1.11 Partition larger numbers

Lesson

We have looked at how to break up  four digit numbers  and use a number expander to help us see the parts in our number.

Examples

Example 1

We have written the number 4050 in a number expander.

Fill in the boxes to make the sentences correct.

a

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

Worked Solution
Create a strategy

Use the given number expander.

Apply the idea

The number expander shows that there is 4 in thousands.

We can break up this number into 4 thousands and 5 tens.

b

We can break up 4050 into hundreds and 50 units.

Worked Solution
Create a strategy

Use the given number expander closing the "thousands".

Apply the idea

We can break up 4050 into 40 hundreds and 50 units.

Idea summary

Another word that we can use to describe the ones place is 'units'.

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 ones

Partition and build larger numbers

Let's look at how we can break up larger numbers using place value.

Examples

Example 2

We're going to write 56\,713 in expanded form.

a

Fill in the number expander for 56\,713.

56\,713=⬚ \, \text{ Ten-Thousands }⬚ \, \text{ Thousands }⬚ \, \text{ Hundreds }⬚ \, \text{ Tens }⬚ \, \text{ Units}

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

56\,713=5 \, \text{ Ten-Thousands }6 \, \text{ Thousands }7 \, \text{ Hundreds }1 \, \text{ Tens }3 \, \text{ Units}

b

56\,713=⬚+⬚+⬚+10+3

Worked Solution
Create a strategy

Use the number expander in part (a).

Apply the idea

5 is in ten thousands, 6 is in thousands, and 7 is in hundreds, so the values are 50\,000, 6000, and 700.

56\,713=50\,000+6000+700+10+3

Example 3

We have written the number 21\,476 in the following number expander:

Fill in the boxes below to make the sentences correct.

a

We can break up this number into ten thousands, hundreds, and 76 units.

Worked Solution
Create a strategy

Use the number expander closing the "thousands" for the value of hundreds.

Apply the idea

We can break up this number into 2 ten thousands, 14 hundreds, and 76 units.

b

We can also break up 21\,476 into only hundreds and units.

Written in this way, the number is made up of hundreds and 76 units.

Worked Solution
Create a strategy

Use the number expander closing the "ten-thousands" and "thousands" for the value of hundreds.

Apply the idea

We can also break up 21\,476 into only hundreds and units.

Written in this way, the number is made up of 214 hundreds and 76 units.

Idea summary

Every number can be made in different ways, and it doesn't change the value of the number. The number 246\,000 has the same value as:

• 2 hundred thousands and 46 thousands

• 2 hundred thousands and 40 thousands and 6 thousands

• 246 thousands,

• 2460 hundreds,

• 24\,600 tens, or

• 246\,000 units.

Outcomes

MA2-4NA

applies place value to order, read and represent numbers of up to five digits