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Find what you need using this resource finder. All you need to know is the numeracy strategy level from NZ Maths.

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Welcome to the nzmaths Resource Finder.Use this section of the site to browse our mathematics learning resources.Login or sign up for a free account, and you can save collections of resources for lesson planning. Please read the Help File for information on how to create plans.

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An online K-8 math program designed to complement math lessons. Try sample lessons here: http://www.dreambox.com/k-8-math-lessons
Individual subscriptions - $99.95, Family plan - $149.95

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Monitor student activity
Measure student growth
Predict future proficiency

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Welcome to DreamBox Math!

DreamBox is a K-8 digital math program designed to complement your math curriculum whether in the classroom or at home. Our rigorous and interactive lessons adapt to each student providing the ultimate personalized learning experience. Available in English and Spanish!
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DreamBox personalizes instruction, complements remote learning and boosts student confidence.

DreamBox dynamically adapts based on in-the-moment formative assessment tools that determine how students solve problems, providing powerful data to identify gaps and personalized learning pathways. Our digital program helps schools and districts meet students where they are - regardless of remote learning conditions - and provides effective insights for planning.
Learn how DreamBox can help your district

Adaptive technology for every child. Powerful insights for every teacher.

With over 2,000 lessons designed by math teachers and aligned to state standards, DreamBox helps build conceptual understanding, increase procedural fluency, and raise student achievement. We've combined rigorous, standards-aligned lessons, with professional development to support strong implementations and complement instruction no matter where it takes place. DreamBox is available in English and Spanish, because every child learns best in their primary language.
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Make screen time FUNctional!

Keep kids engaged and learning- on a platform they'll love. DreamBox complements your child's remote learning schedule and is proven to boost math performance. Whether your learner is a math whiz or needs help filling some gaps, DreamBox provides individualized instruction and builds confidence.

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Building math confidence

We believe a positive mindset goes a long way. Students build math confidence as they strengthen their social-emotional skills - skills that include grit, perseverance and goal-setting. As many schools engage in distance learning this Fall, DreamBox has three simple tips for helping your child build confidence in math from home.
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Creating student engagement in a virtual environment

As many shift to remote learning models, traditional teacher engagement strategies have been flipped upside down. Enter online learning, which speaks to a different type of engagement needed. DreamBox Math was built by educators with student engagement top of mind. Learn how our program ensures engagement and discover best practices from DreamBox teachers.
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Remote learning ready

DreamBox Math can be used in all instructional models; in person, virtual or hybrid learning. Keep students engaged, gain insight into student progress and access reports on classroom, school and district math proficiency.
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With a STRONG rating from ESSA and multiple third-party studies, DreamBox Math is proven to increase student achievement. DreamBox has won more than 40 industry awards and is used by 150,000 teachers and 3.5 million students in the U.S. and throughout Canada, and Mexico.
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Center Point Urbana Intermediate School
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Predict student efficiency - no testing required

Predictive Insights for K-5 is an innovative new reporting tool that can predict future proficiency for year-end state math assessments throughout the school year. Gain a deeper understanding of where students are at, regardless of remote learning conditions.
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See the DreamBox difference in action

Over 2,300 engaging, standards-aligned lessons in English and Spanish that are proven to build problem-solving strategies, hone critical-thinking skills, and develop math fluency.

New DreamBox features to support all learning models

New product capabilities provide educators with critical tools to engage, connect with and motivate students whether learning inside the classroom or remotely.
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DreamBox Learning - Online Math Learning for Students, K-8

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↓ Skip to Main Content Monitor student activity Measure student growthPredict future proficiency See What's New DreamBox is a K-8 digital math program designed to complement your math curriculum whether in the classroom or at home. Our rigorous and interactive lessons adapt to each student providing the ultimate personalized learning experience.

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Free Online Math Learning

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Great online resource with fantastic explanations.

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Math explained in easy language, plus puzzles, games, worksheets and an illustrated dictionary. For K-12 kids, teachers and parents.

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An article from Stanford University about a different approach to teaching mathematics.

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For many students, math class is the subject of nightmares. Many who enthusiastically show off their counting skills in pre-school years later consider math class the most loathed hour of the school day. The problem, according to a Stanford education professor, is a matter of mindset.

"All children are different in their mathematical thinking, strengths and interests," said Jo Boaler, a professor of mathematics education at Stanford Graduate School of Education.

Boaler has studied how students learn math, to identify why so many students end up hating or fearing math, and, too often, underachieve. She has followed thousands of students through middle and high schools to ascertain exactly how they learn and what are the most effective ways they reach their potential.

