step 1 of 6
A school trip costs $240. Families have already paid 3/4 of the cost.
First look at the fraction 3/4. What does the bottom number 4 mean?
Moving between situations, diagrams and equations
Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents
What a learner can do afterwards
- Write an equation with three-digit numbers to match a measurement or money word problem
- Draw a bar model to represent a fraction problem and use it to solve
- Explain how a number line diagram relates to the quantities in a word problem
1 · Read
A story problem with numbers can be shown in more than one way. You can draw a picture, like a bar cut into equal parts. You can jump along a number line. Or you can write an equation with numbers and a fraction. All three show the same amounts, just in different forms.
Tap to shade 3 of the 4 parts.
Try it together
A school trip costs $240. Parents have already paid 3/4 of that. Split $240 into 4 equal parts: 240 ÷ 4 = 60. Then take 3 of those parts: 3 × 60 = 180. Parents paid $180, and the bar model shows it as 3 shaded parts out of 4.
Tap to shade 3 of the 4 parts.
Try it together
The same $240 fits on a number line. Start at 0, and the whole cost sits at 240. Four equal hops of $60 reach it, and 3 hops land on $180. A number line also shows taking away: start at the amount you had and hop back by what you spend. Where you land is what is left.
When you switch between a picture, a number line, and an equation, check that they agree. If your bar is cut into 4 equal parts, your equation uses fourths and your number line hops in fourths too. Two pictures that cut the same amount into different-sized parts are not showing the same thing.
A diagram, a number line, and an equation can all show the same fraction problem, and when they match, you know your answer is right.
2 · Watch
3 · Play
Try it yourself
Shade parts of the bar and watch the fraction change.
Take it off screen
Print a worksheetA4 with an answer key page for grown-ups. No screen, no internet.
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
Then practise
24 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.