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This resource is appropriate for grades 3 - 12 . The New York Times provides multiple graphs for students to look at and talk about what is happening. They can analyze these graphs for bias and trends, engage is mathematical discourse, and develop curiosity about how data informs our daily lives.

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Graphs, maps and charts from The Times — and an invitation to students to discuss them live.

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These slow reveal graphs can help students at all levels of proficiency and math understanding think about what graphs might represent and get them talking about data. This fosters curiosity, inquiry, and discourse around data and mathematics. Appropriate for grades 4-12

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Slow Reveal Graph is an instructional routine that promotes sensemaking about data. This highly engaging routine uses scaffolded visuals and discourse to help students (in K-12 and beyond) make sense of data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways.

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A FREE K-5 math curriculum that integrates computational thinking using screen free resources.

Students scan coding cards that put their mathematical thinking into action!

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Scratch was founded my Massachusetts Institute of Technology (MIT) to let kids
create animations and games using block-based coding. Scratch teaches structured
thinking and creativity, supports math practice through game design, and builds digital literacy, which are areas in high demand for career training. This tool is great for students in grades 3+ and is free!

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Scratch is a free programming language and online community where you can create your own interactive stories, games, and animations.

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This fun resource engages students in a game-based process for learning number skills and is great for PK-1 students, or 2nd grade students in need of remediation. The web-based version is free, and the app-based version can be made free for school districts, though for the general population, there is a cost after the free trial.

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Did you know that Lego offers STEAM lessons teachers can download for free? They also have tons of teacher resources including professional development, STEAM sets, and activities for students in PK - 8th grade!

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LEGO® Education SPIKE™ Essential - Lesson Planning - Lessons by Subject

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Estimation 180 offers free daily tasks to use in your classroom that will get your students working with number sense and reasoning! These are excellent for warm ups, engaging discussions, and for building critical thinking skills in 3-8 students.

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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7 Generation Games has decided to offer all of its games for free. These games help students develop math and social studies skills for grades 3-8 and will help prevent summer learning loss!

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Growing Math | Classroom-ready learning resources for Grades 3-8

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This organization, backed by the Maier Math Foundation and the Math Learning Center create activities that can be used by students, families, and teachers to enrich mathematical learning - for free! These resources are available for PK-5 concepts.

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Native Teaching Aids is a company based in St. Ignatius, Montana, that works with Indigenous communities to preserve language and culture. They create a multitude of materials - from games to posters - to bring authentic, meaningful context to classrooms across the U.S.

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Starting a language project with us is simple! Reach out today, and our team will be ready to assist you from Monday to Thursday, 9:00 AM to 5:00 PM MDT.

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Ted Talk - Math isn't Hard, it's a Language - Randy Palisoc 

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Ted Talk - Math isn't Hard, it's a Language - Randy Palisoc 

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In this short (9-minute) Ted Talk, Randy Palisoc describes the importance of humanizing mathematics and treating math as a language to increase student outcomes.

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Math isn't hard, it's a language | Randy Palisoc | TEDxManhattanBeach

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Department of Education - OHIO - Free PD Bank 

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Department of Education - OHIO - Free PD Bank 

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The Ohio Department of Education has multiple pre-recorded webinars for self-guided learning in mathematics teaching & learning!

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Professional Learning for Mathematics | Ohio Department of Education and Workforce

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The Ohio Department of Education and Workforce, in partnership with the Ohio ESC Association, offers a professional learning series to expand educators’ understanding of Ohio’s Learning Standards for Mathematics and the Standards for Mathematical Practice.
This four-part webinar series supports educators in fostering mathematical discourse and language routines in the classroom:

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The Little Shell Tribe provides a high volume of cultural resources on their website. Though these aren't specifically identified as being math-related, there is no shortage of mathematical thinking present. For example, understanding traditional herbs and medicines can connect to measurement and data, counting and cardinality, numbers base ten, algebraic thinking and beyond! The same is true for the impact of the fur trade, living within the four seasons, and so many more of these lessons, stories, and creations teachings. I encourage teachers to start from a place of trying to understand, then explore the idea - where are mathematics present in these cultural expressions?

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OUR CULTURE The ancestors of today's Little Shell Tribe are first documented being in the land now known as the State of Montana as early as 1692 guiding Henry Kelsey of the Hudson's Bay Company. In the 1730s, as part of the Nehiyaw Pwat Confederacy (i.e, Cree Assinboine, aka, Iron Alliance) ancestral Little Shell peoples [...]

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While the Confederated Salish and Kootenai Tribes have not identified these resources as math-specific, there is no shortage of mathematical thinking present in Indigenous Ways of Knowing. The Tribes offer a number of resources that can be leveraged in mathematics lessons, particularly regarding measurement and data and spatial reasoning or geometry.

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&nbspCSKT | NRD Division of Fish, Wildlife, Recreation & Conservation

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Online Resources | &nbspCSKT | NRD Division of Fish, Wildlife, Recreation & Conservation

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Bring the Museum of the Rockies into your classroom with real fossils and artifacts, unique hands-on activities and lesson plans, and current research on science and history. These resources support STEM education, Montana Content Standards, and Indian Education for All, highlighting MOR’s best resources for children. Help your students learn MORE without being at MOR.

Outreach Kits include:

Lesson plans and materials for hands-on learning

Background information for educators

Lists of recommended resources for parents, educators, and students

Checklists of applicable Montana Content Standards

Outreach Kit Rental Fees
All trunks have a rental fee of $35 per week to support the purchase of new materials. Scholarships are available, as this cost is not meant to prohibit schools with restricted budgets. All items are available for pick-up at MOR or can be shipped to your school. You will be responsible for the cost of the return shipping back to MOR. Shipping rates vary depending on the weight of the item but are usually $25-$30.

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In 2016, Carter County Museum (CCM) and its sister museum, Museum of the Rockies, embarked on a collaborative educational project known as MAIA: Mobile Science Lab.

This classroom lab explores the mathematical and biologic concepts of growth curves while connecting students with Montana's agricultural economy and rich fossil history. A lesson developed by the science and math departments at Carter County High School (CCHS) and recently piloted at CCHS in Ekalaka, Montana, engages students in measuring femurs of cattle, chicken, deer, and the dinosaur Maiasaura. MOR and CCM provided access to materials and content oversight.

This traveling outreach program combines the osteology collections of CCM, one of the world's best-studied dinosaur growth series from MOR, and partnership with Carter County High School. The result is an engaging learning experience that connects Montana rural students to mathematical concepts, agriculture, and natural science.

Download our letter to teachers here: MAIA Letter to Teachers
For more information, check out our press release: MAIA Press Release
The teacher's guide and student workbook are available upon request.

The trunk is available for use to Montana high schools upon request. The first priority for MAIA will be given to teachers and schools in southeastern Montana. To reserve the trunk or for further questions, contact Sabre Moore at smoore@cartercountymuseum.org.

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Learn about and sign up for one of the astronomy, paleontology, Indian Education for All, or Yellowstone outreach kits to supplement your classroom curriculum.

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Glacier National Park Math Lesson Plans 

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Glacier National Park Math Lesson Plans 

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Did you know that the National Park Service has mathematics lesson plans? Ground your students in place-based learning around lodge painting, bird watching, temperature tracking, rock collecting, and more!

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Search Lesson Plans - Glacier National Park (U.S. National Park Service)

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Alert 1, Severity closure, Going-to-the-Sun Road Seasonal Closure

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Confederated Tribes of Grand Ronde Lesson Plans  K-12

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Confederated Tribes of Grand Ronde Lesson Plans  K-12

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Although the Tribal Nations of the Grand Ronde are not specific to Montana, this tribe offers substantial resources and lesson plans (aligned to common core standards) that could be implemented in classrooms in Montana, or could serve as a way to relate or compare Tribes in Montana to these Tribes in Oregon. This tribe has done incredible work presenting K-12 curriculum in Science, Math, ELA, and History. Give their resources a look!

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Mission Statement:

Welcome to the Confederated Tribes of Grand Ronde Tribal History curriculum unit. We appreciate that you are taking the time to learn and teach this curriculum to your class. This curriculum was created from the need for historically accurate and culturally relevant curriculum in Oregon schools about Oregon Native Americans and as a response to countless requests from Oregon teachers for classroom-ready materials on Native Americans. Our hope is that these lessons can be taught in a variety of settings and subjects - creating a more culturally responsive atmosphere for all students throughout all areas of their education experience. We hope you find these units useful and appreciate the positive difference you are making by teaching this as it will have an incredible impact on generations to come.
CTGR Tribal History Curriculum Feedback Form
Implementation

It is the intent that these lessons will be integrated into pre-existing school curriculums throughout the school year. They should be introduced to students as any other lesson would and can be applied in a variety of subject levels. While target "Native American Lessons and/or Learning Weeks" can convey much of the information and concepts, we encourage educators to approach these units/lessons as a classroom culture shift and use them to "sprinkle" culture throughout their curriculum. This conveys a message of inclusiveness and acceptance to students as they understand the concept of Native Americans' role in the present-day. While the lessons can be taught as small units, many also serve as stand-alone lessons and can be taught in conjunction with other non-Native curriculums.

The Tribal History Curriculum covers a wide variety of topics throughout multiple subjects.

o English Language Arts

o Science

o Social Studies

o Government

o World Trade

o US History

o Health

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Curriculum | Confederated Tribes of Grand Ronde

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Welcome to the Confederated Tribes of Grand Ronde Tribal History curriculum unit. We appreciate that you are taking the time to learn and teach this curriculum to your class. This curriculum was created from the need for historically accurate and culturally relevant curriculum in Oregon schools about Oregon Native Americans and as a response to countless requests from Oregon teachers for classroom-ready materials on Native Americans.

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Make Math Moments - How to Group Students In Math Class 

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Make Math Moments - How to Group Students In Math Class 

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What Listeners Will Get From This Episode: Practical strategies for grouping students in math class—when to use ability-based groups for targeted support and when to use heterogeneous groups for richer discussions. Guidance on choosing the right math tasks—how to match math tasks with the most effective grouping strategy. Ideas for keeping groups dynamic—ways to ensure students aren’t stuck in fixed-ability groups and have opportunities to grow. Techniques to foster equitable participation in math class—how to structure groups so all students contribute and benefit, regardless of skill level. Ways to prevent unintentional tracking—tips for avoiding the pitfalls of long-term ability grouping.

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Ep347: How To Group Students In Math Class: Similar Abilities or Mixed Abilities in Math Classrooms?

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Montana PBS has so many classroom resources available! Did you know nearly 8,000 resources appear when you search "Indian Education for All"? Take this fish sampling lesson plan for example: https://montana.pbslearningmedia.org/resource/midlit11.math.splsamp/population-sampling-fish/

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Search Classroom Resources | PBS LearningMedia

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Find classroom resources for teachers and students. Search for videos, lesson plans, and games aligned to state and national standards.

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Billings Public Schools K-5 Math Lessons 

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Billings Public Schools K-5 Math Lessons 

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Billings Public Schools offers a cache of K-5 model lesson plans, with videos, that support educators in working with IEFA in Math, through the use of stories.

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BPS K-5 Math - BPS OPI/IEFA Model Lessons

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Through grant funding from OPI & Indian Education for All, the following resources were developed to make connections between MCCS, IEFA Model Teaching Units, and our Montana Content Standards and Lead 21 Literacy Resources. Research based best practices and strategies were the common thread

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This bank of Free K-12 math problems utilizes the open middle model where each problem has a set starting parameter and a set answer, but an "open middle" meaning that there are many strategies or methods students can utilize to reach the solution. This strategy helps reduce math anxiety - students are no longer afraid of getting the wrong answer - and shifts the focus of mathematical engagement from one that prioritizes finding solutions to one that values creative thinking and mathematical inquisition. For additional learning about this strategy, consider purchasing Robert Kaplinsky's book: "Open Middle Math".