In her new book, Mathematical Mindsets, Boaler describes how society has traditionally valued one type of math learner - one who can memorize well and calculate fast - as opposed to others who have the same potential but may be deeper, slower and more creative. The book offers research evidence and resources for teachers and parents to help children learn math well, in the classroom and at home.

Test-taking pressures

The "testing culture" in American schools is a major problem for math learners, Boaler said, noting that exams and tests are far more pervasive in math than other subjects.

"Students from early ages realize that math is quite different than other subjects, and that it depends heavily on taking tests and answering uninteresting questions."

This combination of frequent testing, procedural teaching and uninteresting questions disconnected from students' lives causes many students to regard math as a "cold, lifeless subject" without a human connection, she said.

Many students, she said, believe incorrectly that to be good at math they need to be fast at math - too many classes emphasize speed in math and memorization.

Boaler has published research and strategies on the best ways for students to learn math "facts" without the fear and anxiety that many students feel when given timed tests and flash cards.

For example, speed pressure in math causes the early onset of math anxiety for many students, she said. And children who think more slowly and deeply are often turned off by math because they see it as a subject of shallow recall of facts and rules.

Opening up mathematics

The good news is that any student's negative perception of math can dramatically change, Boaler said. In her recent summer math camp for seventh- and eighth-grade students, which can be seen in this video, students learned to enjoy math and they improved their achievement dramatically through open, creative math lessons.

Boaler works with Stanford psychology Professor Carol Dweck to deliver growth mindset interventions to teachers and students. A "growth mindset" is built around the idea that most basic abilities can be developed and expanded upon through dedication and hard work. By contrast, with a "fixed mindset," people believe their basic qualities, like their intelligence or talent, are simply fixed traits.

"When we open up mathematics and teach broad, visual, creative math, then we teach math as a learning subject instead of as a performance subject," Boaler said.

Boaler offers resources on how to develop growth mindsets for math learners. Her new Stanford center, youcubed, which is funded by the Bill & Melinda Gates Foundation, provides free mindset math lessons that were used in over 100,000 schools last fall. The website has attracted millions of visitors in the last month alone. She also has online courses for teachers and parents and for students to help them teach and learn math.

When schools teach young people growth mindset mathematics, Boaler said, the outcome is that the subject becomes deeper and filled with more connections, so students enjoy it more and achieve at higher levels.

Math for today's tech world

Boaler has also worked with the Program for International Student Assessment tests team, analyzing their data set of 13 million students worldwide. They found that the lowest achieving students are those who use a memorization strategy. The highest performers are those who see math as a set of connected, big ideas.

Boaler agrees with high-tech leaders such as Conrad Wolfram, who supports "broad, multidimensional" mathematics, which involves problem solving, modeling, reasoning, making connections and thinking deeply.

She points out that students entering the 21st-century workplace need to be able to ask questions of data, map out mathematical pathways and reason quantitatively - routine calculations, after all, will be performed by machines. She cites research studies that demonstrate how such an approach can engage more young people and put them on a path to success.

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Research shows how children can enjoy and succeed in math, Stanford expert says

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For many students, math class is the subject of nightmares. Many who enthusiastically show off their counting skills in pre-school years later consider math class the most loathed hour of the school day. The problem, according to a Stanford education professor, is a matter of mindset.

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A "Week of Inspirational Math" lessons designed for students in grades 1 - 12 from Stanford University.

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Choose your own maths adventure with our interactive tools that allow you to build a custom playlist of inspirational activities!

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Online PD offered by NZ maths.

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nzmaths | Numeracy Workshops | Assessment | Using GloSS: Global Strategy Stage Assessment

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The GloSS assessment enables you to identify the strategy stage students are operating at across all three strategy domains, known as the global strategy stage. It consists of a series of strategy questions which can be administered to individual students in a few minutes or less.

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"Global Strategy Stage (GloSS) forms can be used to determine stage information for all three strategy domains".
https://nzmaths.co.nz/gloss-forms

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"Global Strategy Stage (GloSS) forms can be used to determine stage information for all three strategy domains".
https://nzmaths.co.nz/gloss-forms

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"Global Strategy Stage (GloSS) forms can be used to determine stage information for all three strategy domains".
https://nzmaths.co.nz/gloss-forms

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"Global Strategy Stage (GloSS) forms can be used to determine stage information for all three strategy domains".
https://nzmaths.co.nz/gloss-forms

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Objectives and activities to support each strategy level for Number Knowledge

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Addition, Subtraction, and Place Value - Book 5

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Addition, Subtraction, and Place Value - Book 5

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Objectives and activities to support each strategy level for Addition, Subtraction, and Place Value

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Explanation behind the number framework of NZ Maths.

