step 1 of 6
You know a fraction and a decimal can share one point on the line. A third costume joins now: the percent. A grid of 100 squares has 47 squares shaded.
Which trio all name that shaded amount?
Moving between bar models, number lines and equations
Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connections between representations
What a learner can do afterwards
- Represent a scaling problem as both a bar model and a multiplication equation
- Show how 0.35, 35/100, and 35% all represent the same quantity on a hundredths grid
- Translate a line-graph reading into a subtraction equation to find the difference
1 · Read
You already know fractions, decimals, and multiplication on their own. That helps when pocket money, a game score, or a plant height shows up in a new form. The same number can show up as a bar model, a number line, or an equation, and they all tell the same story.
Tap to fill the grid, one at a time: 2 rows of 8.
Try it together
A bar model shows multiplication as equal groups. Two strips with 8 blocks in each are 2 lots of 8, so the equation is 2 x 8 = 16. Scaling works the same way: if one strip is 9 tiles long and you want it 3 times as long, that is 3 strips of 9, or 9 x 3 = 27. The picture and the equation carry the same numbers.
Tap to fill the grid, one at a time: 2 rows of 8.
Try it together
0.47, 47/100, and 47% are the same amount. Picture a grid of 100 squares. If 47 are shaded, you can write that as the decimal 0.47, the fraction 47/100, or the percent 47%.
Try it together
A line graph shows a tomato plant 6 cm tall in May and 13 cm in July. To find how much it grew, read both points and subtract: 13 - 6 = 7. The plant grew 7 cm.
Some amounts come in tenths instead of hundredths. A strip split into 10 big parts and a grid split into 100 small squares are the same size, so each big part covers 10 small squares. That makes 7/10 the same as 70/100, 0.7, and 70%. When two amounts are written in different ways, change them to the same way first, then compare them.
Good to know
If you're not sure your equation is right, try drawing it as a bar model or a number line. If the picture and the equation tell the same story, you've got it.
Bar models, number lines, and equations are different pictures of the same math. Learn to move between them.
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
30 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.