Topics
2. Addition and subtraction
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Australia
Year 4

2.07 Estimation and multistep questions

Lesson
Practice
Lesson

Are you ready?

Do you remember how we can  round numbers  , to help us simplify some number problems?

Examples

Example 1

Round 3322 to the nearest thousand.

Worked Solution
Create a strategy

Plot the number on a number line and choose the thousand it is closest to.

Apply the idea

Looking at the number line below, 3322 is closer to 3000 than to 4000.

30003100320033003400350036003700380039004000

So 3322 rounded to the nearest thousand is 3000.

Idea summary

To round a number to the nearest 1000, plot it on a number line and choose the multiple of 1000 that it is closest to.

Add and subtract by estimating first

When we solve addition and subtraction problems, estimating our answer gives us an idea of what to expect. In this video, we see how we can estimate the answer to addition or subtraction problems, using a number line to help us.

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Examples

Example 2

We want to estimate the answer to 258-26.

a

Round each of the two numbers to the nearest and then subtract them.

Worked Solution
Create a strategy

Use a number line to round each number to the nearest ten.

Apply the idea

Looking at the number line below, 258 is closer to 260 than to 250.

250251252253254255256257258259260

So 258 rounded to the nearest ten is 260.

Looking at the number line below, 26 is closer to 30 than to 20.

2021222324252627282930

So 26 rounded to the nearest ten is 30.

To find 260-30 we can plot 260 on a number line and jump back by 30:

220230240250260270

260 - 30 = 230

b

Find the value of 258-26.

Worked Solution
Create a strategy

Use a number line to subtract.

Apply the idea

Start at 258 and jump back 26 units.

230235240245250255260

258-26=232

Reflect and check

We can see that the answers are very similar, so the estimation of 230 was a good approximation for the actual answer of 232.

Idea summary

If we don't need an exact answer to a problem, we can use estimating to find out a close-enough answer. We can also use estimating to check our answers, so it is a great skill to learn.

Add and subtract three numbers

How can we solve a problem with more than one part? Have a look at this video to see some different ways to do this.

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Examples

Example 3

Find the value of 570+25+4.

Worked Solution
Create a strategy

Use a place value table to add the numbers.

Apply the idea

Write the digits in the place value table.

HundredsTensUnits
570
25
+ 4
=

Add the digits in each place value column.

HundredsTensUnits
570
25
+ 4
=599

570 + 25 + 4 = 599

Idea summary

By adding in a different order, we may be able to use strategies such as Bridge to 10, to help us solve a problem. The number lines below show how we can solve 7 + 5 + 3 by changing the order, and still arrive at the same answer of 15.

Number lines showing addition of 7, 5, and 3 in two different orders. Ask your teacher for more information.

Outcomes

ACMNA073

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

ACMNA076

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder

ACMNA083

Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction

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