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Fraction, Decimals and Percentages - Book 7

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Fraction, Decimals and Percentages - Book 7

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Objectives and activities to support each strategy level for Fraction, Decimals and Percentages.

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An example of how to structure Math Workshop.

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Objectives and activities to support each strategy level for Multiplication and Division.

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Math Instruction for Struggling Students

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Math Instruction for Struggling Students

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A short guide outlining important aspect of instruction.

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Mathematics Instruction LD Guide for Teachers.pdf

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How to start Number Talks in a classroom.

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Teacher Guide: How Visual is Your Math Teaching?

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Teacher Guide: How Visual is Your Math Teaching?

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A great Teacher Guide from YouCubed.org.

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An example of how to incorporate visual math activities from YouCubed.org.

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SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning. 

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SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning. 

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An article from Jo Boaler about the "Importance of Visual Mathematics for our Brain and Learning."

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Objectives and activities to support each strategy level for Fractions, Decimals, and Percentages.

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Objectives and activities to support each strategy level for Number Sense and Algebraic Thinking.

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Measurement, Geometry, Algebra and Statistics

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Measurement, Geometry, Algebra and Statistics

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Objectives and activities to support each strategy level for Measurement, Geometry, Algebra and Statistics.

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* For Tier II and III
* Requires Level B qualification for purchase.

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The KeyMath3 Diagnostic Assessment is an individually administered measure of essential mathematical concepts and skills. keymath,keymath 3,math skills,math test,math assessment,teaching math,math problems,elementary math

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Two teachers use books to start their math lessons in Pre-Algebra and Calculus.

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"Context and prior knowledge are critical components in fostering comprehension, regardless of the topic," according to Faith Wallace, co-author of Teaching Math Through Reading. Reading literature is one of several ways to build that context and background knowledge. "When math is integral to the story students can learn the concepts in a natural way, become inquisitive, engage in thoughtful conversation, and more," said Wallace.

The combination of mathematical, literary and personal reflection, along with students' genuine interest in the story, leads to higher student engagement, Bezaire said. Year after year, his students who previously kept quiet raised their hands during discussions of The Curious Incident . "Very often, this continues into the rest of the year after our novel study is done," he said. "Often when middle school students get momentum in a certain class, they are hardy enough to allow it to continue even when the unit of study changes."
Calculus Book Club
Two years ago, when a schedule change created extra periods in Sam Shah's multivariable calculus course, he instituted a class book club. The students started with the satirical science fiction novel Flatland by Edwin Abbott and later read several nonfiction texts about mathematicians and mathematical ideas. Book club meetings took place during a block of 30 to 40 minutes a few times per month, with a rotating pair of students leading each discussion.

In the first year, Shah said, his biggest challenge was deciding how much to chime into the discussions. It's as important to create a relaxed atmosphere for the meetings as it is to keep students focused on the text, he said.

During the second year of book club, he made an effort to intervene less often. "When I reflected upon what my goal was ... it wasn't to teach kids how to do close readings and feel like drudgery. The readings were picked to inspire kids to think, to have strong feelings about, to be curious about something mathematical that showed up, to see and think about math differently."

That's what the readings did.

"What I appreciated most is how humanizing our conversations were of mathematics - in terms of who was doing it - and how much curiosity students brought to the mathematical ideas they were exposed to."

One student, for example, used The Calculus of Friendship by Steven Strogatz as the model for her final course project , in which she explored her identity and mathematical experiences using calculus concepts.

Although another schedule change this year forced Shah to drop book club from calculus, he has continued the club outside class with interested students.

"If you have the time, it's a magical way to get kids to see mathematics through a number of different lenses," he said.

Shah created a list of titles that would work well in a math book club, and Bezaire's curriculum for The Curious Incident of the Dog in the Night-Time is available on his website . MindShift asked the two teachers to share their advice for educators who want to try incorporating literature into their own math classrooms.

Lay the groundwork for the unit by communicating with parents, other teachers, administrators, students before diving in. There may be resistance: the book has been removed from some schools because of profanity.

Stock up on throat lozenges or tea with honey. "I speak out loud in front of classes for a living, and it's still a stretch for me to read the book out loud four times per day," Bezaire said.

Pre-read each day's reading passage to find teachable moments: clues, red herrings and math worth expanding on. Make notes in your copy of the novel to make things easier the second year.

