Primary 1 Methods and Model Drawing
Use these drawings and step-by-step methods to make a word problem easier to see and solve.
Keywords
Use these words while your child points to a part of a drawing or explains a step.
- Method
- A way to organise the information and solve a problem.
- Systematic listing
- Write possible answers in order and check each clue.
- Bar model
- Draw bars to show how amounts are related.
- Part / whole
- A whole amount can be made from smaller parts.
- Difference
- How much more one amount is than another.
- Equal unit
- One of several bar parts that all represent the same amount.
- Before / after
- Compare amounts before and after a change.
- Working backwards
- Start at the result and reverse the actions, beginning with the last one.
Method: Systematic listing
List possible whole numbers in order, then test each condition. This is a problem-solving strategy to use with number knowledge, not a separate required syllabus topic.
What whole numbers are more than 5 but less than 10? List 6, 7, 8, 9. The words “more than” and “less than” exclude 5 and 10.
May has more than 5 apples. Lim has 2 more apples than May. The total number of apples they have is less than 20. How many apples could May have?
Scroll sideways to see every possible value.
| May: more than 5 apples | 6 | 7 | 8 | 9 | … |
|---|---|---|---|---|---|
| Lim: 2 more than May | 6 + 2 = 8 | 7 + 2 = 9 | 8 + 2 = 10 | 9 + 2 = 11 | … |
| Total: less than 20? | 6 + 8 = 14 ✓ | 7 + 9 = 16 ✓ | 8 + 10 = 18 ✓ | 9 + 11 = 20 ✗ | larger ✗ |
May could have 6, 7 or 8 apples. Stop at 9: the total is already 20, so every larger value also fails.
Common mistake: Including 5 when the clue says “more than 5”, or accepting a total of 20 when it must be less than 20. Test every clue for each candidate.
Ask: “What is the smallest number we may try? When can we stop listing?”
What whole numbers are more than 12 but less than 16?
Reveal the answer
13, 14 and 15. Both endpoints are excluded.
Model drawing: Part–whole model
Draw two attached parts when a story joins amounts or asks for a missing part. Label the known parts first and put ? on the amount the question asks for.
Mira has 24 stickers. She gets 13 more stickers. How many stickers does she have now?
Model first: 24 + 13 = ?. Add ones 4 + 3 = 7, then tens 2 + 1 = 3. Mira has 37 stickers.
Important: The question asks for the whole, so the question mark spans both attached parts.
Common mistake: Drawing 24 as the whole and 13 as a part. “Gets 13 more” means the final whole is larger than 24.
Ask: “What are the two parts? Is the question asking for a part or the whole?”
There are 46 pencils altogether. 18 are red. How many are blue?
Reveal the answer
28 blue pencils. Put 46 on the whole and 18 on one part. The missing part is 46 − 18 = 28. Check 18 + 28 = 46.
Model drawing: Comparison model
Draw aligned bars for two amounts. The extra piece on the longer bar is the difference. This helps a child see why “how many more?” is a subtraction question.
Asha has 32 shells. Ben has 19 shells. How many more shells does Asha have than Ben?
Model first: 19 + ? = 32. Find the extra piece: 32 − 19 = 13. Asha has 13 more shells.
Important: Both bars start at the same point. The question mark marks only the extra part, not Asha’s whole bar.
Common mistake: Adding 32 and 19 because both quantities are in the story. Ask the child to point to the extra section between the two bar ends.
Ask: “Which bar is longer? Where is the extra part? What equation finds just that part?”
Lee has 45 marbles. Noor has 28 marbles. How many more marbles does Lee have?
Reveal the answer
17 more marbles. Draw aligned bars of 45 and 28; the extra part is 45 − 28 = 17.
Method: Before and after
Show how many are in each box before and after the move. No balls are added or taken away.
Box A has 30 balls. Box B has 10 balls. Some balls move from Box A to Box B. Now both boxes have the same number of balls. How many balls moved?
Before
↓ Move one 10-ball part from Box A to Box B
After
The after bars are the same length. The orange part is the group that moved.
Box A has 30 balls. Box B has 10. How many more does Box A have?
- Find the difference: 30 − 10 = 20 balls.
- Cut the 20-ball difference in half: 10 + 10 = 20. One 10-ball part stays and one moves.
- Move one 10-ball part. Box A has 30 − 10 = 20 and Box B has 10 + 10 = 20.
Answer: 10 balls moved.
Important: The balls leaving Box A go into Box B. The total stays 40.
Common mistake: Answering 20 because 30 − 10 = 20. That is the gap at first. Moving 20 balls would swap the box counts, not make them equal.
Ask: “How many more balls does Box A have? If the boxes end equal, how can we split that difference?”
Ravi has 70 cards and Mei has 30. Ravi gives some cards to Mei until they have the same number. How many cards does Ravi give?
Reveal the answer
20 cards. They have 100 cards altogether, so each ends with 50. Ravi gives 70 − 50 = 20; Mei has 30 + 20 = 50.
Method: Working backwards
When the final number is known but the starting number is hidden, reverse the last action first. Addition and subtraction reverse each other.
I think of a number. I add 7, then subtract 3, and get 12. What number did I start with?
Forward story
Work backwards from 12
What happened last in the story? Reverse that action first.
- Reverse “subtract 3” by adding 3: 12 + 3 = 15.
- Reverse “add 7” by subtracting 7: 15 − 7 = 8.
- Check forwards: 8 + 7 = 15, then 15 − 3 = 12. The starting number was 8.
Important: Reverse the order of the actions as well as each operation: reverse “subtract 3” before reversing “add 7”.
Common mistake: Subtracting 7 from 12 first. Adding 7 happened first in the story, so reverse it last.
Ask: “What happened last? How can you reverse it? Can you check by following the story forwards?”
I think of a number. I subtract 5, then add 9, and get 18. What was my number?
Reveal the answer
14. Work backwards: 18 − 9 = 9, then 9 + 5 = 14. Check: 14 − 5 = 9, then 9 + 9 = 18.
Model drawing
Draw equal-sized units to show how two amounts are related. Start the bars at the same point, then use the known total or difference to find the value of one unit. The examples below show how to find each person's amount.
Find each person's stickers
Asha has 3 times as many stickers as Ben. Together they have 24 stickers. How many stickers does each person have?
Parent prompt: “Can you match each of Asha's three parts to Ben's one part?” Count the units before using the known total or difference. Each unit must represent the same number of stickers.