Facebook group. You can even request a skill through the website (at the top under the question mark symbol).

Should you upgrade to the Plus version?

At the time of writing, DeltaMath Plus costs $75 for a year subscription and is one of the most valuable subscriptions I have.
Some features in DeltaMath Plus that have been lifesavers during the coronavirus pandemic:

You can create an Assessment.

This is an awesome feature and has continued to improve since it was first launched. For example, recently they added the ability for students to change their answers before they submit the assessment.

Read my blog post about How to Give a Math Test During Distance Learning

You can create your own problems.

I like this feature because there are often times when I cannot find the types of problems I need, but I don't love it as much as I thought I would. Students get accustomed to having multiple problems to try. When you assign your own problem, if a student gets it wrong, they cannot try another one similar to it. You can, of course, give multiple attempts.

Adding your own question is especially helpful on assessments.

You can assign a specific problem to students.

This is awesome for when you find a problem that you want everyone to try, but, like with creating your own problems, if students get it wrong, they cannot try another one similar to it. You can give multiple attempts, though.

You can post an assignment to an individual or group

This feature is particularly useful for giving assessments when you have students that are permitted extra time as part of their accommodations.

There are help videos available to watch for every skill.

You have the ability to hide the videos from students, and you can also see how much of a video a student watched.

(I recently had a student email me to say "I've been trying DeltaMath for hours. I watched the video and I just can't do it, so I gave up." When I looked at his stats, he had only tried 2 problems, had watched 10 seconds of a 10-minute video, and had spent a total of 23 minutes on the assignment. After I shared those stats with him, he finished the assignment.)

Ability to assign sub-types

I like this feature a lot. An example is the module, "Exact Values of Trig Functions (All Six)." When I look at this module, there's an option to click on "Problem types." From there I can choose from options such as, "sin/cos/tan quadrant 1" or "csc/sec/cot quadrants 2,3,4."

If you are not yet in the DeltaMath Official Facebook group, join the helpful community where you can ask questions and share in the delight of using DeltaMath.

If you don't have an account with DeltaMath (why don't you? It's free!) but want to see the types of problems available, you can go to deltamath.com/explore
*Note: with regards to what DeltaMath cannot (yet) do, Mr. DeltaMath (a.k.a. Zach Korzyk) tells me that everything on that list is in some stage of development. The highest priority is the ability to sync with popular LMS platforms. Look for that to be available by August 2021!

Check out my infographic about what DeltaMath can and cannot do!

Have you had the chance to join my email list? You can be one of the first people to find out about new blog posts, free stuff, new resources, and giveaways!

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Start Using DeltaMath.com Today (and what DeltaMath can and cannot yet do)

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"DeltaMath is the bomb dot com." That is what I said to a former colleague when he admitted to having never used DeltaMath.com. He and I have been teaching high school math for over 20 years (which you could probably guess by my use of the very trendy "dot com" joke).

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Brought to you by the team that created the Desmos calculators and activities. Math 6–8 is available now. Algebra 1 will be available for the 2022–2023 school year.

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Rebecca Moore, Math Coach, Naugatuck, CT

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Celebrate every student’s brilliance with the Desmos 6-8 Math Curriculum.

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Singapore Math | The world's top PK-8 math education.

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25 YEARS OF SINGAPORE MATH!

25 years ago my parents introduced the original Primary Mathematics textbooks and workbooks to a few parents in our community of West Linn, Oregon. We had just moved from Singapore where I had attended public school, and, unimpressed by the math education at my new school, my parents wondered if other students and parents might benefit from the Singapore math curriculum...

The Secrets to Singapore's World-class Math Curriculum

This book provides an inside look at Singapore math. Written by Wenxi Lee, a Singaporean who grew up using the method and is now a math education researcher, The Secrets to Singapore's World-class Math Curriculum explains how and why Singapore math works. She weaves personal experience with fascinating research in this approachable yet highly informative read.

DIMENSIONS MATH AT HOME™️ Videos

This comprehensive subscription provides in-depth video lessons for all Dimensions Math Grades 1-6 chapters.

