Primary 5 Four Operations of Whole Numbers Study Guide
Primary 5 whole numbers in six short steps: tens, hundreds and thousands, brackets and the order of operations, then four kinds of word problem. Each step has something to tap and a question to try.
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What are the four operations of whole numbers in Primary 5?
Find the right amount first, then calculate in order.
In Primary 5 your child calculates without a calculator, splitting off the tens, hundreds and thousands, and writing one operation per line. The word problems then ask which amount to find before anything else: what stays the same, the value of one group, a supposed total, or the number before a wrong step.
In this chapter, your child learns to:
- multiply and divide by 10, 100, 1000 and their multiples;
- work out brackets first, then times and divide, then plus and minus;
- spot whether the total or the difference stays the same;
- find the value of one repeating group, then count the groups;
- suppose every item is one kind, then swap;
- undo a wrong step, then do the step that was meant.
Step 1
Multiplying and dividing by 10, 100 and 1000
Split the multiple into two factors. 300 is 3 times 100, so multiplying by 300 means multiplying by both factors: by 3, then by 100. Times 100 moves every digit two places to the left. To divide by 600, divide by 100 first, then by 6. The power of ten is only one factor; the other is still part of the divisor.
Tap Next step
What is 7200 ÷ 80?
Step 2
Order of operations with brackets
Finish each amount before joining them. Brackets are worked out first. Then times and divide, from left to right, and then plus and minus, from left to right. In 56 ÷ 7 + 3 × 5, the divide and the times sit inside two amounts, so both are finished before the plus joins them. Put brackets round 56 ÷ 7 + 3 and that becomes one amount, made first.
Tap Next step
What is 60 − 24 ÷ 4 × 2?
Step 3
Total unchanged and difference unchanged
Ask what the change leaves alone. When one person gives some to the other, nothing is added and nothing is thrown away, so the total stays the same. When both spend or receive the same amount, both bars change together, so the difference stays the same. Write the unchanged amount in units first, then find 1 unit.
Tap Next step
Hana has 3 times as many beads as Lin. After Hana gives Lin 30 beads, they have the same number. How many beads did Hana have at first?
Raj has $95 and Wei has $35. They each spend the same amount. Then Raj has 4 times as much money as Wei. How much does each of them spend?
Pei has 36 more stickers than Rui. Pei gives Rui some stickers, and then they have the same number. How many stickers does Pei give Rui?
Step 4
The grouping method
Value one group, then count the groups. When items come in a repeating pattern, such as 3 notebooks for every file, that pattern is one group. Write what one group contains and find its value. Divide the total by that value to get the number of groups, then multiply to answer in the items the question asks for.
Ken buys some notebooks at $2 each and some files at $5 each. For every 3 notebooks, he buys 1 file. He spends $66. How many notebooks does he buy?
Tap Add a group
Lily buys bowls at $3 each and plates at $2 each. For every bowl, she buys 2 plates. She spends $56. How many plates does she buy?
Step 5
The supposition method
Suppose they are all one kind, then swap. There are two kinds of item, a known number of items and a known total. Suppose every item is the cheaper kind; that gives a starting total. Compare it with the real total, find what one swap adds, then divide the missing amount by what one swap adds.
20 tickets were sold for a school concert. Adult tickets cost $8 and child tickets cost $5. The tickets sold for $121 altogether. How many adult tickets were sold?
Tap Swap a ticket
A pen holds 15 chickens and rabbits. They have 42 legs altogether. How many rabbits are there?
Step 6
Working backwards from a wrong step
Undo the wrong step, then do the one that was meant. Start from the result that was actually reached. Undo the wrong operation with its inverse: a divide undoes a times, a minus undoes a plus. That recovers the starting number; then carry out the step that was meant. When a length is cut into the wrong number of pieces, the same length is in both bars, so the extras gather into the missing piece.
Tap Next step
Aisha planned to cut a rope into 6 equal pieces. She cut it into 5 equal pieces instead, so each piece was 4 cm longer than planned. How long is the rope?
Ben should have divided a number by 4. He multiplied it by 4 instead and got 192. What is the correct answer?
Primary 5 whole numbers questions, worked step by stepCover the working and try each one on paper. Then open the hint, or show the lines one at a time.
Find the value of 81000 ÷ 900.
- 900 = 100 × 9.
- 81000 ÷ 100 = 810.
- 810 ÷ 9 = 90.
Find the value of 72 − (15 + 9) ÷ 3 × 2.
- = 72 − 24 ÷ 3 × 2
- = 72 − 8 × 2
- = 72 − 16
- = 56
Mei and Jun have 360 marbles altogether. Jun gives Mei 45 marbles. Then Mei has 3 times as many marbles as Jun. How many marbles did Mei have at first?
- After: Mei 3 units, Jun 1 unit. 4 units = 360.
- 1 unit = 360 ÷ 4 = 90.
- Mei after = 3 × 90 = 270.
- Mei at first = 270 − 45 = 225.
Mr Goh paid $151 for 25 flower pots. Large pots cost $7 each and small pots cost $5 each. How many large pots did he buy?
- If all were small: 25 × 5 = $125.
- Still to make: 151 − 125 = $26.
- One swap adds 7 − 5 = $2.
- Large pots: 26 ÷ 2 = 13.
Nadia thought of a number. She should have multiplied it by 6 and then added 15. Instead she divided it by 6 and then added 15, and got 27. What answer should she have got?
- Undo the plus: 27 − 15 = 12.
- Undo the divide: 12 × 6 = 72. That is the number.
- As meant: 72 × 6 = 432.
- 432 + 15 = 447.
Step 7
Check yourself
Five quick questions on the word-problem steps and brackets. Nothing is saved, and each answer suggests a practice set.
1. What is 40 − (12 + 8) ÷ 4?
2. Ivan is 32 and his son is 4. In how many years will Ivan be 5 times as old as his son?
3. Erasers are sold in packs of 3 for $2. Ken spends $14 on erasers. How many erasers does he get?
4. 9 spiders and beetles have 62 legs. A spider has 8 legs and a beetle has 6. How many spiders are there?
5. Mr Ng should have subtracted 18 from a number. He added 18 instead and got 75. What is the correct answer?
Using this guide at home. Steps 1 and 2 are best done with a pencil: let your child write each working line before tapping, then compare. In Steps 3 to 6, ask what the question wants found first, and why, before the next tap. Each step takes a few minutes.
The worked examples climb from a straight calculation to a story that has to be undone. Ask your child to say which method fits before revealing a line; naming the method is half the work in these questions.
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P5 Four Operations of Whole Numbers lessons and practice
6 lesson videos and 57 questions across eight subtopics, from Basic to Challenge, each with a worked solution.
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