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Week of Inspirational Math: Beginning of the year building foundations in math

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

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Common Core Math Standard Lessons

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New to CPALMS?

CPALMS is an online toolbox of information, vetted resources, and interactive tools that helps educators effectively implement teaching standards. It is the State of Florida's official source for standards information and course descriptions.

Click here to watch an introduction video!

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CPALMS is an online toolbox of information, vetted resources, and interactive tools that helps educators effectively implement teaching standards. It is the State of Florida's official source for standards information and course descriptions. Click here to watch an introduction video!

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@ Michigan State University

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The CMP teacher materials are organized around an instructional model that supports "inquiry-based" teaching. The Launch, Explore, and Summarize are described in more detail in the Philosophy, Instructional Model.

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Wonderful resource for Number Talks, Counting Collections, 3-Act Math and many other instructional activities.

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Lessons are broken down by grade level and CC Standards.

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Online Number Talk ideas

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Problem Based Math Lessons & CC Curriculum Maps Grades 3-12

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

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

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

- Geoff

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Common Core Problem Based Curriculum Maps

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

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Math Talks Planning Resources & Math Talk Sources

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Math Talks Planning Resources & Math Talk Sources

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San Francisco Unified School District

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Read about how Math Talks can strengthen accuracy, efficiency, and flexibility in this article by Sherry Parrish from Teaching Children Mathematics.

More sources for Math Talks:

Other Tools
This folder includes a variety of helpful tools for deepening math talks, planning, and assessing. Including:

Another source of information and resources for Math Talks from Math Perspectives is here.

30 ways to make number strings more inclusive...

Anchor number strings in context.

Never underestimate the importance of models.

Explicitly represent language that helps students be precise mathematically.

Explicitly ask students to try new strategies

​More on NumberStrings.com

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Read about how Math Talks can strengthen accuracy, efficiency, and flexibility in this article by Sherry Parrish from Teaching Children Mathematics. More sources for Math Talks: Other Tools This folder includes a variety of helpful tools for deepening math talks, planning, and assessing.

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Gradel Level Lesson Ideas

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Article

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Performance Assessment Tasks grades 2-5. There are also other helpful resources throughout this website.

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Performance Assessment Tasks | Inside Mathematics

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These tasks are grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics. You may download and use these tasks for professional development purposes without modifyi…

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Support with understanding the standards

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Support with understanding the standards

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We understand that it's challenging for teachers to find resources to support students in building an enduring understanding of mathematics. Only the IM Certified Experience helps teachers catalyze mathematical proficiency with an engaging and inclusive approach that lifts students up to the skills, understandings, and practices that will stay with them for a lifetime. IM K-12 Math gives you exclusive access to engaging content and professional learning and to an inclusive community.

Help students become lifelong math learners. Preview IM K-12 Math™.

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Illustrative Mathematics | K-12 Math | Resources for Teachers & Students

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We understand that it's challenging for teachers to find resources to support students in building an enduring understanding of mathematics. Only the IM Certified Experience helps teachers catalyze mathematical proficiency with an engaging and inclusive approach that lifts students up to the skills, understandings, and practices that will stay with them for a lifetime.

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Number Routines, Mental Math Strategies, Number Translations, Silent Board Games, "Diamond" Problems

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Building number sense each day

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Supporting mathematical argument

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Daily Routines, Tasks, Math Tools, Workshop Resources

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This post contains affiliate links for your convenience. By clicking on these links I may earn a commission at no additional cost to you.

Some kids (and adults too!) have negative feelings about math. It can seem abstract and difficult. But there are lots of fun ways to make it less intimidating. Starting with the very basics, using play and activities there are lots of hands-on counting activities for kids! We've done so many activities to teach counting! There are way too many to list them all but here are a few of our themed favorites.

30+ Hands-On Counting Activities

More Counting Activities

Below you'll find some of the best ideas to include counting skills within other activities like games, crafts, stories and sensory play.

