5.06 Estimation and multistep questions

Lesson

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.

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.

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.

So 258 rounded to the nearest ten is 260.

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

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:

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.

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.

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.

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.

Add the digits in each place value column.

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.

Outcomes

MA2-5NA

uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers

MA2-8NA

generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values