# Representing numbers in different ways

## In a nutshell

You can represent numbers in many different ways: number lines, tally charts, counters, place value charts and models. Visual representations can help you to understand place value, and are useful when introducing new topics such as the four operations.

## Number lines

You can represent numbers by using a number line. Count the marks on the number line to determine what value each jump of a small division represents.

**Example 1**

*What number is represented on the following number line?*

*There are $10$ "jumps" between the numbers $600$ and $650$. You can use this information to work out what each small "jump" is.*

*$650 - 600 = 50\\50 \div 10 = 5$*

*This means that the number line goes up in fives. The arrow points the number seven marks away from* $600$.

$600 + (7\times5) = 635$

*This means that the number represented on the number line is $\underline{635}$.*

## Counters

Counters are used as visual representations of numbers. The following number counter represents the number $66$. There are $6$ full rows of $10$ and $6$ ones.

$(6\times 10) + 6 = \underline{66}$

## Tally charts

Tally charts use lines to represent values. Each line represents a one. When there are five tally lines, the fifth is marked across the previous four, looking like a "gate". Grouping tally charts in fives makes it quicker to add up the total at the end, as long as you know your times tables.

##### Example 2

*What number is represented below using the tally charts?*

*Counting up in fives, the *$8$ *"gates" represent *$40$* and the *$3$* lines represent *$3$*.*

*The number represented on the tally chart is $\underline{43}$.*

## Part whole model

Part whole models show a full number and the parts that make up that number. The smaller numbers always make up the bigger number using this model. A part whole model can help you understand how addition and subtraction work.

**Example 3**

*Construct a part whole model for the calculation*

$17+38 = 55$

*The two smaller numbers that make up the larger number are $17$ and $38$. Place them into a part whole model connecting each of them to the bigger number, $55$.*