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The name "Open Middle" might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:

a "closed beginning" meaning that they all start with the same initial problem.

a "closed end" meaning that they all end with the same answer.

an "open middle" meaning that there are multiple ways to approach and ultimately solve the problem.

Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.

Some additional characteristics of open middle problems include:

They generally have multiple ways of solving them as opposed to a problem where you are told to solve it using a specific method. Example

They may involve optimization such that it is easy to get an answer but more challenging to get the best or optimal answer. Example

They may appear to be simple and procedural in nature but turn out to be more challenging and complex when you start to solve it. Example

They are generally not as complex as a performance task which may require significant background context to complete. Example

We hope you enjoy these problems. Please be sure to send us any ideas for problems we can add.

Thanks!
Co-founders Nanette Johnson and Robert Kaplinsky

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The name "Open Middle" might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have: a "closed beginning" meaning that they all start with the same initial problem.

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The Virginia Department of Education provides a wonderful bank of resources and lesson plans on open-ended math tasks, organized by grade level and connected standard. As most are aware, open-ended math tasks provide a rich opportunity for students to engage at many levels, including students with accommodation and supportive needs and culturally and linguistically diverse students.

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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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MSU Explore: Earth & Space Science Camp is a 5-day summer camp program encouraging Montana middle school students to learn more about science, technology, engineering and math (STEM). It inspires students to consider science-related careers, encourages them to pursue a college education, and gives them a taste of college life. The camp typically runs in June.

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MSU Explore: Earth & Space Science Camp - Academic Technology and Outreach | Montana State University

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This summer camp, which serves Native American students from 6 th – 10 th grade, students will have an opportunity to access rich learning experiences in math and science, receive support and mentoring throughout the year, and, have an opportunity to earn money for continuing to succeed in their academics! The program has three pathways, determined by age group and program experience, and typically takes place in June.

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Montana American Indians in Math and Science (MT AIMS)

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This online platform houses all of the K-12 Math Standards in a downloadable format. When we have our new standards up, this framework will include associations to the 2011 standards, IEFA integrations, Notes and Guidance, Instructional Examples, and more!

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A list of activities to support math learning for elementary students.

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Here's a collection of LEGO math activities that kids will love! These activities are perfect for kids in the elementary grades, or ages 5 - 10.

We love using LEGO® bricks for hands-on math learning. There are so many math concepts that you can explore - addition, subtraction, measurement, estimation, fractions, multiplication, division, and more.

Why purchase math manipulatives when you have LEGO bricks? HA!

Here's how this post works. Each activity has a link that will take you to the full instructions (and printable file if applicable) for that activity.
FIRST AND SECOND GRADE LEGO MATH ACTIVITIES
Get started with the concept of addition by using these LEGO Addition Mats. Perfect for young students who need to see the objects being added.

Build a LEGO Number Line and then use it for addition, subtraction, and more.

These LEGO Math Challenge Cards have been extremely popular! Each card has a task for the child to complete using LEGO® bricks. The cards are perfect for first and second graders, and they cover the concepts of addition, subtraction, fractions, measurement, estimation, place value, and grouping.

LEGO Place Value: Help kids understand the concept of place value by building two-digit numbers as tens and ones. There is a printable mat to go with this!

Print this awesome LEGO First Grade Math Pack. There are activities for measurement, finding the missing addend, and number bonds (addition activities).

Teach probability and graphing with LEGO bricks! This feels more like a game than a math assignment.

Build a LEGO Balance. This simple LEGO balance really works, and will allow kids to compare the weights of different objects. So fun!
UPPER ELEMENTARY LEGO MATH ACTIVITIES - THIRD GRADE AND UP
I have 4 different ways to teach multiplication with LEGO® bricks, and I'd recommend trying them all so that the child can approach the concept of multiplication from different angles.

First, there is this Printable Multiplication Towers activity. This approaches multiplication as grouping (or repeated addition).

Then you can try this LEGO Multiplication Game that teaches the geometric model of multiplication.

Here's a really cool way to build a 3D LEGO Multiplication Graph - it's a way to visualize the multiplication tables.

Kids will also enjoy this LEGO Arrays Multiplication Game. Just grab some dice, basic bricks, and some 16 x 16 plates. Then race to cover the plate!

LEGO Prime Numbers: Use LEGO® bricks to figure out which numbers are prime numbers! This is a concrete way to help kids understand the concept. This post has printable activity sheets with instructions.

Teach fractions with LEGO bricks! Here are Four LEGO Fraction Activities.

Build LEGO Math Patterns: These patterns go way beyond simple red-blue-red-blue patterns! Kids can explore all kinds of cool ways to build mathematical structures.

If you're looking for LEGO STEM ideas, be sure to check out our LEGO machines book!

Genius LEGO Inventions with Bricks You Already Have is full of 40 cool machines to build with real moving parts. Create robots, a wind-up catapult, a candy machine, a drummer that really plays the drums, and tons more. The book also has explanations of the physics and engineering concepts involved in each of the projects. Build and learn!

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LEGO Math Activities for Elementary Kids - Frugal Fun For Boys and Girls

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Make math fun with these LEGO math activities! Ideas for addition, subtraction, measurement, place value, multiplication, and more.

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This episode covers the new MP#3 for Montana as part of the Digging Deeper Series.

Accompanying Facilitator Guide:

https://opi.mt.gov/LinkClick.aspx?fileticket=MZFO_OoEaao%3d&portalid=182

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Digging Deeper into Montana Mathematical Practice #3: Justify and Prove (2026)

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Did you know that NCTM offers free online professional development webinars to its members? Members can participate in live sessions, or access previous recordings! This is an incredible resource for educators to access evidence-based, and timely information to support their work in classrooms.

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NCTM – Professional Development Webinars

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What kinds of resources would you like to see more of in this space? 

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Lesson Plans and Activities - I want fresh ideas for instruction!

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IEFA and Math Integration - I want to implement for IEFA in my class!

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Podcast Episodes, Research and Ted Talks - I want to learn more about best practices!

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Differentiation - I want to know how to meet the needs of each student!

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NCTM - Guide for Selecting Mathematics Instructional Materials 

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NCTM - Guide for Selecting Mathematics Instructional Materials 

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This brief article (10-minute read) offers some advice for key considerations in selecting mathematics instructional materials.

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By NCTM President Diane J. Briars
November 2014

Adoption of curriculum materials is one of the most important decisions a teacher, school, or district can make. While state standards describe what students are expected to learn and be able to do, what is taught in classrooms-the implemented curriculum-is heavily influenced by textbooks and other instructional materials. The instructional materials affect lesson content, depth and duration of instruction for particular topics, and topic sequence. So, while we may talk about curriculum materials as just "resources," the fact is that they strongly influence classroom instruction-for better or worse.

Not surprisingly, evaluating curriculum materials has been a hot topic of conversation at recent meetings I've attended. "Which materials are best aligned with 'the Standards'-Common Core or other state standards?" "What criteria, rubrics, or evaluation processes will result in the selection of the 'best' curriculum materials for implementing 'the Standards'?"

During my tenure as mathematics director for the Pittsburgh Public Schools, I led many mathematics materials adoption committees-and I learned a great deal about productive and nonproductive practices. From that work and my experiences with other districts and states, large-scale materials review projects, and national recommendations, I offer my "Top Lessons Learned" about effective curriculum materials evaluation.

Review Criteria and Process: Top Lessons Learned

1. Focus on the central evaluation question: What curriculum materials best support students' learning of the standards? Wording the question in terms of students' learning of content, rather than implementation of standards, puts students' learning front and center. What students learn and how well they learn it depend on both mathematics content and instruction. Framing the review in terms of students' learning makes support for effective teaching and learning a critical feature for review, along with content.

2. Remember that content analysis is much more than alignment. Alignment of content with standards is often represented through "crosswalks" that connect the two, indicating whereand when content addresses particular standards. While such an approach can be useful, effective content analysis examines how materials address standards, that is, it looks for the following:

The treatment of content is consistent with that described in the standards. For example, the grade 7 Common Core State Standards for Mathematics (CCSSM) emphasize understanding and using unit rates and equivalent ratios to solve problems involving proportional relationships, building a foundation for understanding slope. Thus, a critical content "look for" is whether materials build this understanding and emphasize use of these methods, instead of emphasizing solving proportions by using cross multiplication, with little or no attention to unit rates and equivalent ratios.

The development of conceptual understanding, procedural fluency, and applications is balanced, with explicit connections among the three ("rigor" in CCSSM). A critical review criterion is the extent to which procedural fluency builds on conceptual understanding. With respect to applications, important "look fors" include applications that require problem solving and reasoning, as well as more routine use of concepts and skills; the use of applications to introduce new content, as well as to apply concepts and skills after initial instruction; real-world" applications; and, especially at the high school level, opportunities for using mathematics to model real-world situations.

The development of content reflects what is known about how students learn that content most effectively. Ideally, this knowledge is incorporated in the standards, so it would be addressed in content treatment review. (CCSSM's attention to learning progressions, especially in grades K-8, is one of its strengths.) If it is not, or standards do not provide sufficient detail to reflect this knowledge, it is an important review criterion. For example, research clearly indicates that students learn their basic facts more efficiently and effectively when instruction focuses on fact families and strategies that relate unknown facts to known facts (doubles plus one, for example), instead of rote memorization of individual facts. Although CCSSM explicitly includes such strategies, other college- and career-ready standards may not. Regardless, the treatment of basic facts is an important consideration in materials review for grades K-4.

The development of students' problem solving, reasoning, and other mathematical habits of mind-the set of processes identified in the CCSSM Standards for Mathematical Practice-receives explicit and regular attention. These experiences should be embedded in content development, not separate activities or lessons that can easily be skipped. This analysis is also part of the review of support for effective instructional practices described in #3 below.

The materials are focused. Curriculum materials should give sufficient attention to the critical topics identified in the standards for each grade (in CCSSM, the "major work" of the grade), so that students have the time and support to develop the identified proficiencies. That does not mean simply adding more content to each grade so the books become larger! It means devoting more attention to focus topics and less to secondary topics, while omitting topics that are not in the standards.

Content treatment is coherent. The content is effectively organized so that students can clearly see how ideas build upon, or connect with, other ideas both within and across grades. This analysis requires looking at the development of content across grades and courses, in addition to looking at the development within a grade or a course.

The mathematics in the materials is accurate. That the materials should be as close to error-free as possible goes without saying.

Student Achievement Partners' Publishers Criteria provides a more detailed discussion of the preceding criteria.

3. Analyze the nature of the instructional tasks and activities-this is as important as analyzing content. This analysis examines how the materials support students' learning though opportunities to engage in tasks that promote reasoning and problem solving and teachers' implementation of effective teaching practices as described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Critical questions include the following:

To what extent do lessons regularly feature tasks that engage students in problem solving, reasoning, and making sense of mathematics as core instructional activities, rather than special features that can be omitted?

What is the quality of these tasks? Do they permit multiple entry points and approaches? To what extent do they address the learning goals of the lesson?

Do the tasks constitute a coherent series designed to address specific mathematical goals across lessons? Do the tasks build procedural fluency from conceptual understanding across lessons?

What supports do the teachers' editions provide for effective implementation of these lessons? Do they provide, for example, information about likely student solutions, questions to support students as they work on tasks and in subsequent debriefing discussions, and suggestions about ways to structure the summary discussion?

Understanding the intended instructional model is essential for this analysis. Be sure to read the teacher's edition or other explanatory materials, view supporting webinars, etc., that describe the instructional model and where particular supports are located. Reviewing only the student materials may not provide sufficient understanding of how the materials are intended for use in the classroom to support an adequate analysis.