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How Reading Novels in Math Class Can Strengthen Student Engagement

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"Context and prior knowledge are critical components in fostering comprehension, regardless of the topic," according to Faith Wallace, co-author of Teaching Math Through Reading . Reading literature is one of several ways to build that context and background knowledge.

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Various Tasks to fit your classroom. Choose the concept, grade, mathematical topic and practice you are going over in class.

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Ideas from Edutopia.

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Math used to be all rote memorization and pencil-to-paper equations disconnected from the real world, but more and more teachers are realizing the importance of making practical, relevant connections in math.

We asked our audience of educators: How do you use the real world to teach math? We've collected some of the most interesting answers, ways teachers are connecting math to the everyday lives of their students.

The Real-World Math Wall

To get her fifth-grade students thinking about the math in their lives-and to head off the inevitable "we'll never use this in the real world" complaint-Samantha Baumgardner, a teacher at Woodrow Petty Elementary School in Taft, Texas, has them bring in a common item and write three ways it relates to math on a notecard. These objects form the class's real-world math wall.

An interesting rule: Once something is placed on the wall, the same item can't be brought in again-pushing students to think outside the box to make real-world math connections. Students bring in objects like playing cards, cake pans, softball score sheets, and cookie recipes. One student brought in a medicine dropper and by way of explanation wrote, "The medicine dropper helps you measure water, and it also helps you with cooking steak."

A School Water Audit

At North Agincourt Jr. Public School in Scarborough, Canada, Krista Dunlop-Sheppard, a bilingual resource and home school teacher for grades 1-6, has her students conduct a water audit at home and at their school. Her students have a wide range of math ability: In a single class, she has students with learning disabilities, students who are gifted, and students who have no diagnoses but need extra support. Modifying a pilot project created by the Toronto Zoo Education Department, students add, subtract, find averages, and measure liquids-like the flow rate of all the water fountains, toilets, and urinals-to measure the amount of water their school uses in a day.

They also interview custodians to discover their daily water usage while mopping floors, and do online research to find out how much water the cafeteria dishwasher uses. When finished, students suggest ways for the school to conserve-like collecting rainwater in a barrel to water plants, and cleaning paint brushes in a bucket instead of using running water. In June, students repeat the water audit and see if the changes they implemented made a difference.

Acting Out Restaurant Scenarios

There's nothing wrong with using money to teach negative and positive numbers, or pizza to introduce fractions, but Justin Ouellette-a third- to fifth-grade International Baccalaureate educator at Suzhou Singapore International School in China-takes these exercises a memorable step further, bringing in menus so students can act out true-to-life restaurant scenarios. Going dutch on dinner and tipping reinforces addition, subtraction, decimals, and percents, Ouellette says.

If you need a good resource: Ouellette has used this free lesson plan about a fictional eatery called the Safari Restaurant.

Integrating Math Into English and History

Making real-world math connections can happen outside of math class, too.

While reading Elie Wiesel's Night, 12th-grade students at Kittatinny Regional High School in Hampton Township, New Jersey, calculate the volume of 11 million pennies to help them imagine the impact of the lives lost during the Holocaust. Ashley Swords, a resource center English teacher for grades nine to 12, uses pennies because they are small and plentiful and allow her to recontextualize a familiar, everyday object.

Students perform other calculations to amplify the impact of the lessons-at the school's football field, for example, they determine the volume of Swords herself and then calculate how many football fields would be needed to bury the 11 million Holocaust victims if they were each Swords's size and were buried in graves 10 feet deep. Guesses ranged from two to 20 football fields, with students finally concluding that it would take about 343 football fields.

Swords knew this lesson was a success when a group of six seniors got emotional after completing it and realizing the magnitude of the deaths in World War II.

Math Recipes

Recipes were perhaps the most popular idea among the elementary teachers who responded to our request for real-world math examples. Fifth-grade teacher Gabi Sanfilippo of Meadow Ridge in Orland Park, Illinois, for example, asked her students to write down one to two ways they used math outside of the classroom during spring break-and more than half of her students wrote that they practiced using measurements and fractions while baking and cooking with their families.

In class, students practice halving, tripling, or quadrupling recipes based on how many people they'd cook or bake for. Most teachers don't actually cook in class, but often students cook at home to practice their new skills.

Another educator, Elizabeth Eagan of Bastrop Independent School District in Texas, brings in a toaster oven to bake in class. She teaches the visually impaired, from newborns to 22-year-olds, using recipes in large print, braille, or audio to show the real-world application of adding and subtracting fractions.

