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You have dressed fractions as bars before. Today the fraction gets an exact home: a spot on the number line.
Where does 3/4 live on a number line that runs from 0 to 1?
Moving between diagrams and equations with fractions
Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows
What a learner can do afterwards
- Represent a sharing problem as both a fraction diagram and a division equation
- Explain how a bar model for 4 × 23 connects to the area model and the written method
- Translate a decimal on a number line into a fraction and explain the equivalence
1 · Read
A number line is a straight line with numbers marked on it in order. Whole numbers like 0, 1, and 2 are easy to spot. Fractions live between the whole numbers too. A fraction like 3/4 sits between 0 and 1, closer to 1.
To name a point, first count how many equal steps make one whole. That count is the bottom number. Then count the steps you take from 0. That count is the top number. Two steps on a line cut into five equal steps is 2/5. Every step has to be the same size, or the names stop working.
Try it together
Mia has 3 pizzas to share equally among 4 friends. She draws a bar split into 4 equal parts and shades 3 of them. That is the same as 3 divided by 4, and it lands at 3/4 on the number line.
Tap to shade 3 of the 4 parts.
Try it together
A bar model shows multiplication too. Draw 4 equal bars, each worth 23. Split every bar into 20 and 3, and you have an area model: 4 lots of 20 make 80, and 4 lots of 3 make 12. The written method adds those same two pieces: 80 + 12 = 92.
Good to know
You have drawn fraction bars before: split a whole into equal parts, then count how many parts you have. The same bar connects the picture to the number line and to the written fraction.
A number line can also show decimals, and the two ways of naming land on the same points. Split 0 to 1 into ten equal steps, and the second step is 2/10 as a fraction and 0.2 as a decimal. One point, two names. Count the steps to name the fraction first, then say that same fraction the decimal way.
Fractions and decimals are just different names for the same point on a number line.
2 · Watch
3 · Play
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.