Ratios
A ratio compares quantities multiplicatively. The tools, in order: bar (tape) diagrams, then ratio tables, then “multiply both parts by k.” Students write a:b and a:b:c in lowest terms, build equivalent ratios, and share a quantity in a given ratio — which means adding the parts first to find the size of one part. Three-term ratios and sharing problems are the Grade 6 upgrades. The classic error is reading 2:3 of 20 as “2 and 3” instead of 8 and 12. Ratios, rates, and percents (the next two units) are one language.
Specification · for a parent or teacher
- ratios-grade6
- Advanced Math 6 · Unit 5
- High School Math 1
- Applied
- 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
- 5 items
Students can
and in lowest terms; share a quantity in a ratio; equivalent ratios; tape diagrams and tables.
Ready when
share $84 in the ratio 2:5, then 2:3:7, without being told to add the parts first.
Formulas
Watch for
2:3 of 20 as 2 and 3 rather than 8 and 12.