Eagan prints out recipes at 129 percent for her low-vision students or converts the text to braille using braille transcription software, and then prints them using a braille printer. She purchased , a cookbook in both braille and print that makes it easier for families and teachers to help their students if they haven't mastered the tactile language. Students may use electronic magnifying glasses like Pebble and Ruby. For audio, Eagan records herself reading the recipes, has a peer or parent help, or uses the app Seeing AI, which can scan and read recipes aloud.

Grocery Store Field Trip

Many teachers make real-world math connections to grocery shopping. Leanna Agcaoili's second-grade students at Joseph J. Fern Elementary School in Honolulu, Hawaii, are tasked with creating a healthy meal for their family on a $20 budget. On a grocery store field trip, students practice adding and subtracting one- and two-digit whole numbers-and learn about money and budgeting in the process.

Agcaoili says she'll do a practice run in class next year, noting that the first time through some students had difficulty finding their ingredients.

Graphing Favorite Halloween Candy Wrappers

After Halloween, Dottie Wright Berzins, a retired public school teacher, had her students bring in wrappers from their favorite Halloween candy. Depending on the age, the students then created graphs showing their favorite candies.

Younger ages built life-size candy bar graphs, marking the x- and y-axis with masking tape on the floor and using the wrappers to represent the bars. Older students constructed tally charts and paper graphs, and followed ads, tracked which brands advertised more, interviewed peers about their favorite candy, made predictions, and created what-if scenarios-like what if the price of chocolate increased-how would that variable impact the graph?

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Math used to be all rote memorization and pencil-to-paper equations disconnected from the real world, but more and more teachers are realizing the importance of making practical, relevant connections in math. We asked our audience of educators: How do you use the real world to teach math?

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K-12 Online Learning

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A great way to explore math concepts using Desmos.

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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Math curriculum, modules, and activities from the state of NY (aligned to Common Core).

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The New York State Education Department discontinued support for the EngageNY.org website on July 7, 2022. The NYSED encourages educators to download any EngageNY content they wish to use in the future from our archive sites below.

All ELA and mathematics curriculum files will be available at the links below, and will remain free and licensed under the Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA) license.

Archived EngageNY Curriculum Files:

Grades 3-8 ELA and Mathematics Test Materials:
Questions regarding this change may be directed to the EngageNY Help Desk.

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The New York State Education Department discontinued support for the EngageNY.org website on July 7, 2022. The NYSED encourages educators to download any EngageNY content they wish to use in the future from our archive sites below.

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Take a course with YouCubed.Org (Stanford University) for $99.00.

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Inspire ALL Students with Open, Creative Mindset Mathematics

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Journal Prompts explaining concepts and student thinking.

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Math Games for Conceptual Understanding and Fluency (Grade 5).

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Explanation of Rich Tasks in Math.

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Criteria for Rich Tasks.

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Analyzing Student Tasks.

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Recommended Manipulatives for Math Education (Grade 5).

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A research paper by Jo Boaler at Stanford University.

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A free resource for teachers and students! By entering a teacher code, students can play math games to work on their skills.

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Another free resource for teachers and students! By entering a teacher code, students can work on individual math lesson to work on the skills they need to close the gap.

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It's simple to get started!

Simply send an email to sarah@mobymax.com, with the following information for each teacher that you would like to include in the school or district pilot:

Teacher full name

Teacher email address

School name

That's it! We'll do all the work to get your teachers started with MobyMax.

If you have any questions, please give us a call at 888-793-8331.

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Award-winning MobyMax helps struggling learners quickly catch up to grade level and closes learning gaps for all your students. Find and fix missing skills with personalized learning, pinpoint assessments, and motivating rewards.

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This is so cool. It is an interactive math developmental continuum to foster mathematical mindset.

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Mathematical Mindset Teaching Guide, Teaching Video and Additional Resources - YouCubed

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We have designed a Mathematical Mindset Guide to help teachers create or strengthen a growth mindset culture. This guide contains five Mathematical Mindset Practices along with links to teaching videos. […]

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Mathematics help design the optimal instrument in terms of shape and sound.

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Seven examples how math became art using ratios, patterns, and formulas.

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While maths might seem like a purely formulaic pursuit, the patterns and ratios it produces can help create some of history's most striking works of art - as anyone who's read The Da Vinci Code will know.

Just take a look at Leonardo Da Vinci's geometric sketches inside Luca Pacioli's book, De Divina Proportione (The Divine Proportion), or M. C. Escher's mathematically accurate prints, and you'll realise that the purity and patterns found within numbers and forumulae can transform the world into a more beautiful place.

