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Math Playground has hundreds of interactive math word problems for kids in grades 1-6. Solve problems with Thinking Blocks, Jake and Astro, IQ and more. Model your word problems, draw a picture, and organize information!

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MATH PRACTICE Skills to Practice:  Math and Language  

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MATH PRACTICE Skills to Practice:  Math and Language  

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k-6

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IXL | Online math and English language arts practice.

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IXL is the world's most popular subscription-based learning site. Used by over 7 million students, IXL provides unlimited practice in more than 4,500 math and English language arts topics. Interactive questions, awards, and certificates keep kids motivated as they master skills.

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Building Number Sense with

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Text Book-  used to support observations, conversations and products

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Great resource for building vocabulary, word meaning and pronunciation -
Pre recorded  Grades 2-6

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Wordly Wise i3000 - More Activities, More Engagement, to Reach More Students

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Wordly Wise i3000, now with more activities and more engagement to reach more students

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Brain Teasers & Math Puzzles : Puzzle & Brain Teaser Collection

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Syvum's Math Puzzle & Brain Teaser Collection contains free online interactive brain teasers & math puzzles with answers & explanations

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Multiple Step Problem Solving Using Singapore Model Math

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Thinking Blocks Addition Model: Multistep Comparison

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This is a tutorial for using the iPad app, Thinking Blocks Addition.

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ADDITION TO RATIOS - On- Line Practice CD's Available

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An interactive math lesson about Place Values.

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Homework and Practice
Text Book-  used to support observations, conversations and products

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GRADES 3/4
used to support observations, conversations and products Some basic questions for review

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You can use the previous year' s worksheets as a review at the beginning of the year. mental math c) a Predict what would happen if you took 10 free

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Text Book-  used to support observations, conversations and products

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Using Dominoes

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Dominoes have become a staple in most primary classrooms. They build upon dice patterns and are often used to model decomposition of numbers, building student knowledge of addition facts. They are an excellent manipulative for primary students to use and these are some examples of how students might use dominoes in the math center.

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Text Book-  used to support observations, conversations and products Homework and Practice

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K-3

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MATH ACTIVITIES: Number Sense: Student having problems remembering "teen" numbers 

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MATH ACTIVITIES: Number Sense: Student having problems remembering "teen" numbers 

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It is very common for students to have difficulty with the numbers 11- 19. Their names do not follow the common rule and they are the sight words/ numbers of mathematics. Teachers must ACTIVELY help students develop meaning for both the words and the corresponding numerals.

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Whole Class -Multiple Choice Math Questions : Grades 1-6

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Whole Class -Multiple Choice Math Questions : Grades 1-6

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Some test taking strategies

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Kids' Place Houghton Mifflin Mathematics

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MATH ACTIVITIES You might find some good stuff here 

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MATH ACTIVITIES You might find some good stuff here 

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Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents.

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Math Word Problems (K-12) with scoring rubrics... 

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Math Word Problems (K-12) with scoring rubrics... 

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IMPORTANT : NOTE COPYRIGHT

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Please Note: Balanced Assessment printed materials are available from this site, except for those indicated below. Please use the order form and follow the ordering directions carefully as they have changed. Current prices can be found on our order form.

Please also note that the Balanced Assessment Primary & Elementary Tasks have been published by Corwin Press. The Balanced Assessment Transition & Middle School Tasks have been published by Teachers' College Press. These tasks may still be viewed in.pdf format on this website but they may not be copied or printed.

About the program

From 1993 to 2003, the Balanced Assessment in Mathematics Program existed at the Harvard Graduate School of Education. The project group developed a large collection of innovative mathematics assessment tasks for grades K to 12, and trained teachers to use these assessments in their classrooms.

The library of over 300 mathematics assessment tasks developed during the project remains freely available through this web site. Teachers may use these materials in their own classrooms at no cost.

This site also offers reports on our approach to mathematics assessment and our distinctive objects x actions scoring system. A more detailed overview of the project is also available.

One of the most satisfying results of this ten-year project was the enthusiastic response of teachers to our assessment tasks and publications. We hope that you will continue to find the Balanced Assessment tasks to be a valuable resource.

Ordering Balanced Assessment publications

It is possible to purchase printed Balanced Assessment publications using our order form.

Our library of assessment tasks

If you are looking for a specific task, you can find it by name or by number.

If you're just getting to know our materials, we'd like to suggest a few of our favorite tasks:

Our approach to assessment and scoring

These reports and materials were developed while the Balanced Assessment program operated at the Harvard Graduate School of Education, between 1993 and 2003.

