Decomposing and composing numbers to 5

General

Students learn to decompose and compose numbers to 5. They learn to recognize decompositions in images, but also line charts and numbers. They learn to compose numbers by counting on.

Relevance

It is useful to know this when you want to divide objects. Sometimes you can be unfair in your division. If you want to split 4 eggs into two basket, you can do that in different ways.

Introduction

Students practice counting amounts to 5 by counting the animals in the image shown and holding up the correct number card.

Development

You can decompose numbers in different ways. Explain, using the eggs, that you can decompose 5 into 1 and 4, but also 3 and 2, and doing this is called decomposing. If you already have one of the numbers, you count on to see how many more you need. Explain that this is called composing numbers. Show decomposing numbers by dividing the 4 eggs shown into the 2 baskets and then also showing how to compose those numbers. Show all possible decompositions of 4. Explain that you can sometimes see what the decomposition is because the objects in the picture are in different colors, but that you can turn those numbers around too. Discuss that you can also use a decomposition frame. Practice recognizing the numbers in the images with beads and discuss with the students which numbers they can turn around and how they can be written in a decomposition frame.
Explain to students that if you can't see the decomposition with colors, you need to count by first looking at the amount they have, and counting on. Practice this together and ensure students count on. There are also decompositions without images or object representations. Ask students to try decomposing in their heads, or allow students to work with blocks.

Check that students understand decomposing and composing numbers to 5 by asking the following questions:
- What does decomposing mean? And composing?
- Can you demonstrate how to decompose 3?
- Which numbers can you swap in a decomposition?

Guided Practice

Students practice decomposing and composing by first filling in the missing number in a decomposed number. They then see the number with objects that they can use for counting for composing, and finally a number without objects.

Closing

Check that students have understood by asking them to drag blocks to compose to 5. Have them say how many blocks are needed to compose the number and check the answer by erasing the covered square. Give pairs of students blocks to practice decomposing 3. They can also practice other decompositions. Discuss why it is useful to decompose numbers and have them come up with other situations in which they would need to be able to use this.