But it's not just historically - even today, mathematicians and artists are bringing their skills together to create some truly beautiful works. And with the help of computers, they've taken things to a whole new level.

Below are seven of our favourite recent adventures in maths and art.
1. Simon Beck's snow art
Simon Beck is a mapmaker by trade, but his passion for art inspired him to create these epic 'snowscapes' in the European Alps.

Each one takes 11 hours and Beck makes them using nothing but a compass and his snowshoes, and most of them depict mathematical formation such as a Koch snowflake or a Sierpinski triangle, which you can see below.

He chooses to draw with maths because of the simplicity of the patterns, he told Alex Bellos over at The Guardianin 2014. "You can get to drawing much sooner," he says. "You are just following simple rules. You don't have to keep referring to a diagram. You can do it from memory. And they just look the best."

See more here.
2. Hamid Naderi Yeganeh's computer illustrations
Iranian arist Hamid Naderi Yeganeh uses mathematical formulae to create intricate, computer-generated illustations - his program can create thousands a day. The emerging shapes were always beautiful, but he began to realise that some of them also randomly represented real-life objects.

"I change the formulae to find better shapes. But I don't know anything about the results of the programs before running them. For example, I found [the] boat and animals accidentally," he told Science Friday.

He now tweaks his data to make more of these recognisable shakes, in order to help share "the power of mathematics" with the world. He's also made his formulae and illustrations open to the public on his website so anyone can create their own.
3. Tom Beddard's Fabergé Fractals
Fractals are patterns that repeat at every scale - creating never-ending swirls, lines, and curves that have been loved in the natural, math, and art worlds for centuries. To show his appreciation, UK physicist Tom Beddard decided to create digital renderings of 3D Fabergé eggs covered in these detailed fractal patterns.

"The 3D fractals are generated by iterative formulae whereby the output of one iteration forms the input for the next," Beddard told My Modern Met. "The formulae effectively fold, scale, rotate or flip space. They are truly fractal in the fact that more and more detail can be revealed the closer to the surface you travel."

Either way, they're incredibly beautiful. See more of his work here.
4. Liz Blakenship and Daniel Ashlock's taxonomy of fractals
Even if you're a die-hard fractals fan, what you might not know is that there are many different types of fractals out there, and they don't all look like the ones above. That's why Liz Blakenship and Daniel Ashlock have created a taxonomy of fractals, complete with illustrations to show them off in all their glory.

These L-system fractals, for example, look more like exotic ferns than mathematical diagrams. But they're still made up of repeating patterns. "These L-systems use two angles, given by the letters A and B and two distances given by the letters C and D," Ashlock and Blakenship write.

See more fractals in their taxonomy.
5. Henry Segerman's 3D models
Australian mathematician Henry Segerman creates illustrations and 3D printed models that express mathematical formulae and concepts, to help his students better understand them.

"Students should be given time to understand the language of mathematics and to creatively apply it to solve problems. Often, maths classes never go beyond rote exercises, in contrast with an English class in which we would use the language to create a new idea, a story or poem," Segerman says.

"The language of mathematics is often less accessible than the language of art, but I can try to translate from one to the other, producing a picture or sculpture that expresses a mathematical idea."

6. The Hevea Project's models of isometric embedding

Isometric embedding is a little complex to understand, but it was fundamental work done by A Beautiful Mind mathematician John Nash, along with Nicolaas Kuiper - and it explains how the entire world can be contained in grain of sand.

"This sounds ridiculous. For instance, take a sphere - say the surface of a tennis ball - and imagine shrinking it down to have a nanometre radius," writes Daniel Matthews about isometric embedding. "Nash and Kuiper show that by 'ruffling' the surface sufficiently (but always smoothly; no creasing or folding or ripping or tearing allowed!) you can have an isometric copy of your original tennis ball, all contained within this nanometre radius."

A French team of mathematicians calling themselves the Hevea Project have now created digital constructions of what this would look like, and the results are spectacular.

Read more about their work here.
7. Kerry Mitchell's celebration of the Curiosity landing on Mars
If there's one thing better than mathematical art, it's mathematical art that celebrates space exploration, like this image created by renowned artist and former NASA engineer, Kerry Mitchell, in 2012 to celebrate the Curiosity rover landing on Mars.

Although it looks like a regular painting, Mitchell creates all his art using algorithms and fractals.