Assessing Mathematical Understanding and Skills Effectively (AMUSE)
Also available as a Word document.
This 1995 report describes our project group's approach to mathematics assessment.

Mathematics Content and Process Scoring System (MCAPS)
Also available as a Word document.
This report describes our objects x actions approach to scoring assessment tasks.

MCAPS Scoring Tool
Requires Microsoft Excel or compatible spreadsheet.
This spreadsheet implementation of the MCAPS scoring system enables teachers to efficiently use the system in their classes.

Judah L. Schwartz,
Principal Investigator/Director
Joan Kenney,
Project Coordinator/Director
Susan Ilias
Kevin Kelly
Teresa Sienkiewicz
Yesha Sivan
Victor Steinbok
Amy Warren
Michal Yerushalmy

For information on using BA tasks in the classroom, professional development for teachers and administrators, and issues regarding orders, please contact:
Joan Kenney
Joan_Kenney@post.harvard.edu

For technical web site issues, contact:
dan@mathshell.org

The materials on this web site were developed under National Science Foundation grants MDR-9252902 and ESI-9726403 (subcontracts from the University of California at Berkeley and Michigan State University), with additional funding from the American Academy of Arts and Sciences, the Boston Public Schools, the Cambridge Public Schools, and the Noyce Foundation..

All documents are Copyright © 1995-2003, President and Fellows of Harvard College.With the exceptions listed above in the heading to this page you are hereby granted the right to duplicate or print these materials for use in your classroom or school. Otherwise, these materials are protected by copyright.

This web site was originally designed by Kevin Kelly.

Last Update: 10/17/2015
Copyright © 2020, The Concord Consortium. All rights reserved.

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Please Note: Balanced Assessment printed materials are available from this site, except for those indicated below. Please use the order form and follow the ordering directions carefully as they have changed. Current prices can be found on our order form. Please also note that the Balanced Assessment Primary & Elementary Tasks have been published by Corwin Press.

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Number Talks (extract from online course) - YouCubed

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This teaches the pedagogical strategy called 'Number Talks' with some interesting different methods shared by Stanford students. The full online course is available at: Stanford Online - How to Learn Math for Teachers

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STANFORD UNIVERSITY

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Great stuff!

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David Weiss is sited  by - Stanford's YouCUBED  (Boaler

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David Weiss is sited  by - Stanford's YouCUBED  (Boaler

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In 1992, Deborah Loewenberg Ball wrote an article called Magical Hopes: Manipulatives and the Reform of Mathematics Education. This article is intended to draw some connections between our use of manipulatives and our use of technology in math education, and hopefully offer some suggestions for improving the use of technology.

There is a similar magical hope that technology can be used to reform mathematics education and I think that some of this reform is misguided, and this is in fact why I no longer work as an educational technologist. Without reforming work we as educators do to make links between the resources we use and the learning outcomes we hope to see borne out by children, there will be little effective change in the overall learning experiences for children.

Here is a paragraph from Dr. Ball's article that stood out to me. For some context, Dr. Ball starts her article describing a student explaining how they understand odd versus even numbers. For further detail, I recommend reading her article.

Some teachers are convinced that manipulatives would have been the way to prevent the students' "confusion" about odd and even numbers. This reaction makes sense in the current context of educational reform. In much of the talk about improving mathematics education, manipulatives have occupied a central place. Mathematics curricula are assessed by the extent to which manipulatives are used and how many "things" are provided to teachers who purchase the curriculum. Inservice workshops on manipulatives are offered, are usually popular, and well attended. Parents and teachers alike laud classrooms in which children use manipulatives, and Piaget is widely cited as having "shown" that young children need concrete experiences in order to learn...

Here is an updated paragraph with the current reform efforts focused on utilizing technology in mathematics education.

Some teachers are convinced that [technology] would have been the way to prevent the students' "confusion" about odd and even numbers. This reaction makes sense in the current context of educational reform. In much of the talk about improving mathematics education, [the use of technology has] occupied a central place. Mathematics curricula are assessed by the extent to which [technology is] used and how many "things" are provided to teachers who purchase the curriculum. Inservice workshops on [technology] are offered, are usually popular, and well attended. Parents and teachers alike laud classrooms in which children use [technology], and [Papert] is widely cited as having "shown" that young children need [access to technology] in order to learn...

