Grade 6 Ratios - Hard Practice
A hard grade 6 worksheet for Ratios & Proportions.
Worksheet snapshot
- Ratios & Proportions
- Key concepts: Understanding core ratios & proportions concepts for Grade 6; Applying ratios & proportions strategies appropriate to Grade 6
- Students master ratios & proportions at Grade 6 level, working with challenging problems, explaining their reasoning, and applying concepts to new situations.
- Apply it: Ratios & Proportions at the Grade 6 level connects to everyday situations students encounter: problem-solving in daily life, making sense of quantities and relationships, and building mathematical literacy for future learning.
- Write the ratio 20:6 in simplest form.
- Write the ratio 19:9 in simplest form.
- Write the ratio 9:11 in simplest form.
About Ratios & Proportions
Ratios compare two quantities, showing their relative sizes. Students learn to write ratios in multiple forms, find equivalent ratios, and solve problems using proportional reasoning.
Ratios are fundamental to proportional thinking, which underlies fractions, percentages, slope, rates, scaling, and countless real-world applications from cooking to architecture. Ratio understanding is essential for success in algebra and beyond.
Ratios & Proportions
Write ratios, build tables/double number lines, find unit rates, and solve proportion problems in real contexts.
This hard level worksheet:
Multi-step contexts with mixed units; create and solve proportions from word problems; justify solutions using multiple representations.
Key Concepts
- Ratios, equivalent ratios, and unit rates
- Tables/double number lines/graphs for proportions
- Proportion equation solving and reasoning
Prerequisite skills
Fluent with multiplication/division facts; fraction equivalence; coordinate graph basics.
Teaching Strategies
Use ratio tables and double number lines before equations; link to unit rate; graph proportional relationships to highlight constant of proportionality.
Assessment ideas
Have students write ratios from descriptions or pictures. Test equivalent ratio understanding. Include rate problems (unit rates). Ask students to solve proportion problems. Use contextual problems requiring ratio reasoning (recipes, maps, scale drawings).
Common Challenges
Mixing up order in ratios; treating additive changes as proportional; unit confusion in rates.
Real-World Applications
Recipes, maps/scales, speed/unit pricing, and mixture problems.
Extension Activities
Compare two rates and defend the better value; create a proportional table and graph from a story; solve a proportion two ways (table and equation).
Parent Tips
When shopping or cooking, ask for unit prices or scaled amounts and have your child explain the ratio relationship.