"This image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration. 'Curiosity' celebrates both the unsung measure of central tendency, the harmonic mean, and the Curiosity rover's landing on Mars in August 2012," writes Mitchell.
H/T: The Science Explorer

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7 Times Mathematics Became Art And Blew Our Minds

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While maths might seem like a purely formulaic pursuit, the patterns and ratios it produces can help create some of history's most striking works of art - as anyone who's read The Da Vinci Code will know. Just take a look at Leonardo Da Vinci's geometric sketches inside Luca Pacioli's book, De Divina Proportione (The Divine Proportion), or M.

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An article that explains math and art from the American Mathematical Society.

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Our mission is to further the interests of mathematical research, scholarship and education.

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A TED talk by Emmanuel Schanzer about the importance of teaching concepts and process.

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Why is algebra so hard? | Emmanuel Schanzer | TEDxBeaconStreet

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A TED talk on mathematics as the secret to understanding our world through patterns, formulas, and numbers.

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Math is the hidden secret to understanding the world | Roger Antonsen

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Calculus is used to solve motion, heat, marginal cost & revenue, birth/death rates and etc.

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What is Calculus? When Do You Use It In The Real World?

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One of the foremost branches of mathematics is calculus. The formal study of calculus started from the 17th century by well-known scientists and mathematicians like Isaac Newton and Gottfried Leibniz, although it is possible that it has been at use as early as the Greek era.

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Grade 3 - 12 online application for exploring functions, expressions, and equations!

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Great ways to integrate novels into algebra at all age levels.

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For a number of years I have been studying a novel with my students in my Pre-Algebra classes. It has been a fantastic experience, and I think every math teacher should at least consider whether a novel study would enhance their students' experiences in their math class.

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By creating a free account, you have access to real-life simulations and applications for budgeting and finance. Some interactive activities do not require a log-in.

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financial literacy terms and definitions

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curriculum open access resources in economics core

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Empower your students with financial skills with NGPF's free, teacher-vetted curriculum for Grades 6-12 Personal Finance, Financial Math, and Economics Classes.

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Article: Growth Mindset "There is No Such Thing as a 'Maths Brain'..."

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Article: Growth Mindset "There is No Such Thing as a 'Maths Brain'..."

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An article from World Economic Forum

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There's no such thing as a 'maths brain'. It's your attitude that's holding you back

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A MOOC targeting the mindsets of students studying mathematics has seen improved grades.

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A game for improving numeracy and number manipulation skills for younger students.

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Who would benefit from playing?

The Number Catcher is primarily designed for children aged 5 to 10 but its higher levels can be fun for adults too!

Children who are making their first steps with numbers will learn the basic concepts of number and arithmetic. Older children, who are already familiar with numbers, will build their fluency in arithmetic.

The game is especially designed to address mathematical learning disabilities (dyscalculia), by strengthening the brain circuits for representing and manipulating numbers.

The Number Catcher focuses on two-digit numbers. For children who make their first steps with numbers, consider using our more basic game The Number Race.

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The Number Catcher - Teaching Arithmetic and Treatment of Dyscalculia

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The Number Catcher is primarily designed for children aged 5 to 10 but its higher levels can be fun for adults too! Children who are making their first steps with numbers will learn the basic concepts of number and arithmetic. Older children, who are already familiar with numbers, will build their fluency in arithmetic.

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Resource for parents, teachers, and students with dyscalculia.

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About dyscalculia

Dyscalculia is a specific learning difficulty that affects roughly 5% of the population. It is often described as "like dyslexia, but for maths". I find this a helpful analogy because we have all, nowadays, heard of dyslexia but not everyone has, yet, heard of dyscalculia.

Dyscalculia is a relatively new field. In the UK, the first official government recognition of its existence came in 2001 when a definition was published by the DfES (as it was then), a definition that has not since been added to or amended; compare this date with the UK's earliest government definition of dyslexia in 1970.

Recent and current research will gradually increase our understanding of dyscalculia so that, in time, teachers and other practitioners will have enough information to underpin a consensus about the best way to help dyscalculic learners. In the meantime, there is a general feeling that the best approach is to build on what has proved to be successful with dyslexic learners, namely multisensory teaching methods combined with an awareness on the part of teachers and schools of the precise nature of the students' difficulties.

Dyscalculia is often called a 'maths' difficulty but it actually only affects those aspects of mathematics to do with number. For example, a dyscalculic learner may have no problems at all with geometry or algebra but be unable to remember a simple multiplication fact. It would be more accurate, therefore, to think of dyscalculia as a difficulty with arithmetic, or perhaps as a specific arithmetic difficulty, rather than a difficulty with maths as a whole. Dyscalculia need not be a bar to understanding mathematical concepts or to taking a degree in a scientific or mathematical subject.

