Draw a bar model before calculating. Draw the whole as one long bar and mark the parts under it. Put a question mark on the part you need. Then decide: to find a whole, add the parts; to find a part, take the other parts from the whole. For equal groups, draw equal units and multiply. When one amount is more than another, take away the extra to make equal units.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- bar model
- a drawing of bars that shows how the numbers in a story fit together
- whole
- the total amount
- part
- one of the amounts that make up the whole
Worked examples
A farmer picks 250 apples. She sells 86 apples at the market and gives 57 apples to her neighbours. How many apples does she have left?
- 1.Whole bar: 250. Parts that went: 86 and 57.
- 2.86 + 57 = 143.
- 3.250 − 143 = 107.
= 107
Mia buys 5 packs of stickers with 12 stickers in each pack. She gives 9 stickers to her brother. How many stickers does she have now?
- 1.5 equal units of 12: 5 × 12 = 60.
- 2.60 − 9 = 51.
= 51
Ali and Ben have 150 marbles altogether. Ali has 30 more marbles than Ben. How many marbles does Ben have?
- 1.Take away Ali's extra 30: 150 − 30 = 120, which is 2 equal units.
- 2.One unit: 120 ÷ 2 = 60.
= 60
For parents
Method: Bar model (part–whole)
What to say: What is the whole? What are the parts? Where does the question mark go?
Common mistakes:
- Does the first step of a two-step problem and gives that as the answer.
- Works out a different quantity from the one the question asks for (the part that went, or the other person's amount).
- Uses the right first step but adds at the second step when the story takes away.
- Adds every number in the story (keyword or 'altogether' thinking) instead of modelling it.
- Adds the number of groups and the size of each group instead of multiplying.
- Halves the total, ignoring that one person has more than the other.