Here is an example of technology intended to be used in mathematics education. This is a virtual manipulative I created which is intended to draw students attention to how function rules can be represented as visual sequences. Try changing the sliders and keeping track of what you notice and what you wonder.

Now consider, what do you think children might notice when looking at this manipulative? What will they wonder? And most importantly, what will they learn as a result of using it?

If you have time, I recommend actually trying this activity out with a variety of children at different age levels. What I have learned is that children rarely see things the same things as adults (especially if those adults are mathematicians and/or mathematics teachers). In particular most children with whom I have used this particular manipulative do not attend to the differences between terms in the same way that adults do, and very few children even notice that the manipulative above includes an equation. They tend to focus almost entirely on the elements of the virtual manipulative over which they have control (the sliders) and the elements that change the most (the visual pattern) and in particular generally ignore features not immediately visible (the difference between terms) or recognizable (the equations).

Technology that relies on children independently making mathematical discoveries is likely to fail for some children. Given that one's current mathematical knowledge is a large factor in how easily one makes mathematical discoveries, this use of technology may increase educational inequity rather than decrease it.

Recommendation: Utilize instructional strategies intended to make the sharing of mathematical ideas explicit for all students.

Here is another paragraph from Dr. Ball's article:

Manipulatives -and the underlying notion that understanding comes through the fingertips- have become part of educational dogma: Using them helps students; not using them hinders students. There is little open, principled debate about the purposes of using manipulatives and their appropriate role in helping students learn...

Fortunately, there is tremendous debate about the use of technology in mathematics education, but most of this debate has centered on grain sizes of discussion that are far too broad to be helpful. Instead of questions like, "Is technology helpful in mathematics education?" we should be asking ourselves much more specific questions that have the same form as "is this use of this technology helpful for these students in this situation?" And then when we come up with a first draft answer for that question, we should make sure that our second draft includes some evidence from our students that the learning experience in question was actually improved by the use of the technology.

Recommendation: The links between what we hope children will learn from a particular activity and the evidence that they have learned should be made clear and investigated.

Here is another insightful quote from Dr. Ball:

My main concern about the enormous faith in the power of manipulatives, in their almost magical ability to enlighten, is that we will be misled into thinking that mathematical knowledge will automatically arise from their use. Would that it were so! Unfortunately, creating effective vehicles for learning mathematics requires more than just a catalog of promising manipulatives. The context in which any vehicle-concrete or pictorial-is used is as important as the material itself. By context, I mean the ways in which students work with the material, toward what purposes, with what kinds of talk and interaction. The creation of a shared learning context is a joint enterprise between teacher and students and evolves during the course of instruction. Developing this broader context is a crucial part of working with any manipulative. The manipulative itself cannot on its own carry the intended meanings and uses.

I sometimes see the same kind of thinking from mathematics educators (myself included); that just because a particular Desmos activity or Geogebra applet contains some mathematical idea, that children will learn the mathematical principles that are potentially generative in the activity. Sometimes some children see the mathematical principle, we have them present their work, and then we either hope or assume that this sample of children is representative of the whole class. Unfortunately, selection of students to present is a challenging activity that tends towards sharing strategies deemed as correct rather than surfacing a mathematical idea (like Sean's observation in Deborah Loewenberg Ball's article) that is fruitful to present and discuss even though an outside observer would consider the idea incorrect.

Recommendation: Before students engage in a technological activity, anticipate how we think they may consider the mathematical features. While students engage in a particular activity, listen to students talk, watch them work, and ask them questions to probe at their actual mathematical thinking. Use this information to potentially revise the activity.

Dr. Ball continues with this argument:

If we pin our hopes for the improvement of mathematics education on manipulatives, I predict that we will be sadly let down. Manipulatives alone cannot and should not-be expected to carry the burden of the many problems we face in improving mathematics education in this country. The vision of reform in mathematics teaching and learning encompasses not just questions of the materials we use but of the very curriculum we choose to teach, in what ways, to whom, and in what kinds of classroom environments and discourse. It centers on new notions about what counts as worthwhile mathematical knowledge. These issues are numerous and complex. For instance, we need to shift from an emphasis on computational proficiency to an emphasis on meaning and estimation, from an emphasis on individual practice to an emphasis on discussion and on ideas, reasoning, and solution strategies. We need to alter the balance of the elementary curriculum from a dominant focus on numbers and operations to a broader range of mathematical topics, such as probability and geometry. We need to shift from a cut-and-dried, right-answer orientation to one that supports and encourages multiple modes of representation, exploration, and expression. We need to increase the participation, enthusiasm, and success of a much wider range of students. Manipulatives undoubtedly have a role to play in these aims, by enhancing the modes of learning and communication available to our students. But simply getting manipulatives into every elementary classroom cannot possibly suffice to fulfill these aims.

