Topics
1. Number and place value
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Australia
Year 3

1.10 Partition 4 digit numbers

Lesson
Practice
Lesson

Are you ready?

We looked at how to  break numbers in the hundreds up by place value  , and how to model them with blocks.

Examples

Example 1

We have written a number in the number expander below.

A number expander that shows 3 tens and 2 units.
a

What is the value of the units?

Worked Solution
Create a strategy

Use the given number expander.

Apply the idea

The value of units from the number expander is 2.

b

What is the value of the tens?

Worked Solution
Create a strategy

Use the given number expander. Add 0 as a placeholder.

Apply the idea

We can see from the number expander that we have 3 tens which is equal to the value of 30.

c

Now look at the number 67. What is the value of the tens?

Worked Solution
Create a strategy

Use a number expander to break the given number into tens and units.

A number expander where the number of tens and units are blank.
Apply the idea

We can place 6 in tens and 7 in units.

A sumber expander showing 6 tens and 7 units.

We can see that we have 6 tens which is equal to the value of 60.

Idea summary

We can use a number expander to identify the value of a digit of a number.

Partition and built of numbers to ten thousands

This lesson looks at how we can use place value to break up numbers up in different ways.

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Examples

Example 2

Express 2704 in expanded form. 2704=⬚ \, \text{ Thousands }⬚ \, \text{ Hundreds }⬚ \, \text{ Tens }⬚ \, \text{ Units}

Worked Solution
Create a strategy

Use a place value table.

Apply the idea
ThousandsHundredsTensUnits
2704

2704=2 \, \text{ Thousands }7 \, \text{ Hundreds }0 \, \text{ Tens }4 \, \text{ Units}

Idea summary

A place value table is useful to expand numbers in thousands.

Number expanders for ten thousands

Let's look at how a number expander can help us understand the place value of a number in different ways.

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Examples

Example 3

We have written the number 6275 in a number expander.

A number expander with 6 thousands, 2 hundreds, 7 tens, and 5 units.

Fill in the boxes to make the sentences correct.

a

We can break up this number into ⬚ thousands, ⬚ tens, and 5 units.

Worked Solution
Create a strategy

Since we can't use hundreds, break the hundreds into 10 tens and add the original tens value.

Hundreds blocks turned into 10 tens blocks.
Apply the idea

Breaking 200 into tens will give 20 tens.

Adding the original tens value: 20+7=27

We can break up this number into 6 thousands, 27 tens, and 5 units.

b

We can break up 6275 into 6 thousands and ⬚ units.

Worked Solution
Create a strategy

Break the hundreds and tens into units and add the original units value.

A hundreds block turned into 10 tens blocks turned into 100 units blocks.
Apply the idea

Breaking 270 into units will form 200+70=270 units.

Adding the original units value gives: 270+5=275.

We can break up 6275 into 6 thousands and 275 units.

Idea summary

Every number can be made in different ways, and it doesn't change the value of the number. The number 3800 has the same value as:

  • 3 thousands and 8 hundreds

  • 38 hundreds

  • 380 tens, or

  • 3800 units

Outcomes

AC9M3N01

recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000

AC9M3N03

add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator

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