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The most inspirational video you will ever see    Nick Vujicic

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Marilyn Burns

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Monday, August 17th, 2015

Several issues come up regularly when teachers seeking help with their math instruction ask me questions. One is a general question: How can I motivate my students to enjoy math more? Another relates more to managing instruction in the classroom: What can I do during math lessons when some students finish their work quickly while others need more time? Another is a concern about practice: How can I give students the practice they need without relying on more worksheets?

One suggestion I offer to respond to all of these questions is: Make games an integral part of math instruction. One game that has become a standard in my teaching repertoire is Four Strikes and You're Out. I've taught this game at different grade levels to give students practice with mental computation, adjusting the numbers, operations, and number of blanks to be appropriate for the particular class. The game is sort of a mathematical version of the word game Hangman. (If your students know how to play Hangman, it may be helpful to reference it when you teach this game.)

When I introduced the game to a class of third graders, I began as I typically do. I wrote Four Strikes and You're Out on the board as I explained to the class that this is the name of a game I was going to teach them. Sammy's hand shot up and asked me the question I typically get.

"Don't you mean three strikes?" he asked, thinking about baseball.

And I gave my typical response, "We could play the game with three strikes, but let's try it first with four strikes and then you can see which would be better." Next I wrote a blank frame for a math problem that I knew the children could solve. And next to the problem frame, I listed the numbers from 0 to 9.

"One number goes in each blank," I explained, pointing to the six blanks I had drawn," and your job is to figure out the numbers in the problem." I showed the students a folded slip of paper and told them that inside I had written the problem they were to guess. (I didn't tell them the problem: 35 + 10 = 45.)

"Here's how we play," I continued. "You guess a number, and if it's in my problem, I'll write the number in all the places it belongs. But, if you guess a number that's not in my problem, you get a strike. To win, you have to figure out all of the numbers before you get four strikes."

As with all new investigations, some students were confused. I've found that the best way to resolve confusion is to move forward. "There's no way to know at this point in the game what my numbers may be-you just have to guess," I said. "But after you make some correct guesses, you'll have some clues that can help."

I called on Celia to make the first guess. "Three," she said. I referred to my "cheat sheet" with the problem written on it and said, "Yes, that's one of the numbers in the problem." I wrote 3 where it belonged in the problem and crossed it off the list to indicate that it had been guessed.

"Two," Hiroshi guessed next. I referred to my cheat sheet and said, "No, there's no 2 in my problem, so that counts as a strike." I crossed out the 2 and wrote an X next to the title to indicate a strike.

"Nine," Amanda guessed next. I referred to my cheat sheet again and said, "No, that's strike two." The students groaned.

"It's good that we have four strikes," Sammy commented. I wrote another X.

"Five," Maria guessed. I again referred to my cheat sheet. Even though I had memorized the problem, I checked to model for the students what they were to do after each guess when they later played the game independently.

"That's a useful guess," I said, recording the 5 in the two places it appeared and crossing it out on the list.

A buzz of conversation broke out. A few students realized that the two 5s meant that there had to be a zero in the ones place of the second number. Others, however, didn't notice this. I brought the class back to attention. "Now that you have some clues in the problem," I said, "talk at your tables about what you now know, and what might be a good next guess. Raise your hand when you're ready to make the next guess." After a moment or so, about half the hands were raised. I called on Charlotte.

"There has to be a zero," she said.

"Can you explain why?" I asked.

"Because you're adding something to 35 and the answer ends in a 5. So the number you're adding has to end in zero." Some students nodded in agreement and others looked confused. I've learned that after playing the game several times, more students begin to reason numerically about how the clues can help. This thinking calls for computing mentally, thinking about numerical structures, and helps develop number sense. At this point, I focused on being sure they all at least knew how to play.

"So you'd like to guess a zero?" I asked. Charlotte nodded and I recorded.

Conversation broke out again at their tables. After a few moments, I called the students back to attention and asked, "Who would like to share an idea about what you now know?" I called on Nelson.

"You can't be sure about the missing numbers," he said. "But if you guess one of the numbers right, then you'll know the other."

Anna had something else to add. "Eight won't work in either place," she said. "Can I come up to the board and show why?" I agreed. She came up and pointed at the first remaining blank. "Look," she said, "if it's 35 plus 80, you'd have three numbers in the answer because it would be more than 100." She then pointed at the blank in the sum and continued, "If the answer is 85, the second number would have to be 50, but we already used up the five." I could see that some students didn't follow Anna's explanation, so I asked the class again to turn and talk at their tables about Anna's idea and what they might want to guess next.

After a moment I asked, "Who wants to make the next guess?" I called on Tom

"Lucky seven," he guessed.

I checked the problem and responded, "Strike three." The students groaned as I recorded a strike and crossed out the 7.

"Let's see what choices are left," I said. Together we read the numbers that weren't crossed out-1, 4, 6, and 8. Max reminded us that eight wouldn't work, but I didn't cross it out since it hadn't been guessed.

"Six won't work either," Angela said. "We already know nine is wrong, so you can't have 35 plus 60, and if the answer was 65, there would have to be another 3, and we already guessed that number."

"I guess a one," Beatrice said.

"And the other number is a four. It has to be 35 plus 10 equals 45," Sammy said.

I recorded the numbers and said, "Let's check the addition to be sure it's right." Everyone agreed that it was correct.

"You figured out the problem with only three strikes," I said, "so you win." The class cheered.

I repeated the game for two more problems (50 + 26 = 76 and 29 + 13 = 42). The next day, we played two more games, and this time I changed the number of blanks in one game and the operation from addition to subtraction in the other (37 + 87 = 124 and 70 - 12 = 58). Later in the year, I used problems that involved multiplication and division, choosing problems that related to what the students were learning and practicing (for example, 6 x 5 - 4 = 26 and 5 = 40 ÷ 8).

Tips from the Classroom
This is an example of a game that works well as a whole-class investigation, for the class to play as one team against the teacher. When the students understand how to play, they can learn to play the game independently. For this, I organize the class into partners so that each pair of students could play against another pair. I've found that having students work in pairs helps avoid errors in their responses and encourages communication about how they are reasoning.

First I had each pair think of a problem and, as I had modeled, write it on a slip of paper and fold it. On a half sheet of paper, they wrote the blanks for the problem and the list of the numbers from 0 to 9. Then they were ready to play. Pairs took turns, first one pair guessing and then switching roles. I added Four Strikes and You're Out to the class list of Math Games and it became a favorite option.

I've learned that it's important that students have the skills they need to play any game I teach, whether the game is intended to develop understanding, provide practice, and/or offer challenges. I was careful to introduce the game using an addition problem that I knew the students could solve. When the math is accessible, students can more easily focus on learning how to play.

I've also learned that when I first introduce a game, just as when I present anything new in the classroom, some confusion is typical. For that reason, I like to teach a new game to the entire class so that everyone receives the same information. I play sample games as many times as needed to resolve all issues of confusion before I expect students to be successful independently.

Competitive or Cooperative?
Four Strikes and You're Out is an example of a competitive game where the goal is to win. From their experience playing games like Tic-Tac-Toe, children have learned to play competitive games where someone wins (or sometimes the game ends in a tie). Competitive games help students test their skills, take risks, and learn to be graceful winners and losers. However, it's important to foster communication and cooperation among students. Having the students play in pairs allows for both cooperation and competition. Throughout the year, I like to teach a mix of games that can be played competitively, cooperatively, or either way.

Note: This blog is excerpted from the Fourth Edition of my book About Teaching Mathematics. The game originally appeared in Teaching Arithmetic: Lessons for Addition and Subtraction by Bonnie Tank and Lynne Zolli.

