Step-by-step Maths Level 4: Choosing the operation and explaining why
Part of the Step-by-step Maths Level 4 solving problems with the four operations chapter. Chapter overview · whole chapter on one page
Choosing the operation and explaining why
Sometimes a question asks which operation to use and why. A good answer names the operation and gives a reason about the story.
Your reason can say what the numbers mean, such as equal groups, putting together, or taking away.
Key ideas
- Name the operation.
- Give a reason that uses the story.
- Check the operation would give the right 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 bags each hold the same number: equal groups.4 groups of 9
- Choose the operation. Equal groups of the same size use multiplication.4 × 9 = 36
- 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 and gives a reason about equal groups.
Check. Check: 4 × 9 = 36 is the total.
Watch out. The reason matters as much as the operation.
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.380 and 245
- Choose the operation. Putting two amounts together is addition.380 + 245 = 625
- 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 and gives a reason about putting amounts together.
Check. Check: 625 - 245 = 380.
Watch out. The reason matters as much as the operation.
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.520 take away 185
- Choose the operation. Taking away is subtraction.520 - 185 = 335
- Give the reason. A good reason mentions taking away or what is left.some are taken away, so the rest 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 and gives a reason about taking away.
Check. Check: 335 + 185 = 520.
Watch out. The reason matters as much as the operation.
Watch out
Watch out. Saying “multiply” with no reason is not enough. Say what the groups are.
Exam tip
Grown-up tip. Accept any sensible reason that uses the story. Ask: “Why would you use that operation here?”
Exercise 9E Practice: choosing the operation and explaining
Non-calculatorMethod. 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.424 into 8 groups
- Choose the operation. Sharing into equal groups is division.424 ÷ 8
- Work out the answer. Ask: how many groups of 8 make 424?8 × 53 = 424
- Write the answer. This is the number for each child.53
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.147 into 3 groups
- Choose the operation. Sharing into equal groups is division.147 ÷ 3
- Work out the answer. Ask: how many groups of 3 make 147?3 × 49 = 147
- Write the answer. This is the number for each child.49
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. Taken away means subtract.561 take away 451
- Choose the operation. Taking away is subtraction.561 - 451
- 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 561 - 451) 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. 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.567 take away 101
- Choose the operation. Taking away is subtraction.567 - 101
- 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 567 - 101) 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 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.84 into 6 groups
- Choose the operation. Sharing into equal groups is division.84 ÷ 6
- Work out the answer. Ask: how many groups of 6 make 84?6 × 14 = 84
- Write the answer. This is the number for each child.14
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 (subtraction), then work out the answer.
- Find the key words. “sold” and “left” mean some are taken away.7434 and 5576
- Choose the operation. Taking away is subtraction.7434 - 5576
- Work out the answer. Use exchange if a column is too small.7434 - 5576 = 1858
- Write the answer. This is how many are left.1858
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. Taken away means subtract.607 take away 283
- Choose the operation. Taking away is subtraction.607 - 283
- 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 607 - 283) 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. 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.842 take away 434
- Choose the operation. Taking away is subtraction.842 - 434
- 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 842 - 434) 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 the key words, choose the operation (multiplication), then work out the answer.
- Find the key words. Equal groups: the same number in each bag.6 bags of 6
- Choose the operation. Equal groups are multiplication.6 × 6
- Work out the answer. Use a times table fact, or add in steps.6 × 6 = 36
- Write the answer. This is the total.36
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 (multiplication), then work out the answer.
- Find the key words. Equal groups: the same number in each bag.8 bags of 81
- Choose the operation. Equal groups are multiplication.8 × 81
- Work out the answer. Use a times table fact, or add in steps.8 × 81 = 648
- Write the answer. This is the total.648
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 bags each hold the same number: equal groups.8 groups of 8
- Choose the operation. Equal groups of the same size use multiplication.8 × 8
- 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 8 × 8) 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. 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. 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.4 groups of 8
- Choose the operation. Equal groups of the same size use multiplication.4 × 8
- 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 4 × 8) 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. 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.621 and 669
- Choose the operation. Putting two amounts together is addition.621 + 669
- 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 621 + 669) 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. 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.236 and 542
- Choose the operation. Putting two amounts together is addition.236 + 542
- 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 236 + 542) 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. 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.672 and 348
- Choose the operation. Putting two amounts together is addition.672 + 348
- 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 672 + 348) 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.