I have met and worked with many learners with developmental dyscalculia over the years and the most striking thing they have in common is their lack of 'number sense'. For those of us who are more numerate, it can be difficult to imagine what it means to have absolutely no feel for numbers. To give you some idea of what it might be like to live in a world in which everything to do with numbers feels alien and challenging, here are three examples from my own experience of working with learners with dyscalculia. Note that these pupils were all of average, or above average, intelligence.

Learners with dyscalculia have no sense of the size of the quantity that is represented by a number. For example, immediately after establishing that there were 13 glass nuggets in a group, by touching and counting them, an 8-year old was presented with a group of roughly 30 of the same nuggets. The challenge was to estimate how many. After much thought (but no opportunity to count them) the pupil guessed that there were 11, without noticing that this guess was less than 13, despite seeing me add to the previous quantity. Another example comes from a highly intelligent 9-year old who was trying to work out what to add to 4 to make 9, by reasoning from a known doubles fact. The pupil said, "Could it be 5? No, because, well, 4 + 4 is 8 but 5 is a much bigger number than 4, so 4 + 5 would be much bigger than 9."

Learners with dyscalculia may have no idea that there are repeating patterns within our decimal number system. For example, a 9-year old trying to add 14 + 10 used fingers to count up 10 steps, one at a time, starting from 14. Another child of the same age, who produced a fast and correct answer to 14 + 10 was unable to work out 26 - 6 without using fingers to count back, one by one.

Learners with dyscalculia may have very little ability to conjure up an accurate mental number line in their heads. I have lost count (no pun intended!) of the number of children who have counted out aloud for me as follows: "... 95, 96, 97, 98, 99, 100, 200, 300 ...".

Indicators for dyscalculia are:

No 'feel' for numbers and relative quantities

an inability to subitise (see without counting) even very small quantities

an inability to estimate whether a numerical answer is reasonable

weaknesses in both short-term and long-term memory

an inability to count backwards reliably

a weakness in visual and spatial orientation

directional (left/right) confusion

slow processing speeds when engaged in maths activities

trouble with sequencing

a tendency not to notice patterns

a problem with all aspects of money

a marked delay in learning to read an analogue clock to tell the time

an inability to manage time in their daily lives.

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About dyscalculia Dyscalculia is a specific learning difficulty that affects roughly 5% of the population. It is often described as "like dyslexia, but for maths". I find this a helpful analogy because we have all, nowadays, heard of dyslexia but not everyone has, yet, heard of dyscalculia. Dyscalculia is a relatively new field.

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Common Core Problem Based Curriculum Maps

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Common Core Problem Based Curriculum Maps

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Problem Based Learning curriculum maps based on the Common Core. Activities were submitted by various contributors and curated by the owner of the website.

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The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online.

The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math 9 (Integrated), Math 10 (Integrated), and Math 11 (Integrated) are from Pearson. Other Scope and Sequences were developed by me, modeling a similar visual style.
Grade 3 CCSS PrBL Curriculum Map Grade 4 CCSS PrBL Curriculum Map Grade 5 CCSS PrBL Curriculum Map Grade 6 CCSS PrBL Curriculum Map Grade 7 CCSS PrBL Curriculum Map Grade 8 CCSS PrBL Curriculum Map Math 9 (Integrated) CCSS PrBL Curriculum Map Math 10 (Integrated) CCSS PrBL Curriculum Map Math 11 (Integrated) CCSS PrBL Curriculum Map Algebra 1 CCSS PrBL Curriculum Map Geometry CCSS PrBL Curriculum Map Algebra 2 CCSS PrBL Curriculum Map
Be sure to check back often as these curriculum maps are bound to change when new cool activities are added on math blogs worldwide. I'll be adding more and more curriculum maps in due time. Also, if you have a favorite particular task that isn't here (or just comments in general), let me know in the comments!

For more on Problem Based learning, you can check out my previous posts on the topic.

- Geoff

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Common Core Problem Based Curriculum Maps

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The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online. The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math...

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Thought provoking and engaging math problems for K-12.

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Open Middle - Challenging math problems worth solving

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Open Middle offers interactive math problems designed to foster critical thinking. Explore unique challenges that boost problem-solving skills and creativity.

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Online resource for Algebra. You can play or build Mystery Grid, Who am I?, and Mobiles.

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Use logic to solve visual, interactive mathematical puzzles. Create your own puzzles to share with your friends or the SolveMe Community.