Hands-On Counting Activities and Games

Math Caps: A Math Facts Game from Mosswood Connections

Easy Preschool Watermelon Counting Game from Homeschool Preschool

Spider Web Number Lacing Activity from Artsy Momma

Fine Motor Activity: Turkey Feather Counting from Artsy Momma

Nuts and Bolts More or Less Game from Preschool Powol Packets

Flower Counting Activity from Teaching 2 and 3 Year Olds

Counting Game for One-to-One Correspondence from Buggy and Buddy

Counting Stamp Match Activity from Weaving Ideas

Dinosaur Busy Bag Number Activity from Clare's Little Tots

Contact Paper Fall Tree Counting Game from Simple Fun for Kids

Felt Leaf Number Line Activity from Something 2 Offer

Foam Cup Construction with Numbers from Simple Fun for Kids

Simple Montessori Counting Activity from My Mundane and Miraculous Life

100 Items to Use to Count to 100 from Edventures with Kids

Learning to Count with Pipe Cleaners from School Time Snippets

Hands-on Preschool Counting with Rings on Fingers from School Time Snippets

Skip Counting Activities from What Do We Do All Day

Gross Motor Counting Activities

Teach Counting with a Stair Jumping Game from Homeschool Preschool

Teach Counting with Simon Says from Homeschool Preschool

Gross Motor Math Game: Counting Action Dice from Buggy and Buddy

Bubble Wrap Number Hop from Clare's Little Tots

Hands-On Crafts for Counting

Recycled K Cup Frog Craft and Counting Activity from Artsy Momma

Spider Counting Craft from Teaching 2 and 3 Year Olds

Pretend Play for Counting

Preschool Math Activity with Bear Counts from Teaching 2 and 3 Year Olds

Personalized Felt Counting Set with Ten Apples Up On Top from Buggy and Buddy

Pretend Play and Number Recognition from My Mundane and Miraculous Life

Counting 1 to 5 with 5 Little Ducks from Red Ted Art

Hands-On Sensory Activities for Counting

Exploring Numbers with Playdough from Simple Fun for Kids

Dinosaur Sensory Bin: Counting and Math from My Mundane and Miraculous Life

With a little creativity math doesn't have to be intimidating at all. These hands-on counting activities are sure to be a hit!

More Counting Activities You'll Love!
Ocean I Spy Counting Printable for Preschoolers Free Printable Goldfish Counting Cards

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30+ Hands-On Counting Activities for Kids

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This post contains affiliate links for your convenience. By clicking on these links I may earn a commission at no additional cost to you. Some kids (and adults too!) have negative feelings about math. It can seem abstract and difficult. But there are lots of fun ways to make it less intimidating.

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​Indicator of progress

Students count the number of objects in a small set. Success depends on several understandings, one of the most important of which is using one-to-one correspondence.

While some students can recite the number sequence accurately (i.e. say 1, 2, 3, etc.) they have difficulty maintaining one-to-one correspondence when counting a set of objects.

For more information, see: Learning to count

Illustration 1: Matching names to objects

To ascertain whether students can use one-to-one correspondence, ask students to count a set of counters you have placed in a pile in front of them. Children not using one-to-one correspondence will not co-ordinate saying the number names with taking the counters one by one. Some will say more than one number per object; others will take more than one object per number.

Illustration 2: Conservation of number

Show the student two sets of 6 counters arranged as shown below, spread out or in a group. Ask the student which group has more. Successful students will count each of the sets of counters and find that they contain the same number of counters. Some students will look at the two sets and say that the longer row of counters contains more. Even when they have counted both sets, some students will say that both sets have six counters but the top line of six has more. The appearance dominates the students' judgement.

Illustration 3:

Examples of the types of tasks that would be illustrative of one to one correspondence concepts, aligned from the Mathematics Online Interview:

Question I - 'First year of schooling detour' - Selecting and counting 4 yellow, 3 green, 5 blue teddies

Question 8 (b) (c) - Read cards from 0-10, show 7 and get that number of teddies

Teaching strategies

The following activities involve students using all their senses to develop the co-ordination that is essential to one-to-one correspondence. That is, the teaching strategies use movement of the body, hearing sounds, using eyes and feeling with hands.

Activity 1: Counting and body movements provides several ideas to help to use one-to-one correspondence while counting movements using their bodies.

Activity 2: Counting sets of objects provides several ideas to help students to use one-to-one correspondence while counting concrete materials.

Activity 3: Matching the written number to the quantity provides several ideas to help students to use one-to-one correspondence while counting representations of objects.

Activity 4: Variations on counting suggests some very important counting variations.

These activities simultaneously extend students' verbal counting skills and improve the use of one-to-one correspondence.

Note on Subitising
Subitising is the ability to identify the number of objects in a set without counting and when there is no special arrangement (e.g. not in a dice pattern).