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Using games has long been standard in my teaching, and for several reasons. Games capture students' interest and engages them in learning math. They're ideal when students have extra time. And they're effective options for the paper-and-pencil practice. Here's one of my favorites.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Sharing these fun puzzles with your kids is a great way to get them thinking mathematically and solving problems in a fun and engaging way! Try these free puzzles with YOUR kids today!
Do you want the latest Free Math Puzzles for All Grade Levels in your inbox every week? ➜ Sign-up for our weekly newsletter and start getting free stuff today!

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Sharing these fun puzzles with your kids is a great way to get them thinking mathematically and solving problems in a fun and engaging way! Try these free puzzles with YOUR kids today! Do you want the latest Free Math Puzzles for All Grade Levels in your inbox every week?

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ABCya! * Number Chart - Use to Learn Number Patterns & More

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The interactive number chart is a great way for students to discover number patterns, skip count, and learn multiplication tables. Color the interactive number charts to find patterns in numbers or use them for counting exercises. Children can print their charts too!

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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After introducing the downloadable Maze Hundreds Chart yesterday, this post details some strategies for using the interactive chart in your classroom. If you have not yet watched the first post, I encourage you to take a quick look at it before viewing these strategies.

I have many more resources I am excited to share, so I encourage you to subscribe to the blog so that you will be notified as soon as they are posted. Then you will be able to use them in your classroom right away.

Here are some strategies for using The Maze Hundreds Chart.

You can download The Maze Hundreds Chart here.

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

You may also enjoy the post that surprises many readers entitled "How to Create 9 Identical Dot Patterns in 10 Seconds or Less."

Another downloadable resource I recommend is 180 Opportunities to Notice.

Thank you for your time! If you find these resources valuable, I encourage you to take a moment to subscribe to the blog so you will be notified as soon as I post more resources for you to download.

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Strategies for Using the Maze Hundreds Chart - Steve Wyborney's Blog: I'm on a Learning Mission.

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After introducing the downloadable Maze Hundreds Chart yesterday, this post details some strategies for using the interactive chart in your classroom. If you

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Digital Flipped 100's Chart Routines (with animated numbers chart!)

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Digital Flipped 100's Chart Routines (with animated numbers chart!)

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Curious Thoughts of Elizamath Brandenbook

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It seems that my first two posts on turning the hundreds charts (grid) upside down has generated a good bit of buzz. I really appreciated all the feedback from teachers across the country and from the teachers in my own building (special thanks to Andrew Stadel and John SanGiovanni)! What I thought was going to be a one shot blog post deal has taken on a life of its own.

The great part about being a lead teacher is being in a large elementary school (750 students) with lots of teachers who love to volunteer their classrooms up to me to model and try things out with their students. So when I pitched this idea to my grade 1 team they were eager to have me try it out. At that same meeting I came up with the idea of using Steve Wyborney's digital hundreds chart version to make this into a math routine. I was able to modify his original hundreds chart into several different upside down versions to use in my routine.

So, the very next day I went off, ipad and tripod in hand, to video myself on my first attempt to Spencer Taylor's first grade classroom. Spencer has a group of first graders who have many special needs (a quarter of them already have an IEP) as well as 1 or 2 students who are English Language Learners. I knew that in our first grade classrooms had spent a good amount of instructional time with place value and using the hundreds chart early in the year. From our planning the teachers decided to again revisit and expand on their instruction in place value to addition and subtraction in this upcoming marking period (we are really going to focus on those 1.NBT standards). Spencer warned me that he wasn't sure how they might respond but, undeterred I forged ahead!

I began by exposing only the 1 and the 100 on the board. These are what I call the "anchor numbers"; numbers that help students make sense of the board and the arrangement without showing them the entire board. Then I turned 9 other squares white. With the students I first just had them simply NOTICE and WONDER about what they saw. The students quickly able to see that these numbers were in a different place then they were used to but, as you will see in the video, they adapted quickly and were not phased by the change. Next, for the routine we played a game of the class against me. I told them that for every number on the marked spaces, that they could identify correctly they would get a point and for every number that they incorrectly identified I would get the point. Throughout the idea was that the student identifying the number had to explain to the class how they used their math thinking to determined the solution.

Side note....the video quality is not fabulous (sorry) as the lights had to be off to see the blue outline of the boxes on Steve's chart.

What I saw from these students during the short routine was a tremendous amount of thinking and reasoning! I also saw how easily they could reason through the changes given their knowledge of numbers and patterns. This has spurred me on to think about creating lots of different number charts (with numbers in different locations) and building routines around them to build number sense through reasoning with patterns.

Side note...I would love to create a program where you could have a board with 100 or 120 spaces, fill the smallest number you want into one cell and the largest number into the last cell and then the board would automatically populate so you could use it like the board I modified from Steve or this Classworks board. If this is a skills you have contact me so we can make this happen! In the meantime I'll create some different boards on this page and start posting them for teachers.

Something else you might notice from the video is that you will see me try to redirect them to talk to their classmates instead of just me. Students tend to just respond to the teacher but it is very important for them to communicate with each other instead of just the teacher. This is something that could easily be built in this classroom through routines and activities.

Even after a successful routine with this group of first graders, I realized that this journey was taking on a life of its own. First, I'm going to call change the routine name to Number Chart Routine. My plan is that the boards will have many different configurations. They may be right side up or upside down, sometimes they will end with 100 and sometimes they will go way beyond that into digits in the thousands or even start below 1 with decimals, fractions, negative number (yes even elementary students can understand that concept), etc... For now, until I can figure out a way to automate the chart as I mentioned above, I will just begin by creating more variations on the board for teachers use and archiving them here on my blog (and on my school's google page) for anyone to use and modify for FREE.

Here is the link to the folder that I'm going to continue to add versions of the Number Chart Routine. I created 10 number charts to start with (5 regular and 5 upside down). I will be adding more over the next few weeks. Be sure to drop in again and make suggestions of other variations that you would like to see created! This post will also be added to a new Math Resources page titled Number Chart Routine.

So...after all of this I hope you will dive in with me and try out this routine and share your experiences, thoughts, and feedback!

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Upside Down and All Around: The Hundreds Chart 3.0

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It seems that my first two posts on turning the hundreds charts (grid) upside down has generated a good bit of buzz. I really appreciated all the feedback from teachers across the country and from the teachers in my own building (special thanks to Andrew Stadel and John SanGiovanni)!

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The concept of 10 more/less is a beast in the primary grades.Last week I realized that I've been feeding the monster that I'm continually trying to defeat. Almost every day, in every K-2 classroom across the United States students encounter this guy:

I made a conscious effort to pop my head in every K-2 classroom in the schools I visited this week.It was great to see that every classroom had a traditional 0-99 or hundreds chart posted like one above.

While visiting, one of the teachers asked if I could come back today and model a lesson using a 0-99 chart because her students "just weren't getting it."I gladly accepted her invitation and showed up with this guy:

I didn't use manipulatives for this lesson because I was specifically focusing on the rote counting process which precedes one-to-one cardinality when counting by ones OR tens.

This 30 minute lesson is about as unscientific as it gets when it comes to research but here's my take-aways:

The traditional hundreds chart is counter-intuitive to how students understand and recognize number. When numbers increase by 10 or more, they go down.

The hundreds chart is set up to mirror reading (left-to-right, top-to-bottom).But just because we do it in reading, does it mean that we have to apply that same idea to math?

By inverting the chart and starting with zero at the bottom, students were able to explain that when the number increase by ten it gets larger/taller/bigger/greater which are all modeled when they move "up".

A student made the best connection EVER when she said "It's like my carton of chocolate milk. When I drink some there's less and it goes down. But when I spit it back in there's more milk and it goes up."

I took that student's reasoning and applied it to the traditional hundreds chart (which I didn't share).When we put more in, it goes down.When we take milk out, it goes up.When in life does this ever happen?

It comes back to the ol' " which way does a ten frame go? "I think students should see the ten-frame both ways.I just don't think I'm giving the hundreds chart the same opportunity.If anyone has some or knows of official research on this please share.

