Understanding fractions (age 10+)
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 algebraic equation 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
The lesson
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.
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 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.
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.
Watch it
Where it sits
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.