Research shows that children as young as two years of age can subitise 2 or 3 objects*. There is quite a lot of evidence that babies and some animals* can do it too.

Adults can subitise about 5 or 6 objects. Test yourself; the objects can be randomly arranged, not in a standard pattern e.g. as on a die.

* of course they may not know the name of the number - but they know how many there are as a quantity!

Activity 1: Counting and body movements

Keeping track of counting

Students need to track the counting sequence as they are saying and pointing to numerals. The numbers 1 to 10 (and later beyond) can be written on a strip of paper or individual cards (marked 1 - 10) can be placed in order (download below). Students must put their fingers on the written symbols as they are saying the number words. Gradually increase the number sequence.

Number Cards (PDF - 11Kb) - PDF document with numbers 1-20 to be presented as a strip or cut into separate numbers to make number cards.

How many movements?

Students count the number of claps the teacher makes. This can be the number of beats on a drum, taps on a triangle. Students count aloud and aim for rhythm.

Can you do this?

Can students make the number of movements given by the teacher e.g. clap three times, hop three times, skip five times, nod six times? Students count aloud as the actions are done.

How many stairs?

A good task for young students is counting the number of stairs in a staircase. They find it extremely difficult to coordinate walking up or down stairs while reciting the verbal sequence in co-ordination. Some students think the number of stairs appears to change depending on whether the students count faster or slower than they step.

Activity 2: Counting sets of objects

Place a group of objects (e.g.: shells, leaves, counters, teddies, boats, cars) on the table. Ask the student to count how many objects there are. Watch carefully and see if you can determine how the student decides how many objects there are.

Does the student give an instantaneous response? Was this response correct or incorrect? Can they explain how they worked out how many objects there were?

Does the student touch each object as they count?

Does the student move each object as they count?

Does the student track the objects with their eyes while touching their face, tapping their leg or under the table as they count?

These behaviours demonstrate that students have an understanding of one-to-one correspondence.

Activity 3: Matching the written number to the quantity

Shuffle the Number cards (PDF - 11Kb) and ask the students to choose a card.

Can they place that number of objects next to the card?

Can they draw that many objects?

Can students predict how many objects there are if

one more is added to the group?

two more are added to the group?

if one object was taken away?

if two objects were taken away?

Introduce the counting of pictures of objects on a printed page. How do students keep track of the objects they have counted?

Does the student look at the objects and give an instant answer (i.e.: can they subitise)?

Does the student touch each picture?

How does the student check that they have counted every object only once?

Activity 4: Variations on counting

Counting objects in a row is not all there is to counting. Students need to develop good strategies for keeping track of what objects they have counted in many other situations. This is an important skill that can be discussed in class.

Counting objects in a circle.
How do you remember where you started? (e.g.: "I keep a finger of my left hand on the starting object and point at the other objects in one-to-one correspondence with my right hand").

Counting a pile of objects.
How do you remember which ones you have counted? (e.g.: "I move them across to the other side of the table one by one").

Counting moving objects.
How do you know which ones you have counted? Very hard, and it is important to recognise that this will be a difficulty. (When a student recognises that this task will be difficult for them, they are demonstrating metacognition).

References

Kalmus, H. (1964) Animals as Mathematicians, Nature 202, 1156 - 1160

Gelman, R. & Gallistel, C.R., (1978) The Counting Model. In The Child's Understanding of Number. (pp 73-82) Cambridge Ma: Harvard

University Press.

Reys, R., Suydam, M. & Lindquist, M. (1984) Helping children learn mathematics. New Jersey. Prentice-Hall

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Students count the number of objects in a small set. Success depends on several understandings, one of the most important of which is using one-to-one correspondence. While some students can recite the number sequence accurately (i.e. say 1, 2, 3, etc.) they have difficulty maintaining one-to-one correspondence when counting a set of objects.

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5th Grade

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Response to Intervention (RTI): If you've been in the classroom within the last ten years, there is a large chance that you've heard of (and utilized) this reinforcement and recovery measure.

After first learning about RTI models, many educators (and myself) asked, " Is this just another complicated, drawn-out mandate by bureaucrats that never set foot in a classroom?"