This leads to some questions that we educators can ask ourselves before we embark on using some new technology with students (in the same way that at the time of Deborah Loewenberg Ball's article was published that manipulatives were a new technology for many teachers).

Does using this technology help my students learn mathematics that they can use without the use of this technology?

How will someone who does not yet know the mathematics embedded within this technological tool see the mathematics?

Does this technology focus solely on the acquisition of a limited set of mathematical knowledge or is it possible for students to use deliberate practice to identify patterns across different problems and acquire new mathematical ideas?

Does this technology make it harder for my students to interact with each other and with me?

How will I learn how my students understand the mathematical ideas that are the focus of this lesson?

Who is the audience of this technology?

Does this technology exacerbate existing inequities in mathematics education?

Some of these questions were originally in this post.

I don't have answers to all of these questions unfortunately but I think as a community of mathematics educators, we should be at least trying to answer them. I also have not unpacked some really large scale and potentially damaging initiatives around online learning and personalized learning. Stay tuned for a Part 2 to this post focused more on these uses of technology.

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In 1992, Deborah Loewenberg Ball wrote an article called Magical Hopes: Manipulatives and the Reform of Mathematics Education. This article is intended to draw some connections between our use of manipulatives and our use of technology in math education, and hopefully offer some suggestions for improving the use of technology.

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ARTICLE: Math Fluency - research and strategies 

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ARTICLE: Math Fluency - research and strategies 

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LOTS OF VIDEOS K-

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number talks - Yahoo Video Search Results

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The search engine that helps you find exactly what you're looking for. Find the most relevant information, video, images, and answers from all across the Web.

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A Collection on Viemo : Small, Lawson, etc.

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Alex Lawson: The Power of the Number Line

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ENGAGE MATH: HIGH YIELD STRATEGIES: ONTARIO VIDEO 

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ENGAGE MATH: HIGH YIELD STRATEGIES: ONTARIO VIDEO 

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This is "High Yield Strategies Math" by LearnTeachLead (1) on Vimeo, the home for high quality videos and the people who love them.

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MATH RESOURCE: A GUIDE TO EFFECTIVE INSTRUCTION VARIOUS STRANDS  

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MATH RESOURCE: A GUIDE TO EFFECTIVE INSTRUCTION VARIOUS STRANDS  

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Guides to Effective Instruction in Mathematics - OCDSB Ministry Resources

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A living document containing all Ministry Policy and Resource Documents

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These guides provide teachers with practical applications to help students
K - 6 achieve the curriculum expectations in mathematics. Home Connections

Click < here > to access the Guides in French.
Click < > to view which publications are available in print form or online only.
Click < > for instructions on ordering materials from Services Ontario.

Understanding Addition and Subtraction of Whole and Decimal Numbers (ppt)
Number Sense and Numeration, Grades 4 to 6 (with reference to Volumes 2 and 6)

Understanding Multiplication and Division of Whole and Decimal Numbers (ppt)
Number Sense and Numeration, Grades 4 to 6 (with reference to Volumes 1, 3, 4, and 6)

Understanding Relationships Between Fractions, Decimals, Ratios, Rates, and Percents (ppt)
Number Sense and Numeration, Grades 4 to 6 (with reference to Volumes 1, 5, and 6)

Data Management and Probability (pdf)

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These guides provide teachers with practical applications to help students K - 6 achieve the curriculum expectations in mathematics. Home Connections Click to access the Guides in French. Click to view which publications are available in print form or online only. Click for instructions on ordering materials from Services Ontario.

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Jo Boaler on Complex Instruction and Group Work in Math

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Jo Boaler on Multidimensional Math

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Inspire ALL Students with Open, Creative Mindset Mathematics

Our Mission

Our main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math into accessible and practical forms. We know from research how to teach math well and how to bring about high levels of student engagement and achievement but research has not previously been made accessible to teachers.

