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A 3 minute illustration of the concept of number sense by Professor Jo Boaler, in English and Spanish versions.

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Eddie Gray & David Tall are two British researchers who worked with students, aged 7 to 13, who had been nominated by their teachers as being low, middle or high achieving students. All of the students were given number problems, such as adding or subtracting two numbers. The researchers found an im…

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3-Act Tasks | Questioning My Metacognition (gfletchy.com)

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3 Act Tasks for K-2 Students

There's lots of room for improvement with these materials. Please leave comments about what should be added or revised. If you try them with students, share what you learn!

(Note: A few tasks are in-progress!) Also, see the links at the bottom of this page for more great 3 Act Task resources.

More 3 Act Tasks

The tasks here are inspired by the work of Dan Meyer and many others. Check out these excellent resources for more tasks:

Dan Meyer - 3 Act Tasks (grades 6-12)

Graham Fletcher - 3 Act Tasks (grades K-7)

Mike Wiernicki - 3 Act Tasks (grades 2-8)

Andrew Stadel - 3 Act Tasks (Elem-HS)

Kyle Pearce - 3 Act Tasks (grades 3-HS)

Dane Ehlert - 3 Act Tasks (grades 3-HS)

Andrew Gael - 3 Act Tasks with particular considerations for a range of learners

Mike Flynn - creating a first 3 Act Task

Annie Fetter - more on using I Notice & I Wonder

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3 Act Tasks for K-2 Students There's lots of room for improvement with these materials. Please leave comments about what should be added or revised. If you try them with students, share what you learn! (Note: A few tasks are in-progress!) Also, see the links at the bottom of this page for more great 3 Act...

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Elementary 3 Act Tasks DESMOS Collection My 3 Act Tasks: Dart Throw (Structuring 5) K.OA.A.1-3, K.OA.A.5 On Your Mark V1 K.OA.A.3 On Your Ma…

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The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.

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Notice and Wonder Images (shared by Sara LaHood, Cohort 3 TL).pptx

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Notice and Wonder PPT (shared by Nan Prausa, Cohort 3 TL).pptx

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Your browser does not support JavaScript! This site uses JavaScript but is fully functional without it.

Mathematics

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
Implementing Rich Mathematical Tasks in the Grades K-2 Classroom Implementing Rich Mathematical Tasks in the Grades 3-5 Classroom Implementing Rich Mathematical Tasks in the Grades 6-8 Classroom Implementing Rich Mathematical Tasks in the Grades 9-12 Classroom
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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The page you are trying to reach does not exist or has been moved. You can either search for the item you are looking for or go to our home page.

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The Inside Problem Solving problems are non-routine math problems designed to promote problem-solving in your classroom. Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity. The problems were developed by the Silicon Valley Mathematics Initiative and are aligned to the Common Core standards.

To request the Inside Problem Solving Solutions Guide, please get in touch with us via the feedback form.

Why Problem Solving?

Problem solving is the cornerstone of doing mathematics. George Polya, a famous mathematician from Stanford, once said, "A problem is not a problem if you can solve it in 24 hours." His point was that a problem that you can solve in less than a day is usually a problem that is similar to one that you have solved before, or at least is one where you recognize that a certain approach would lead to the solution. Bu t in real life, a problem is a situation that confronts you and you don't have an idea of where to even start. Mathematics is the toolbox that solves so many problems. Whether it is calculating an estimate measure, modeling a complex situation, determining the probability of a chance event, transforming a graphical image or proving a case using deductive reasoning, mathematics is used. If we want our student s to be problem solvers and mathematically powerful, we must model perseverance and challenge students with non-routine problems.

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Inside Problem Solving | Inside Mathematics

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The Inside Problem Solving problems are non-routine math problems designed to promote problem-solving in your classroom. Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.

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Clothesline Math has been a growing trend in mathematics education. I saw Andrew Stadel give a talk on it (back in 2015), however it was geared toward middle school and high school math. My mind, never shutting off, was pondering how to make it fit for my elementary teachers. And in my research, there aren't many elementary clothesline cards out there.

Clotheslines become interactive number lines. Students are able to manipulate cards to show proportional reasoning, precision, equality between numbers, and magnitude. The clothesline builds students' number sense. It's a routine that can work from kindergarten through high school.

