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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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Decide and Defend is an instructional routine in which students make sense of another’s line of mathematical reasoning, decide if they agree with that reasoning, then draft an argument defending their decision. The routine fosters math practice 3, construct viable arguments and critique the reasoning of others.

The type of task that sits at the center of the Decide and Defend routine is a worked example. The worked example can be taken from a book, created by the teacher, or produced by a student. It can be mathematically correct or incorrect. Whatever task you choose, it should position your students to make sense of a line of reasoning that is not their own, and decide for themselves if it is correct or incorrect.

When selecting worked examples for #DeciDefend, ask yourself:

Does the worked example highlight a common error students make?

Does the worked example draw attention to a classic misconception students hold?

Does the worked example contain a representation that will serve to deepen students’ conceptual understanding?

Does the worked example present a unique solution strategy that sparks consideration of underlying math concepts?

You can use the following planner to help you plan a Decide and Defend task

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K-8 Non-Curricular Tasks to start off the year!

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Introduction

Rich mathematical tasks engage students in sense-making through deeper learning that require high levels of thinking, reasoning, and problem solving. The VDOE Rich Mathematical Task Committee, composed of mathematics teacher leaders from across the Commonwealth, created mathematically rich tasks aligned to the 2016 Mathematics Standards of Learning. The committee created task implementation templates prior to administering the tasks in classrooms. For many of the tasks, the committee scored the tasks individually, calibrated their scoring with a team, provided scoring rationales and selected student work to serve as anchor papers. The Virginia Department of Education would like to extend a special thank you to the Rich Mathematical Task Committee, as well as their colleagues who supported this work in their divisions.

Planning for Remote Implementation of Rich Mathematical Tasks

These resources, along with the Planning for Remote Implementation of Rich Mathematical Tasks guidance document, are provided to support teachers in implementing the 2016 Mathematics Standards of Learning in their classrooms. Teachers are encouraged to not only use these tasks with their students, but also to endeavor to implement them with fidelity by utilizing the detailed information provided in the task implementation templates.