4. Focus initial reviews on student materials and teacher editions of the materials.These have the primary influence on classroom teaching and learning. Analyze ancillary materials and other supports for effective teaching and learning-such as assessments, technology integration, additional practice, and professional learning-after you have narrowed your choices to materials that adequately meet the content and instructional support criteria. All the flashy supplementary materials in the world won't make up for flawed content or lack of high-quality instructional activities.

5. Consider equity, diversity, and access. High-quality content and instructional practices are critical for the success of all students; therefore, reviews of these aspects are essential first steps in addressing equity and access. After narrowing your choices, however, consider specific ways in which materials promote equity and access. To what extent, for example, do they-

provide teachers with strategies and materials for meeting the needs of a range of learners, including both struggling and advanced learners?

suggest accommodations and modifications for English language learners that will support their regular and active participation in learning mathematics?

provide a balanced portrayal of various demographic and personal characteristics?

See the CCSSO-NCSM Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Tools for a more complete list of equity, diversity, and access criteria.

6. Recognize that all omissions or gaps are not the same. No materials are perfect. Inevitably, an evaluation process will uncover gaps, omissions, or inadequate treatment of some content. The key question is how easily teachers, the school, or the district can fill the gaps. For example, providing additional practice on a skill may be relatively easy; providing lessons to address a gap in concept development is probably more difficult. Gaps that are most difficult or impossible to fill are consistent lack of instructional tasks that engage students in problem solving, reasoning, and the mathematical practices. Expecting teachers, schools, or districts to create or find high-quality tasks for almost every lesson is unreasonable-and, most likely, will not provide the consistent quality or coherence needed for effective teaching and learning.

7. Recognize that additional content is less problematic than gaps that are difficult to fill. Given the variation in standards across states, materials are likely to contain content beyond that addressed in your standards. The issue is how that extra content affects the treatment of content addressed in the standards. If the extra content can easily be skipped, or if it contributes positively to students' learning the content addressed in the standards, then it doesn't matter. It does matter, however, when it decreases time and attention on content addressed in the standards, disrupts the focus and coherence of the materials, or is so great that the books are huge.

8. Request all series and materials produced by each publisher. When you call for materials to review, remember that some of the large companies publish more than one program, so you may have to ask to see them all. Also, request programs from smaller, alternative publishers and developers as well as the large publishers. You want to review all the options, not just the traditional best sellers.

9. Allocate sufficient time for your review process. Thoughtful analysis of the content, instructional activities, and other features of curriculum materials described above takes time. Materials that are adopted are likely to be used-and to influence instruction-for a number of years. So time spent reviewing materials carefully is time well spent.

10. Use a "narrowing choices" strategy to make the review process as efficient as possible. Clearly, thorough content analyses are time-consuming-and may seem overwhelming. To make the process manageable, first review all materials for their treatment of only one or two key content domains. Retain for further review only those materials that give adequate treatment to those domains. Then make a second cut based on your evaluation of the nature of the instructional tasks and support for effective teaching practices within those domains. After these cuts, you're likely to have a manageable number of materials for further review. For example, to review middle school materials with respect to CCSSM, you might first review all materials for their treatment of ratios and proportional relationships (grades 6 and 7) and functions and expressions and equations related to proportional relationships (grade 8). Then review materials that treat that content well from the standpoint of the nature of their instructional tasks, and so on, for that content. Submit the materials that adequately address both criteria to additional review, starting with the remaining content domains, instructional tasks, and other review criteria such as equity, diversity, and access, ancillary materials, and so on.

11. Rate and discuss rather than score. Analysis of materials is qualitative, rather than quantitative; that is, reviewers are judging the quality of content treatment, instructional activities, and so forth, in different materials. Consequently, qualitative rubrics with categories such as "Not Found," "Low," "Marginal," "Acceptable," and "High" can be more useful than numeric scales. Qualitative ratings also provide useful guidance for subsequent within- and across-grade discussions of the quality of different materials.

12. Provide adequate professional learning for the members of the review team. It is essential that all reviewers both understand the standards and are knowledgeable about the effective teaching practices for implementing them. To ensure this common base of knowledge and understanding, consider engaging reviewers in collaborative study of the standards. For CCSSM, read and analyze the progression documents in addition to the standards themselves. APrinciples to Actions book study can be a good way to build knowledge of the effective teaching practices.

13. Try out your top choices in the classroom. The real test of the quality of any materials is the learning that they support in the classroom. If at all possible, try out at least a unit or two from the materials under final consideration in several classrooms. Even if the review committee is in unanimous agreement, using the materials in some classrooms is important before finalizing the decision. When you test the materials in this way, recognize that they may use unfamiliar instructional models, so students-and teachers-will need some adjustment time. My experience has been that trying out materials has been invaluable in helping review committees adopt materials that strongly support effective teaching and learning.

A number of rubrics and tools are available to support materials evaluation. I have used the CCSSO-NCSM Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project Tools referred to earlier. The strengths of these tools are that they provide qualitative rubrics for analysis of different review criteria, along with worksheets that are specifically designed to support cross-grade as well as within-grade analysis of treatment of core content domains. As you consider rubrics for your process, be sure that they (1) support cross-grade analysis of content coherence as well as the quality of individual lessons or units and (2) promote discussion of strengths and weaknesses of particular materials rather than only numerical ratings.

Even though this list of review criteria and processes may seem overwhelming, in practice, these "lessons" have worked very well to guide the review process and support adoption of materials that will promote all students' learning of the standards. Selection of curriculum materials is one of the most important responsibilities of teachers, schools, and districts. And careful analysis of how materials address standards and instruction is a necessary foundation for this work and critical to the learning of all students.

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Curriculum Materials Matter: Evaluating the Evaluation Process - National Council of Teachers of Mathematics

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By NCTM President Diane J. Briars November 2014 Adoption of curriculum materials is one of the most important decisions a teacher, school, or district can make. While state standards describe what students are expected to learn and be able to do, what is taught in classrooms-the implemented curriculum-is heavily influenced by textbooks and other instructional materials.

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EdReports: A Guide for Selecting Instructional Materials. 

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EdReports: A Guide for Selecting Instructional Materials. 

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Need help selecting quality instructional materials? Checking out this guide is a great first step.

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All students deserve high-quality materials. Less than 20 percent of the materials in use in classrooms are aligned to standards.

What you select and how you select matters. Schools and districts have more options than ever from which to find high-quality materials that meet their local priorities. The selection process is a critical lever for ensuring that quality materials are adopted and then used well in classrooms. Current adoption practices are simply not good enough.
We believe that:

Selecting materials is a decision worthy of study and prioritization

Local context and instructional vision should drive decision-making

Educator voice and expertise must be at the center of the decision

Materials should be aligned to high standards, attend to instructional shifts and be based on research

Professional learning and implementation needs to be considered from the beginning of selection processes.

We work with teams across the country to implement the steps below, improve their selection processes, and find the right materials for their students and teachers. Explore our case studies to see how different districts have applied these key steps. Additional activities, resources, and protocols we use with teams are embedded within the steps for you to use or adapt within your own process.

We've also collected resources and best practices from these districts and included them here for your inspiration. We will be adding to this collection on a regular basis.

Contact us if you would like to share a best practice from a recent adoption process or consult with one of our experts as you plan your next instructional materials selection,
contact@edreports.org.

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All students deserve high-quality materials. Less than 20 percent of the materials in use in classrooms are aligned to standards. What you select and how you select matters. Schools and districts have more options than ever from which to find high-quality materials that meet their local priorities.

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Asset Based Teaching Perspectives - A Joint Statement from Association of State Supervisors of Mathematics
(ASSM) and the Association of Mathematics Teacher Educators (AMTE)

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Asset Based Teaching Perspectives - A Joint Statement from Association of State Supervisors of Mathematics
(ASSM) and the Association of Mathematics Teacher Educators (AMTE)

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This 4.5-page brief will take educators a short while to read but can potentially bring new perspectives to the forefront regarding student skills. A brief excerpt: "Asset-based perspectives start with recognizing that all students bring knowledge, experiences, strengths, talents, and resources to the learning process and can contribute meaningfully. Student thinking is valued, and the teacher facilitates discussions that build on what students know. Asset-based perspectives cultivate an inclusive classroom environment where students see themselves and others as capable learners and doers of mathematics. This is important for all students, but especially students who have historically been marginalized in mathematics education."

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A Guide for Assessing Mathematical Understanding - Education Northwest (REL) 

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A Guide for Assessing Mathematical Understanding - Education Northwest (REL) 

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This guide, published by Education Northwest, supports educators in understanding a key component of differentiation - understanding and assessing what students know and can do. This is a rather large document, and will take significant time to read fully, however, many educators may have familiarity with some of the topics already.

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This episode covers the new MP#1 for Montana in a video with built-in activities for self or group study. Study on your own, or, partner with educators you know to dig deeper in understanding MP1. The facilitator guide is also offered to support your engagement with this video and comes with a participant worksheet.

Accompanying facilitator guide: https://opi.mt.gov/LinkClick.aspx?fileticket=4WR_IVCp_gU%3d&portalid=182

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Digging Deeper into Montana Mathematical Practice #1: Problem-Solving & Perseverance (2026)

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This episode covers the new MP#2 for Montana in a video with built-in activities for self or group study. Study on your own, or, partner with educators you know to dig deeper in understanding MP2. The facilitator guide is also offered to support your engagement with this video and comes with a participant worksheet.

Accompanying facilitator Guide: https://opi.mt.gov/LinkClick.aspx?fileticket=sJvcBJBY1cY%3d&portalid=182

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Digging Deeper into Montana Mathematical Practice #2: Abstracting and Generalizing (2026)

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Joint Position Statement NCTM and CEC on Teaching Mathematics to Students with Disabilities 

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Joint Position Statement NCTM and CEC on Teaching Mathematics to Students with Disabilities 

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This short position statement will take approximately 8-10 minutes to read. It covers statements regarding the rights of students to access grade-level learning, declarations of position, and suggested action items for schools, educators, state agencies, researchers, and beyond.

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This great resource is good for helping P-6 students work with representing data. The story about a loveable dragon who wants to use data to make friends is great for younger students, while the dynamic pictures and printable resources highlighting the different data representations would be great for older students and teachers.

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Daphne Draws Data: a storytelling with data adventure

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Daphne Draws Data: a storytelling with data adventure

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Daphne shares the superpower of numbers and graphs through her adventures! Explore activities for kids, guidance for parents, and STEM resources for educators to make learning about graphs fun and accessible.

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Teacher Learning Hub - Tech-ify Your Classroom: The Basics of K-5 Technology Integration

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Teacher Learning Hub - Tech-ify Your Classroom: The Basics of K-5 Technology Integration

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The lessons in this course will guide you through the basics of meaningful, effective technology integration in grades K-5. Young learners are capable of leveraging technology to learn, do and create amazing things, and this course will guide you in thinking about technology and how it can enhance the curriculum and learning in your classroom. Technology is a powerful tool for differentiation and learning how to integrate it in instructional practice will support educators in meeting the needs of all students. Participants in this course can earn up to 4 PDUs.

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Built with Open LMS, a Moodle-based product. Copyright © 2024 Open LMS, All Rights Reserved.

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Teacher Learning Hub - More Than Making the Grade: An Introduction to Standards-based Grading and Reporting

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Teacher Learning Hub - More Than Making the Grade: An Introduction to Standards-based Grading and Reporting

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This course, available on the teacher learning hub, can support educators in exploring standards-based grading. This strategy is highly effective when paired with differentiated instruction strategies. Participants in this course can earn 2 Professional Development Units.

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Built with Open LMS, a Moodle-based product. Copyright © 2024 Open LMS, All Rights Reserved.

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7-8th Grade: Exploring Geometric Concepts Through Engaging with Shadows! 

