These exercises and activities are for students to use independently of the teacher to practice number properties

- Solve problems involving simple ratios.

Proportions and Ratios, AP (Stage 8).

- Practice exercises with answers (PDF or Word)
- Homework with answers (PDF or Word)

### Prior knowledge

- Add 2 digit numbers or multiply by a 2 digit number (stage 7)
- Double 2 digit numbers

### Background

In using these data tables, there are 2 ways of generating the sets of numbers required, either working horizontally or vertically. With the numbers provided in the table, working horizontally does not invoke skip counting, but can be solved easily using a multiplicative strategy. Be wary of introducing this as students may rapidly move beyond their knowledge of basic facts if this is introduced. (For example, in question 2 students are using a ratio of 1:4, and have to work out 4 lots of 24). However, discuss with students how to construct the answers using a mixture of strategies. For example, by working vertically on questions 1 and 2 students could construct their answers using addition strategies and/or doubling. (For example, 4 × 24 is double 24 = 48 and double 48 = 96). Alternatively, when working horizontally, the answer for 4, when doubled will give the answer for 8.

### Comments on the Exercises

**Exercise 1**

Asks students to complete ratio tables and use the tables to answer questions