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Number and place value

Representing numbers in different ways

Representing numbers in different ways

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Tutor: Toby

Summary

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?


Maths; Number and place value; KS2 Year 3; Representing numbers in different ways


There are 1010 "jumps" between the numbers 600600 and 650650.  You can use this information to work out what each small "jump" is.

650600=5050÷10=5650 - 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 600600.

600+(7×5)=635600 + (7\times5) = 635​​


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



Counters

Counters are used as visual representations of numbers. The following number counter represents the number 6666. There are 66​ full rows of 1010​ and 66​ ones.

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


Maths; Number and place value; KS2 Year 3; Representing numbers in different ways


​​

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?


Maths; Number and place value; KS2 Year 3; Representing numbers in different ways


Counting up in fives, the 88 "gates" represent 4040 and the 33 lines represent 33.

The number represented on the tally chart is 43\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=5517+38 = 55


The two smaller numbers that make up the larger number are 1717 and 3838. Place them into a part whole model connecting each of them to the bigger number, 5555.


Maths; Number and place value; KS2 Year 3; Representing numbers in different ways


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FAQs - Frequently Asked Questions

Why are visual representations useful?

How do I represent a number using a tally chart?

How can I represent numbers in different ways?

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