Primary 5 maths · Whole numbers · About 12 minutes
Use the order of operations and brackets without a calculator
Match the grouped part of the expression to the grouped objects in the story.
Start the interactive lesson →Open practice activity
What you will learn
- Use the order of operations and brackets without a calculator
Models used: number sentences, stories, tables.
Before you start
What do the packets mean?
There are 3 loose pencils and 2 packets. Each packet holds 4 pencils.
Each counter stands for one object. The separate groups are parts; count all the groups to find the whole.
There are 3 loose pencils and 2 packets. Each packet holds 4 pencils.
A multiplication can describe packets inside a larger total. Brackets can change what belongs inside each packet.
loosepacketpacketThere are 2 groups, with 4 objects in each group. Count a group before counting them all.
Find the pencils in the packets first: two groups of four make eight.
3 + 2 × 4 = 3 + 8
4 + 4 = 2 × 4 = 8
The complete bar is the whole. Each labelled section is one part of it.
Now join the 3 loose pencils. There are 11 pencils.
3 + 8 = 11
There are 5 groups, with 4 objects in each group. Count a group before counting them all.
Brackets would tell a different story: (3 + 2) × 4 means five groups of four.
(3 + 2) × 4 = 20
4 + 4 + 4 + 4 + 4 = 5 × 4 = 20
What did the picture help us see?
Brackets would tell a different story: (3 + 2) × 4 means five groups of four.
Worked example: A new example, together
Work out 5 + 8 × 6.
| Loose objects | Packets | In each packet |
|---|---|---|
| 5 | 8 | 6 |
Separate amount and equal groups. Read each value with the heading above its column.
Match the grouped part of the expression to the grouped objects in the story.
Multiplication forms one grouped amount before it is added.
Separate amount and equal groups Loose objects Packets In each packet 5 8 6 Separate amount and equal groups. Read each value with the heading above its column.
Do multiplication before addition: 8 × 6 = 48.
Separate amount and equal groups Loose objects Packets In each packet 5 8 6 Work out 5 + 8 × 6.
53
Separate amount and equal groups. Read each value with the heading above its column.
Do multiplication before addition: 8 × 6 = 48.
Separate amount and equal groups Loose objects Packets In each packet 5 8 6 Separate amount and equal groups. Read each value with the heading above its column.
5 + 48 = 53.
Separate amount and equal groups Loose objects Packets In each packet 5 8 6 Separate amount and equal groups. Read each value with the heading above its column.
Brackets would change the grouping: (5 + 8) × 6 is different.
Separate amount and equal groups Loose objects Packets In each packet 5 8 6 Separate amount and equal groups. Read each value with the heading above its column.
Check the result against the question we started with.
53 − 5 = 48.
We found 53. Multiplication forms one grouped amount before it is added.
Separate amount and equal groups Loose objects Packets In each packet 5 8 6
Common mistakes to discuss
- Longer looks larger. Compare the greatest place first, not the number of digits on the page. 0 thousands beats nothing: 998 is less than 1002 because the thousands differ.
Check your understanding
- Use the order of operations and brackets without a calculator
- explain the order of operations using the amounts being grouped
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
Try this lesson →Related Primary 5 lessons
- Read and write numbers to 10 millionRead and write numbers to 10 million · About 12 minutes
- Multiply and divide by 10, 100, 1000 and their multiplesMultiply and divide by 10, 100, 1000 and their multiples · About 12 minutes