However, after taking a closer look at the basis behind Response to Intervention models, you can quickly see the merit of a three tiered classroom system. RTI is based on valid research completed on teacher-proven methods for instructing and assessing all students (across the entire learning spectrum).
Read below to the break to learn about four quick strategies and activities you can use in your math classroom to optimize the "teacher-proven methods" of your RTI model to meet the unique learning needs of each and every student.
RTI Activities for your Math Classroom

1) Math Journaling

Implementing a math journal allows your students to " think about their thinking" (metacognition) and record it in a way that makes sense to them. This journaling process gives you a window into each student's mind to determine where he or she needs help or enrichment.

Encourage students to draw, write and calculate in a math journal to solve problems, work through processes, and explain their actions. Assign math journals once a day, once a week or even once a month to create an invaluable, ongoing formative assessment.

In respect to RTI, you can differentiate journal assignments for Tier 1 students by providing open-ended questions, like "How would you quickly count all of the toes in this classroom?" Differentiate further for Tier 2 and Tier 3 students by asking more concrete questions, based on the concepts they are currently working on.

Additionally, with the advent of free student blogs and discussion boards, you can facilitate an open online classroom forum that encourages your students to post their journals and findings online. Each student can curate and comment on one another's journal entries, creating an element of collaboration and peer reasoning.

Looking for good examples of a math journal? Look no further than Pinterest user Susan Cardin's "Math Journal" board. It contains over 80 examples of fun journal ideas and templates.

2) Manipulatives

Consider a kindergarten classroom. It's likely stocked with colorful bins full of plastic toys, connecting cubes, blocks and three-dimensional shapes. Now, somewhere along the way to middle school those toys got left behind, but the cubes, blocks, and three-dimensional shapes still serve as valuable manipulative materials.

Manipulatives help students of all ages learn and understand math concepts, from counting to multiplication and division. Break out these manipulatives - foregoing toys in an effort to respect the maturity of eighth graders - to introduce more complex math concepts in a way students can see and touch (and talk about).

These manipulatives do not necessarily have to be concrete either! Recent educational technology developments even allow students to use virtual manipulatives on a touchscreen or laptop.

Your students will benefit from "seeing" math concepts in a new way. As they progress, some Tier 1 students will likely leave the tactile manipulatives behind as they "get it." Tier 2 and 3 students can continue to refer back to the objects (virtual and/or physical) for to help form better understandings and reinforce prior knowledge.

3) Introduce and Review Math Vocabulary

As you know, math is its own language. Beginning in the early grades, your students learned terms like " sum", " difference", or " addend ". These words (hopefully) became part of their everyday vocabulary. However, these mathematics terms often require revisiting and scaffolding, regardless of the student's current learning level and goals.

Post a running list of math vocabulary in the classroom and review it often. Harkening back to strategy one, ask students to journal about specific terms and real world application. It will be interesting to see how each student uniquely describes the term " factor" or " exponent." Allow students to draw, diagram or provide examples of terms rather than memorizing a textbook definition. Learning the vocabulary will help all students become more familiar with math concepts.

In respect to your RTI model, you can stratify the complexity of the terms and the method of reviews between the tiers. For example, Tier 1 students might be best suited to learn more complex terms, as necessary, while Tier 2 and 3 students can continue to revisit learned terms via differentiated modalities as they develop needed comprehension.

4) Think Aloud

When teaching, or re-teaching, math concepts, using a "Think Aloud" activity is a great method for students to understand, hear, and see what's going on in your head as you solve the problem or work through a mathematical process.

Walk students through several examples by thinking aloud each step of the way. Encourage struggling students to model the " think aloud " process by asking them to explain each step as they go. This can be done in a whole-class, small group, or partner setting.

While Tier 1 students often "get it" without further explanation, thinking aloud helps break complex processes down into manageable steps for Tier 2 and 3 students. Also, by hearing and seeing explanations from their peers, students often have "light bulb" moments that may not have clicked during your teacher-led instruction.

Tell us about strategies you use in your RTI math classroom!

These four strategies and activities are only the tip of the iceberg of what is possible within your math classroom. There are many more flexible ways to meet the mathematics learning needs of your students, and we'd love to hear your great strategies and ideas!
Start your conversation on our Facebook Page or Tweet us at @Wowzers!
Sign up for the FREE Pilot from Wowzers Online Math!
Photo credit: Pinterest

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4 Response to Intervention (RTI) Strategies for the Math Classroom

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Response to Intervention (RTI): If you've been in the classroom within the last ten years, there is a large chance that you've heard of (and utilized) this reinforcement and recovery measure. After first learning about RTI models, many educators (and myself) asked, "Is this just another complicated, drawn-out mandate by bureaucrats that never set foot...