If you flip the chart please let me know how it unscientifically goes!

Bottoms up and stay thirsty my friends!

Update October 2016: Jenny Bay-Williams recently shared this article from 1974 regarding a flipped hundreds chart. Not surprising to see that we haven't changed a thing.

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Bottoms Up to Conceptually Understanding Numbers

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The concept of 10 more/less is a beast in the primary grades.Last week I realized that I've been feeding the monster that I'm continually trying to defeat.

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More Ideas (from 1974!) for the Flipped 100's Chart

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More Ideas (from 1974!) for the Flipped 100's Chart

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The Flipped 100's Chart Teaching Ideas #3

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The Flipped 100's Chart Teaching Ideas #3

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Helping children conceptualize numbers and find meaningful ways to think about their relationships is a goal in our kindergarten classroom. We encourage problem solving and working with number strategies in daily number talks, and are always on the lookout for interesting ways to compliment the rich math learning opportunities we are observing in the children's play.

Recently I became a member of the National Council of Teachers of Math (NCTM https://www.nctm.org/). A highlight of membership is that I have access to the journal Teaching Children Mathematics, which is filled with research-based articles outlining interesting and developmentally appropriate practice for the early years. In the December 2017 (24, 3) issue there is a fascinating article by Jennifer M. Bay-Williams and Graham Fletcher called A Bottom-Up Hundred Chart? In this piece the authors challenge educators to consider the potential for enriching children's learning if the popular math tool is flipped upside down.

Bay-Williams and Fletcher share that a flipped hundred chart makes sense because when children use the chart to solve equations, the language they use to describe direction on the chart matches their understanding of the operation - if adding the number appears to get taller, bigger and greater as physically modeled when children track the addition sentence by moving up on the chart and if subtracting the number appears to shrink, moving downwards and getting smaller by descending the chart (e.g., if a child is solving 13 + 12 s/he would first point to the thirteen, move upward one space and then to the right two). The authors also suggest a number of different activities for exploring the chart including cutting one into a 'number puzzle', encouraging children to find mystery numbers, and assigning children a number and challenging them to find all the number's 'neighbours'. These activities are great ways for children to physically and mentally manipulate the chart, helping them to become more comfortable working with the numbers.

After reflecting upon our math program I have created five additional activities that I believe will continue to challenge children and encourage them to strengthen their understanding and confidence working with the numbers 1 - 100.

Guess my number!

Display a flipped hundred chart and mentally think of a number that the children will have to guess. Give children one clue at a time to help guide them to your number (e.g., my number is less than 50, my number doesn't have a 6 in it, my number is odd). The children can consider the clues and cross out the numbers that don't follow the clues. With additional clues more numbers will be crossed off the chart until children guess the correct one. Reverse roles and invite the children to think of a number and give the clues to you!

Our children love to manipulate pentominoes - using them to fill frames and trays and solving intricate puzzles. Children can also be encouraged to use them as tracers, matching them to the chart and outlining the numbers contained within. Once a collection of numbers has been traced, encourage children to find something that all numbers have in common (e.g., they each have a 4 in them; they are all greater than 36). Tip - ensure your flipped hundred chart is printed to the same size as your pentomino set to ensure an accurate match.

Our children love to write with dry erase markers. Create a variety of 'missing number' flipped charts, laminate, and invite the children to practise filling in the missing numbers.

Flipped Hundred Chart Coding

We spend a lot of time coding in our classroom and see potential for incorporating coding directions and spatial reasoning into exploring the flipped hundred chart. Display the chart and determine a starting number. Provide children with a series of verbal or written coding directions as they move from the starting number and reach the end number. Once the final number is determined encourage children to create an statement or equation that describes the relationship between the two numbers.

The number is 48!

What do you know about 3 and 48? (48 - 3 = 45, 3 + 45 = 48, 3 + 5 + 40 = 48)

Roll, Subtract and Race!

Use an enlarged copy of the flipped hundred chart as a board game. Two (or more players) can use recycled board game pieces and place them on the starting point 100 spot. Each player takes a turn rolling one die and moving their player backwards on the chart (or 2 to make the game more difficult). Students can be encouraged to think in equations (If I start at 100 and roll 5, 100 - 5 places me on the 95 spot). First player to move off the board into the 0 spot wins!

What other ways can children learn with the flipped hundred chart?

Feel free to share other ideas in the comment section below or tweet #flipped100schart!

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Helping children conceptualize numbers and find meaningful ways to think about their relationships is a goal in our kindergarten classroom. We encourage problem solving and working with number strategies in daily number talks, and are always on the lookout for interesting ways to compliment the rich math learning opportunities we are observing in the children's play.

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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100 Subitizing Slides & 10 Challenge Patterns - Steve Wyborney’s Blog: I’m on a Learning Mission.

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I have a new resource for you. 100 Subitizing Slides & 10 Challenge Patterns.

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Steve Wyborney's Blog: I'm on a Learning Mission.

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I made multiplication table using and went on to discover some very interesting relationships within the table.

You will see several here. Click here to download the table. (After downloading, your first step will be to click the multiplication symbol to clear the table.)

Other posts that may interest you:

You may also be interested in viewing and downloading The Green Light Hundreds Chart.

See the updated video: Is This Claim Always True? A powerful post to use in your classroom.

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The Animated Multiplication Table - Steve Wyborney's Blog: I'm on a Learning Mission.

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I made multiplication table using PowerPoint and went on to discover some very interesting relationships within the table. You will see several here. Click here to download the table. (After downloading, your first step will be to click the multiplication symbol to clear the table.) Other posts that may interest you: The Maze Hundreds Chart...

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Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

This post includes 50 (fifty!) free, downloadable PowerPoint math lessons!

Watch the video, download some (or all) of the lessons, and experience what happens when you unleash this resource in your classroom!

I've been excited to click the Publish button on this post for several weeks! It's time!
UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

Splat Through 10
How many dots are under the Splat?

Splat Through 20
How many dots are under the Splat?

Multiple Splats
(Note: Splats that are the same color must cover the same number.)
Splat 3.1 - multiple splats Splat 3.2 - multiple splats Splat 3.3 - multiple splats Splat 3.4 - multiple splats Splat 3.5 - multiple splats
Instant Multiple Splat
(Note: An additional feature of this level is the opportunity to ask, "What could the total be?")

Splat 4.1 - Instant Multiple Splats Splat 4.2 - Instant Multiple Splats Splat 4.3 - Instant Multiple Splats Splat 4.4 - Instant Multiple Splats Splat 4.5 - Instant Multiple Splats
2-Color Splat
(Splats of different colors must have different values.)

Splat 5.1 2-color Splat Splat 5.2 2-color Splat Splat 5.3 2-color Splat Splat 5.4 2-color Splat Splat 5.5 2-color Splat Splat 6.2 Instant 2-color Splat Splat 6.3 Instant 2-color Splat Splat 6.4 Instant 2-color Splat Splat 6.5 Instant 2-color Splat
Instant 2-Variable Splat
(Splats of different colors must have different values. Splats of the same color must have the same value.)
Splat 7.1 Instant 2-variable Splat Splat 7.2 Instant 2-variable Splat Splat 7.3 Instant 2-variable Splat Splat 7.4 Instant 2-variable Splat Splat 7.5 Instant 2-variable Splat
Number Splat
(Note: Only the numbers circled on the screen may be used.)
Splat 8.1 - Number Splat Splat 8.2 - Number Splat Splat 8.3 - Number Splat Splat 8.4 - Number Splat Splat 8.5 - Number Splat Splat 9.1 - Instant Number Splat Splat 9.2 - Instant Number Splat Splat 9.3 - Instant Number Splat Splat 9.4 - Instant Number Splat Splat 9.5 - Instant Number Splat
Instant Number Splat with 2 Variables
(Note: Only the numbers circled on the screen may be used, and Splats of different colors must have different values.)
Splat 10.1 - Instant 2-Variable Number Splat Splat 10.2 - Instant 2-Variable Number Splat Splat 10.3 - Instant 2-Variable Number Splat Splat 10.4 - Instant 2-Variable Number Splat Splat 10.5 - Instant 2-Variable Number Splat
NOTE: I wrote each of these lessons using PowerPoint, so I recommend playing them in PowerPoint. If you do not have PowerPoint, you may want to download the PowerPoint viewer so that you can play the lessons.

UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Other Posts and Resources Which May Be of Interest Tiled Area Questions The Maze Hundreds Chart
Introducing Cube Connectors
Provide Massive Space to Notice
Primary Tile Questions
3 Powerful Tile Strategies (and 40 new downloadable pages)
Please take a moment to subscribe to the blog so you'll be notified each time new resources are posted!

I would treasure hearing about your experiences using Splat! to promote number sense in your classroom!

All my best,
Steve

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Splat! - Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

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Savvy Subitizing Cards

These cards contain the numbers 1-10, but for each number it has a card that shows the numeral, finger pattern, ten frame, rekenrek, tally marks, and dot patterns. If you don't want to make your own, you can purchase a deck of the cards on my shop page.

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These cards contain the numbers 1-10, but for each number it has a card that shows the numeral, finger pattern, ten frame, rekenrek, tally marks, and dot patterns. If you don't want to make your own, you can purchase a deck of the cards on my shop page.

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

Which One Doesn't Belong?

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

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Teaching Tools | Resources for Teachers from Scholastic

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Four years ago, I shared Subitizing to Foster Multiplicative Thinking. Since then, I've really enjoyed hearing back from folks like you about how the cards are supporting your work. Along the way, I've received "a few" emails asking about for...

These Geometric Subitizing Cards have been in beta the past two years. I asked our buddy Joe Schwartz to take them for a test drive last spring and he reported back. Joe's all in. How do they work? Let's play... Last week I took them for another spin...

What's the purpose of flashcards? There's 2 answers I frequently hear and only one I agree with. Answer 1: help kids know/memorize their facts Answer 2: help students build fluency through the automatization of strategy I know how Tracy and many...

UPDATE 3/17/19: The updated cards can be found in this post (Multiplication Subitizing Cards: An Upgrade to Building Fluency) ---------- Learning basic facts through tricks or a mnemonic song lead students...

*** Slides: Full Day K-2 Addition & Subtraction Tasks: Graham Fletcher's 3-Act Tasks Websites Referenced Open Middle Estimation 180 - Andrew Stadel Which One Doesn't Belong? - Mary Bourassa Same Different Images Worthwhile Posts &...

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Search results for "subitizing cards" | Questioning My Metacognition

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Four years ago, I shared Subitizing to Foster Multiplicative Thinking. Since then, I've really enjoyed hearing back from folks like you about how the cards are supporting your work. Along the way, I've received "a few" emails asking about for... These Geometric Subitizing Cards have been in beta the past two years.

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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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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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

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51 Esti-Mysteries - Steve Wyborney's Blog: I'm on a Learning Mission.

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This activity can be a daily classroom ritual. The first few times it is important to reinforce for students the purpose of the activity. Over time, this will become unnecessary. Share the purpose with students and stress that analyzing the wrong answer is a great opportunity for learning and not about punishing students publicly for wrong answers.

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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With the implementation 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.

Gain knowledge of how kids learn math so that you can confidently close your textbook and do fun lessons that meet your students where they are.

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Build Math Minds | Learn to LOVE Teaching Math

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With the implementation 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. Gain knowledge of how kids learn math so that you can confidently close your textbook and do fun lessons that meet your students where they are.

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GeoGebra - the world's favorite, free math tools used by over 100 million students and teachers

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Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more

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Where’s Poly? An Exploration in Geo-Dotting

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Download the Resource What’s geo-dotting? I have no clue but that’s what I’m calling this lesson. We started by asking, “What do you notice?” Our favori…

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Your browser either doesn't support Javascript, or you've turned it off. To use Mentimeter, please make sure to turn Javascript on. How do I enable Javascript?

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We think that this is a very good time to wish for peace. Above is a picture of the wreath that I made for this winter's season. Do you know this symbol? Where did it originate? Do you ever use a different symbol for peace (for instance, sideways "V"s)?

In this activity students learn about the semaphore flag symbols and how this peace symbol was first designed. They design their own symbol and try to figure out how many possibilities there are in this kind of communication.

The activity: PeaceSymbol.pdf

How should I cook my turkey? - Students judge timing, cost, tastiness, and quantity necessary as they plan for the feast. 4.MD, 5.NBT, 4.MD, 6.RP, 6.NS, 7.NS + Great video on a deep frying fire with William Shatner.

Shopping season already! - Students will be able to add some understanding and analysis to holiday shopping trips after calculating savings in dollars and percents with this timely investigation. 6.RP, 7.EE, 7.EE

Not enough mashed potatoes - Use Brian's famous mashed potatoes recipe to practice changing decimals to fractions; calculating ingredient measure for various-sized Thanksgiving servings; have students explain their reasoning; and to have students figure out how many servings 7½ pounds of potatoes would make. 5.NF, 6.RP, 7.RP

Consumers in the U.S. spend a lot of money. In this activity we look at historical data to see if there are any patterns in our spending. How does our holiday spending show up in these graphs? What accounts for spikes or drops in spending? What patterns do you notice? Which patterns will likely continue and which patterns won't? Let the class see, think, wonder and discuss in this timely activity.

Soo Yeon is a Mathematics teacher at an international school in Asia and has be an avid user of YummyMath. Formerly she was a chemical engineer and shares our intent of providing practical, relatable, and real-world contexts in teaching mathematics.

She would like to share the following with YummyMath users:

"As you know Leslie and Brian's hard work and vision of exploring math in real life contexts has been instrumental in helping students develop critical thinking, questioning skills, and a positive attitude towards Mathematics. I wholeheartedly share their vision and am dedicated to upholding their mission. Moving forward, YummyMath will continue to evolve, enhancing content and user experiences to better meet your needs both now and in the future. I understand the challenges teachers and parents face in balancing engaging activities with time management. To address this, I kindly request your input through a survey ( ) to ensure that YummyMath effectively supports your needs.

Thanks so much for your support as YummyMath starts this new chapter. "

In this activity, students work through the nomenclature to understand the possibilities of nano science and quantum dots. Questions that are answered; How many nanometers are in a millimeter? What is a semiconductor? What and why does this nano technology increase our ability to closely examine, understand and modify our tools?

The activity: Quantum-dot.pdf

On Veterans Day we honor the men and women that have served in the Armed Forces of the United States. There are now 16.2 million living veterans. We found these maps that show where veterans live in the U.S.

What do you notice and what do you wonder when seeing these maps?

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We think that this is a very good time to wish for peace. Above is a picture of the wreath that I made for this winter's season. Do you know this symbol? Where did it originate? Do you ever use a different symbol for peace (for instance, sideways "V"s)?

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"I'm so glad I live in a world where there are Octobers." ( Anne of Green Gables, chapter 16). Living in the gorgeous mountains of east Tennessee, I can deeply resonate with Anne's sentiment. Fall is the most beautiful time of the year here, and I love everything about it. But one of the things I love most (and definitely the thing my kids love most) is pumpkins. The excitement of going to a farm and exploring, picking out the very best one. Discovering the variety in shapes, sizes and colors. It makes my heart happy. 🙂 So of course, you know I'm going to have an idea or two ( or ten) for learning math with pumpkins! So whatever the ages of your kids, you are bound to find some fun pumpkin math to explore in this list.
*Please Note: This post includes affiliate links which help support the work of this site. Read our full disclosure here.*
Pumpkin Math for Early Elementary:

MY LATEST VIDEOS

Work on counting to ten, addition and subtraction with this "Runaway pumpkins" printable board game.