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7-8th Grade: Exploring Geometric Concepts Through Engaging with Shadows! 

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This engaging activity will support your students in making mathematical discoveries related to Similarity and Dilations. The lesson is aligned to CCSS standards and offers three separate activities!

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NCTM - Understanding and Reframing “Learning Loss” in Mathematics: Goals, Policies, and Practices for Strengths-Oriented and Equitable Solutions

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NCTM - Understanding and Reframing “Learning Loss” in Mathematics: Goals, Policies, and Practices for Strengths-Oriented and Equitable Solutions

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This free hour-long webinar recording will address how a range of leaders have been working to address “learning loss,” which may be better thought of as unfinished learning, and how to think about, organize, and define their goals; implement new practices and avoid other practices; use and shape policies; and create positive opportunities for their students.

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NCTM – Professional Development Webinars

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Presented by Donna Leak , Levi Patrick and Zachary Champagne

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Differentiation: What it is and what it isn't

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Differentiation: What it is and what it isn't

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This article, from ASCD explains what instructional differentiation is, and breaks down common myths. It will take approximately 7 minutes to read.

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NCTM Guidance on Differentiated Learning 

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NCTM Guidance on Differentiated Learning 

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This article summarizes effective, evidence-based differentiation strategies to use when teaching mathematics. This article will take approximately 5-7 minutes to read.

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Get real. It's impossible to look at any classroom and pretend that each and every student is alike. Instead, focus on the differences that exist, value the diversity , and allow each student the opportunity to shine. Teachers should be open to different approaches and strategies as long as students are able to explain their reasoning. Students want the chance to be original, resourceful, or ingenuous.

Blend whole-class, group, and individual instruction. It is more effective and efficient to use different strategies in different situations. When using groups, rotate students based on demonstrated knowledge, interest, and/or learning style preferences with the aim of moving students to a higher level of achievement. Use the groups to set up learning activities that: teach new concepts, apply concepts previously learned, and also revisit skills not mastered.

Be proactive. Embrace accountability. You as a teacher are responsible and obligated to plan a variety of ways to facilitate learning. Instruction may be differentiated in content, process, or product according to the students' readiness, interests, or learning style. Students must be able to express themselves in what they learn, how they learn it, and how they demonstrate their understanding. As you progress as a great teacher, you will become more comfortable using multiple instructional strategies and a variety of representations at the same time to increase the chances of reaching each and every student.

Acknowledge that students have different learning styles, learn at different speeds, are at different comfort levels of thinking abstractly, and differ in abilities to make connections. Offer choices and flexibility in the classroom. When appropriate, set up learning centers to provide choices. Make sure the centers include varied activities such as skill practice, problem solving, manipulatives, games, working with technology such as computers or calculators, graphs and other visuals, and writing opportunities. This will provide for a more comfortable, engaging, and inviting learning environment for students with different levels of understanding and different interests.

Never separate assessment from instruction; rather integrate assessment into instruction by making informal assessments a way of life in your classroom. In the classroom, focus on qualitative assessment more than quantitative assessment. It is imperative to get to know each student's achievement levels and strengths and weaknesses. Pre-assessment is a critical first step that should be used before designing any lesson. Don't assume what your students know or don't know; find out!

Get to know your students! Outside of the classroom, keep up on your students' interests. Try to find time to make a basketball game or a theatre production to show that you are interested in them outside of mathematics class. In the classroom, use personal interest inventories regularly. Once you know your students interests, you will be able to better create assignments that fit your students' interests. Students will be more engaged in the learning if they feel it was developed around their interests.

Use a variety of forms of assessment: formal tests, homework assignments, journals, discussions, and presentations. Equally important is that you follow through; use the results of assessments to continuously plan lessons on skills that are not yet mastered by your students.

Reflect on lessons, projects, evaluations, and everything else that goes on in your classroom. Focus on how you could modify lessons to better fit the students' needs and interests.

Focus on the students! It may be easier for you to lecture and assign drill and practice, but remember that your ultimate goal is to be in the best interest of your students' learning. Use more inquiry-based teaching practices and investigations.

Realize that teaching is evolutionary. Great teaching doesn't happen overnight. It takes patience and consistent dedication. Focus on becoming comfortable differentiating one new lesson at a time. Your plan must include more than the content. You also will need a plan for managing time and keeping students focused. You may worry about disruptions, but in a collaborative learning environment, students will be more engaged and disruptions may decrease. Students are unique, so the same approaches aren't going to work year to year or even day to day. As teachers, we must monitor each learner, their learning, and make continuous adjustments.

Take the time to briefly pre-teach or even re-teach to meet the needs of students before introducing new content goals. Use heterogeneous groups to facilitate a tutoring and mentoring relationship between students, but be careful not to overuse this strategy. Hold students accountable for their own learning. The more skilled students deepen their understanding by articulating concepts, and the less skilled have a chance to learn ideas from a different source. Sometimes a peer's words are easier to internalize and may be less intimidating than working one-on-one with the teacher.

When differentiating your classroom, don't leave out the gifted students. Be cautious that you are assigning open-ended rich inquiry activities instead of more work or always using peer-tutoring and mentoring relationships. Differentiating should allow each and every student to be enriched. Differentiating is NOT adjusting the workload assigned based on ability levels or grading differently based on perceptions of students' capabilities.

Arrange your classroom in clusters to promote mathematical literacy. Get your students comfortable with the norms associated with collaborative learning; it's a necessary prerequisite to differentiated instruction, and it also creates more opportunities for interaction. Imagine a teacher in a classroom of 32 students. In a 50 minute class period, she can't dedicate even two minutes to a student individually, but in groups of 4, she could dedicate more than 6 minutes to a group. Additionally, when working with one group, the other groups would be on task communicating and making progress.

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Differentiated Learning - National Council of Teachers of Mathematics

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Get real. It's impossible to look at any classroom and pretend that each and every student is alike. Instead, focus on the differences that exist, value the diversity , and allow each student the opportunity to shine. Teachers should be open to different approaches and strategies as long as students are able to explain their reasoning.

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Digital Resources from National Indian Education Association 

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Digital Resources from National Indian Education Association 

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Looking for some lesson plan resources, parent resources, professional development, or digital access to native texts? Check out the National Indian Education Association's resource bank!

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Digital Resources for Parents and Teachers - National Indian Education Association

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Who We Are Programs Resources Events Get Involved Other Ways to Give Come Work for Us Teach.NIEA.org Job Board Other Positions in Native Education Log Into Your Member Record Contact Your Senator Contact Your Representative Annual Events 2024 Hill Week 2023 NIEA Convention & Trade Show NIEA Golf Tournament 2022

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Indigenous Mathematics and the Power of Stories: Conversation with Kori Czuy

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Indigenous Mathematics and the Power of Stories: Conversation with Kori Czuy

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Kori shares how Indigenous Stories showcase mathematical concepts and demonstrate the mathematics fluency of Indigenous Knowledge Keepers. This video is 50 minutes long. Kori has a PH.D in Indigenous Mathematics and Story Mathematics.

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Indigenous Mathematics and the Power of Stories: Conversation with Kori Czuy

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Culturally Relevant Pedagogy In Mathematics: A Critical Need | Shelly Jones | TedxCCSU

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Culturally Relevant Pedagogy In Mathematics: A Critical Need | Shelly Jones | TedxCCSU

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This short, 15-minute video introduces teachers to the applications of culturally relevant pedagogy applications in mathematics and through this, empower students to learn and become mathematically fluent.

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CULTURALLY RELEVANT PEDAGOGY IN MATHEMATICS: A CRITICAL NEED | Shelly Jones | TEDxCCSU

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IRIS Center - Self Guided Course - Evidence Based Math Instruction 

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IRIS Center - Self Guided Course - Evidence Based Math Instruction 

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Looking to learn a little more about Evidence-Based Math Instruction Strategies? This quick, free, and self-guided course from the IRIS center can help get you started. It even comes with a quick assessment at the end to help you ensure you understand the key takeaways. Not sure what the IRIS Center is? It is a highly respected professional learning organization out of Vanderbilt University that is funded by the Department of Education.

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Page 1: The Importance of High-Quality Mathematics Instruction

One of the core academic subjects in the United States and throughout the world, mathematics is key to many of our most common daily activities and routines, things like shopping, banking, cooking, and home repair. Further, in today's increasingly technologically reliant society, more and more jobs require some level of proficiency in mathematics and science. Students who lack sufficient mathematical knowledge and skills are more likely to experience negative outcomes as adults, including fewer opportunities for meaningful employment and a reduced likelihood of economic independence. Because of these factors, it is critical that students begin to develop essential math concepts and skills at an early age. Unfortunately, studies conducted since the 1970s have shown that students in the United States do not perform as well on mathematics assessments as do their peers in other countries.

Research Shows

Studies, such as those below, have raised concerns about the adequacy of mathematics instruction in the United States.

This bar graph illustrates the results of the 2017 National Assessment of Educational Progress (NAEP) mathematics achievement test for 4th and 8th grades and the 2015 data for 12th grade. The table is divided into three columns-one for 4th-grade results, one for 8th-grade results, and the last for 12th-grade results-and each column is divided into two rows. The top row is labeled "Students Proficient & Advanced," while the lower is labeled "Students Basic & Below Basic."

The test results are displayed for three categories of test takers: "All Students," "Students with Disabilities," and "ELLs." The "All Students" bars are colored aqua. The "Students with Disabilities" bars are peach. Finally, the "ELLs" bars are yellow.

In the 4th-grade column, "All Students" are 40% in the Proficient & Advanced range and 60% in the Basic & Below Basic range. "Students with Disabilities" are 17% in Proficient & Advanced and 83% in Basic & Below. Likewise, "ELLs" are 15% in Proficient & Advanced and 85% in Basic & Below.

In the 8th-grade column, "All Students" are 34% in the Proficient & Advanced range and 66% in the Basic & Below Basic range. "Students with Disabilities" are 9% in Proficient & Advanced and 91% in Basic & Below. Finally, "ELLs" are 6% in Proficient & Advanced and 94% in Basic & Below.

In the 12th-grade column, "All Students" are 25% in the Proficient & Advanced range and 75% in the Basic & Below Basic range. "Students with Disabilities" are 3% in Proficient & Advanced and 97% in Basic & Below. Finally, "ELLs" are 6% in Proficient & Advanced and 94% in Basic & Below.

What Do These Data Indicate?

The NAEP test is designed so that students who have learned the knowledge and skills deemed important for their grade level should score at the "Proficient" level at a minimum. However, the NAEP data show that a majority of students perform at the "Below Basic" and "Basic" levels, indicating little to partial mastery. And, of course, this lack of mastery will likely create new hurdles in subsequent grade levels, where a foundational understanding of mathematical concepts and procedures is required for success. Students who do not master foundational mathematics skills in early grades are likely to fall further behind as they progress through school.

With all of this in mind, take another look at the data in the table above. Note that many 4th-grade students (60%) have yet to master the expected mathematics knowledge and skills, a percentage that is even greater (75%) for students in the 12th grade. And the results are even worse for students with disabilities as well as for English language learners (ELLs).

The purpose of this module is to explore why some students struggle with mathematics and what steps teachers can take to give their students a significantly improved chance to succeed in the classroom.

Consider This

In recent years, a greater emphasis on college- and career-readiness has led to higher standards for student mathematics proficiency, as well as to more rigorous graduation requirements. Whereas in the past high school students in most states were required to complete Algebra 1 prior to graduation, those students are now often required to complete Algebra 1, Geometry, and Algebra II. Once more, reflect on the NAEP data presented above and consider the number of students who will struggle to meet these new requirements.

Why Do Some Students Struggle More with Math?