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Lessons, Math Workshop, RTI, Number Talk Resources

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Review the Rubric with Students

Most teachers use rubrics to score student responses to open-ended questions. Make sure students understand the rubric so that they know exactly what they must provide to get the best score. Teachers use a variety of strategies to provide this training:

Student Scoring: Save student responses from previous years. Show a sample response on the overhead (without student name) and ask small groups to decide what score the response would get and why. Lead a discussion about what is missing from the response and have students suggest what might be added to get the highest score.

Peer Editing: Pair students to read each other's response, assign a rubric score and make suggestions or comments.

Write-On Bulletin Board: Regularly display student work that exemplifies the best response to open-ended questions. Try to include different strategies for organizing information (table, graph, list, drawing, factor tree, etc.) so that students consistently see proof that there are MANY right ways to respond.

Use the Writing Process Approach

Students are accustomed to editing their first drafts in language arts, reworking their writing to craft a better response. Regularly include these practices in math class. After writing, students should use the rubric to examine their response and annotate, clarify or reorganize, as needed, to craft a tight response. Students should be encouraged to use words, pictures and/or numbers to capture their thinking process in these open-ended questions. They must also understand that there are many different ways to achieve a perfect score as long as they accurately show their thinking toward a correct answer.

Math Portfolios: Keep folders of students' open-ended problem solving with first draft, revised draft and annotated rubric attached.

Remember to...Checklist: Have students generate a list of things (in their own words) that they should check before deciding their open-ended response is complete. Add more items, based on student performance or assessed weaknesses -- e.g. label all graphs, write the unit (centimeter, inch, packages, etc.)

Math Word Wall: Encourage students to check that they have used the best math words and that they have spelled them correctly.

Writing Conferences: Conference with students to review their responses and provide detailed feedback on what they did correctly and/or how they might improve their response, as per the rubric.

Provide Independent Practice

Mathwire Dr.Seuss Day Math Activities

Mathwire St. Patrick's Day Math Activities

Shamrock Paths challenges students to use Pascal's Triangle to figure out how many different ways there are to spell Shamrock. Included in the PDF file are an explanation of how this problem relates to Pascal's Triangle and the numerical solution to the challenge.

Shamrock Patterns requires students to rotate shamrocks to complete the pattern. Download some copies of Extra Shamrocks for students to cut apart and glue on to complete the patterns.

Top of the Morning challenges students to identify the 100th and 1000th letter that will be printed on the electronic signboard.

Featured Data Collection Activity: Cereal Toy Investigation

Strategy of the Month: Organizing Data

There are many different ways to organize data: graphs (bar, line, circle, glyph, etc.), line plot, stem-and-leaf plot, table, list, picture, etc. Be sure to meaningfully plan opportunities for students to use these different methods in problem-solving exercises. As part of class discussion, display different student responses on the overhead or whiteboard, commenting on how one student used a table and another used a graph, etc. At times, teachers might encourage students to use a table or draw a graph, etc. so that they demonstrate proficiency in using the different approaches.

Tip of the Month: Have Students Write Original Math Problems

Students use higher-order thinking skills when they write original problems similar to those they have done in class. Have students proof and solve each other's problems before publishing them on the computer, along with the author's name and the date. These problems may be used as do-nows, homework assignments, or placed in the math center. Teachers who regularly include student writing find that students are highly motivated to solve problems created by their peers AND teachers develop a larger bank of appropriate word problems over time.

Mathwire Blog

Don't miss the new Mathwire Blog for the latest updates on Mathwire! The Mathwire blog will feature new activities as they are added to the Mathwire collection and it will also spotlight classic Mathwire activities, adding suggestions for classroom implementation and/or modifications to best meet the needs of varied students in a classroom.

Best of all, the Mathwire Blog format allows users to comment on the activities and add their own ideas to the mix. This should benefit all of us as we try to engage students in learning mathematics.

Check out the new Mathwire Blog and be one of the first to become an active contributor to the Mathwire family. The Mathwire Blog replaces the old Mathwire subscription e-mail lists so that you are constantly up-to-date on Mathwire happenings.

Mathwire Search Options

New to Mathwire.com? There are several ways to search the site for activities by Math Standard, Math Topic, or using an alphabetical search.