Explore estimation, counting and skip counting as you determine how many seeds are in a pumpkin.

Increase fact fluency with these pumpkin number bond cut and paste pages.

Help your Kindergartner work on counting and number recognition with these pumpkin counting cards.

Or practice counting with these count and clip cards (includes numerals and number words)

Display numbers with these playdough ten frame counting mats.

Or make a pumpkin number line to work on a variety of skills.

Practice shape recognition with these adorable pumpkin shape matching cards.

Or if you prefer, try this set of pumpkin shape puzzles.

Practice early measurement skills with these pumpkin measuring tools.

Explore shapes and patterns with your own DIY pumpkin geoboard! This looks so fun!

Practice subitizing and counting to ten with this cute pumpkin freebie.

This set of pumpkin task cards will give your kids extra practice with subtraction word problems.

Work on addition with these cute pumpkin addition mats.

And this post includes two cute ten frame pumpkin activities.

Explore measurement and more with this simple, low prep pumpkin investigation.

Combine math and a light table with this cute activity.

Use these pumpkin mazes as a fun roll and cover counting game.

Create an interactive pumpkin number line for working on addition and subtraction.

Plus, check out this post of "cook and learn" ideas with pumpkins.

Have fun exploring all sorts of measurement with pumpkins.

Pumpkin Math for Upper Elementary/Middle:

Practice order of operations and mental math with these fun pumpkin puzzles.

Practice mental math, addition, subtraction, multiplication and more with this game kids are sure to love.

This "roll a pumpkin patch activity" looks like such a fun way to practice addition, subtraction and multiplication.

And this HUGE pumpkin-themed math pack covers math skills for kids ages 4-10.

This pumpkin unit study includes math, science, social studies, language arts and more! All related to pumpkins!

Practice all those multiplication facts with a free set of pumpkin multiplication matching cards for all facts from 2-10 ( free for subscribers-sign up here!)

Or create a pumpkin patch array for visual and hands-on multiplication practice.

Work on fractions with this fun combination of math and art with pumpkins.

Pumpkin Math for High School:

Explore linear equations with this three part lesson: How much does a pumpkin cost?

Practice order of operations with this cute set of pumpkin puzzles.

Or play this pumpkin smash order of operations game.

Practice graphing linear equations to make a fun jack-o-lantern.

Work on quadratic equations with this engaging pumpkin chunkin activity.

Hopefully this huge list has given you lots of ideas and resources for exploring all kinds of math concepts with pumpkins, large and small.

Do you have a fun pumpkin math idea that wasn't included? Share in the comments!

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Ultimate Collection of Pumpkin Math Ideas for K-12

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"I'm so glad I live in a world where there are Octobers." ( Anne of Green Gables, chapter 16). Living in the gorgeous mountains of east Tennessee, I can deeply resonate with Anne's sentiment. Fall is the most beautiful time of the year here, and I love everything about it.

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A guide to finding math work at every level of cognitive demand for elementary students, including problems that push their thinking.

©Shutterstock/Monkey Business Images

The internet can be a great resource for finding math tasks at every level of cognitive demand. While elementary students need exposure to tasks at all levels-lower as well as higher-an emphasis should be placed on those at the higher levels. That means we need the skills to evaluate what is and isn't cognitively demanding.

To determine the quality of online activities, my research partners and I used Margaret Schwan Smith and Mary Kay Stein's 1998 Task Analysis Guide (TAG), which consists of four distinct levels of cognitive demand: memorization, procedures without connections, procedures with connections, and doing mathematics.

With memorization, critical thinking isn't necessary, no connections are made to understanding why the answer works, and procedures are bypassed. This type of task can look like recalling facts. Procedures without connections are algorithmic; students come up with an answer without making connections to other math concepts and aren't required to explain their work. Problems that follow simple procedures, like requiring the U.S. standard algorithm for addition, fall under this category. Memorization and procedures without connections are low cognitive demand tasks because they don't require a lot of thinking.

Teachers often present visual diagrams or manipulatives like Unifix cubes or base 10 blocks to solve math tasks that are procedures with connections, which allow students to approach the problem from multiple angles. These problems use procedures, such as the partial product algorithm for multiplication, to help students understand why the answer works as opposed to only knowing how to find the answer.

The highest level problems, doing mathematics, require non-algorithmic thinking, demand self-monitoring, and allow for multiple strategies to be used-students at this point are exploring mathematical concepts.

Procedures with connections and doing mathematics are high cognitive demand tasks because students need to make connections, analyze information, and draw conclusions to solve them, according to Smith and Stein.

Math Tasks Need to Be Chosen Critically

In order to present elementary students with problems at every cognitive level, teachers must be critical consumers of the resources available. In our research, the following points helped my colleagues and me evaluate the cognitive demand and quality of online tasks.

Age matters. The level of cognitive demand can change depending on the age of the children a problem was created for. For example, completing a worksheet of basic one-digit addition problems would be coded as memorization for a fourth grader, who is expected to have them memorized (even more so if the student is being timed), but it would be considered doing procedures without connections for kindergarteners, who are just learning what it means to add two parts to make one whole.

If you're looking for high cognitive demand tasks, a resource that meets any of the following criteria can be considered a procedure with connections; to be classified as doing mathematics, there must be multiple ways to solve the task:

The problem usually involves manipulatives (e.g,. 10 frames, base 10 blocks, number lines, number grids).

There are directions calling for students to provide explanations of how they found the answer (through models, words, or both).

There is a high level of critical thinking required. For example, students decide how to tackle a problem that can be solved in more than one way, make real-world connections to the math, or explain their mathematical thinking.

When evaluating a math task, teachers should also evaluate any images that accompany it. Is an image included solely for decorative purposes, or does it have a functional role in solving the problem? Images with functional roles include clock faces, 10 frames, and graphs. If an activity has a decorative image, it is significantly more likely to be a low cognitive demand task; if it has a functional image, it is much more likely to be coded at a high level of cognitive demand. While an activity might be popular because of its decorative, cute images, visual appeal does not correlate with high levels of cognitive demand. It's important to focus on the content rather than the art.

Where to Find Cognitively Demanding Math Tasks

You have a notably higher chance of finding math activities at a high level of cognitive demand on websites where resources are reviewed before publication as opposed to sites like Teachers Pay Teachers or Pinterest where anyone can post. The following websites publish reviewed resources:

Illustrative Mathematics allows teachers to search for tasks based on content standards by domain or grade for K-12 (free).

EngageNY is a set of pre-K to grade 8 English language arts and mathematics curricula created by the New York State Department of Education. It also has math curricula for higher grades-Algebra I and II, Geometry, Precalculus, and above (free).

NRICH, run by the University of Cambridge in England, provides a library of resources and curriculum-mapping documents for students ages 3 to 18 (free).

youcubed, founded by Stanford University mathematics education professor Jo Boaler, provides high-quality math tasks that can be searched for by grade (K-12) or topic. Some tasks have been created by the researchers who run youcubed, while others are drawn from a variety of sites, including NRICH (free).

Illuminations is an online resource available through the National Council of Teachers of Mathematics (NCTM) that provides materials based on both NCTM standards and Common Core State Standards for grades pre-K to 12. Access requires an NCTM membership (cost: $49 to $139 a year).

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A guide to finding math work at every level of cognitive demand for elementary students, including problems that push their thinking. ©Shutterstock/Monkey Business Images The internet can be a great resource for finding math tasks at every level of cognitive demand.

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The great people at Brilliant.org contacted me about this post and connected me to the great new puzzles they create every summer in the UPDATE AUGUST 2019: 100 Day Challenge and also to l ink to printouts. Such great stuff. Check out the links in the sentence before! Thanks Brilliant! ( and follow them on twitter!)

