# Teaching Addition and Subtraction, Part Two

I remember my first experience in a Mathematics Methods Course of a Part/Part Whole Mat. I really liked how the mat could be used for both addition and subtraction. This was the beginning of my pedagogical understanding of composing and decomposing as an addition and subtraction situation. I have already written a series of posts about decomposing numbers, so today I will give you a few ideas and explain why composing and decomposing is important.

I will never forget sitting with some teachers who were discouraged by the new common core standard K.OA.5, “Fluently add and subtract within 5.” The teachers initially interpreted that as having to do flash cards with their students. Flash cards don’t help us create thinkers.

Do not fear! Composing and decomposing can help students fluently know math facts and be done visually through a variety of activities:

Five Frame                                            Ten Frame

Dot Cards                                              Unifix Cubes

Base Ten Blocks                                     String of Beads

In Mathematics Learning in Early Childhood, the authors describe decomposing and composing as put together/take apart situations. This requires the students to think of a total in relationship to the two addends. Definitely a challenge for some students! In the last situation, Change Plus/Change Minus, students rely on their counting strategies to supply them with the result. Now they have to see a quantity as the total and the two parts.

One way to help students make a natural connection is to take a stack of six unifix cubes and break them apart somewhere. Write the total number of cubes and then under the total write the expression, or if your students are not ready for the symbols, use the part/part whole mat. Here is an example you can download.

Take apart is different then take away. When you take something apart, each part is still there and can be talked about. “Students need to make sense of the procedures for themselves. They need to describe and explain what they are doing in natural and then mathematical language.” (Clements & Sarama 2009)

Let’s work together to build a foundation that promotes thinking and making sense of mathematics! The foundation the students have will either empower students to understand or feed the misconception that math is boring and just has to be memorized.

Leave a comment about how the student pages worked or how you have taught decomposing and composing numbers.

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### 5 Responses to Teaching Addition and Subtraction, Part Two

1. […] I remember my first experience in a Mathematics Methods Course of a Part/Part Whole Mat. I really liked how the mat could be used for both addition and subtraction. This was the beginning of my ped…  […]

2. […] Now I would like to help her see how three situations are in that file: Change Plus/Change Minus, Decomposing/Composing, and Comparison. (If you want to explore these categories in more depth, you can click on each […]

3. […] are the four scenes for Decomposing/Composing. You can click here to learn more about this addition and subtraction situation. I have used color to distinguish sets of pencils and flowers. I just printed them on two different […]

4. […] series on teaching addition and subtraction. Part One talks about the Change Plus/Change Minus, and Part Two talks about Composing/Decomposing. Our last situation is […]