Preview videos here to see why this is a game-changing addition to your Singapore math toolkit.

Dimensions Math PK-5 Resources

Blackline Masters (BLM), Printouts, and more.

Access all Dimensions Math PK-5 resources to use alongside your Dimensions Math Home Instructor's Guides and Teacher's Guides here.

Dimensions Math Resources

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A coherent framework of the mathematics that I learned in elementary and middle school.

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My Mathematics Reference Framework in Detail

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My Mathematics Reference Framework in Detail

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You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

\[f\left( x \right) = 0\]

1. Find the vertex. We'll discuss how to find this shortly. It's fairly simple, but there are several methods for finding it and so will be discussed separately.

2. Find the \(y\)-intercept, \(\left( {0,f\left( 0 \right)} \right)\).

3. Solve \(f\left( x \right) = 0\) to find the \(x\) coordinates of the \(x\)-intercepts if they exist. As we will see in our examples we can have 0, 1, or 2 \(x\)-intercepts.

4. Make sure that you've got at least one point to either side of the vertex. This is to make sure we get a somewhat accurate sketch. If the parabola has two \(x\)-intercepts then we'll already have these points. If it has 0 or 1 \(x\)-intercept we can either just plug in another \(x\) value or use the \(y\)-intercept and the axis of symmetry to get the second point.

5. Sketch the graph. At this point we've gotten enough points to get a fairly decent idea of what the parabola will look like.

Example 1 Sketch the graph of each of the following parabolas.

1. \(f\left( x \right) = 2{\left( {x + 3} \right)^2} - 8\)

2. \(g\left( x \right) = - {\left( {x - 2} \right)^2} - 1\)

3. \(h\left( x \right) = {x^2} + 4\)

Show All Solutions Hide All Solutions
Show Discussion

Okay, in all of these we will simply go through the process given above to find the needed points and the graph.

a \(f\left( x \right) = 2{\left( {x + 3} \right)^2} - 8\) Show Solution

First, we need to find the vertex. We will need to be careful with the signs however. Comparing our equation to the form above we see that we must have \(h = - 3\) and \(k = - 8\) since that is the only way to get the correct signs in our function. Therefore, the vertex of this parabola is,

\[\left( { - 3, - 8} \right)\]

Now let's find the \(y\)-intercept. This is nothing more than a quick function evaluation.

\[f\left( 0 \right) = 2{\left( {0 + 3} \right)^2} - 8 = 2\left( 9 \right) - 8 = 10\hspace{0.25in}y - {\mbox{intercept : }}\left( {{\mbox{0,10}}} \right)\]

Next, we need to find the \(x\)-intercepts. This means we'll need to solve an equation. However, before we do that we can actually tell whether or not we'll have any before we even start to solve the equation.

In this case we have \(a = 2\) which is positive and so we know that the parabola opens up. Also the vertex is a point below the \(x\)-axis. So, we know that the parabola will have at least a few points below the \(x\)-axis and it will open up. Therefore, since once a parabola starts to open up it will continue to open up eventually we will have to cross the \(x\)-axis. In other words, there are \(x\)-intercepts for this parabola.

To find them we need to solve the following equation.

\[0 = 2{\left( {x + 3} \right)^2} - 8\]

We solve equations like this back when we were solving quadratic equations so hopefully you remember how to do them.

\[\begin{align*}2{\left( {x + 3} \right)^2} & = 8\\ {\left( {x + 3} \right)^2} & = 4\\ x + 3 & = \pm \sqrt 4 = \pm 2\\ x & = - 3 \pm 2\hspace{0.25in} \Rightarrow \hspace{0.25in}x = - 1,\,\,x = - 5\end{align*}\]

The two x-intercepts are then,

\[\left( { - 5,0} \right)\hspace{0.25in}{\mbox{and}}\hspace{0.25in}\left( { - 1,0} \right)\]

Now, at this point we've got points on either side of the vertex so we are officially done with finding the points. However, let's talk a little bit about how to find a second point using the \(y\)-intercept and the axis of symmetry since we will need to do that eventually.