Students with Learning Disabilities

Compared to the overall population, a much smaller percentage of students with disabilities demonstrate proficiency in mathematics. Although every learner is unique, students with a mathematics learning disability (MLD) tend to display any of a number of characteristics that affect their mathematics performance, including:
mathematics learning disability (MLD)
Condition characterized by significant difficulty in mathematics calculation and/or problem solving; a specific learning disability (SLD) in the area of mathematics, sometimes referred to as dyscalculia.

Difficulty processing information

Difficulty identifying relevant information in mathematics problems, especially in word problems

Difficulty translating information into a mathematical expression or equation

Problem maintaining attention

Difficulty selecting an effective problem-solving strategy

Poor reasoning and problem-solving skills

Working through a problem without making sure all steps are completed or that the answer makes sense

Deficits in the areas of mathematics facts and computational skills

Memory and vocabulary difficulties

Difficulty solving multi-step problems

Weak visual/spatial representational skills

Difficulty reading about mathematics

Difficulty understanding the language, or vocabulary, of mathematics

Difficulty understanding mathematics concepts and how concepts relate to procedures

Mathematics anxiety

Learned helplessness-that is, having low motivation, being a passive learner, and attributing both successes and failures to external, uncontrollable factors (e.g., luck)

Diane Bryant, who conducts research on mathematics interventions for students with LD, describes why students with mathematics learning disabilities and those who struggle with mathematics are often grouped together in research in this area (time: 1:01).

Diane Pedrotty Bryant, PhD
Project Director, Mathematics Institute for
Learning Disabilities and Difficulties
University of Texas at Austin

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View Transcript
Transcript: Diane Pedrotty Bryant, PhD

Students who struggle with mathematics and those who have been identified as having mathematics learning disabilities share similar characteristics. For example, both groups of students may have difficulty with what's called number sense, just understanding numbers and the meaning of numbers and certainly calculation. Problem solving is another area. So I think this is one reason that these two groups are often included in studies. Another reason has to do with ensuring that you have a large enough sample size so that you can look at the treatment effects of practices that may become evidence-based practices. Therefore, it's not uncommon to see both students with mathematics difficulties and students with identified mathematics learning disabilities included in the sample.

English Language Learners

ELLs, too, have difficulty with mathematics, though their struggles are more likely to be a result of linguistic issues. It is important for teachers to understand that mathematics consists of more than just numbers; it includes a significant amount of content-specific vocabulary. When teachers discuss mathematical procedures and concepts, they typically use academic language, which is composed of content-specific vocabulary-for example, words like factor, estimate, and sum-vocabulary with multiple meanings-for example, table -and complex language structures. Not surprisingly, then, many ELLs struggle to solve mathematical word problems.
academic language
The language used in academic settings to communicate information orally and in writing about discipline-specific content.

What Can Teachers Do?

To improve student mathematics performance, more and more school and districts have implemented high-quality mathematics instruction. This instruction involves the implementation of both:

A standards-based curriculum - The concepts and skills believed to be important for students to learn

Evidence-based practices (EBP) - Strategies or practices proven through research to be effective for teaching mathematical concepts and procedures

Research Shows

When they provide effective mathematics instruction, teachers can reduce the performance gap between students who are at risk for mathematics difficulty and their average and high-performing peers.
(Clarke, Smollkowski, Baker, Fien, Doabler, & Chard, 2011)

Students with learning disabilities who receive effective mathematics intervention can develop critical skills like problem-solving and abstract reasoning, which are necessary to achieve mathematics proficiency.
(Gersten, Chard, Jayanthi, Baker, Morphy, & Flojo, 2008; Allsopp, Lovin, & van Ingen, 2017)

Activity

Among the factors that sometimes influence effective high-quality mathematics instruction are teacher and student perceptions and beliefs about mathematics itself.

Click here to discover your own attitudes and beliefs about mathematics and to reflect on how they might influence your instruction.
Perceptions and Beliefs Regarding Math
Are the statements about mathematics ability in the boxes below True or False? Read each and click "True" or "False" to find out the answer.
(Close this panel)

If you are completing this activity in class, with a small group, or with a partner, discuss how your attitudes and beliefs about mathematics might influence or have already influenced your instructional practices. Next, brainstorm ideas for improving your mathematics instruction.

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IRIS | Page 1: The Importance of High-Quality Mathematics Instruction

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One of the core academic subjects in the United States and throughout the world, mathematics is key to many of our most common daily activities and routines, things like shopping, banking, cooking, and home repair. Further, in today's increasingly technologically reliant society, more and more jobs require some level of proficiency in mathematics and science.

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Dan Meyer's website contains many 3-Act Math tasks that are free for educator use and aligned to Common Core State Standards. These activities will engage problem-solving and modeling practices in instruction.

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3 Act Math Tasks By Kyle Pearce, Dan Meyer and Others

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3 Act Math Tasks by Kyle Pearce, Dan Meyer and many others to spark curiosity and fuel sense making.

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DREME has prepared a number of great family resources for educators to share with the families in their school community. These resources will foster family engagement and partnership in student learning.

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Free, Research-Based Materials for Supporting Family Math.

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Advances in Early Math Education Webinar

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Advances in Early Math Education Webinar

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This free professional learning webinar is from the Development and Research in Early Mathematics Education (DREME) Network based out of Stanford. This webinar will help all teachers better understand the important considerations in early math education.

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Advances in Early Math Education: Critical Issues in Policy and Practice - DREME

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The Development and Research in Early Mathematics Education (DREME) Network, in collaboration with the Stanford Center on Early Childhood, hosted a conference on May 3, 2024, celebrating the progress made in the last decade in research and practice around early math teaching and learning.

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Teacher Learning Hub: Indian Ed. & Math Integration Course 

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Teacher Learning Hub: Indian Ed. & Math Integration Course 

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Need some professional development units or just want to learn more about integrating IEFA and Math? This 2-unit Hub Course will provide you with resources to learn more and give you an opportunity to try your hand at making a lesson, with helpful feedback at the end.

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Summary of Indian Ed & Math Seamless Integration | Learning Hub

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Ms. Tailfeathers from Browning Public Schools shares this great integration of IEFA and math in her classroom, using data from Tribal Elections! This lesson could be adapted to address standards related to data or percentages, and meet a variety of learning standards, however this lesson is specifically designed around middle school standards.

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Adriane Tailfeathers and Math (IEFA Across the Content Webinar Series 2023-24)

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The talented OPI IEFA team has curated many lesson plans that integrate mathematics through the cultural practices and histories of Montana's Indigenous Peoples. Take a look today!

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Looking for some problem-based learning activities for your students? This resource has numerous examples of learning activities, complete with lesson plans and customization abilities. These would serve great as an intervention strategy for students at any level of their learning, whether they are advanced and ready to move on, or need more time to grasp the concept. Tailor the questions to the students' needs and abilities, or design heterogeneous groups to puzzle out the riddle.

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Everything you ever wanted to know about early numeracy but didn't know to ask. 

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Everything you ever wanted to know about early numeracy but didn't know to ask. 

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This 10-minute read will provide readers with a research-supported overview of early numeracy - what it means and how it can support learning and love of math. Complete with resources for teachers, this is a good introduction and professional learning article.

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Everything you ever wanted to know about early numeracy but didn’t know to ask - Teach. Learn. Grow.

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The science of reading is a hot topic. Early numeracy is equally important and can even be a predictor of later reading proficiency.

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This free online program is FULL of visualization tools, enrichment activities, and lessons. Use the virtual manipulatives to support your instruction, let your students engage with a treasure hunt, explore the applications of mathematics, or use any of the fully developed and interactive lesson plans.

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Discover Mathigon, the Mathematical Playground. Learning mathematics has never been so interactive and fun!

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Town Pump Foundation - Education Grants 

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Town Pump Foundation - Education Grants 

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Town Pump has expended over $2.2 Million to Montana schools since 2002! Check it out and see how your great idea to improve mathematics instruction for your students could qualify for this outstanding grant opportunity.

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Town Pump Foundation | Montana Education Grants

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The National Council of Teachers of Mathematics offers many grant opportunities to fund math classrooms, some of which range up to $10,000! Deadlines are November 1 and May 1 depending on the grant.

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Grants - National Council of Teachers of Mathematics

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The University of Montana offers many K-12 learning experiences at limited, or often, no cost to teachers and schools. Schedule a visit from a mathematician, let your students experience drone aviation sciences, check out the fossils in the paleontology exhibit, or visit the planetarium!

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University of Montana K-12 Group Visits and Classroom Experiences

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Medical Detectives is a half-day program developed by the Office of Health Research & Partnership for high school students to learn about the cross-section between genetics, medicine, and biomedical research. High school students and their teachers would visit the UM campus to conduct biotechnology procedures to diagnosis a medical disorder for a family, learn about opioid addiction, or try to detect antibiotic resistance in the environment.

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Discovery Education, which the OPI provides to all K-12 Montana teachers at no cost during the 2024-2025 school year, offers a number of virtual field trips related to mathematics. Let your students learn about numbers through examining polar bear population trends, or, see data at work through a career in the NBA!

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Join us for our Virtual Field Trips or watch them on-demand after their premieres. Each no-cost Virtual Field Trip comes with a companion guide packed with standards-aligned, hands-on learning activities! Select one of the options below to register.

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Take students beyond the classroom and into some of the world's most iconic locations with virtual field trips. Learn more!

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This STEM and Manufacturing experience list from Boeing and Discovery Education allow students to see math in action through aerospace technological development!

This resource is free.

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Boeing FUTURE U. inspires the next generation of innovators, equipping them for tomorrow's careers. Launch your mission today. www.boeingfutureu.com #boeingfutureu

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This museum offers outstanding virtual field trips for students at a fee, but Title One schools can apply for sponsored trips at no cost to the school! These enriching experiences are sure to captivate your students and challenge their minds through fun mathematical applications.

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At the Museum, online, or in your school - you choose!

MoMath is pleased to present its group offerings. MoMath field trips can accommodate over 500 students daily, with educator sessions spread throughout the course of the day.

Please note that these prices represent a discount available only to class groups from US schools, pre-K through 12th grade, Monday through Friday from September through June. For all other groups, please email groupsales@momath.org.

If you are a Title One school and are interested in applying for a sponsored field trip (online or in person) for your students in the 2021-2022 school year, please visit titleone.momath.org. Title One sponsored trips are held at various times during the school year; acceptance is not guaranteed.

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In-Person Field Trip Packages

MoMath Morning

$625 per group of up to 25 students, $25 per extra student up to 35 students

Arrival any time before 1:00 pm

Private educator-led, hands-on session in classroom

Up to 90 minutes free exploration on exhibit floor

$575 per group of up to 25 students, $23 per extra student up to 35 students

Arrival any time between 1:00 pm and 3:00 pm

Private educator-led, hands-on session in classroom

Up to 90 minutes free exploration on exhibit floor

Afternoon Exploration

$525 per group of up to 25 students, $21 per extra student up to 35 students

Arrival any time after 3:00 pm

Private educator-led, hands-on session in classroom

Up to 90 minutes free exploration on exhibit floor

Double Discovery

$700 per group of up to 25 students, $28 per extra student up to 35 students

Arrival any time after 10:00 am

Two private educator-led, hands-on sessions in classrooms

Up to three hours free exploration on exhibit floor

Optional 30-minute reservation of classroom space for lunch ($150 additional facility fee)

Exhibit Exploration (no educator session)

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Online Field Trip Packages

For the packages below that include an educator session, pricing is based on a flat rate for groups of up to 32 students with an additional fee if there are more than 32 students, up to a total of 96 students.

Package A: Up to 32 students

$395 for up to 32 students

Private online educator-led, hands-on session

Package B: Up to 64 students

$775 for up to 64 students

Private online educator-led, hands-on session

Package C: Up to 96 students

$1,150 for up to 96 students

Private online educator-led, hands-on session

Please note that these prices represent a discount available only to class groups from US schools, pre-K through 12th grade, Monday through Friday from September through June. For all other groups, please email groupsales@momath.org.

