step 1 of 6
By now you can dress one amount as a fraction, a decimal, a percent, or a picture. Zara has $20 and spends 2/5 of it on a book.
What is 2/5 of $20?
Moving between representations of a relationship
Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations
What a learner can do afterwards
- Translate a word problem into an equation, with a bar or symbol standing for the unknown and also represent it on a bar model
- Plot data from a table onto a coordinate grid and interpret the relationship
- Explain how a pie chart, a fraction, and a percentage all represent the same proportion
1 · Read
A math relationship can be told in more than one way. A story about sharing cookies, a picture split into equal parts, an equation with a fraction, a table of numbers, and a graph can all describe the exact same amount. Once you can move between them, math stops feeling like separate tricks and starts feeling like one connected idea.
Tap to shade 3 of the 4 parts.
A fraction, a percent, and a pie chart slice can all name the same part of a whole. Percent means out of 100. To turn a fraction into a percent, rename it in hundredths: 3/5 is 60/100, which is 60%. To go back, read the percent as hundredths and simplify: 60/100 is 3/5. The picture changes, the amount does not.
Try it together
Zara has $20 and spends 2/5 of it on a book. The equation is 2/5 x 20 = 8, so she spent $8 and has $12 left. A bar model splits the $20 into 5 equal strips: 2 strips ($8) spent, 3 strips ($12) left. Story, equation, and bar model all agree.
A bar model also runs backwards. If you know what one strip is worth, multiply it by the number of equal strips to get the whole. A bar cut into 3 equal strips where one strip holds 11 pencils has 3 x 11 = 33 pencils in the whole bar. A part plus the number of equal parts is enough to rebuild the total.
Try it together
A shop's price table shows: 1 shirt costs $10, 2 shirts cost $20, 3 shirts cost $30. Plot these as points on a coordinate grid, shirts on one side and cost on the other. The points line up in a straight line through zero, because the price per shirt never changes.
Good to know
When you switch between a story, a bar model, an equation, and a table, check that the numbers match in every version. If the story says 'a quarter', your equation should use 1/4, not 4/1.
A fraction, a percent, a pie chart slice, a bar model, a table, and a graph can all describe the same relationship, just in different clothes.
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.