First, notice that the \(y\)-intercept has an \(x\) coordinate of 0 while the vertex has an \(x\) coordinate of -3. This means that the \(y\)-intercept is a distance of 3 to the right of the axis of symmetry since that will move straight up from the vertex.

Now, the left part of the graph will be a mirror image of the right part of the graph. So, since there is a point at \(y = 10\) that is a distance of 3 to the right of the axis of symmetry there must also be a point at \(y = 10\) that is a distance of 3 to the left of the axis of symmetry.

So, since the \(x\) coordinate of the vertex is -3 and this new point is a distance of 3 to the left its \(x\) coordinate must be -6. The coordinates of this new point are then \(\left( { - 6,10} \right)\). We can verify this by evaluating the function at \(x = - 6\). If we are correct we should get a value of 10. Let's verify this.

\[f\left( { - 6} \right) = 2{\left( { - 6 + 3} \right)^2} - 8 = 2{\left( { - 3} \right)^2} - 8 = 2\left( 9 \right) - 8 = 10\]

So, we were correct. Note that we usually don't bother with the verification of this point.

Okay, it's time to sketch the graph of the parabola. Here it is.

Note that we included the axis of symmetry in this graph and typically we won't. It was just included here since we were discussing it earlier.

b \(g\left( x \right) = - {\left( {x - 2} \right)^2} - 1\) Show Solution

Okay with this one we won't put in quite a much detail. First let's notice that \(a = - 1\) which is negative and so we know that this parabola will open downward.

Next, by comparing our function to the general form we see that the vertex of this parabola is \(\left( {2, - 1} \right)\). Again, be careful to get the signs correct here!

Now let's get the \(y\)-intercept.

\[g\left( 0 \right) = - {\left( {0 - 2} \right)^2} - 1 = - {\left( { - 2} \right)^2} - 1 = - 4 - 1 = - 5\]

The \(y\)-intercept is then \(\left( {0, - 5} \right)\).

Now, we know that the vertex starts out below the \(x\)-axis and the parabola opens down. This means that there can't possibly be \(x\)-intercepts since the \(x\) axis is above the vertex and the parabola will always open down. This means that there is no reason, in general, to go through the solving process to find what won't exist.

However, let's do it anyway. This will show us what to look for if we don't catch right away that they won't exist from the vertex and direction the parabola opens. We'll need to solve,

\[\begin{align*}0 & = - {\left( {x - 2} \right)^2} - 1\\ {\left( {x - 2} \right)^2} & = - 1\\ x - 2 & = \pm \,i\\ x & = 2 \pm \,i\end{align*}\]

So, we got complex solutions. Complex solutions will always indicate no \(x\)-intercepts.

Now, we do want points on either side of the vertex so we'll use the \(y\)-intercept and the axis of symmetry to get a second point. The \(y\)-intercept is a distance of two to the left of the axis of symmetry and is at \(y = - 5\) and so there must be a second point at the same \(y\) value only a distance of 2 to the right of the axis of symmetry. The coordinates of this point must then be \(\left( {4, - 5} \right)\).

Here is the sketch of this parabola.

This one is actually a fairly simple one to graph. We'll first notice that it will open upwards.

Now, the vertex is probably the point where most students run into trouble here. Since we have by itself this means that we must have \(h = 0\) and so the vertex is \(\left( {0,4} \right)\).

Note that this means there will not be any \(x\)-intercepts with this parabola since the vertex is above the \(x\)-axis and the parabola opens upwards.

Next, the \(y\)-intercept is,

\[h\left( 0 \right) = {\left( 0 \right)^2} + 4 = 4\hspace{0.25in}y - {\mbox{intercept : }}\left( {0,4} \right)\]

The \(y\)-intercept is exactly the same as the vertex. This will happen on occasion so we shouldn't get too worried about it when that happens. Although this will mean that we aren't going to be able to use the \(y\)-intercept to find a second point on the other side of the vertex this time. In fact, we don't even have a point yet that isn't the vertex!

