January 30th, 2026
Hello families — hard to believe this semester is in the final weeks! Your child(ren) will begin a unit on ratios and proportions. Below is a clear overview of what students will learn, how you can support them at home, and simple examples and practice ideas you can try together.
How to read and write ratios in different forms (e.g., a:b, \frac{a}{b}, “a to b”).
How to simplify ratios and determine equivalent ratios.
How to set up and solve proportions (equations that state two ratios are equal).
Using proportions to solve real-world problems (scaling recipes, maps, rates).
Visual strategies: ratio tables, double number lines, and tape diagrams.
Checking solutions for reasonableness (does the answer make sense in context?).
Ratio — comparison of two quantities (e.g., red to blue = 3:2).
Equivalent ratios — ratios that express the same relationship (e.g., 3:2 = 6:4).
Proportion — an equation stating two ratios are equal (e.g., \frac{3}{2} = \frac{9}{6}).
Unit rate — amount per one (e.g., miles per hour, price per item).
Writing and simplifying ratios
Scenario: A fruit bowl has 6 apples and 4 oranges.
Ratio of apples to oranges: 6:4.
Simplified: divide both by 2 → 3:2.
Equivalent ratios with scaling
Start with 2:5.
Multiply both parts by 3 → 6:15 (equivalent).
Solving a proportion (cross-multiplication)
Problem: If \frac{3}{4} = \frac{x}{12}, find x.
Cross-multiply: 3\times 12 = 4\times x → 36 = 4x.
Solve: x = \frac{36}{4} = 9.
Check: \frac{3}{4} = \frac{9}{12} (both equal 0.75).
Real-world scaling (recipe)
Recipe for 4 people needs 2 cups of flour. How much for 10 people?
Set proportion: \frac{2}{4} = \frac{x}{10}.
Cross-multiply: 2\times 10 = 4x → 20 = 4x → x = 5 cups.
Ratio table: Make a small table showing how quantities grow together (useful for doubling/tripling).
Double number line: Draw two parallel number lines and mark matching pairs to visualize scaling.
Tape diagram: Draw bars representing quantities for comparison.
Unit rate approach: Convert to “per one” when helpful (e.g., cost per item).
Ask them to explain their thinking — verbalizing helps solidify understanding.
Cooking: Adjust a recipe for more or fewer servings; ask your child to compute new ingredient amounts.
Shopping: If 3 shirts cost \$45, what’s the price per shirt? (Unit rate: \frac{45}{3}=15 → \$15 each.)
Sports stats: Compare win ratios (e.g., 8 wins and 2 losses → win ratio 8:2 → simplified 4:1).
Driving: If a car travels 150 miles on 5 gallons, what is miles per gallon? (Unit rate: \frac{150}{5}=30 mpg.)
Ask guiding questions: “How did you set up that ratio?” or “Does that answer seem reasonable?”
Encourage sketches: number lines or tape diagrams are quick and powerful.
Let them try first; prompt them to check their work and explain steps.
Praise process and effort — reasoning matters more than speed.
Short lessons, guided practice, collaborative problem solving, and periodic exit tickets/quizzes.
Use of visual models (tables, number lines) and transition to algebraic methods (proportions and cross-multiplication).
Opportunities for real-world application and word problems.