6.RP.3.a: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Hands-on Activities

1. Recipe Adjustment

Adjust a recipe's ingredients based on different servings. Create a table of ratios for the original recipe and calculate the new amounts needed for increased or decreased servings.

2. Scale Models

Build a scale model using ratios. Choose an object like a building or a car, decide on a scale (e.g., 1:50), and calculate the dimensions of the model based on the actual object's size.

3. Sports Statistics

Analyze sports stats by creating ratios of wins to losses for various teams and plotting these on a coordinate plane to compare performance visually.

4. Budget Planning

Help plan a family budget by creating a table of income to expenses ratio. Adjust the table to see how spending less or more in certain categories affects the overall budget.

5. Gardening Project

Use ratios to plan a garden, determining how much space to allocate to different types of plants based on their required spacing and expected growth.

Strategies When Your Child Struggles

1. Simplify the Concept

Break down complex ratio problems into simpler parts by using smaller numbers or more familiar contexts, like comparing pieces of fruit.

2. Visual Aids

Use visual aids such as diagrams or ratio blocks to make abstract concepts more tangible and easier to understand.

3. Repetition Practice

Encourage regular practice with different sets of ratios to build confidence and familiarity with the concept.

4. Peer Learning

Arrange study sessions with peers to discuss and solve ratio problems together, which can provide different perspectives and solutions.

5-Minute Activities

Activity 1: Quick Ratio Quiz

Ask your child to solve three quick ratio problems before dinner. This keeps the mind sharp and focused on mathematical thinking.

Activity 2: Estimate and Check

Have your child estimate the ratio of everyday items (e.g., windows to doors in your home) and then check by counting.

Activity 3: Flashcard Ratios

Use flashcards with different ratio problems. Time your child as they solve each one, aiming for quicker and more accurate responses.

Activity 4: Graph It Out

Use graph paper and have your child plot ratios from their daily life, like hours spent on homework versus play.

Mid-Year Expectations

By the middle of 6th grade, your child should be able to:

• Students should be able to create simple ratio tables and identify equivalent ratios.
• Students should begin to feel comfortable plotting ratios on a coordinate plane.

End-of-Year Expectations

By the end of 6th grade, your child should be able to:

• Students can independently make tables of equivalent ratios and find missing values.
• Students can accurately plot and compare ratios on a coordinate plane.

Mastery Signs

Your child has mastered this standard when they can:

• Ability to explain the concept of ratios and their practical applications.
• Confident in manipulating and comparing complex ratios both numerically and graphically.

Questions to Ask:

Ask your child to solve these problems and explain their process:

• Create a table of equivalent ratios for 4:3 and find three missing values.
• Plot the points (3,9), (4,12), and (5,15) on a coordinate plane. What ratio do these points represent?
• How many different equivalent ratios can be formed from the ratio 6:8? List at least two.
• Compare the ratios 2:3 and 4:6. Are they equivalent? Explain your reasoning.