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Composing and Decomposing Numbers

One of the reasons I love teaching math is that it is so much different now than when I was in elementary school (Google paleolithic age for a frame of reference). Take composing and decomposing numbers. I don’t remember ever “playing” with numbers. I learned to count, I learned to write my numbers, I learned addition and subtraction facts, but I don’t remember ever learning that there are lots of ways to make 5, or any number for that matter.

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John Van de Walle devotes pages to explaining the importance of composing and decomposing numbers, and parts and wholes (also called part-part-whole) are foundational to Singapore Math.

Under a Rock is my take on an activity that is commonly used in classrooms to explore parts and wholes. In this activity, the child knows the whole and one of the parts. It is their task to determine the missing part. Do you hear the algebraic thinking going on there? Students will work with a partner, and each pair of students needs counters and a plastic cup (can’t be transparent). Students choose, or are given, a target number. They count out that many counters and the number is recorded as the whole. Player 1 covers their eyes, while Player 2 puts some of the counters “under the rock” (the plastic cup). Player 1 opens their eyes and tries to determine how many counters are under the rock. The cup is lifted to check Player 1’s answer, and the two parts are listed on the recording sheet. The partners repeat the process with another combination for the target number. Oh, did I mention that this is concrete learning, so there’s that CRA sequence of instruction again!

Click here to grab your freebie! I hope you enjoy this activity!

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  1. I’ve played this game with my kindergarten kids before, but never had a name for it. Now I do! (And a cute recording sheet to go along) Thanks!

  2. Just found your blog via pinterest! I needed to find a good math blog. Thanks for all you do!! New Texas follower!

  3. As a Math Recovery Teacher, this is fantastic! We play this game too, but never had a name for it either! I love the recording sheet. I will be using this in my classroom!

  4. Donna-
    I just want you to know that you are an answer to prayer tonight! I needed new ideas and a math mentor to give me some fresh ideas and understanding in home-educating my kindergarten-and-preschool-age mathematicians, and I am so excited to have found your site. Thank you for what you are doing!

  5. I’ve got 5 year old grandson and this is what he’s been doing the last couple of months at school. I’m going to be tutoring my 12 year old great niece and she said she doesn’t understand numbers, so this looks like a good blog for me to follow. I just need to figure out how to do it via Skype!

  6. We play a game like this called “Penny Plate” to help students understand addition & subtraction to 20. They just love it, and they all think they’re doing “math magic” because they’re figuring out how many pennies are hiding under the plate…and they’re almost always right:)

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