Learn More

Jo Boaler

Dr Jo Boaler is a Professor of Mathematics Education at Stanford University, and the faculty director of youcubed. She is the author of the first MOOC on mathematics teaching and learning. Former roles have included being the Marie Curie Professor of Mathematics Education in England, a mathematics teacher in London comprehensive schools and a lecturer and researcher at King's College, London. Her PhD won the national award for educational research in the UK. She is an elected fellow of the Royal Society of Arts (Great Britain), and a former president of the International Organization for Women and Mathematics Education (IOWME). She is the recipient of a National Science Foundation 'Early Career Award,' the NCSM Kay Gilliland Equity Award (2014) and the CMC Walter Denham Mathematics Leadership award (2015). She is the author of nine books and numerous research articles. She formed youcubed to give teachers, parents and students the resources and ideas they need to inspire and excite students about mathematics. Her work has been published in the New York Times, TIME magazine, The Telegraph, The Atlantic, The Wall Street Journal and many other news outlets. She was named by the BBC as one of 8 educators "changing the face of education."

Join Our Facebook Community

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Inspire ALL Students with Open, Creative Mindset Mathematics Our main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math into accessible and practical forms. We know from research how to teach math well and how to bring about high levels of student engagement and achievement but research has not previously been made accessible to teachers.

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SCOPE AND SEQUENCE - EDUGAINS Grades 1-8

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SCOPE AND SEQUENCE - EDUGAINS Grades 1-8

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TARGETED IMPLEMENTATION

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OPEN FILE USING PDF/ADOBE

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Will be trying this with ISSP students

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Easy $1.00 Way to teach PLACE VALUE, Standard Form, Expanded Form

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USE cheap FOAM CUPs to make an addictive MATH TOOL that helps students understand PLACE VALUE, standard form and expanded form. FREE easy to use MATH GAMES and activities! Go to http://www.mbstead.com I made this video because I wanted to make a online learning station that students could follow that would help meet the common core standards.

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DEVELOPMENTAL CHART  OVERVIEW  K-12  MATH- PLANNING DOCUMENT 

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DEVELOPMENTAL CHART  OVERVIEW  K-12  MATH- PLANNING DOCUMENT 

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Instructional programs from prekindergarten through grade 12 should enable each and every student to-

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https://www.pinterest.ca/pin/284008320234941070/

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Numberless & Numbered Word Problems (Story Problems within 100)

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Help students understand and solve addition and subtraction word problems within 100 by using an AMAZING and effective strategy called, Numberless Word Problems. Students will no longer absentmindedly add or subtract numbers they see, because there aren't any numbers there - at first, anyway. Click to find out how it works.

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A Step by Step approach to Numberless Word Problems

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Numberless Math Word Problems: A Strategy that Works!

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﻿﻿ Is your wish to help students feel successful and confident when solving math word problems? If so, you will want to read about a strategy that has significantly helped students become better problem solvers.

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Learned about the idea of using numberless word problems from Bruno Pullara. I then found this video on how one teacher launched this strategy in her classroom

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Using the Notice and Wonder Math Routine is a great way to launch into numberless word problems with 2nd grade students. Watch a complete lesson in action that includes a group discussion followed by individual journal work.

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SPIRAL MATH - PLANNING FOR MATH EVERY DAY - UNIVERSITY OF CHICAGO 

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SPIRAL MATH - PLANNING FOR MATH EVERY DAY - UNIVERSITY OF CHICAGO 

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I learned about this idea from Burno Pullara in a Professional Development session at our school. I then found this site from the University of Chicago.

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Access guides to assessment, computation, differentiation, pacing, and other aspects of Everyday Mathematics instruction.

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Scaffolded Problems  Preparing for EQAO- Most EQAO QUESTIONS are Part-Part Whole. One of many great ways to introduce word problems or mathematical stories to students... Supporting student Metacognition.

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PLANNING FOR EVERY DAY MATH- TEACHER SAMPLE

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TEACHER SAMPLE WEBSITE

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TRANSFORMATIONAL  PRACTICES 2.0  PDSB DOWNLOAD FROM APPLE  I BOOKS 

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TRANSFORMATIONAL  PRACTICES 2.0  PDSB DOWNLOAD FROM APPLE  I BOOKS 

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A Great Resource by Tina Zita -Peel Modern Learners Teacher

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Transformational Practices 2.0 by Peel District School Board on iBooks

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Read a free sample or buy Transformational Practices 2.0 by Peel District School Board. You can read this book with iBooks on your iPhone, iPad, iPod touch or Mac.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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Word Problems Made Easy by creating a visual Model 

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Word Problems Made Easy by creating a visual Model 

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A revolutionary, online math program comprising games, animated books and downloadable materials.