So, we'll need to find a point on either side of the vertex. In this case since the function isn't too bad we'll just plug in a couple of points.

\[\begin{align*}h\left( { - 2} \right) & = {\left( { - 2} \right)^2} + 4 = 8\hspace{0.25in} \Rightarrow \hspace{0.25in}\left( { - 2,8} \right)\\ h\left( 2 \right) & = {\left( 2 \right)^2} + 4 = 8\hspace{0.25in} \Rightarrow \hspace{0.25in}\left( {2,8} \right)\end{align*}\]

Note that we could have gotten the second point here using the axis of symmetry if we'd wanted to.

Here is a sketch of the graph.

Let's graph some parabolas.

Example 2 Sketch the graph of each of the following parabolas.

1. \(g\left( x \right) = 3{x^2} - 6x + 5\)

2. \(f\left( x \right) = - {x^2} + 8x\)

3. \(f\left( x \right) = {x^2} + 4x + 4\)

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a \(g\left( x \right) = 3{x^2} - 6x + 5\) Show Solution

For this parabola we've got \(a = 3\), \(b = - 6\) and \(c = 5\). Make sure that you're careful with signs when identifying these values. So we know that this parabola will open up since \(a\) is positive.

Here are the evaluations for the vertex.

\[\begin{align*}x & = - \frac{{ - 6}}{{2\left( 3 \right)}} = - \frac{{ - 6}}{6} = 1\\ y & = g\left( 1 \right) = 3{\left( 1 \right)^2} - 6\left( 1 \right) + 5 = 3 - 6 + 5 = 2\end{align*}\]

The vertex is then \(\left( {1,2} \right)\). Now at this point we also know that there won't be any \(x\)-intercepts for this parabola since the vertex is above the \(x\)-axis and it opens upward.

The \(y\)-intercept is \(\left( {0,5} \right)\) and using the axis of symmetry we know that \(\left( {2,5} \right)\) must also be on the parabola.

Here is a sketch of the parabola.

In this case \(a = - 1\), \(b = 8\) and \(c = 0\). From these we see that the parabola will open downward since \(a\) is negative. Here are the vertex evaluations.

\[\begin{align*}x & = - \frac{8}{{2\left( { - 1} \right)}} = - \frac{8}{{ - 2}} = 4\\ y & = f\left( 4 \right) = - {\left( 4 \right)^2} + 8\left( 4 \right) = 16\end{align*}\]

So, the vertex is \(\left( {4,16} \right)\) and we also can see that this time there will be \(x\)-intercepts. In fact, let's go ahead and find them now.

\[\begin{align*}0 & = - {x^2} + 8x\\ 0 & = x\left( { - x + 8} \right)\hspace{0.25in} \Rightarrow \hspace{0.25in}x = 0,\,\,x = 8\end{align*}\]

So, the \(x\)-intercepts are \(\left( {0,0} \right)\) and \(\left( {8,0} \right)\). Notice that \(\left( {0,0} \right)\) is also the \(y\)-intercept. This will happen on occasion so don't get excited about it when it does.

At this point we've got all the information that we need in order to sketch the graph so here it is,

In this final part we have \(a = 1\), \(b = 4\) and \(c = 4\). So, this parabola will open up.

Here are the vertex evaluations.

\[\begin{align*}x = - \frac{4}{{2\left( 1 \right)}} = - \frac{4}{2} = - 2\\ & y = f\left( { - 2} \right) = {\left( { - 2} \right)^2} + 4\left( { - 2} \right) + 4 = 0\end{align*}\]

So, the vertex is \(\left( { - 2,0} \right)\). Note that since the \(y\) coordinate of this point is zero it is also an \(x\)-intercept. In fact it will be the only \(x\)-intercept for this graph. This makes sense if we consider the fact that the vertex, in this case, is the lowest point on the graph and so the graph simply can't touch the \(x\)-axis anywhere else.