Last school year I had a student who at least once a week announced LOUDLY (and at times with swearing) that they hated math. HATED IT! The student would frequently shut down (head down, headphones on) or threaten to walk out. Multiple times a week I was working to convince this student that they were a mathematician, that they could do anything we were doing in class. Honestly, it felt like I was a therapist with this student all year. I knew something for sure that this student knew in their innermost secret place - that they were totally a mathematician and despite all the bluster (more than almost any student in my 25 year career) this student loved solving problems and loved math. This student was one of my favorite students last year. I love the challenge of changing the pathways in students brains that cause them to react out of frustration.

Last year this student claimed to hate me. This year this student seeks me out when they are frustrated. (Don't you love how much your students love you once you are not their current teacher!) Several weeks ago this student skipped their math class (out of frustration) can came to the math center where I was working. I was not on my game that day and did not realize they were skipping until the end of the hour. After talking through their frustration about not being able to do math, I told the student to chill out for the remaining 10 minutes so I could work with another student. 2 minutes later this is what I saw the student doing on their phone.

The student was solving a math puzzle I had posted in the hallway several days prior. This student had no idea I had posted it. This student claims to hate math, yet they took time out of their passing time to snap a picture of the puzzle so they could solve it later. When I saw this I shouted, "HA! I caught you. You do like math. Look, I told you to just chill and you are choosing to do math." This student smiled at me and just nodded in agreement. Yes! I love days like this.

AN EXPERIMENT

Sometime at the beginning of February I decided to do a little experiment. My gut told me that all of us love solving problems. I wanted to see what would happen if I posted a math problem in the hallway. Would anyone stop and try and solve it?

Since returning to the classroom 4 years ago I've become much more of a minimalist in my classroom. If I am not referencing the things on the was regularly and/or no one is regularly looking at the things on my wall, then I don't put it up there. I have removed a bunch of 'visual noise' that use to clutter my walls. If I was going to put something in the hallway, then I wanted people to look at it. The walls of my school are littered with tons of announcements I am not sure anyone ever looks at. I did not want this to be one of those things.

So I started with 2 basic rules for posting math puzzles in the hallway of my school.

Whatever I placed in the hallway needed to be something that could be solved fairly quickly. Our passing time at our school is 4 minutes. I wanted it to be possible that at least a few students could solve the problem in 4 minutes or less. I was totally OK knowing that it may take many others much more time. I wanted problems that invited all learners in.

I also wanted to post puzzles that did not require the students to do much writing.

Following those 2 rules I posted this puzzle - in color - on an 8.5×11 inch sheet of paper. Someone I know posted this problem on Facebook - I think it may be from the Brilliant app -though I'm not sure. I did NOT include my name. There were no prizes announced. I have never told my classes about this. I just posted it mid-day on a Tuesday.

Then I watched. Nothing happened. At least, I did not see many people looking at it. I was a bit disappointed.

The next morning, I added this sign to the top of the problem.

Things changed immediately. Every time I looked in the hall I saw single students or groups of students or even staff stopping and looking at the problem. I saw students pointing and explaining. At times I watch as students argued over the problem. I heard students excitedly calling over other students so they could explain the solution. They had no idea I was watching. They were solving the problem out of the pure joy of solving things. Lesson learned. If you are going to post a puzzle - make sure you challenge others to solve it.

This slideshow requires JavaScript.

Then this happened.

Student's insisted on writing down the solution. So I laminated the 'Can you solve this puzzle?' sign. This stopped the writing.

Other teachers would excitedly tell me they caught students in their math classes who do not do well looking at the puzzle.

A couple of weeks later I changed the puzzle. This time I used a puzzle I use in math class with my students.

Most people who solve this problem the first time (including a lot of math teachers) shout out '16', When students are solving it I tell them after a minute that the answer is NOT 16. They groan (I've just ruined what they thought for sure was the answer) and keep working on it. I use this problem in class to have a discussion about the importance of watching the details in the problem. My student teacher can be often heard in class reminding students to 'watch for bananas and coconuts' as they solve other problems. When I posted this problem in the hallway I decided to add a post-it note to the puzzle.

Then this happened.

So I replaced the post-it note with a Desmos post-it note.

Not even the power of Desmos could stop people from writing down the correct answer. So I begged for them not to share the answer in my next post-it note.

That did not work either - people kept writing down correct & incorrect (15) solutions on the post-it note. . Finally I laminated the statement. Problem solved.

Almost everyday I catch people looking at, talking about the problems I post. They do it more when they think no teachers are around. I knew it. At some level we all love doing math. The structure of the classroom can take some of that joy away - even with the best teachers.

So what are my next steps?

I want to continue to look for ways for math to be fun for students. What can I do in my classroom and school so students engage in math out of their free will. I do have one other way that I am doing this in my classroom (PLAY TABLE) that I will blog about soon.

I want to frequently (more frequently than I currently take the time to do) change these problems out. To do this I plan to collect 30-60 good problems, print them out & laminate them so I always have a puzzle ready to go. Here are some potential problems I may use, including the 2 pictured above. (Word Doc: Math Problems for hallway fun ) I would love it if you send other problems my way. Tweet me @Saravdwerf or email me at [email protected] Remember, I want problems that can be solved relatively quickly & not require students to write much down.

I want to continue to use classroom tasks that build off of students curiosity.

I want to continue to watch students and observe when they engage in math naturally. My students have the answers to my questions. I just need to be open to watching for them. What I've noticed so far is that students of all achievement levels are trying to solve these problems.

I want to remember that despite what students are telling me - I never know what they are doing when I am not looking. Even my most challenging students may be out there somewhere right now solving a math problem I gave them on their phone.

As always, I love hearing from you! Let me know what you think. What have you done to encourage students to engage in mathematics outside of the things you do in class?

p.s. After posting this blog, I was reminded that the inkling to do this started last summer during Twitter Math Camp when I introduced Dave Sabol to Jucy Lucy's at an iconic Minneapolis Restaurant. During our lunch he was telling me about posters he had used the prior year in the hallway's of his school. He was looking for a new idea and somehow the idea of ' Which One Doesn't Belong' problems came up. I had wanted to do something similar for a while, but he made it happen at his school right at the start of the school year. Check out Dave's resources at his blog for WODB posters from his school.

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Even if they say they don't like doing math, they secretly do. An Experiment you should try. - Sara VanDerWerf

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The great people at Brilliant.org contacted me about this post and connected me to the great new puzzles they create every summer in the UPDATE AUGUST 2019: 100 Day Challenge and also to l ink to printouts. Such great stuff. Check out the links in the sentence before! Thanks Brilliant!

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The mathies Standalone Player has not yet loaded.

Please check if:

Javascript is enabled

the Flash Player plugin is installed

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your Flash Global Security Settings trust this location

other flash based sites, like Gizmos, work

refreshing the page fixes things

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your system administrator is placing restrictions on Flash content

you can open the .swf directly in the browser

If it still will not load, please use a machine/environment where it does and use the Feedback link to share with us any helpful information about the issue including the browser, operating system, school board etc.

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Please check if: Javascript is enabled the Flash Player plugin is installed active content is allowed your Flash Global Security Settings trust this location other flash based sites, like Gizmos, work refreshing the page fixes things clearing your cache fixes thing restarting your browser fixes things your system administrator is placing restrictions on Flash content you can open the .swf directly in the browser If it still will not load, please use a machine/environment where it does and use the Feedback link to share with us any helpful information about the issue including the browser, operating system, school board etc.

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Play Broken Calculator. Sam's calculator got smashed, but some of it still works.
Can you help Sam get the answers?

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Welcome to our Free Math Puzzles for 4th graders.

Here you will find our range of 4th Grade Math Brain Teasers and Puzzles which will help your child apply and practice their Math skills to solve a range of challenges and number problems.

Math Puzzles

Using puzzles is a great way to learn Math facts and develop mental calculation and thinking skills in a fun and easy way.

