## Reflection: Diverse Entry Points Understanding Subtraction - Section 3: Independent Practice

As I spoke to students about the ways they were solving the subtraction problems they had in front of them, I could see the differences in understanding of what subtraction is. Students who understood that subtraction would yield a smaller number than the quantity they started with, were able to show a way to start with that larger number and compare it to a smaller number to find the difference, or to count back by tens and ones, or even by ones to get to their answer.

Students who still struggle with the concept of subtraction didn't seem to realize the solution wasn't correct when they ended up with a quantity bigger than they had started with, even though the problem asked how many were left.

One child read the problem that there were 14 birds in a tree and 6 flew away, how many are left in the tree and she said 20. When I asked her how she got the answer she said she used her number grid. I asked her to show me what she did. She started at 14 and counted up 6 to get to 20. I asked her if we could draw a picture to check her answer. She drew the tree with 14 tally mark birds. She crossed out 6 and counted what was left and told me 8. I asked her why the 2 answers might be different, i.e. her 20 and her 8 and she said, I counted on the number grid and then with tally marks so my answer is different.

Here is a lack of understanding about what is actually happening when we add or subtract. This is a misunderstanding that needs to be addressed now as a foundational skill, before trying to move on to more complex numbers.

(I don't doubt that if I had given her the two problems in number form 14 + 6 = and 14 - 6 = that she would have been able to get the right answer, but that is rote learning and not understanding what she is trying to do.)

This child showed that she did not clearly understand the number grid and its directionality for adding and subtracting. Next time she could use counters on the grid. If she put on the 14 and then took away the 6 that flew away, she would see where her original answer was incorrect.  She could also use a double ten frames for addition / subtraction as a way to check her work. I also encourage students to draw the pictures because this often shows them visually what has happened.

Diverse Entry Points: Differences in Student Thinking

# Understanding Subtraction

Unit 2: Adding and Subtracting the Basics
Lesson 14 of 18

## Big Idea: Understanding subtraction is as key to Common Core Standards as is understanding addition and it is usually much harder for students to grasp.

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50 minutes

### Beth McKenna

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