The fact that this parabola has only one \(x\)-intercept can be verified by solving as we've done in the other examples to this point.

\[\begin{align*}0 = {x^2} + 4x + 4\\ & 0 = {\left( {x + 2} \right)^2}\hspace{0.25in} \Rightarrow \hspace{0.25in}x = - 2\end{align*}\]

Sure enough there is only one \(x\)-intercept. Note that this will mean that we're going to have to use the axis of symmetry to get a second point from the \(y\)-intercept in this case.

Speaking of which, the \(y\)-intercept in this case is \(\left( {0,4} \right)\). This means that the second point is \(\left( { - 4,4} \right)\).

Here is a sketch of the graph.

Example 3 Convert each of the following into the form \(f\left( x \right) = a{\left( {x - h} \right)^2} + k\).

1. \(f\left( x \right) = 2{x^2} - 12x + 3\)

2. \(f\left( x \right) = - {x^2} + 10x - 1\)

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Show Discussion

Okay, as we pointed out above we are going to complete the square here. However, it is a slightly different process than the other times that we've seen it to this point.

a \(f\left( x \right) = 2{x^2} - 12x + 3\) Show Solution

The thing that we've got to remember here is that we must have a coefficient of 1 for the term in order to complete the square. So, to get that we will first factor the coefficient of the term out of the whole right side as follows.

\[f\left( x \right) = 2\left( {{x^2} - 6x + \frac{3}{2}} \right)\]

Note that this will often put fractions into the problem that is just something that we'll need to be able to deal with. Also note that if we're lucky enough to have a coefficient of 1 on the term we won't have to do this step.

Now, this is where the process really starts differing from what we've seen to this point. We still take one-half the coefficient of \(x\) and square it. However, instead of adding this to both sides we do the following with it.

\[{\left( { - \frac{6}{2}} \right)^2} = {\left( { - 3} \right)^2} = 9\] \[f\left( x \right) = 2\left( {{x^2} - 6x + 9 - 9 + \frac{3}{2}} \right)\]

We add and subtract this quantity inside the parenthesis as shown. Note that all we are really doing here is adding in zero since 9-9=0! The order listed here is important. We MUST add first and then subtract.

The next step is to factor the first three terms and combine the last two as follows.

\[f\left( x \right) = 2\left( {{{\left( {x - 3} \right)}^2} - \frac{{15}}{2}} \right)\]

As a final step we multiply the 2 back through.

\[f\left( x \right) = 2{\left( {x - 3} \right)^2} - 15\]

And there we go.

b \(f\left( x \right) = - {x^2} + 10x - 1\) Show Solution

Be careful here. We don't have a coefficient of 1 on the term, we've got a coefficient of -1. So, the process is identical outside of that so we won't put in as much detail this time.

\[\begin{align*}f\left( x \right) & = - \left( {{x^2} - 10x + 1} \right)\hspace{0.25in}{\left( { - \frac{{10}}{2}} \right)^2} = {\left( { - 5} \right)^2} = 25\\ & = - \left( {{x^2} - 10x + 25 - 25 + 1} \right)\\ & = - \left( {{{\left( {x - 5} \right)}^2} - 24} \right)\\ & = - {\left( {x - 5} \right)^2} + 24\end{align*}\]

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In this section we will be graphing parabolas. We introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas. We also illustrate how to use completing the square to put the parabola into the form f(x)=a(x-h)^2+k.

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Whelp, it looks like Mathshare is defunct. I loved the concept of technology that railed the learners towards a step-based approach. Site still kinda stands, but don't try to build anything too meaningful on it unless they start better releases.

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Help students share and organize their math work

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High production, high standard, engaging videos about almost any branch of mathematics. How can you not be engaged by Brody and his antics across the UK? My favorite Brody episode will always be his building a pi of pies. And Cliff Stoll nearly burning the house down with his birthday cake of fractions. Hannah Fry trying to measure the radius and circumference of the earth from the top of the Shard building with her astrolabe and giant protractor.

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