Each set of cards has been designed to have equal cards as well as multiple representations. They are all PDF files.

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Clothesline Math has been a growing trend in mathematics education. I saw Andrew Stadel give a talk on it (back in 2015), however it was geared toward middle school and high school math. My mind, never shutting off, was pondering how to make it fit for my elementary teachers.

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What Makes Teachers Special? - Pedagogical Content Knowledge

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Mathematical Knowledge for Teaching (MKT) with Dr. Deborah Loewenberg Ball

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Mathematical Knowledge for Teaching (MKT) with Dr. Deborah Loewenberg Ball

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Shared Perspectives - Deborah Loewenberg Ball

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Teaching Habits that Promote Productive Struggle in Math

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0:00 / 0:15•Watch full video

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Assessments for Learning Encourage a Growth Mindset

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Compare formative and summative assessments

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The Progression of Early Number & Counting

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The Progression of Early Number & Counting

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The Progression of Early Number & Counting

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Fairfax Network - Fairfax County Public Schools

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Classroom Management Strategies To Take Control Of Noisy Students

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This video is a great demonstration of how teachers can create a culture for math learning in their classrooms. From School Improvement Network

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Zaretta Hammond: Culturally Responsive Teaching 101 | #PLtogether

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What Is The Concrete Representational Abstract Approach

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Connecting concrete learning to the abstract algorithm for subtraction with regrouping

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My growing list of free real world problem-based lessons for grades 2 through high school. Includes links to download multimedia and teacher guide.

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Dan Meyer introduced the idea of 3-Act Math Tasks with his TED Talk: Math Class Needs a Makeover.

Below is a table of the 3-Act Tasks that I've created. Those marked with a * are newly added to this website as of 8/21/2023.

5.NBT.7, 5.MD.5

Multiplying Decimals, Volume

How much money is that?

Card House
3.OA.3, 3.OA.7, 3.NBT.3, 5.NBT.7, 8.G.7

Multiply Whole Numbers
Multiply Decimals
Pythagorean Theorem

How tall will the card house be when finished? How many cards/decks were used to build the card house? How many card triangles were used to build the card house?

For more tasks to try, check out the work offered by these amazing mathematics educators:

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Dan Meyer introduced the idea of 3-Act Math Tasks with his TED Talk: Math Class Needs a Makeover. Below is a table of the 3-Act Tasks that I've created. Those marked with a * are newly added to this website as of 8/21/2023. Task Name with LinkStandard(s)Big Idea(s)Main Question/WonderSweet Tart Hearts4.NF.4, 3.NF.1Multiplying Fractions and Whole...

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If you know the name of the case study you want to see, click on the appropriate letter range to quickly get to that section of the table, otherwise just scroll thru the table. To go to a specific case study, click on the picture.

Given a map of an amusement park, students are asked to design a schedule and divide visitor students into groups so that they can optimize their field trip visit.

Looking at the pictures, students compare the modern day animals with their prehistoric cousins. How do they think they are different? How are they the same?

By looking at any footprint, students must develop a method in order to find the height of the person.

Students must figure out how to be able to park as many cars as possible on a lawn while having enough room for cars to get out when the sports event is over.

NEW!
This is a new case study that may not yet have been field tested and piloted in a classroom. Teachers are encouraged to use them with their students and to share their results with others here."

Given aerial photographs of caribou herds, students are asked to develop a process for estimating population numbers.

NEW!

Students study the map of the Moreno Valley Trash Collection schedule. Students then figure out which areas they think have a bigger need for trash pick-up and how many workers they think are needed to pick up the trash in each district daily.

NEW!
This is a new case study that may not yet have been field tested and piloted in a classroom. Teachers are encouraged to use them with their students and to share their results with others here."

Students are given weather maps for four days and are to predict what the fifth map should look like.

NEW !
This is a new case study that may not yet have been field tested and piloted in a classroom. Teachers are encouraged to use them with their students and to share their results with others here."

Students are asked to do a layout of a mini-golf course, given 18 designs and area constraints.

Back to Top

Students are asked to develop a ranking system to determine which airlines are more likely to arrive on-time.

