A ratio compares amounts without needing their size: 3 red beads to 5 blue beads is the same comparison as 6 to 10. This unit builds the idea up in six steps: what a ratio says and in which order, how to simplify it, how to share an amount in a ratio, why multiplying keeps a ratio and adding does not, how to solve proportion problems by finding the value of one, and how a table, a straight line through the origin and y = kx describe one proportional relationship.
Every idea is something you can move: groups of counters, bars cut into equal parts, a ratio scaled against the same ratio with an amount added, a pack scaled to one item and back, and a line with a start amount you can slide to zero. No lesson needs a calculator.
The lessons, in order
- Lesson 1 · What a ratio says Writing a ratio of two or three amounts in a stated order, reading a ratio as parts of a whole, and putting amounts in the same unit first. Slide two groups of counters from 1 to 9 and read the ratio in both orders and the share of the whole. No calculator
- Lesson 2 · Simplifying ratios Equal ratios, simplifying with the highest common factor, converting to one unit first, the form 1 : n and ratios of three amounts. Slide two lengths from 1 to 24 and see them cut into equal groups; the groups are the simplest form. No calculator
- Lesson 3 · Sharing in a ratio Sharing an amount in a ratio of two or three parts, finding the value of one part, working back from one known share or from a difference. Slide the two parts of a ratio and the value of one part and watch the bar of equal parts, the total and both shares. No calculator
- Lesson 4 · Equal ratios and scaling A proportion as two equal ratios, scaling with a scale factor, why adding to both parts changes a ratio, and the cross-product check. Multiply 3 : 5 by a factor and add an amount to both parts, and compare each result with the ratio you started with. No calculator
- Lesson 5 · Solving proportion problems Solving proportion problems by the value of one and by a scale factor, comparing best value, and recognising a relationship that is not proportional. Set a known pack and a number wanted, and see the value of one item turn the known cost into the cost wanted. No calculator
- Lesson 6 · Proportional relationships Recognising a proportional relationship from a table, a graph and an equation, the constant of proportionality k, and why a start amount breaks it. Move a line y = kx + c with a slope and a start amount, and compare y divided by x at two points. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.