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To book a summer group trip, please visit summergroups.momath.org.

Questions? Email schoolgroups@momath.org.

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Field Trips - National Museum of Mathematics

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MoMath is pleased to present its group offerings. MoMath field trips can accommodate over 500 students daily, with educator sessions spread throughout the course of the day. Please note that these prices represent a discount available only to class groups from US schools, pre-K through 12th grade, Monday through Friday from September through June.

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The Montana Council of Teachers of Mathematics offers a rolling grant opportunity is a great way for teachers to fund their instructional needs! Possible examples where you could apply this $500 include (but aren't limited to) - calculator purchase, student project materials, a classroom set of the game "set", or a virtual field trip from the Mo-Math Museum! Bring your ideas to this very short (5-10 minute) application form. You do not need to be a member of MCTM to apply, though it is highly encouraged you consider joining this outstanding community of math educators!

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Join your Science and Math content specialists as they address the issues you want to hear about - straight from the educators currently working in Montana classrooms and with Montana teachers. Topics requested by the field that we plan to cover include educator self-care, differentiation in the classroom, teacher retention, working with special student populations, and more! Learn how to leverage these episodes as professional development opportunities through our collaborative or independent listener guides.

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The Montana Office of Public Instruction is pleased to offer a new approach to professional learning. The Mission of the Last Best Learning Podcast is to del…

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Mathematics activities through a global perspective. 

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This outstanding website offers math activities with global integrations - offering traditional and modern applications of mathematics and allowing students to connect mathematical concepts to cultures across the world! Each activity includes cultural relevance, modern considerations, and related math questions and activities. Two IEFA applications to Montana are featured as well - through Bitterroot harvesting and Stick Game - two significant practices to the Sqelix w (Salish), Ktunaxa (Kootenai), and Qlispe (Pend d’Oreille) who call the Flathead Reservation home, as well as many other Native Nations in Montana.

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Building Thinking Classrooms - Peter Liljedahl 

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Building Thinking Classrooms - Peter Liljedahl 

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This hour-long video delivers Peter's view of building thinking classrooms, the conception of his project, and the strategies you can use to build thinking classrooms in your school.

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Peter Liljedahl: Building Thinking Classrooms

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Students' Awareness of Their Cognitive Processes Facilitates the Learning of Math, finds study. 

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Students' Awareness of Their Cognitive Processes Facilitates the Learning of Math, finds study. 

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This 5-minute read from phys.org discusses the importance of self-assessment in students' learning.

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Credit: Unsplash/CC0 Public Domain

The purpose of education is to ensure that students acquire the skills necessary for succeeding in a world that is constantly changing. Self-assessment, or teaching students how to examine and evaluate their own learning and cognitive processes, has proven to be an effective method, and this competence is partly based on metacognitive knowledge.

A new study conducted at the University of Eastern Finland shows that metacognitive knowledge, i.e., awareness of one's cognitive processes, is also a key factor in the learning of mathematics. The work is published in the journal Cogent Education.

The study explored thinking skills and possible grade-level differences in children attending comprehensive school in Finland. The researchers investigated 6th, 7th and 9th graders' metacognitive knowledge in the context of mathematics.

"The study showed that ninth graders excelled at explaining their use of learning strategies, while 7th graders demonstrated proficiency in understanding when and why certain strategies should be used. No other differences between grade levels were observed, which highlights the need for continuous support throughout the learning path," says Susanna Toikka of the University of Eastern Finland, the first author of the article.

The findings emphasize the need to incorporate elements that support metacognitive knowledge into mathematics learning materials, as well as into teachers' pedagogical practices.

Self-assessment and understanding of one's own learning help to face new challenges

Metacognitive knowledge helps students not only to learn mathematics, but also more broadly in self-assessment and lifelong learning. Students who can assess their own learning and understanding are better equipped to face new challenges and adapt to changing environments. Such skills are crucial for lifelong learning, as they enable continuous development and learning throughout life.

"Metacognitive knowledge is a key factor in learning mathematics and problem-solving, but its significance also extends to self-assessment and lifelong learning," says Toikka.

In schools, metacognitive knowledge can be effectively developed as part of education. Based on earlier studies, Toikka and colleagues have developed a combination of frameworks for metacognitive knowledge, which helps to identify students' needs for development regarding metacognitive knowledge by offering an alternative perspective to that of traditional developmental psychology.

"This also supports teachers in promoting students' metacognitive knowledge. Teachers can use the combination of frameworks to design and implement targeted interventions that support students' skills in lifelong learning."

According to Toikka, the combination of frameworks enhances understanding of metacognitive knowledge and helps to identify areas where individual support is needed: "This type of understanding is crucial for the development of metacognitive knowledge among diverse learners."

More information: Susanna Toikka et al, Combined conceptualisations of metacognitive knowledge to understand students' mathematical problem-solving, Cogent Education (2024). DOI: 10.1080/2331186X.2024.2357901

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Students' awareness of their cognitive processes facilitates the learning of math, finds study

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The purpose of education is to ensure that students acquire the skills necessary for succeeding in a world that is constantly changing. Self-assessment, or teaching students how to examine and evaluate their own learning and cognitive processes, has proven to be an effective method, and this competence is partly based on metacognitive knowledge.

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This AMAZING (and free) story series includes translated videos in English, Blackfeet and Cree, as well as many Canadian First Nations' languages. The stories discuss mathematical concepts, and have themes such as community, family, generosity, and more!

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Small Number Counts to 100

Written by Veselin Jungic & Mark MacLean
Illustrated by Simon Roy

The first story, Small Number Counts to 100 was inspired by narration from Ms. Rina Sinclair of the Siksika Nation. The story can be shown to elementary school students as a counting practice/puzzle or as a pattern recognition problem. For high school students it can be a way to introduce arithmetic progressions, modular addition, or an idea of number systems with a base different than 10.

Group shot of Small Number and grandparents
Small Number is a 5 year-old boy who gets into a lot of mischief. He lives with his Grandma and Grandpa, who patiently put up with his antics, in a small settlement with 7 tipis arranged in a circle.

Wanting to take the cat home to show Grandma, he tries to catch it and learns that the black cat is really a skunk.

Small Number receiving a bath
Grandma doesn't want Small Number spending time in their tipi until he smells better, so she decides to set him a task she thinks will take him a long time. She knows Small Number can count to 100.

Small Number counting fingers
...and then runs in to see his Grandma and yells: "It is Auntie Rena's tipi!" which is one tipi south of his grandparents'.

Question: How did Small Number know that the 100 th tipi is the one just south of his grandparents' tipi without actually counting them?

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Written by Veselin Jungic & Mark MacLean Illustrated by Simon Roy The first story, Small Number Counts to 100 was inspired by narration from Ms. Rina Sinclair of the Siksika Nation. The story can be shown to elementary school students as a counting practice/puzzle or as a pattern recognition problem.

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This link offers a preview of the book Shota and the Star Quilt. This would make an excellent addition to your reading time, and introduce concepts such as geometry, and patterns to students.

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3-5 Lesson: Native American Star Quilts 

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3-5 Lesson: Native American Star Quilts 

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This neat Code.org lesson engages coding and the recognition of mathematical and geometric patterns as they relate to star quilts. Although it is designed for 3rd-5th graders, this lesson could be adaptable for younger ages and some resources for younger students are included.

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Native American Star Quilts - Lesson 1 - Code.org

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Anyone can learn computer science. Make games, apps and art with code.

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I bet you knew that Desmos offered a free online calculator, but did you know that Desmos Classroom has discovery-based lessons and activities? This free program allows teachers to use one of the plug-in-play activities, or modify or design their own. Teachers can monitor student learning, make student answers anonymous, and deliver immediate feedback to students for support. Check it out!

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A complete list of NCTM resources for math classrooms (K-12). Some of these resources require an NCTM membership, however, there are free items available for classroom use!

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Classroom Resources - National Council of Teachers of Mathematics

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Struggling to help your students achieve their greatest level of success? This article, from the Region 7 Education Service Center, a national non-profit that supports schools and government agencies, provides insight into how you can leverage acceleration and remediation to lift your students' achievement bar higher. This will take about 10 minutes to read.

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Acceleration vs. Remediation: What Works for My Students

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What is the difference between acceleration and remediation and how do I know which is best for my students?

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Kristen Moore talks about the real issues teachers of mathematics run into in her "Pool-Side PD" in short (less than 20 minutes) episodes. Consider listening to her podcast, you'll learn about building capacity for yourself, finding a balance between instructional tools, assessment, and project ideas!

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Kristen Moore, Project Based Learning Coach

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Ep 57: Fitting It All In: Balancing Effective Teaching Practices

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Kristen Moore, classroom teacher and instructional coach at Moore Than Just X, empowers middle and high school math teachers to transform the student experience with the strategies and the confidence to implement project-based learning, mastery-based assessment, and more student-centered practices to boost engagement in their classrooms. Teaching math has never been this fun!Whether you’re a math teacher newbie or a seasoned veteran, you’ll find something new and inspiring in every episode that’s sure to start changing the way you’re teaching math. You’re already a listener, why not join the Movement inside ✨The Modern Math Teachers Movement Facebook group? Join the community of middle and high school math teachers who are not afraid to shake things up and make math class the best part of the day for our students. So tune in each Tuesday, have some fun, and let’s elevate our math teaching game together!

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This article, published by Edutopia, discusses the ways that teachers can promote resiliency in math learners - a necessary skill as students age and interact with the world, not just for its applications to difficult math problems, but for its applications to life! This quick, 6-minute read includes links to resources and further reading if you find yourself wanting to learn more!

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Support provided by early childhood educators can put students on a path that will lead to success in math for years to come.

Working in schools during the global Covid-19 pandemic has highlighted the need for students to be resilient in many aspects of their lives. As students and teachers work to rebuild relationships, we can plan ways to best support students' resilience and continued learning as well as to inspire students to engage with and enjoy math. This is especially true for young learners in preschool and elementary school. If students learn to be resilient when it comes to math at an early age, it will serve them well throughout their academic careers.

What is mathematical resilience?

Resilient learners have a growth mindset with respect to learning. They are comfortable with challenge and the idea of mathematical struggle. Resilient learners recognize when they are stuck and have the language to ask for support when they need it. Most important, they hold a belief that they can "do math."

Why do students need to be mathematically resilient?

Many students believe that they are not good at math. These learners need to overcome any negative attitudes they might hold about math class, which may be attributed to a number of factors. For example, many students hold a belief that math should come easily, and when they don't know an answer right away, they come to the conclusion that they are not good at math, leaving them unmotivated to keep trying.

The Teacher's Role in Building Resilience

Building resilience takes time but is achievable in a classroom environment that not only fosters a positive culture of learning and collaboration but also values mathematical struggle-an environment where students' learning needs are understood using formative assessments and observations and where teachers spend quality time with individual students and encourage discussion between students. Problems may need to be worked through to develop persistence and risk-taking.

Regular math chats, along with noticing and talking about the math around us in everyday experiences, help students develop a positive attitude toward math from a young age. Teachers can explicitly teach technical language and how to show understanding using multiple representations such as objects, drawings, and symbols.

It's important to make math visual. For example, teachers can use a hundreds chart to support learning about the relationships between different numbers. Some students may need extra work developing their number sense using manipulatives and organizational tools such as ten frames for counting collections.

Tasks That Help Build Resilience

Mathematics is not just a set of skills to be learned. Supporting students to become numerate involves developing both mathematical skills and knowledge. Focusing on the big ideas ensures that lessons not only involve developing fluency in the required mathematics skills but also help develop understanding and knowledge in a variety of contexts. For example, in Australia the areas of focus in primary school include trusting the count, place value, and multiplicative thinking.