About Mathwire.com

Mathwire.com is designed to provide activities and appropriate worksheets for teachers to use in their classrooms. &nbsp All activities and worksheets support the constructivist approach to learning mathematics and the NCTM Standards.

Activities: &nbsp The activities on this site were developed by Terry Kawas and the teachers in districts where she has worked as a math consultant and coach or with students she has taught in college math-methods courses. &nbsp The activities are classroom-tested by teachers and appropriate modifications have been made to reflect this field-testing. &nbsp These activities are posted online in an effort to share quality activities and routines within the mathematics community.

Read A Note from Terry and see what users are saying about Mathwire.

Terms of Use: &nbsp Teachers are welcome to download any of the activities for free use in their classrooms. &nbsp No activities may be copied for use on other websites or included in commercial products without permission in writing from Terry Kawas, webmaster. &nbsp Contact Terry Kawas

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Most teachers use rubrics to score student responses to open-ended questions. Make sure students understand the rubric so that they know exactly what they must provide to get the best score. Teachers use a variety of strategies to provide this training: Student Scoring: Save student responses from previous years.

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Centers should be designed to:

It is important to build a community of learners so that students will be able to work independently at centers since you will be engaged with other students during this time. When introducing Centers for the first time it is important to:

communicate clear, explicit, high expectations and develop a few non-negotiable rules established jointly by both you and your students;

be available to assist students during center time and reinforce appropriate behaviors;

instruct, model and provide guided practice opportunities before placing new tasks in centers;

hold very brief 'mini lessons' every day prior to children going to centers focusing on how to use the equipment and materials, how to share materials, how to take turns, put things away etc. During this time you might have two students role-play the use of the materials while others critique their efforts or model how to solve a problem without teacher assistance (e.g. introduce the "Ask Three before Me" strategy to encourage students to ask three different classmates to help solve an issue during center time before coming to you with a problem).

Students can be scheduled at centers using either a rotation system or a self selected system. When using a rotation system a designated amount of time is given to each center before students may move on to the next. Using a self selected system students move themselves through centers in a systematic way, using contracts or planning sheets to record what activities have been completed.

Looking for ways to incorporate more writing into your centers? Download copies of these Reflection Templates and have them available to students during Math Centers sessions.

Whenever possible center activities should be open-ended, allowing for multiple responses to allow students to learn in their zone of proximal development, and provide for a mixture of independent as well as paired tasks. In order to encourage students to talk with one another, problem solve together, and assist one another in their learning a center should generally have between two and six students.

The possibilities for math center activities are endless. For examples of a range of activities to use in Centers see our Math Centers eBooks for K - 5th Grade. FREE sample centers can be downloaded on the Number, Geometry, and Measurement/Data pages for your grade level on our website.

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Centers should be designed to: It is important to build a community of learners so that students will be able to work independently at centers since you will be engaged with other students during this time.

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Number Talks, Estimation, and other Math Routines

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With the implement of new standards, assessments, and (for some) new curriculum, teachers are feeling bogged down and yet left out on their own to make sense of it all.

Especially in this era of education, there is a lot of unknowns about what and how we should be teaching.

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Build Math Minds | Learn to LOVE Teaching Math

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With the implement of new standards, assessments, and (for some) new curriculum, teachers are feeling bogged down and yet left out on their own to make sense of it all. Especially in this era of education, there is a lot of unknowns about what and how we should be teaching.

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Imagine open-ended math tasks that get students asking questions as well as answering them. Creative Math Prompts lead learners to build and test their own ideas.

Check out this fun and challenging problem about skip-jumping patterns from the people at mathpickle.com.

Why do bright math students in the U.S. fall short in international comparisons? Helping these students reach their full potential may mean challenging some popular beliefs.
Mathematical Art

The Mathologer introduces us to beautiful pictures created just from multiplication and "clock arithmetic." Amazing!

The 5280 Math Newsletter

Sign up for the 5820 Math Newsletter. Keep up with work I am doing as well as the latest in math talent development: classroom resources, tools and strategies, challenging and engaging math problems, interesting articles, websites, and blogs.