Most children are much more engaged and motivated solving puzzles than working out pages of traditional math facts.

Using these math puzzles below will help your child to develop their Math fact skills as well as their strategic thinking and reasoning.

There are different versions of each puzzle from 1st to 5th grade, so it is easy to find an easier or harder version of the same puzzle.

Each puzzle comes complete with answers.

Free Math Puzzles

4th Grade Math Challenges and Puzzles

Here you will find a range of challenges and puzzles to develop your child's math skills and number facts in a fun way.

These puzzles have been designed to support the 4th grade skills of adding, subtracting, multiplying and dividing.

Using these sheets will help your child to:

learn and practice their addition facts, including adding negative numbers;

practice their subtraction facts;

practice and apply multiplication and division facts;

develop problem solving skills and reasoning.

4th Grade Free Math Puzzles

Salamander Line-Up

Captain's Square Puzzle

Newton's Crosses Puzzle

Quadra's Square Puzzle

Magic Square Puzzle

Sally's Hexagon Puzzle

Arithmogon Triangle Puzzle

Newton's Number Track Puzzle

Quadra's Operation Puzzle

Tree Adding Puzzle

Make 100 Puzzle

Number Grid Challenge: Target 100 Puzzle

The aim of this grid puzzle is for you to find a path through the grid with a total of 100. Choose your path carefully!

The maze involves adding a series of 6 to 7 numbers (with values up to 26) together to try to get a total of 100.

Number Maze Target 64 Puzzle

Total Difference Puzzles

These puzzles are designed to test your thinking skills, as well as you addition and subtraction!

There are a set of 3 puzzles, of varying difficulty, with the easiest one coming first.

On some puzzles, the two numbers are given, and the total and difference need to be calculated.

On the harder puzzles, only one of the numbers and the total is given, and the other number and difference need to be calculated.

The hardest puzzles involve working out the two numbers, given only their total and difference.

Total Product Puzzles

These puzzles are designed to test your thinking skills, as well as you addition and multiplication!

There are a set of 3 puzzles, of varying difficulty, with the easiest one coming first.

On some puzzles, the two numbers are given, and the total and product need to be calculated.

On the harder puzzles, only one of the numbers and the total (or product) is given, and the other number and product (or total) need to be calculated.

The hardest puzzles involve working out the two numbers, given only their total and product.

Looking for an easier puzzle...?

If these free Math Puzzles are not at the right level for you, try some of our easier 3rd grade math puzzles.

Looking for a harder puzzle...?

If these free Math Puzzles are not at the right level for you, try some of our harder 3rd grade math puzzles.

Number Fill in Puzzles

It's great when kids have fun and are learning math skills without really thinking about it. These number fill in puzzles are a great way to develop thinking skills and getting kids to check all the possibilities.

Number Search Puzzles

Number Search Puzzles are a great way to get children looking for numbers and developing number recognition skills.

They are also a good resource for developing short term number memory skills, and can be a good way to take the fear out of large numbers.

We have a range of different number search puzzles - from easier puzzles to trickier ones to work out.

With the easier puzzles, the numbers only go horizontally (left to right) or vertically downwards.

The numbers get progressively larger on the trickier puzzles, and the grids get larger.

Math Games 4th Grade

Using games is a great way to learn Math facts and develop mental calculation skills in a fun and easy way.

The following games involve different 4th Grade Math activities which your child will enjoy playing.

Games include using negative numbers, decimal addition and subtraction, rounding, multiplying by 10s.

Fourth Grade Math Word Problems

Here is our set of 4th grade math word problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Using these sheets will help your child to:

apply their addition, subtraction and problem solving skills;

apply their knowledge of rounding and place value;

solve a range of 'real life' problems;

attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

Math Riddles

Here is our collection of free math riddles from 1st grade to 5th grade.

You will find a range of number riddles which will help your child to develop their place value skills, as well as developing their problem solving and reasoning.

The riddles are also useful for developing understanding of mathematical language.

How to Print or Save these sheets

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Follow these 3 easy steps to get your worksheets printed out perfectly!

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

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Welcome to our Free Math Puzzles for 4th graders. Here you will find our range of 4th Grade Math Brain Teasers and Puzzles which will help your child apply and practice their Math skills to solve a range of challenges and number problems. Using puzzles is a great way to learn Math facts and develop mental calculation and thinking skills in a fun and easy way.

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Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs.

With support from the Albert I. Pierce Foundation, our fractivities are aligned with common core standards in mathematics and English language arts so you can more easily incorporate teaching fractals in your classroom, combining science, math and art!

You can use our curriculum for free or can hire us to come to your school to lead fun, hands-on activities. Check out our education and outreach page!

Need help in choosing a fractivity?

This summary page shows what grades each activity is appropriate for and what common core math standards they meet.

This page includes the associated English language arts standards met by the activities.

We are sharing these fractivities with teachers for free and request that you provide feedback to us so we can continue to refine and improve our curriculum. Thank you, and have fun!

See what people are saying about us on our feedback page!

These Fractivities were developed with the generous support of the Math & Science Bureau of the NM Public Education Department, Albuquerque Community Foundation and the AI Pierce Foundation.

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Fractivities are hands-on projects that teach fractal concepts in a fun, artistic way. Students utilize their math skills in real-world applications and also work together as a team to create large fractal designs. With support from the Albert I.

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Art, Proportion and Reasoning

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Welcome to Scale City, the biggest, smallest road trip ever! Created for grades 6-8, but fun for everyone! Explore amazing roadside attractions and learn about the mathematics of scale. At each stop, a short video field trip and a fun interactive simulation help you understand proportional reasoning.

If you'd like to explore Scale City's locations by beginning with simpler math concepts and moving on to more complex ones, the suggested order is Dinosaur World, Louisville Slugger Museum, Mural Painting, Miniature Land, World Chicken Festival, Sky-Vue Drive-In, Belle of Louisville, and Kentucky Horse Park. Each video and interactive also can be enjoyed individually. It's up to you!

Visit the Scale City Teacher's Diner for resources designed to help you use Scale City in your classroom. All the lesson plans are aligned with Kentucky state education standards, which are based on national standards.
Scale City's interactives require Adobe Flash Player 10.0.12.36 or higher and will not work on devices that do not support Flash. Visit PBS LearningMedia Resource

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Welcome to Scale City, the biggest, smallest road trip ever! Created for grades 6-8, but fun for everyone! Explore amazing roadside attractions and learn about the mathematics of scale. At each stop, a short video field trip and a fun interactive simulation help you understand proportional reasoning.

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Use a visual tool for adding and subtracting fractions with: 1) like denominators (screens 2-9) 2) unlike denominators (screens 10-13)

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"These kids hate math." As I was working with a struggling teacher this past week, this jarring phrase came out. It is this type of comment that made last Tuesday a two-shower day: I always take one in the morning and then, every so often, I need a second to get rid of the (emotional as well as physical) filth.

In a follow-up conversation, I learned that this particular teacher was having difficulty moving from a sage-on-the-stage mentality (where teachers focus primarily on lecturing and imparting knowledge) to a facilitator of learning. It is this facilitation that not only motivates but also helps all students master challenging standards.

Although I knew that, in the short time I had to work with this educator, I would not be able to solve all of the mathematical woes with which she was struggling, I did know that she was capable and that she could use APPS to help design, develop, and assess learning experiences to redefine her classroom to become a student-centered one focused on the expectations of the Standards.

Before I shared some of my favorite APPS with her, I explained to her that it wasn't enough for me to just teach her these: she had to learn to fish as well so that she could find her own resources in the future. As we worked together, I shared with her my version of the acronym APPS for technology integration within the classroom: how will an application help students Acquire meaningful content standards; how will an application help students Progress through meaningful feedback; how will an application measure Proficiency of student learning, and how will an application S upport the student in learning content.

