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Counting, Composing, and Changing Numbers

A goal of our mathematics instruction should be to help our students develop flexibility with numbers. For that to happen, children need to experience the meaning of numbers with concrete, hands-on experiences. Three keys to developing flexibility are counting, composing, and changing numbers. The activities I’m sharing today are simple to prep and use materials you probably already have. I always recommend introducing activities such as these during small group instruction before moving them to a workstation.

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Students in Kindergarten may come to you able to recite numbers. There is a difference, however, between counting and reciting numbers. Children need lots of opportunities to connect quantities with numerals. These counting cards (download here) have dots representing each number. Using teddy bear counters or linking cubes to have students count out the number shown on the card reinforces one-to-one correspondence. After the student has counted out the corresponding number of counters, be sure to ask them how many? It is an important developmental step to be able to name the number counted. I like to use just one color of counters for this task so students are not distracted by the color. We’ll get to two colors in just a bit.


Learning that numbers can be composed in more than one way sets the stage for both flexibility with numbers and automaticity with basic number facts. Knowing that 5 can be composed of 1 and 4, 2 and 3, or even 5 and 0 really is the basis for understanding the relationship between addition and subtraction. By the end of Kindergarten, children should know all the combinations for the numbers up to ten. It’s important for children to work on their own target number. For example, one student might be working on the combinations for 5 while another is working on the combinations for 7. For more information about that, check out this post.

For this task, I’ll describe two options: using the counting cards and teddy bear counters from the last task or using ten-frames and two-color counters. Switch up the two options, so students see multiple representations. To use the cards and teddy bear counters, place two different colors of teddy bears in a bag. The child should not be able to see through the bag, so I use a lunch bag. Have the student draw their target number of counters out of the bag without looking. The total will be their target number, but the two different colors show a way the number can be composed. For example, 2 and 4 make 6. They keep repeating this process, using the same target number, to find different combinations. It’s important for students to verbalize their combinations (e.g., 2 and 4 make 6) and they can also write them down for accountability.

When using ten-frames, I like these two-sided paddles and magnetic counters, but you can download printable ten-frames here. For a great partner activity, have two students who are working on the same target number share a ten frame. One partner uses the red side of the counters and the other partner uses the yellow side. The red partner puts out a number of counters. The yellow partner adds counters to make the target number. Both partners verbalize the combination. In the picture below, you see 4 and 2 make 6. Partners repeat this process to explore different combinations of the target number.


Finally, we get to changing numbers. This is the understanding that we either add to or take away from one number to make another number and knowing how much to add or take away. Either the number cards or ten-frames are great tools for this activity. During small group instruction, you can control the numbers. So, for example, ask students to show 6. Then say a new number, such as 4, and ask students if they would need to add to their number or take away from it. After they respond, have them change their number to the new number. Continue this same process with additional numbers. Now if we changed the number to 8, would we add or take away. Okay, change your number to 8. With each new direction, they are changing the last number showing on their board so, from 6, they would take off two to make 4. Then they need to add 4 to make 8 and so on. As students gain confidence with this process, question them on how many they added or took away. You might also ask them to predict upfront: If we have 4 and want to make 8 would we add or take away? How many would we add?

To use in a workstation, simply provide number cards from 0 to 10. Players start by turning over one card and making the number. As they turn over additional cards, they change their number to the new number.

While these types of activities are designed for Kindergarten, it is helpful to assess 1st and 2nd-grade students on these concepts as well. If students in 1st or 2nd grade are struggling with their basic addition facts, activities like these will help fill in those gaps.

I’d love to hear your comments and additional suggestions for developing flexibility with numbers. If you found this post useful, I hope you’ll share it using the social share buttons at the very bottom of the post!

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  1. I LOVE your blog – it is my first go to place when teaching new math concepts! I started reinforcing how to compose numbers using the game Heads Up Seven Up with my class. Seven becomes the number we are making. I ask the kids to tell me how many kids to start with (anywhere from 0 to 7). They become my first group of choosers. Then we talk about how many more we need to get to seven. They are the second group. I have seven choosers each round, but as we are composing I just have them stand in two separate spots. The kids quickly see a way to make seven, and then we play the round. For the next round I ask them a different way to make seven. I usually write the ways they come up with on the board as we go, so we can fill in any we missed after playing for a few rounds. And sometimes we play with 6, 8 or 9 choosers just to vary the numbers we are working with. The whole process adds very little time to the game, but it is a super engaging way for them to practice this skill!

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