Novel, real-world, culturally relevant problems help spark student interest and facilitate deep learning. Tasks should allow for struggle so that students understand that they don't have to get the answer quickly. Regular, short "number talks" help all students to become involved and strengthen fluency, intuition, and mental math strategies. Focus is on process and communication rather than speed. Over time and with practice, students' ability to explain and critique situations improves.

There are many websites that offer excellent, free ideas for math tasks. It's well worth spending time finding suitable problems. For example, NRICH Maths has challenging tasks and problems that help develop thinking skills, and Math for Love has great ideas for number talks. The reSolve website features well-researched lessons that foster inquiry.

Supporting Resilience Among Students

Students who are given the opportunity to be involved in regular problem-based tasks and are allowed time for exploration and finding solutions in collaboration with their peers can observe how others persevere. By sharing mental solution strategies aloud, students are exposed to how math concepts can be used and applied.

The way in which information is internalized depends on whether it's within a learner's zone of proximal development (ZPD). ZPD-that range of knowledge that the textbook Elementary and Middle School Mathematics: Teaching Developmentally says might be "out of reach for a person to learn on his or her own, but is accessible if the learner has support from peers or more knowledgeable others"-is important to consider when working to help students develop resilience.

Students may initially feel challenged and uncomfortable as they move into their ZPD and may need support with finding strategies to help them when they feel stuck. All students need opportunities to experience struggle in mathematics. When exposing students to new content, teachers can initially provide scaffolding tools such as manipulatives to help students access a task.

What have you tried?

What do you know?

What are you trying to find out?

The teacher's role is not to step in and show or explain, but to encourage individual approaches to a problem where diversity and risk-taking are honored. It's important to ask questions that help students to make connections between concepts and include clarifying prompts:

The teacher can create variations on each task or problem ("what-ifs") to guide dialogue to a shift in focus and provide more depth of understanding ("That didn't work; what else could you try?").

In order to be successful in math, all students need to value mathematical thinking and discovery and to see themselves as active math learners. Our job is to help foster attributes of resilience and a love of the subject.

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Building Resilience in Young Math Students

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Support provided by early childhood educators can put students on a path that will lead to success in math for years to come.

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Side Step The Scope & Sequence? Problem Based Teaching & Your Curriculum Resources

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Side Step The Scope & Sequence? Problem Based Teaching & Your Curriculum Resources

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This great episode covers balancing curriculum-mandated curriculum with problem-based teaching, and self-reflecting on teacher's own level of contextual knowledge. More importantly, the episode covers how to maximize the materials you have. This episode is only 17-minutes!

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Ep291: Side Step The Scope & Sequence? Problem Based Teaching & Your Curriculum Resources

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Use this facilitator guidebook to strengthen your use of the Humanizing Math video and leverage it into a professional learning experience for yourself - or for your colleagues. All resources referenced within the video are present in the guidebook, with new ones added as they are created!

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This video (30-minutes), accompanied with the facilitator guidebook, can act as a professional learning opportunity. Learn with us as we explore what "humanizing mathematics", low-capacity ways to engage your students, and classroom ready resources for you to use in your instruction!

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Humanizing Math: Grounding Mathematics in the Stories of the Individuals Who Saw its Beauty

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This great journal piece shares some insight into the Cree Tipi, the cultural and communal relevance of the ceremony of its creation, and the mathematical applications of these practices. This resource will help you better understand how the mathematical knowledge of the Cree people manifests organically in the context of building this dwelling, and, serves as a great resource for your lesson planning and application of IEFA in classrooms. It may take about 30 minutes to read, but if you're like me, you'll be too enthralled in what you're learning to notice the time.

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Making Math Moments Matter - How to Build Teaching Confidence. 

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Making Math Moments Matter - How to Build Teaching Confidence. 

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Hosts Jon Orr and Kyle Pearce interview Lori Martin about her experience in building teacher confidence in mathematics teaching. Within this 1-hour episode, you'll find a heavy emphasis on vertical alignment and standardization of language, instructional strategies that build teacher capacity and confidence, and barriers that teachers can meet and tactfully overcome.

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Ep289: How To Build Teaching Confidence: An Interview with Lori Martin

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Brief Study - Integrating History of Math into the Classroom. 

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Brief Study - Integrating History of Math into the Classroom. 

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Have you ever wondered about where it all came from? Who invented 'x' and gave generations of students a headache, anyway? This research paper, published in the Journal of Curriculum and Teaching, can be read in approximately 25 minutes and demonstrates findings related to teacher and student confidence in mathematics through the integration of History of Math in the classroom.

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Discovery Education has been paid for by OPI, making it free for all K-12 teachers in Montana this year. This resource contains learning resources that can excite and support students in learning. They're often interactive in nature and even contain virtual fieldtrips for your classrooms. The interactive tools can help students visualize mathematical behaviors and concepts in action.

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Strengthening Tasks Through Student Talk 

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Strengthening Tasks Through Student Talk 

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Dr. Candela and Dr. Boston discuss math education through the lens of student talk. They highlight the benefit of 'linking' and 'press' in conversation and building accountability to listen to student peers. They delve deeply into listening and understanding while building mathematical reasoning and communication. This episode is 17 minutes long.

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Strengthening Tasks Through Student Talk - Guest: Drs. Amber Candela and Melissa Boston