Webinars to Support Remote Implementation of Rich Mathematical Tasks

Kindergarten

Building Towers Task

Picking Apples Task

Sharing Cookies Task

Shape Riddles Task

Mixed Blocks Task

Morning Routine Task

Grade 1

Comparing Points Task

Toy Cars Task

Nature Walk Task

Doubles Game Task

Playing with Patterns Task

How Can They Be Equal? Task

Grade 2

Mystery Number Task

Sticker Sets Task

Bracelet Task

Brownie Pans Task

Talking Sticks Task

Coins in Pocket Task

How Many Tables Task

Number of Students Task

Grade 3

Packing Pencils Task

Pizza Party Task

Carnival Prizes Task

Baskets of Apples Task

Money in the Piggy Bank Task

Polygon Puzzles Task

Grade 4

Special Delivery Task

Taco Tuesday Task

Trip Transportation Task

Pouring Paints Task

Lunch at Leonardo's Task

Camping Combinations Task

Exploring Quadrilaterals Task

Equality Possibilities Task

Grade 5

Saving for a Bicycle Task

Room for Shoes Task

Trail Mix Time Task

Bus A or Bus B Task

Angle Design Task

Designing Windows Task

Grade 6

Winning the Game Task

Cookie Topping Task

Smart Shopper Task

Tracking Sharks Task

Designing a Dog Park Task

Pizza Delivery Task

Screen Time Task

Grade 7

Which Microscope Task

The Bake Sale Fundraiser Task

Shipping Box Task

A Walk in the Park Task

Spin, Spin, Spin Task

Summer Passes Task

Gardening Task

Grade 8

The Principal's Dilemma Task

Monster Transformations Task

Longest Path Task

It's Your Lucky Day Task

Peanut Butter Task

How Many Stones Will I Need Task

Algebra I

Shopping Translations Task

Flower Gardens Task

Seesaw Fun Task

Full Parking Lot Task

Radical Rocks Task

The Trampoline PartyTask

Bicycle Savings Task

The Soccer Competition Task

We're Playing Basketball Task

Geometry

Logical Drivers Task

Lines and Tigers and Bears, Oh My! Task

Airshow Task

Take Me Out to the Ball Game Task

Sea Cities Task

Shake, Rattle, and Roll Task

Algebra II

Drone's Best Friend Task

Function of a Ride Task

Animate It Task

Wildfires Task

Algae Attack Task

Blank Task Template

Rich Mathematical Task Rubric

Acknowledgments

The Virginia Department of Education would like to extend a special thank you to the Rich Mathematical Task Committee, as well as their colleagues who supported this work in their divisions.

Candice Barkley, Henrico County Public Schools

Jessica Brown, Gloucester County Public Schools

Kaitlyn Bookbinder, Henrico County Public Schools

April Cooke, Fairfax County Public Schools

Kelly Day, Virginia Beach City Public Schools

Michelle Deloach, Chesterfield County Public Schools

Allison Crisher DePiro, Virginia Beach City Public Schools

Katelyn Devine, Henrico County Public Schools

Jenna Filipowicz, Virginia Beach City Public Schools

Kris Gushue, Prince William County Public Schools

Kelly Halpin, Fairfax County Public Schools

Endia Hatcher, Portsmouth Public Schools

Melanie Jenkins, Gloucester County Public Schools

Jenny Jones, Hanover County Public Schools

Tisha Jones, Portsmouth Public Schools

Leslie Laden, Stafford County Public Schools

Kimberly Lawrence, Hanover County Public Schools

Lynn Meade, Henrico County Public Schools

Kathryn Munson, Chesterfield County Public Schools

Anna Papas, Stafford County Public Schools

Sarah Porter, Suffolk Public Schools

Candice Standley, Culpeper County Public Schools

Donna Snyder, Roanoke City Public Schools

Holly Tate, Alexandria City Public Schools

David VanVleet, Fairfax County Public Schools

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Rich Mathematical Tasks | Virginia Department of Education

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Rich mathematical tasks engage students in sense-making through deeper learning that require high levels of thinking, reasoning, and problem solving. The VDOE Rich Mathematical Task Committee, composed of mathematics teacher leaders from across the Commonwealth, created mathematically rich tasks aligned to the 2016 Mathematics Standards of Learning.

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Huge Resource of Quality Problems for K-2

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Huge Resource of Quality Problems for K-2

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Says 2nd Grade, but has tasks that can be adapted for K and 1st.

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Huge Resource of Quality Problems for 3-5

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Huge Resource of Quality Problems for 3-5

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Created for 3rd Grade but easy to adapt for 4th and 5th

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Would You Rather Math – ASKING STUDENTS TO CHOOSE A PATH AND JUSTIFY IT WITH MATH

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don’t go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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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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The Problem of the Week is designed to provide students with an ongoing opportunity to solve mathematical problems. Each week, problems from various areas of mathematics will be posted here and e-mailed to teachers for use with their students from grades 3 and up.

Current Problems

Subscribe Now!

Information for Teachers

Problems are organized into themes. A problem may have more than one theme.

These problems may be used in a variety of different ways including:

posting the problems in a classroom,

discussing the problems with students, and

integrating the problems into the curriculum.

We know that teachers will use these problems in many creative ways!

Solutions to the problems will be sent out to teachers one week after the problems are e-mailed.

Problems & Solutions from 2023-2024

Problem and Solution Archive

The following table has links to booklets containing all the problems and solutions from particular years. The problems are organized into themes, grouping problems into various areas of the curriculum. A problem often appears in multiple themes.

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Design - Graphics, University of Waterloo

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The CEMC has become Canada's largest and most recognized outreach organization for promoting and creating activities and materials in mathematics and computer science.

