This sequence explores the concept of equivalence by asking students to partition numbers into two parts.

This sequence is for students who:

- have one-to-one correspondence skills in counting
- are developing a deeper sense of number
- are familiar with recording equations using symbols, including the use of the equals sign to indicate equivalent values on both sides of an equation.
- would benefit from having some experience in making generalised statements about the structure of number and operations.

### Lesson 1: Red Apples, Green Apples

Students explore the different ways that numbers can be partitioned into two parts. Working systematically, students are asked to find the partitions and show that they have all possibilities. This task affords an exploration of early algebraic thinking and scaffolds students towards seeing a pattern and making a generalisation regarding all possible combinations.

### Lesson 2: 12 Ways to Get to 11

This task uses the picture book* 12 Ways to Get to 11* to investigate how many two-number partitions are possible for any given number. Students apply their learning from Lesson 1: Red Apples, Green Apples to list all the ways that 11 can be made using two numbers. They then look at the number of possible partitions that can be made from some other numbers. Students investigate the fact that for any given number the possible combinations will be always one more than the number itself, and explain why this is the case.

Last updated June 12 2020.