Students are asked to determine the best way in deciding which is the wettest state on any given day. They must present a written plan giving their procedure for establishing which state should be named the rainiest state.

Given a street map, students are asked to design optimal routes for popcorn delivery.

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From a paper folding model used to form 8-sided snowflakes, students are asked to revise the model and develop one that can help them cut out 6-sided snowflakes.

Students are asked to develop a fair rating system to award points to students participating in a summer reading program.

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Paul would like to add at least one additional switch plate for the warehouse lighting. Once the diagram is complete, Paul can begin to actually work on the rewiring job

Students must develop a scheduling system so that the Thompson's may eat on time, since they will be catered for their Thanksgiving dinner

Given information about walking plans and calories burned, students are asked to design a procedure for a health club to meet client's needs.

Students are to determine what the map for wind chill temperatures will look like.

NEW!
This is a new case study that may not yet have been field tested and piloted in a classroom. Teachers are encouraged to use them with their students and to share their results with others here."

Back to Top

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If you know the name of the case study you want to see, click on the appropriate letter range to quickly get to that section of the table, otherwise just scroll thru the table. To go to a specific case study, click on the picture.

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This collection of MEAs was written by educators across the state of Florida who participated in the Model Eliciting Activities Initiative. The goal of the initiative was to provide a rich professional learning experience for participants resulting in original published MEA lesson plans on CPALMS for use by teachers across the nation.

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Video explaining MEAs vs. Traditional Problems

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Video explaining MEAs vs. Traditional Problems

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Unit Chat - Math, Grade 3, Unit 9, Video 1

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Animals Causing Human Deaths in a Year ( LINK)
courtesy of @jennalaib

Type of Graph: pictograph

Source: Steve Jenkins' Animals by the Numbers

Potential Math Content: ratios, fractions, averages (typical/usual), understanding the key, scale

Potential Content Connections: animals, habitats, risk, disease (the mosquito isn't included - why?)

K-8 Math Specialist near Boston, MA View all posts by Jenna Laib

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Click to access the slide deck, and learn more about math & content connections.

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Length of a year (one trip around the sun) of planets in the inner solar system
graph by Steve Jenkins, slow reveal by Jenna Laib () and Amanda Fox (@amanda_renard)
( Slide deck includes notes and questions to elicit discourse)

Type of Graph: bar graph

Source: Jenkins, Steve. Solar System By The Numbers. (2020)

Potential Math Content: bar graphs, estimating values

Potential Content Connections: space, solar system

Published by Jenna Laib

K-8 Math Specialist near Boston, MA View all posts by Jenna Laib

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Length of a year (one trip around the sun) of planets in the inner solar system graph by Steve Jenkins, slow reveal by Jenna Laib () and Amanda Fox (@amanda_renard) ( Slide deck includes notes and questions to elicit discourse) Type of Graph: bar graph Source: Jenkins, Steve.

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Speed of Different Animals in the Air, on Land, and in Water
slow reveal by Amanda Fox (@amanda_renard), graph from the Steve Jenkins'
( Slide deck includes notes and questions to elicit discourse)

Type of Graph: bar graph

Source: Jenkins, Steve. Animals by the Numbers: a Book of Infographics. Houghton Mifflin Harcourt, 2016.

Potential Math Content: bar graphs, speed, rates, horizontal bar graph, scale, determining values

Potential Content Connections: animals, animal adaptations

K-8 Math Specialist near Boston, MA View all posts by Jenna Laib

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Speed of Different Animals in the Air, on Land, and in Water slow reveal by Amanda Fox (@amanda_renard), graph from the Steve Jenkins' ( Slide deck includes notes and questions to elicit discourse) Type of Graph: bar graph Source: Jenkins, Steve. Animals by the Numbers: a Book of Infographics.

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How long can animals hold their breath underwater? (LINK)
courtesy of Jenna Laib ()

( includes notes and questions to elicit discourse)

Type of Graph: bar graph

Source: Simon Rogers and Nicholas Blechwell's Infographics: Animal Kingdom (2014)

Potential Math Content: bar graph, estimating values

Potential Content Connections: animals, animal adaptations

K-8 Math Specialist near Boston, MA View all posts by Jenna

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How long can animals hold their breath underwater?