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Our Favorite Places to go to Find Rich Math Tasks created by Margie Pearse @pearse_margie & Lane Walker @LaneWalker2

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Another Resource with Lots of Recommended Links

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Another Resource with Lots of Recommended Links

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Books Free Resources Problems to Solve Blog Sue's Favorite Links The Math Together Show Same But Different Math Contact

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5th Grade Resources for All Standards (Shared)

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5th Grade Resources for All Standards (Shared)

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Open Up Resources K–5 Math fosters the development of mathematics learning communities in classrooms, gives students access to the mathematics through a coherent progression, and provides teachers the opportunity to deepen their knowledge of mathematics, student thinking, and their own teaching practice.

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We are proud to offer our top-rated full course curricula free of charge on the web.

Interested in high quality print books or our flexible professional learning offerings? Contact us.

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We are proud to offer our top-rated full course curricula free of charge on the web. Interested in high quality print books or our flexible professional learning offerings? Contact us.

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Good resource for math tasks, math talks, and math games.

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Elementary Math materials for distance learning Include a revised scope and sequence adjusted for distance learning, content priority documents, and slide decks for every unit in our curriculum. Many educators are continuing to use these resources, even while teaching in person.

​ Secondary lessons contain proprietary content that is licensed by SFUSD and therefore can not be shared outside of SFUSD.

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﻿ The Math Portals allow teachers to access unit plans and resources, and allow students to access digital versions of the student pages. If you are an SFUSD employee, you may also join our...

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YOHAKU JUNIOR BOOKS 1, 2 AND 3 ARE NOW ON SALE!

A yohaku is a new type of number puzzle that will test your number sense and problem solving skills. Each yohaku is either an additive or a multiplicative puzzle (as indicated by the symbol in the bottom right of the grid). Your task is to fill in the empty cells such that they give the sum or product shown in each row and column.

Great for use in classrooms as a lesson starter, or for the morning commute, or for something to accompany an afternoon cup of tea. Some yohakus will take a few minutes to solve, others will have you puzzling for longer (and you're welcome).

Each yohaku is lovingly created by hand!​

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YOHAKU JUNIOR BOOKS 1, 2 AND 3 ARE NOW ON SALE! A yohaku is a new type of number puzzle that will test your number sense and problem solving skills. Each yohaku is either an additive or a multiplicative puzzle (as indicated by the symbol in the bottom right of the grid).

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Instantly built a devoted audience of children and adults who fell in love with the game's beautiful, colorful display, and connection with deep mathematical understanding.

Honestly, this has got to be one of the most engaging and effective ways of introducing the idea of primes being the 'building blocks' of numbers and building other general logic skills... Overall, Prime Climb is an incredibly flexible game, and certainly met the high expectations it set itself.

This game blew my mind! It blew my wife's mind, it blew my kid's mind... it is one of the coolest visualizations of mathematics and prime numbers I've ever seen ever. It is awesome!

Take a look at Prime Climb, an excellent new game... perfect for adults and children alike.

This game is so rich in mathematical ideas that I literally spent a week investigating it with my class.

Rated #1 Educational Math Game!

Prime Climb is an excellent way to teach about prime numbers, factors, common multiples, and that math is fun!... I loved how Prime Climb engaged my math loving kids and my kids who tolerate math. It was engaging and challenging enough that no one was bored, but easy enough to understand that no one was frustrated. It was the perfect balance. (It was fun for the adults as well.)

This is an amazing game! It is genius actually. You can play this with both young and old and adapt it to anyone's ability. Players must not only use their math skills but their strategy skills as well. I believe this game should be in every classroom in America as well as every home!!

For a game that is a relatively pure experience of math equations, I think you'll be surprised how much fun it can be for players of all ages.

A fun and simple way to bring multiplication, division, and prime numbers all in one easy to play game. Awesome!

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Math for Love is devoted to transforming how math is taught and learned. Offering a free lesson library, plus games, summer curriculum, and more.