Creative Math Prompts
A Creative Math Prompt is an image (often quite simple) that contains the seeds of a deep math investigation. The prompts are open-ended yet connected to content goals. As you and your students make observations and generate questions to explore, you develop your mathematical creativity as well as problem-solving and reasoning skills.
Ten Plus One:
A Tool for Enhancing the
Depth and Complexity of
Math Tasks
Ten Plus One is a free tool designed to help teachers transform traditional math tasks into new tasks that promote learning with deep understanding. It consists of ten strategies to make tasks deeper and one strategy to enhance complexity.
Deep Math Projects
Deep Math Projects are open-ended projects that you can extend by continuing to ask new questions. The problems are self-differentiating and often have multiple solutions and/or solution paths.
Grade 5 Monthly Problem Sets
Each of the nine Monthly Problem Sets for grade 5 contains a grid of 15 problems designed to challenge talented and adventurous students. The problems are organized by content strand: Number and Operation; Algebra; Geometry; and Data and Probability, Rates and Ratios. There is also a General category just for fun!

Math Pickle
mathpickle.com has collection of deep, open-ended, and challenging (some unsolved!) math problems for students of all ages searchable by grade level, including plenty for very young students. Each problem has been found or created by a professional mathematician and fits comfortably into a 45-60 minute time frame.
nrich maths
nrichmaths.org has an extensive collection of rich, engaging math problems searchable by age and concept. There is plenty of support for teachers, and students may submit solutions for possible publication online.
Ken-Ken Puzzles
Ken-ken puzzles are like sudoku, but with a challenging mathematical twist. The puzzles develop not only computational facility but problem-solving skills, number sense, and a deeper understanding of number properties. This website will generate ken-ken puzzles for you based on your choice of grade level, mathematical operations, the size of the grid, and level of challenge.
Zukei Puzzles
Zukei puzzles involve searching for geometric shapes hiding in grids or dots. The focus is on reasoning about properties of two-dimensional figures. The puzzles come in all levels of difficulty. You and students can easily create your own as well.
Exploding Dots
James Tanton's Exploding Dots has taken the math world by storm over the past couple of years. Using a simple visual model, students explore place value, addition, subtraction, multiplication, division, and beyond in different base systems.
Beast Academy
Beast Academy is a full math curriculum for gifted and advanced learners in grades 2 - 5. (I would not recommend it for other students.) It is produced by the Art of Problem Solving people who are known for their materials for gifted secondary students. The focus is on problem solving and deep conceptual understanding. An online version of the program is said to be coming soon.

From the same people who produced Project M3 for upper elementary students, Project M2 "contains eight curriculum units designed for grades K-2 to foster inquiry and engage students in critical thinking, problem solving, and communication activities...[with a] focus on "in-depth" mathematics using research-based practices and standards in mathematics education and early childhood education.

This series from Kendall Hunt is well known throughout the US for providing research-based, deep, challenging math curriculum for advanced learners. Each module comes with extensive teacher support, and you may use the projects as curriculum units or as a supplement. The only downsides: materials are rather expensive and require a fair amount of preparation time for teachers.

Math Building Blocks
Math Building Blocks is a free online book in which colored blocks are used to represent prime numbers and prime factorizations. The blockshelp adventurous learners visualize, analyze, and connect concepts across middle school math standards-everything from factors, multiples, GCFs, and LCMs to fraction computation, properties of exponents and radicals, and algebra.
Creative Math Prompts
A Creative Math Prompt is an image (often quite simple) that contains the seeds of a deep math investigation. The prompts are open-ended yet connected to content goals. As you and your students make observations and generate questions to explore, you develop your mathematical creativity as well as problem-solving and reasoning skills.
Ten Plus One:
A Tool for Enhancing
Depth and Complexity of
Math Tasks
Ten Plus One is a free tool designed to help teachers transform traditional math tasks into more challenging tasks that promote conceptual understanding. It consists of ten strategies to make tasks deeper and one strategy to enhance complexity.
Intrepid Math
Each Intrepid Math problem set contains eight challenging, open-ended math problems for advanced and adventurous learners in grades 4 - 6. With traditional math problems, students learn to solve. With Intrepid Math, students solve to learn.
Grade 6 Monthly Problem Sets
Each of the nine Monthly Problem Sets for grade 6 contains a grid of 15 problems designed to challenge talented and adventurous students. The problems are organized by content strand: Number and Operation; Algebra; Geometry; and Data and Probability, Rates and Ratios. There is also a General category just for fun!

