6.5.A

Math6th Grade

The Standard

represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

Texas Essential Knowledge and Skills for Mathematics

Teacher's field guide

What Students Need to Do: Students identify the multiplicative relationship between two quantities and use it to generate equivalent pairs. They show the same relationship in a table, on a graph, with a scale factor, and as a proportion.
What Mastery Looks Like: A student can show one situation with an equivalent-ratio table, ordered pairs, a graph, and a proportion. The student uses a consistent scale factor and explains what each number means with units.
Common Misconceptions: Students may add the same amount to both quantities instead of multiplying by the same factor. They may reverse ratio order, mix units, or place quantities on the wrong graph axes. Some assume every table is proportional without checking for a constant rate.
How to Assess It: Exit ticket: A recipe uses 3 cups of flour for 4 servings. Complete a table for 8 and 10 servings, graph the points, and solve 3/4 = x/10.

Lesson moves

Use red and blue counters to build a 2:3 ratio, then scale the groups and record each pair in a table.
Ask, "How can you prove that 12 miles in 3 hours and 20 miles in 5 hours show the same rate?"
Give groups matching cards with situations, tables, graphs, and proportions, then have them justify each completed set.
Compare two grocery package sizes by finding unit prices, building tables, and graphing cost against quantity.

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