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Illustrative Mathematics IM K–5 Math | Kendall Hunt

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If you REALLY like exercising your brain,
figuring things 'round and 'round till you explode,
then this is the page for you !

Whosoever shall solve these puzzles shall Rule The Universe!

... or at least they should ...

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If you REALLY like exercising your brain, figuring things 'round and 'round till you explode, then this is the page for you ! Whosoever shall solve these puzzles shall Rule The Universe! ... or at least they should ...

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Grade 3 Comprehensive Math Talks Bank (1)

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Games in the Grade 3 Math Core Curriculum (1)

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Games in the Grade 4 Math Core Curriculum (1)

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Games in the Grade 5 Math Core Curriculum (2)

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Interactive and Engaging Math Problems

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Resources | Building Thinking Classrooms

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BrainBashers - brain teasers, puzzles, riddles, and more

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Looking to enhance your learners' numeracy skills? Numeracy skills are essential for using mathematics in life's contexts and situations. From formative assessment to group work, from estimation to reasoning, from persistence to communication, these numeracy tasks have been collaboratively developed to invite learners into the discourse of mathematics in general, and foster numeracy proficiencies in particular. Best of all, they pair well with the BTC practices and allow for mathematical activity without relying too heavily on pre-requisite knowledge.

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Numeracy Tasks | Building Thinking Classrooms

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Looking to enhance your learners' numeracy skills? Numeracy skills are essential for using mathematics in life's contexts and situations. From formative assessment to group work, from estimation to reasoning, from persistence to communication, these numeracy tasks have been collaboratively developed to invite learners into the discourse of mathematics in general, and foster numeracy proficiencies in particular.

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Encourage problem-solving with 3 Act Math Tasks

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Building Thinking Classrooms?

Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into a set of 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.

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Building Thinking Classrooms | Teaching Practices for Enhancing Learning Mathematics

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Building Thinking Classrooms in Mathematics helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur.

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If you don't know whether or not you are a Recovering Traditionalist, here's how I define us. We are math educators who used to teach math the traditional way.

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Make Math Moments is on a mission to provide an opportunity for all mathematics educators around the world to access professional learning opportunities that will elevate their teaching practice and promote an equitable learning experience for all students. We strive to provide all educators with the opportunity to spark their learning through the Making Math Moments That Matter Podcast as a means to inspire the exploration of new pedagogical practices and to seek out opportunities to deepen their own mathematical content knowledge.

The goal of the podcast is to help more mathematics educators to create a classroom culture where students don't want to stop exploring mathematics when the bell rings by interviewing featured guests such as Jo Boaler, Peter Liljedahl, Sunil Singh, Dan Meyer, Nicki Newton, John Hattie, inviting mathematics teachers on to the show to engage in "Mentoring Moment" episodes where we coach them through a current math classroom struggle, or to simply riff on a specific big idea, tool or strategy for simply.

We strive to positively impact the K-12 mathematical experience for over 1 million students by helping mathematics teachers and mathematics district leadersto strengthen the six (6) key parts of an effective mathematics program.

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Making Math Moments That Matter Podcast - Make Math Moments

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Wondering how to create a classroom culture where students don't want to stop exploring mathematics when the bell rings? Join Kyle Pearce from TapIntoTeenMinds.com and Jon Orr from MrOrr-IsAGeek.com as they team up for EPISODE #1 to uncover how we can Make Math Moments That Matter for every student in the math classroom from Kindergarten through Grade 12.

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Little Minds Big Thinkers is a podcast where educators talk about the magic and messiness of the elementary thinking classroom based on the work of Peter Liljedahl.

Little Minds Big Thinkers is a podcast where educators talk about the magic and messiness of the elementary thinking classroom based on the work of Peter Liljedahl.

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‎Little Minds Big Thinkers on Apple Podcasts

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Little Minds Big Thinkers is a podcast where educators talk about the magic and messiness of the elementary thinking classroom based on the work of Peter Liljedahl.