Using APPS, the five digital tools that I shared with her and will outline below, can redefine a classroom as they can be used to facilitate higher order learning activities that encourage self-directed learning and ongoing assessment. Although this post is tied to math, many of these tools are applicable for usage in all kinds of different content areas. Whether you are tech-savvy or not, all of these free tools are simple to use and require limited know-how. Just in case you want some additional guidance, however, you can find instructions in both written and video form for each of these tech resources at the following link: https://goo.gl/UVv3Ta.

EDpuzzle is a great tool that allows you to help students process content through video. Simply find a Youtube video on a topic of your choice; copy and paste the link into the system, and then embed questions on the video that students answer. The teacher receives responses and then knows where to plan activities to help students improve their mathematical understandings. Students can complete the video task independently or it can be done simultaneously as a whole class.

Here's one activity you can try with EDpuzzle: Give students a link to an EDpuzzle you have created and have them complete the video activity for homework. Then, in class the next day, create several areas where students can work based on the data you have received. One area might be teacher-based direct instruction for students who are really struggling with the concept; another area might an opportunity to work collaboratively with peers on challenging problems, and a third area might require students to create problems that show depth of understanding. Want to increase the caliber a bit with this tool? You could even have students create an EDpuzzle to share with their peers. This not only ensures creativity, but also gives you a great formative assessment: the questions that students embed into the activity really help reinforce their understanding of various topics and help you, as a classroom teacher, figure out what they understand and don't.

I shared the Recap tool in my language arts post, but had to re-share it here as it is equally powerful here, as well. With Recap, teachers provide students with a task and then students record a video response. The teacher receives responses and can provide feedback to students on their video as well as share exemplar videos with students in the class. By using this tool, you can really help students talk about their mathematical understanding.

Here's one activity you can do with this tool: give students various problems and have them record a video explaining how to solve the problem while using diagrams or other manipulatives to show how they solved the problem. Share the responses out with the class. Have students review them to critique the reasoning of other students as well as determine the most precise ways of solving the problems.

ActivePrompt is a website that looks like it came from the late 1990s. However, its simplicity and its versatility make it a must-use in the math classroom. Load an image, either a screenshot or one you've created, into the system. Give students the link and poll them to see where their thinking is. If, for example, you want students to predict where the y-intercept is on a graph, you could upload an image of the graph, have them drag their dots, and then display the information. You'll know very quickly who understands and who does not.

No math tech discussion would be complete without mentioning this tool. GeoGebra is an application that helps students understand math concepts by solving problems and checking solutions. (It can be web-based or app-based.) You can use it for everything from statistics to algebra. It creates a visual representation for just about anything you can think of. Use it as a dynamic worksheet where students can complete their own investigation, as a modeling tool to aid in direct instruction, or even as an authoring tool to create interactive materials for students to explore.

Quizlet is a study tool system designed to practice vocabulary, but it can also be used to help students practice fluency. Released in April of 2016, the new Quizlet Live upped the ante and has students compete against other teams to show their knowledge of terms. While it can be used to develop students' math vocabulary, teachers can also load problems into the system and have students compete to solve them. (This is a great interactive way to help students work on mathematical fluency at the elementary grades.)

Here's how it works: you'll first creates a new Quizlet deck-in one column, type the problem and then, in the second, place the answer. Click Quizlet Live when you are ready to play and give students the game PIN. Students will be placed on random teams: everybody gets the same question, but amongst the team there is only one correct answer. The team has to communicate in order to solve the problems appropriately without making a mistake, or be forced to go back to Start on the game board. Great for fluency as well as determining what types of problems students are struggling with as at the end of the game, Quizlet Live allows you to see commonly confused items that you can then review as a class.

These APPS really take learning to the next level-they transform classrooms into student-centered ones where all students can experience success. Remember my struggling math teacher from the beginning of this post? Three days after working with her, I received the following e-mail: "Dear Bryan, It worked. They got the math, and they thought it was fun."

Through the use of APPS, I know that you, like this teacher, will be able to motivate your students and create that student-centered classroom that is key to all students mastering standards.

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Five APPS to Redefine your Math Class - Achieve the Core Aligned Materials

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"These kids hate math." As I was working with a struggling teacher this past week, this jarring phrase came out. It is this type of comment that made last Tuesday a two-shower day: I always take one in the morning and then, every so often, I need a second to get rid of the (emotional ...

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The desmos.com graphing calculator and its amazing teacher resources at http://teacher.desmos.com are a favorite tool of many in the MTBoS. Activities made by teachers in the site are searchable on Desmos itself to some extent, but not fully. For now, the directory of desmos activities below is still one of the best ways to search for Desmos activities that fit your needs. If you make a polygraph, activity, or other amazing desmos tool, please use this form to add it to the bank!

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The desmos.com graphing calculator and its amazing teacher resources at http://teacher.desmos.com are a favorite tool of many in the MTBoS. Activities made by teachers in the site are searchable on Desmos itself to some extent, but not fully. For now, the directory of desmos activities below is still one of the best ways to search for Desmos activities that fit your needs.

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This is one of my favorite math tricks that can really help your students as they try to understand how to work with equivalent fractions. I learned it at a workshop a couple years ago and have yet to meet a teacher who previously used or was aware of how simple this chart is to help students.

UPDATE: 4/3/2016 This has always been one of my most popular posts on this blog. For years, I have been teaching this using a self-created tool that I call the "Fraction Tracker" with my students. I always thought it would be something great for an iPad, but I don't have those creativity and coding skills. I finally decided to put my "Fraction Tracker" tool up on Teacher Pay Teachers. I included simple directions with photographs on how to use it. If you are interested you can find it here.

Many simple equivalent fractions (most of the ones used in upper elementary years) are easy to find on a regular multiplication chart. I feel it is very helpful to point this out to your students. Many students struggle as they try to learn the many steps that it takes to find equivalent fractions. When you look left to right on the chart you are viewing the multiples of a number. When you view two different rows of multiplies you are viewing equivalent fractions.

For example using the 1's and 2's. Look at the two rows as if they were fractions.
1/2 = 2/4 = 3/6 = 4/8 and so on. You can split rows apart. Look at the rows for 1's and 3's. 1/3 = 2/6 = 3/9 = 4/12 and so on. To show how the chart works with my class I use an overhead projector and circle the numbers to make them easy to locate. To find 1/5 = ? / 30 I circle the 1 and the 5 underneath it on the ones column on the chart. Then I move my finger from the 5 until I get to the number 30 and circle that. I can block out or just cross out other numbers to make it clearer. Then I follow the 1 across and the 30 up until they meet at the number 6. and circle that. If you do it correctly the circles will form a square or rectangle.

Of course, as the students understand how to work the chart, teach them the other ways of finding equivalent fractions. It makes it much easier for them, however, to "see" the equivalent fractions for a number and the students even start memorizing the most common equivalent fractions.

Now for the most important part. When students take a test they usually cannot use a printed multiplication chart. So what! Train them on how to make a multiplication chart from their facts and have them practice often. Then at test time, they can reproduce the chart onto their test before starting the work. It should take less than 5 minutes. Not only can they use the chart for checking fraction, but they can use it as they do multiplication and division problems too! No it is not cheating. It is about being smart, observant, and prepared!

Do play around with the chart on your own. I didn't believe it would work that simply until I practiced with it and used it with my class. There are some other tips and techniques that you can quickly figure out on your own that even make using the chart easier.

Here is a blank multiplication chart template.

It comes from this site which has a bunch of interesting math templates.

If your students have a hard time memorizing their multiplication facts then this book Memorize in Minutes: The Times Tables shows an easy and unique way to help them out.

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Using a Multiplication Chart to find Equivalent Fractions

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This is one of my favorite math tricks that can really help your students as they try to understand how to work with equivalent fractions. I learned it at a workshop a couple years ago and have yet to meet a teacher who previously used or was aware of how simple this chart is to help students.