### Decomposed Dad

This was found on Twitter with the question: if you have 17 goats and 8 leave how many are left? 17-8=9 but my son was told 17-7-1 is the equation. Why?

Dear Decomposed Dad,

Thank you for your question. This activity is designed to help students learn and practice decomposing numbers to subtract numbers within 20. As to your question, there are two main ways someone could know 17-8 is 9 they could: 1) have it dutifully memorized, 2) actually be decomposing the numbers in their head so fast they don’t realize it. The activity helps with the latter way of knowing. Our new Common Core math standards downplay straight memorization of facts in favor of having the skills to figure it out and then memorizing for convenience sake. This takes mathematics out of its current role in many student’s (and parent’s) eyes as “a list of disparate things they have to memorize” and toward “a logical sequence of connected ideas.”

For this problem, at this grade level, students are showing fluency with numbers by decomposing. In the first example they take the 13-5 and decompose it into an expression leading to ten, i.e. 13 – 5 = 13 – 3 – 2 = 10 – 2 = 8. The ten frames above the problem are showing the student what to do. First make a ten, then take the rest from ten. This builds on their work in kindergarten breaking numbers within 10 apart and putting them back together again and builds towards their understanding of place value.

To answer your question, the expressions are mathematically equivalent:

17 – 8 = 17 – 7 – 1 = 9

The reason the 17 – 7 – 1 is the answer for this question is because 17 – 7 makes a ten and then 10 – 1 is 9.

I hope this helps you regain your composure,

Jim Town – Mathematics Specialist at ACOE Core Learning

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