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How long can animals hold their breath underwater?

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Type of Graph: bar graph

Source: Animals by the Numbers, by Steve Jenkins

Potential Math Content: measurement units, scale, interpreting a horizontal bar graph, measurement conversions, metric units, customary units,

Potential Content Connections: animals, migration, geography

K-8 Math Specialist near Boston, MA View all posts by Jenna

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Type of Graph: bar graph Source: Animals by the Numbers, by Steve Jenkins Potential Math Content: measurement units, scale, interpreting a horizontal bar graph, measurement conversions, metric units, customary units, Potential Content Connections: animals, migration, geography K-8 Math Specialist near Boston, MA View all posts by Jenna

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Number of Tornadoes Recorded, by Month, in Alabama (1950-2019) - Slow Reveal Graphs

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When is tornado season? Click to access the slide deck, and learn more about math & content connections.

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How much water do we use doing different household activities? (LINK)
courtesy of Jenna Laib () and Kassia Omohundro Wedekind (@kassiaowedekind)
( Slide deck includes notes and questions to elicit discourse )
Paired Texts:
Type of Graph: bar graph

Source: Scholastic News

Lindstrom, Carole, and Michaela Goade. We Are Water Protectors. Roaring Brook Press, 2020.

Verde, Susan, and Peter H. Reynolds. The Water Princess. G.P. Putnam's Sons, 2018.

Potential Math Content: pictograph, predicting categories based on data

Potential Content Connections: science, #savetheplanet, water

This week so far:
1. Discussed water conservation 💧
2. Read The Water Princess and We are Water Protectors
3. Used a slow reveal graph to analyze how much water we use on a daily basis and how we can work to conserve water 🚿 #STEAM #cgimath pic.twitter.com/5ayaldS0OU
- Lauren Carr (@__LaurenCarr) May 20, 2020

https://platform.twitter.com/widgets.js

K-8 Math Specialist near Boston, MA View all posts by Jenna Laib

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As more dollars were spent on e-cigarette advertising, e-cigarette use amongst teens rose dramatically. This double y-axis graph, that is both a bar and a line graph, reveals a disturbing trend. Click to access the slide deck, and learn more about math & content connections.

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

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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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150 Which One Doesn’t Belong ideas in 2022 | which one doesnt belong, math talk, number talks

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Feb 27, 2022 - Explore Amanda Rindfleisch’s board “Which One Doesn’t Belong” on Pinterest. See more ideas about which one doesnt belong, math talk, number talks.

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I'm guessing you are visiting this page because, like me and the students in my district, you Each WODB on these pages is designed so that can't get enough of the engaged reasoning that occurs when playing Which One Doesn't Belong? We were inspired by the WODB game boards found at Mathematics is all about patterns and relationships, right? Which One Doesn't Belong does an exceptional job of helping to reinforce that concept. any of the images can be eliminated with the other three remaining images having some type of relationship/pattern. To get the most out of this activity, don't just tell why one of the items does not belong, instead, Update: During our CoVID19 learn-at-home time, several teachers have been doing FlipGrids with their students using these WODB boards. I love that they included me in their discussions. And, WOW!, what fantastic insight the students have had and their justifications have been mathematically astute! I think I've been inspired to create more - look for them in the coming weeks. describe the relationship/pattern of the other three (click the link on each category page to see some of the amazing pattern & relationship responses given by students). *Click on EACH image below to see the full set of game boards for EACH category. wodb.ca (be sure to check it out!), but we just couldn't get enough, so I created several new WODB game boards for the teachers and students in my district. And, like everything on this site, I am happy to share them with you for you to enjoy with your students, too!

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I'm guessing you are visiting this page because, like me and the students in my district, you Each WODB on these pages is designed so that can't get enough of the engaged reasoning that occurs when playing Which One Doesn't Belong? We were inspired by the WODB game boards found at Mathematics is all about patterns and relationships, right?

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As far as I know, this idea originated from Chris Shore. He has a site called Clothesline Math , where he shares examples of how this can be used with high school students. Other math educator,...

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3 Ways to Use Numberless Word Problems in Upper Elementary