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Rounding Up Season 2 | Episode 16 – Strengthening Tasks Through Student Talk Guests: Dr. Amber Candela and Dr. Melissa Boston Mike Wallus: One of the goals I had in mind when we first began recording Rounding Up was to bring to life the best practices that we aspire to in math education and to offer entry points so that educators would feel comfortable trying them out in their classrooms. Today, we’re talking with Drs. Amber Candela and Melissa Boston about powerful but practical strategies for supporting student talk in the elementary math classroom. Welcome to the podcast, Amber and Melissa. We’re really excited to be talking with you today. Amber Candela: Thank you for having us. Melissa Boston: Yes, thank you. Mike: So we’ve done previous episodes on the importance of offering kids rich tasks, but one of the things that you two would likely argue is that rich tasks are necessary, but they’re not necessarily sufficient, and that talk is actually what makes the learning experience really blossom. Is that a fair representation of where you all are at? Melissa: Yes. I think that sums it up very well. In our work, which we’ve built on great ideas from Smith and Stein, about tasks, and the importance of cognitively challenging tasks and work on the importance of talk in the classroom. Historically, it was often referred to as “talk moves.” We’ve taken up the term “discourse actions” to think about how do the actions a teacher takes around asking questions and positioning students in the classroom—and particularly these talk moves or discourse actions that we’ve named “linking” and “press”—how those support student learning while students are engaging with a challenging task. Mike: So I wonder if we could take each of the practices separately and talk through them and then talk a little bit about how they work in tandem. And Melissa, I’m wondering if you could start unpacking this whole practice of linking. How would you describe linking and the purpose it plays for someone who, the term is new for them? Melissa: I think as mathematics teachers, when we hear linking, we immediately think about the mathematics and linking representations or linking strategies. But we’re using it very specifically here as a discourse action to refer to how a teacher links student talk in the classroom and the explicit moves a teacher makes to link students’ ideas. Sometimes a linking move is signaled by the teacher using a student’s name, so referring to a strategy or an idea that a student might’ve offered. Sometimes linking might happen if a teacher revoices a student’s idea and puts it back out there for the class to consider. The idea is in the way that we’re using linking, that it’s links within the learning community, so links between people in the classroom and the ideas offered by those people, of course. But the important thing here that we’re looking for is how the links between people are established in the verbal, the explicit talk moves or discourse actions that the teacher’s making. Mike: What might that sound like? Melissa: So that might sound like, “Oh, I noticed that Amber used a table. Amber, tell us how you used a table.” And then after Amber would explain her table, I might say, “Mike, can you tell me what this line of Amber’s table means?” or “How is her table different from the table you created?” Mike: You’re making me think about those two aspects, Melissa, this idea that there’s mathematical value for the class, but there’s also this connectivity that happens when you’re doing linking. And I wonder how you think about the value that that has in a classroom. Melissa: We definitely have talked about that in our work as well. I’m thinking about how a teacher can elevate a student’s status in mathematics by using their name or using their idea, just marking or identifying something that the student said is mathematically important that’s worthy of the class considering further. Creating these opportunities for student-to-student talk by asking students to compare their strategies or if they have something to add on to what another student said. Sometimes just asking them to repeat what another student said so that there’s a different accountability for listening to your peers. If you can count on the teacher to revoice everything, you could tune out what your peers are saying, but if you might be asked to restate what one of your classmates had just said, now there’s a bit more of an investment in really listening and understanding and making sense. Mike: Yeah, I really appreciate this idea that there’s a way in which that conversation can elevate a student’s ideas, but also to raise a student’s status by naming their idea and positioning it as important. Melissa: I have a good example from a high school classroom where a student [...] was able to solve the contextual problem about systems of equations, so two equations, and it was important for the story when the two equations or the two lines intersected. And so one student was able to do that very symbolically. They created a graph, they solved the system of equations where another student said, “Oh, I see what you did. You found the difference in the cost per minute, and you also found the difference in the starting point, and then one had to catch up to the other.” And so the way that the teacher kind of positioned those two strategies, one had used a sensemaking approach based really in the context. The other had used their knowledge of algebra. And by positioning them together, it was actually the student who had used the algebra had higher academic status, but the student who had reasoned through it had made this breakthrough that was really the aha moment for the class. Mike: That is super cool. Amber, can we shift to press and ask you to talk a little bit about what press looks like? Amber: Absolutely. So how Melissa was talking about linking is holding students accountable to the community; press is more around holding students accountable to the mathematics. And so the questions the teacher is going to ask is going to be more related specifically to the mathematics. So, “Can you explain your reasoning?” “How did you get that answer?” “What does this x mean?” “What does that intersection point mean?” And so the questions are more targeted at keeping the math conversation in the public space longer. Mike: I thought it was really helpful to just hear the example that Melissa shared. I’m wondering if there’s an example that comes to mind that might shed some light on this. Amber: So when I’m in elementary classrooms and teachers are asking their kids about different problems, and kids will be like, “I got 2.” OK, “How did you get 2?” “What operation did you use?” “Why did you use addition when you could have used something else?” So it’s really pressing at the, “Yes, you got the answer, but how did you get the answer?” “How does it make sense to you?”, so that you’re making the kids rather than the teacher justify the mathematics that’s involved. And they’re the ones validating their answers and saying, “Yes, this is why I did this because…” Mike: I think there was a point when I was listening to the two of you speak about this where, and forgive me if I paraphrase this a little bit, but you had an example where a teacher was interacting with a student and the student said something to the effect of, “I get it” or “I understand.” And the teacher came back and she said, “And what do you understand?” And it was really interesting because it threw the justification back to the student. Amber: Right. Really what the linking and press does, it keeps the math actionable longer to all of the peers in the room. So it’s having this discussion out loud publicly. So if you didn’t get the problem fully all the way, you can hear your peers through the press moves, talk about the mathematics, and then you can use the linking moves to think through, “Well, maybe if Mike didn’t understand, if he revoices Melissa’s comment, he has the opportunity to practice this mathematics speaking it.” And then you might be able to take that and be like, “Oh, wait, I think I know how to finish solving the problem now.” Mike: I think the part that I want to pull back and linger on a little bit is [that] part of the purpose of press is to keep the conversation about the mathematics in the space longer for kids to be able to have access to those ideas. I want y’all to unpack that just a little bit. Amber: Having linking and press at the end is holding the conversation longer in the classroom. And so the teacher is using the press moves to get at the mathematics so the kids can access it more. And then by linking, you’re bringing in the community to that space and inviting them to add: “What do you agree [with]?” “Do you disagree?” “Can you revoice what someone said?” “Do you have any questions about what’s happening?” Melissa: So when we talk about discourse actions, the initial discourse action would be the questions that the teacher asks. So there’s a good task to start with. Students have worked on this task and produced some solution strategies. Now we’re ready to discuss them. The teacher asks some questions so that students start to present or share their work and then it’s after students’ response [that] linking and press come in as these follow-up moves to do what Amber said: to have the mathematics stay in the public space longer, to pull more kids into the public space longer. So we’re hoping that by spending more time on the mathematics, and having more kids access the mathematics, that we’re bringing more kids along for the ride with whatever mathematics it is that we’re learning. Mike: You’re putting language to something that I don’t know that I had before, which is this idea that the longer we can keep the conversation about the ideas publicly bouncing around—there are some kids who may need to hear an idea or a strategy or a concept articulated in multiple different ways to piece together their understanding. Amber: And like Melissa was saying earlier, the thing that’s great about linking is oftentimes in a classroom space, teachers ask a question, kids answer, the teacher moves on. The engagement does drop. But by keeping the conversation going longer, the linking piece of it, you might get called on to revoice, so you need to be actively paying attention to your peers because it’s on the kids now. The math authority has been shared, so the kids are the ones also making sense of what’s happening. But it’s on me to listen to my peers because if I disagree, there’s an expectation that I’ll say that. Or if I agree or I might want to add on to what someone else is saying. So oftentimes I feel like this pattern of teacher-student-teacher-student-teacher-student happens, and then what can start to happen is teacher-student-student-student-teacher. And so it kind of creates this space where it’s not just back and forth, it kind of popcorns more around with the kids. Mike: You are starting to touch on something that I did want to talk about, though, because I think when I came into this conversation, what was in my head is, like, how this supports kids in terms of their mathematical thinking. And I think where you two have started to go is: What happens to kids who are in a classroom where link and press are a common practice? And what happens to classrooms where you see this being enacted on a consistent basis? What does it mean for kids? What changes about their mathematical learning experience? Melissa: You know, we observe a lot of classrooms, and it’s really interesting when you see even primary grade students give an answer and immediately say, you know, “I think it’s 5 because …,” and they provide their justification just as naturally as they provide their answer or they’re listening to their peers and they’re very eager to say, “I agree with you; I disagree with you, and here’s why” or “I did something similar” or “Here’s how my diagram is slightly different.” So to hear children and students taking that up is really great. And it just—a big shift in the amount of time that you hear the teacher talking versus the amount of time you hear children talking and what you’re able to take away as the teacher or the educator formatively about what they know and understand based on what you’re hearing them say. And so [in] classrooms where this has become the norm, you see fewer instances where the teacher has to use linking and press because students are picking this up naturally. Mike: As we were sitting here and I was listening to y’all talk, Amber, the thing that I wanted to come back to is [that] I started reflecting on my own practice and how often, even if I was orchestrating or trying to sequence, it was teacher-student-teacher-student-teacher-student. It bounced back to me, and I’m really kind of intrigued by this idea, teacher-student-student-student-teacher—that the discourse, it’s moving from a back and forth between one teacher, one student, rinse and repeat, and more students actually taking up the discourse. Am I getting that right? Amber: Yes. And I think really the thought is we always want to talk about the mathematics, but we also have to have something for the community. And that’s why the linking is there because we also need to hold kids accountable to the community that they’re in as much as we need to hold them accountable to the mathematics. Mike: So, Amber, I want to think about what does it look like to take this practice up? If you were going to give an educator a little nudge or maybe even just a starting point where teachers could take up linking and press, what might that look like? If you imagined kind of that first nudge or that first starting point that starts to build this practice? Amber: We have some checklists with sentence stems in [them], and I think it’s taking those sentence stems and thinking about when I ask questions like, “How did you get that?” and “How do you know this about that answer?”, that’s when you’re asking about the mathematics. And then when you start to ask, “Do you agree with what so-and-so said? Can you revoice what they said in your own words?”, that’s holding kids accountable to the community and just really thinking about the purpose of asking this question. Do I want to know about the math or do I want to build the conversation between the students? And then once you realize what you want that to be, you have the stem for the question that you want to ask. Mike: Same question, Melissa. Melissa: I think if you have the teacher who is using good tasks and asking those good initial questions that encourage thinking, reasoning, explanations, even starting by having them try out, once a student gives you a response, asking, “How do you know?” or “How did you get that?” and listening to what the student has to say. And then as the next follow-up, thinking about that linking move coming after that. So even a very formulaic approach where a student gives a response, you use a press move, hear what the student has to say, and then maybe put it back out to the class with a linking move. You know, “Would someone like to repeat what Amber just said?” or “Can someone restate that in their own words?” or whatever the linking move might be. Mike: So if these two practices are new to someone who’s listening, are there any particular resources or recommendations that you’d share with someone who wants to keep learning? Amber: We absolutely have resources. We wrote an article for the NCTM’s MTLT [Mathematics Teacher: Learning and Teaching PK-12] called “Discourse Actions to Promote Student Access .” And there are some vignettes in there that you can read through and then there [are] checklists with sentence stems for each of the linking and press moves. Melissa: Also, along with that article, we’ve used a lot of the resources from NCTM’s Principles to Actions [Professional Learning] Toolkit. that’s online, and some of the resources are free and accessible to everyone. Amber: And if you wanted to dig in a bit more, we do have a book called Making Sense of Mathematics to Inform Instructional Quality. And that goes in-depth with all of our rubrics and has other scenarios and videos around the linking and press moves along with other parts of the rubrics that we were talking about earlier. Mike: That’s awesome. We will link all of that in our show notes. Thank you both so much for joining us. It was a real pleasure talking with you. Amber: Thanks for having us. Melissa: Thank you. Mike: This podcast is brought to you by The Math Learning Center and the Maier Math Foundation, dedicated to inspiring and enabling all individuals to discover and develop their mathematical confidence and ability. © 2024 The Math Learning Center | www.mathlearningcenter.org References and Resources: NCTM: https://pubs.nctm.org/view/journals/mtlt/113/4/article-p266.xml#:~:text=Discourse%20actions%20provide%20access%20to,up%20on%20contributions%20from%20students ERIC: https://eric.ed.gov/?id=EJ1275372 https://www.nctm.org/PtAToolkit/ https://www.nctm.org/uploadedFiles/Conferences_and_Professional_Development/Annual_Meetings/LosAngeles2022/Campaigns/12-21_PtA_Toolkit.pdf?utm_source=nctm&utm_medium=web&utm_campaign=LA2022&utm_content=PtA+Toolkit

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The Math Learning Center offers multiple free math apps for classroom use. From GeoBoards, Fraction tools, and even Math Vocabulary Cards, The MLC has great tools to aid student understanding of math in a visual and discovery-based way. This resource will take less than 2 minutes to check out but may take up to 30 minutes to explore fully.

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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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How to run a math summer camp for students. 

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How to run a math summer camp for students. 

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In this 19-minute episode of the teaching math teaching podcast, Matt Felton-Koestler and Courtney Koestler discuss how they run summer camps for elementary and middle school children.

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Matt Felton-Koestler and Courtney Koestler discuss how they run summer camps for elementary and middle school children.

If you have enjoyed listening to this podcast and are interested in ohter episodes you can see all episodes listed on this website or search by categries at https://evathanheiser.wordpress.com/tmt-podcast/

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Eva Thanheiser, Dusty Jones, Joel Amidon, Jennifer Wolfe

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Courtney Koestler & Matthew Felton-Koestler: How to run math summer camps for kids

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Matt Felton-Koestler and Courtney Koestler discuss how they run summer camps for elementary and middle school children. If you have enjoyed listening to this podcast and are interested in ohter episodes you can see all episodes listed on this website or search by categries at https://evathanheiser.wordpress.com/tmt-podcast/

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PBS Learning media lets you search their database by grade level or resource type. You can find tons of opportunities to enrich your lessons or provide interventions of support to students.

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Find a variety of resources to learn mathematics in the classroom and home. Access videos, games, and activities that all align to state and national standards.

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Tons of activities for integrating coding in your classroom and all free!

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Learn computer science. Change the world.

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Every student in every school deserves the opportunity to study computer science.

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Early Math thinking for infants and toddlers including professional development for teachers, how to have mathematical conversations while reading your favorite stories, and tons of research on early childhood development!

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Erikson Institute Early Math Collaborative

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Book

Our new book extends professional knowledge for mathematics teaching to educators who work with the very youngest learners. How do babies and toddlers understand the precursors of math?

Learn more

The Erikson Institute Early Math Collaborative is transforming the understanding, teaching and learning of early mathematics from the ground up.

Online Learning

Professional development modules

Our self-guided modules provide materials, strategies, and expert guidance for working with adult learners to explore foundational mathematics. Whether you are working with childcare providers, in-service teachers, or pre-service teachers, modules give you what you need to support professional learning in your local context.

Start a module

Children love to count. Counting helps them make sense of the world and to find out how many of something. With time and practice, children develop an understanding of the "rules" or principles of counting.

From an early age, children notice and appreciate patterns in the world around them. Patterns and sequences of different kinds begin to pop up all over the place, especially in the books that children love.

Teachers in four schools recently experimented with a "problem stem" protocol for helping their children understand the math going on in the word problems they face in class. This was part of our Big Shoulders...

In May of 2023, a diverse group of six kindergarten teachers from across the United States were selected from a national pool of talented and committed kindergarten teachers to participate in the RJEM Teaching Fellowship....

From a racial justice centered perspective, books can be powerful tools to engage children in mathematics learning. The worlds, stories, adventures, characters, and possibilities that are made available through books - explicitly math focused and...

RJEM at Work highlights the everyday efforts of caregivers, community organizations, teachers, researchers, and educational institutions to promote racial justice in the mathematical experiences of children. For the RJEM Local Planning Committee, there are multiple...

Get more when you join. More resources and more ways to connect. Save your favorites so that more is at your fingertips.

Best of all, it's free. Sign-up today.

Early math is big.

Learn why we are so passionate about giving every child a strong foundation in math.

Funding for this initiative is generously provided by:

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Early Math Collaborative at Erikson Institute

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The Early Math Collaborative works to improve math instruction for young children in three ways: professional development, research, dissemination.

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PK - 12 Math for Love - Games, Activities, and Curriculum

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PK - 12 Math for Love - Games, Activities, and Curriculum

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This website houses multiple resources for K-12 teachers to use in their classroom as acceleration or supportive interventions. There are free lessons and games, but also supplemental curriculum available for purchase. I am a fan of the openers, these don't require much time commitment!

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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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Dan Finkel - Five Principles of Extraordinary Math Teaching 

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Dan Finkel - Five Principles of Extraordinary Math Teaching 

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Dan Finkel promotes learning math through playing and gives teachers 'permission' to not have all the answers. This inspiring Ted Talk will reinvigorate teachers and encourage them to "teach them (students) that not knowing is not failure. It's the first step to understanding". This video is only 15 minutes long!

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Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainier

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An interesting perspective on math education and balancing student's cognitive load. David Morkunas discusses his emphasized use of the standard algorithm in elementary mathematics and interesting review strategies employed by his school to reduce math anxiety in students, and increase learning outcomes. This podcast episode is about 1 hour long.

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Cognitive load theory in math class with David Morkunas (Ep 26)

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PK - 12 Classroom Resource - Easy to use and free! 

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PK - 12 Classroom Resource - Easy to use and free! 

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Consider sharing this resource with your educators! Which One Doesn't Belong is a fun activity you can use with your students and serves as a great entrance ticket or warm up activity. Get students discussing mathematics or thinking mathematically by justifying their responses and engaging in discourse. This is a K-12 resource.

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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!