## PROPORTIONAL REASONING

## OVERVIEW

This half term focusses initially on the meaning of ratio and uses various models to develop deep and connected understanding of ratio and proportion. The links between ratio and fractions are also explored with pi introduced as the ratio of the circumference of a circle to its diameter. Conversion graphs are used as a contextual introduction to direct proportion with later work with maps and scales.

*Note that Multiplying and Dividing with Fractions has been moved from original WRM scheme to Spring 2 to enable us to fit in the common assessment this half term. *

Medium Term plan here:

## BUILDING ON

Solve problems involving simple ratio relationships.

Understand that two numbers can be related additively or multiplicatively, and

quantify additive and multiplicative relationships.

Use a given additive or multiplicative calculation to derive or complete a

related calculation, using arithmetic properties and inverse relationships.

Solve problems involving similar shapes where the scale factor is known or can be

found.

## POWERFUL KNOWLEDGE

- Divide in a given ratio
- Express ratios in their simplest integer form
- Compare ratios and related fractions
- Solve problems involving ratio of the form 1 : n or n : 1
- Solve proportional problems in the form m : n
- Understand pi as a ratio between diameter and circumference
- Explore conversion graphs
- Convert between currencies
- Understand scale factors as multiplicative representations
- Draw and interpret scale diagrams and maps

**Ratio **

**Lesson 1** – Use a bar model to solve word problems

**Lesson 2** – Use the bar model to solve problems involving ratio

**Lesson 3** – Using the bar model to solve more difficult problems

**Lesson 4** – Simplifying ratio

**Lesson 5** – Work with ratio in the form 1 : n

**Lesson 6** – Maps and scales

**Lesson 7** – Fractions and ratio

**Lesson 8** – Understanding pi as a ratio

**Lesson 9** – Further Circumference Problems

**Multiplicative Reasoning**

**Lesson 10** – Proportional Problems

**Lesson 11** – Money, money, money

**Lesson 12** – Conversion Graphs

**Lesson 13** – Working with similar shapes

**Lesson 14** – Similar shapes and ratio

**Lesson 15**– Enlarging Shapes

**Common Assessment 1 (Week commencing 10th October 2022) **

Updated Sept 2022