Step-by-step Maths Level 4 Solving problems with the four operations: check-up and practice test questions
Part of the Step-by-step Maths Level 4 solving problems with the four operations chapter. Chapter overview · whole chapter on one page
Exercise 9Z Check-up
Non-calculatorMethod. Pick the operation from the key words, then explain why. A good answer names the operation and gives a reason.
- Find the key words. The word more means add.812 and 365
- Choose the operation. Putting two amounts together is addition.812 + 365
- Give the reason. A good reason mentions putting the amounts together.putting the two amounts together
- Write the answer. Accept any answer that names addition and gives a reason about putting amounts together.Accept any answer that says addition (or 812 + 365) and gives a reason, such as putting two amounts together.
Check. Check: the operation you name would give the right answer to the question.
Watch out. The reason matters as much as the operation. Say what the numbers mean.
Method. Solve in two steps: multiply, then subtract. Check the first step before the second.
- Find the total given away. The friends get equal groups, so multiply.9 × 34 = 306
- Take away what was given. Subtract the amount given away from the total.340 - 306 = 34
- Write the answer. This is how many are left.34
Check. Check: work backwards from your answer to see if the story makes sense.
Watch out. In a two-step problem, do the first step, write the answer, then use it in the second step.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 130 ÷ 10. The bottom number tells how many equal parts.130 ÷ 10 = 13
- Take 6 parts. The top number tells how many parts are blue.6 × 13 = 78
- Write the answer. This is the number of blue ones.78
Check. Check: the parts given and the parts left make 130.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Solve in two steps: divide, then add. Check the first step before the second.
- Share the first amount. Equal sharing is division.148 ÷ 4 = 37
- Add the extra in each bag. Each bag gets 15 more.37 + 15 = 52
- Write the answer. This is the number in each bag now.52
Check. Check: work backwards from your answer to see if the story makes sense.
Watch out. In a two-step problem, do the first step, write the answer, then use it in the second step.
Method. Pick the operation from the key words, then explain why. A good answer names the operation and gives a reason.
- Find the key words. Taken away means subtract.881 take away 582
- Choose the operation. Taking away is subtraction.881 - 582
- Give the reason. A good reason mentions taking away or what is left.some are taken away, so what is left is found by subtracting
- Write the answer. Accept any answer that names subtraction and gives a reason about taking away.Accept any answer that says subtraction (or 881 - 582) and gives a reason, such as taking away.
Check. Check: the operation you name would give the right answer to the question.
Watch out. The reason matters as much as the operation. Say what the numbers mean.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 270 ÷ 10. Divide by the bottom number.270 ÷ 10 = 27
- Find the amount given away: 8 × 27. Multiply by the top number.8 × 27 = 216
- Take it away from the total. The question asks what is left.270 - 216 = 54
- Write the answer. This is how many are left.54
Check. Check: the parts given and the parts left make 270.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Pick the operation from the key words, then explain why. A good answer names the operation and gives a reason.
- Find the key words. The bags each hold the same number: equal groups.6 groups of 7
- Choose the operation. Equal groups of the same size use multiplication.6 × 7
- Give the reason. A good reason mentions the equal groups.equal groups of the same size
- Write the answer. Accept any answer that names multiplication and gives a reason about equal groups.Accept any answer that says multiplication (or 6 × 7) and gives a reason, such as equal groups.
Check. Check: the operation you name would give the right answer to the question.
Watch out. The reason matters as much as the operation. Say what the numbers mean.
Method. Find the key words, choose the operation (addition), then work out the answer.
- Find the key words. “altogether” means put the two amounts together.4404 and 3627
- Choose the operation. Putting amounts together is addition.4404 + 3627
- Work out the answer. Add the thousands, hundreds, tens and ones.4404 + 3627 = 8031
- Write the answer. Give the total with the thing it counts.8031
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Find the key words, choose the operation (addition), then work out the answer.
- Find the key words. “altogether” means put the two amounts together.1967 and 737
- Choose the operation. Putting amounts together is addition.1967 + 737
- Work out the answer. Add the thousands, hundreds, tens and ones.1967 + 737 = 2704
- Write the answer. Give the total with the thing it counts.2704
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Work backwards: undo each step in the reverse order, then check forwards.
- Undo the doubling. Halve the result first.334 ÷ 2 = 167
- Undo the take away. Add back the number that was taken away.167 + 247 = 414
- Write the answer. This was the number I started with.414
Check. Check: follow the steps forwards from your answer to get the result in the question.
