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.
When my daughter was first doing addition she would build two different sets and then put them together and add up the total. This is the putting together, but then she learned subtraction as take away, which meant she started with an amount, took some away, and counted the total left. This does not connect to decomposing because she never thought about the ones she took away again. The parts she took away had done their job, and she had her answer. Maybe because we traditionally teach addition as the concept of joining and subtraction as the concept of take away, students don’t have the opportunity to see the connection between addition and subtraction. What do you think? I feel this is why students need to experience these different situations (Change Plus/Change Minus and Composing/Decomposing) in a concrete way. It will allow the students to make a natural connection instead of just believing their teacher that addition and subtraction are connected.
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.