Math Pickle
mathpickle.com has collection of deep, open-ended, and challenging (some unsolved!) math problems for students of all ages searchable by grade level. Each problem has been found or created by a professional mathematician and fits comfortably into a 45-60 minute time frame.
nrich maths
nrichmaths.org has an extensive collection of rich, engaging math problems searchable by age and concept. There is plenty of support for teachers, and students may submit solutions for possible publication online.
Exploding Dots
James Tanton's Exploding Dots has taken the math world by storm over the past couple of years. Using a simple visual model, students explore different base systems, decimals, algebra, and related challenging problems, some of which are unsolved!

This series from Kendall Hunt is well known throughout the US for providing research-based, deep, challenging math curriculum for advanced learners. Each module comes with extensive teacher support, and you may use the projects as curriculum units or as a supplement. The only downsides: materials are rather expensive and require a fair amount of preparation time for teachers.
PBS Infinite Series
This excellent youtube challenge presents videos on popular advanced math topics to a general audience. They also challenge viewers to answer questions and solve related problems. Unfortunately, they recently stopped producing new content, but the original content remains available for viewing.
Mathologer
The "Mathologer" is Australian mathematician Burkard Polster, and he makes beautiful and informative videos about popular math topics such as infinity, rubik's cube, irrational numbers, infinity, higher dimensions, fractals, etc. He also likes to give you challenging problems to think about-and he wears very cool math t-shirts!

The ACCME book series contains challenging, engaging activities that extend and deepen students' conceptual understanding of advanced middle school concepts.

Deep Algebra Projects
Deep Algebra Projects are rich, complex mathematical and real-world investigations that stretch advanced learners out of their comfort zones. The projects enhance students' abilities to think independently, flexibly, and with deep understanding.
Creative Math Prompts
A Creative Math Prompt is an image (often quite simple) that contains the seeds of a deep math investigation. The prompts are open-ended yet connected to content goals. As you and your students make observations and generate questions to explore, you develop your mathematical creativity as well as problem-solving and reasoning skills.

brilliant.org
brilliant.org offers five challenging math or science problems per week at three levels: basic, intermediate, and advanced. You may view solutions submitted by others and compare them to your own. The site also hosts a Wiki of the Day. All of this is free, though if you subscribe, you gain access to additional features including fascinating math and science courses.
Math Pickle
mathpickle.com has collection of deep, open-ended, and challenging (some unsolved!) math problems for students of all ages searchable by grade level. Each problem has been found or created by a professional mathematician and fits comfortably into a 45-60 minute time frame.
nrich maths
nrichmaths.org has an extensive collection of rich, engaging math problems searchable by age and concept. There is plenty of support for teachers, and students may submit solutions for possible publication online.
cut-the-knot
cut-the-knot.org, which the author, mathematician Alexander Bogomolny, calls "Interactive Mathematics Miscellany and Puzzles" contains a massive collection of challenging problems and interesting articles.
PBS Infinite Series
This excellent youtube challenge presents videos on popular advanced math topics to a general audience. They also challenge viewers to answer questions and solve related problems. Unfortunately, they recently stopped producing new content, but the original content remains available for viewing.
3 Blue 1 Brown
This is my personal favorite website of all time. Grant Sanderson creates incredible animations to support the clearest and most beautiful explanations-and explorations-of advanced mathematical concepts that I have ever heard. I wish I had understood half of what I have learned from these videos when I was originally exposed to these ideas!
Mathologer
The "Mathologer" is Australian mathematician Burkard Polster, and he makes beautiful and informative videos about popular math topics such as infinity, rubik's cube, irrational numbers, infinity, higher dimensions, fractals, etc. He also likes to give you challenging problems to think about-and he wears very cool math t-shirts!
Better Explained
Replace memorization by mathematical understanding. Better Explained is an excellent website whose author explains challenging advanced math concepts by emphasizing intuition first. In his words, "Better Explained focuses on the big picture - the Aha! moment - and then the specifics."

Do you know of other excellent resources that support deep conceptual understanding for advanced and adventurous math learners?
If so, please so that I can include them on this site. Thank you!

I have been writing posts for middleweb.com every few months or so. Check them out!

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Imagine open-ended math tasks that get students asking questions as well as answering them. Creative Math Prompts lead learners to build and test their own ideas. Check out this fun and challenging problem about skip-jumping patterns from the people at mathpickle.com. Why do bright math students in the U.S.

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Images to generate questions.

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What is the first question that comes to your mind?