# Multiple Representations

**Multiple representations allow students to gain a deeper understanding.**

**Multiple representations allow students to gain a deeper understanding.**

Comparing multiple methods allows students **make connections** and use the most appropriate method with **fluency**.

Comparing different representations uncovers the **structure** of the mathematics and allows students to make generalisations.

## Using Multiple Representations

Click the image to open the interactive representation in Desmos. You can edit this version and save it to your own account.

DO NOT WORRY ABOUT BREAKING IT! If you accidentally delete something or rescale it and cannot get it back simply come back to this page and click the image again.

Some representations have been embedded into this site. To open in full screen on Desmos, click edit graph on Desmos in the bottom right.

Minimise the control panel in Desmos for the best view (<<)

## Number

**Fractions, Decimals and Percentages**

**Fractions, Decimals and Percentages**

Fractions, decimals and percentages are represented by a 100 grid, decimal number line, percentage number line and bar model. Instruction video link

blank printable templates

**Percentage ****I****ncrease and ****D****ecrease**

**Percentage**

**I**

**ncrease and**

**D**

**ecrease**

Bar model, double number line and ratio table. Instruction video link.

Students often find it hard to visualise beyond 100% using bar models. A double number line allows students to compare % and decimals and links to ratio tables - see Multiplicative Reasoning.

blank printable template

**Multiply ****two digits by two digits**

**Multiply**

**two digits by two digits**

**Multiply ****D****ecimals**

**Multiply**

**D**

**ecimals**

The area model for decimals is represented alongside Dienes blocks. Drag the blocks over the area to clear up any misconceptions.

For example 0.31 x 0.2 = 0.62

The area above is covered by 6x0.01s and 2x0.001s not 6x0.1s and 2x0.01s.

0.31 x 0.2 = 0.062

blank printable template

blank printable template

**Multiply whole numbers and decimals**

**Multiply whole numbers and decimals**