Watch out. Undo the last step first. Addition is undone by subtraction, and multiplication by division.
Total 19 marks. Allow about 19 minutes.
Exercise 9X Practice test questions
Non-calculatorMethod. Find the key words, choose the operation (multiplication), then work out the answer.
- Find the key words. Equal groups: the same number in each bag.4 bags of 52
- Choose the operation. Equal groups are multiplication.4 × 52
- Work out the answer. Use a times table fact, or add in steps.4 × 52 = 208
- Write the answer. This is the total.208
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Pick the operation from the key words, then explain why. A good answer names the operation and gives a reason.
- Find the key words. The word more means add.257 and 672
- Choose the operation. Putting two amounts together is addition.257 + 672
- Give the reason. A good reason mentions putting the amounts together.putting the two amounts together
- Write the answer. Accept any answer that names addition and gives a reason about putting amounts together.Accept any answer that says addition (or 257 + 672) and gives a reason, such as putting two amounts together.
Check. Check: the operation you name would give the right answer to the question.
Watch out. The reason matters as much as the operation. Say what the numbers mean.
Method. Find the key words, choose the operation (multiplication), then work out the answer.
- Find the key words. Equal groups: the same number in each bag.9 bags of 50
- Choose the operation. Equal groups are multiplication.9 × 50
- Work out the answer. Use a times table fact, or add in steps.9 × 50 = 450
- Write the answer. This is the total.450
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Solve in two steps: divide, then add. Check the first step before the second.
- Share the first amount. Equal sharing is division.264 ÷ 8 = 33
- Add the extra in each bag. Each bag gets 20 more.33 + 20 = 53
- Write the answer. This is the number in each bag now.53
Check. Check: work backwards from your answer to see if the story makes sense.
Watch out. In a two-step problem, do the first step, write the answer, then use it in the second step.
Method. Pick the operation from the key words, then explain why. A good answer names the operation and gives a reason.
- Find the key words. Taken away means subtract.611 take away 121
- Choose the operation. Taking away is subtraction.611 - 121
- Give the reason. A good reason mentions taking away or what is left.some are taken away, so what is left is found by subtracting
- Write the answer. Accept any answer that names subtraction and gives a reason about taking away.Accept any answer that says subtraction (or 611 - 121) and gives a reason, such as taking away.
Check. Check: the operation you name would give the right answer to the question.
Watch out. The reason matters as much as the operation. Say what the numbers mean.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 64 ÷ 8. The bottom number tells how many equal parts.64 ÷ 8 = 8
- Take 4 parts. The top number tells how many parts are blue.4 × 8 = 32
- Write the answer. This is the number of blue ones.32
Check. Check: the parts given and the parts left make 64.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find the key words, choose the operation (division), then work out the answer.
- Find the key words. “shared equally” means the same number in each group.35 into 7 groups
- Choose the operation. Sharing into equal groups is division.35 ÷ 7
- Work out the answer. Ask: how many groups of 7 make 35?7 × 5 = 35
- Write the answer. This is the number for each child.5
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Work backwards: undo each step in the reverse order, then check forwards.
- Work backwards. Undo multiplying by dividing.2672 ÷ 4 = 668
- Check forwards. Multiply the number to check.668 × 4 = 2672
- Write the answer. This was the number I started with.668
Check. Check: follow the steps forwards from your answer to get the result in the question.
Watch out. Undo the last step first. Addition is undone by subtraction, and multiplication by division.
Method. Find the key words, choose the operation (subtraction), then work out the answer.
- Find the key words. “sold” and “left” mean some are taken away.5081 and 3384
- Choose the operation. Taking away is subtraction.5081 - 3384
- Work out the answer. Use exchange if a column is too small.5081 - 3384 = 1697
- Write the answer. This is how many are left.1697
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.
Method. Find the key words, choose the operation (division), then work out the answer.
- Find the key words. “shared equally” means the same number in each group.170 into 5 groups
- Choose the operation. Sharing into equal groups is division.170 ÷ 5
- Work out the answer. Ask: how many groups of 5 make 170?5 × 34 = 170
- Write the answer. This is the number for each child.34
Check. Check the answer with the opposite operation to make sure it fits the story.
Watch out. Read the question for the key words first. Then choose the operation before you work out the answer.