Maryland Math 6.AT.A.3.a

Math6th GradeAlgebraic Thinking

The Standard

6.AT.A.3: Use ratio and rate reasoning to solve problems in context by reasoning about tables of equivalent ratios, tape diagrams, double number lines, or the Coordinate Plane.

Generate, compare and find missing values of equivalent ratios and unit rates using multiple representations.

Maryland College and Career Ready Standards for Mathematics (2025) · UNDERSTANDING RATIO CONCEPTS AND USE RATIO REASONING TO SOLVE.

Teacher's field guide

What Students Need to Do: Students fill in missing values in ratio tables by multiplying or dividing both quantities by the same number. They compare ratios and unit rates using tables, diagrams, and double number lines.
What Mastery Looks Like: A student can complete a table showing that 3 apples for $2 matches 9 apples for $6. They can show both on a double number line and explain that each deal gives 1.5 apples per dollar.
Common Misconceptions: Students may add the same number to both parts of a ratio instead of multiplying both parts. They may divide in the wrong order when finding a unit rate or put dollars and items on the wrong lines.
How to Assess It: Exit ticket: Cart A sells 6 pencils for $3, and Cart B sells 10 pencils for $5. Complete a table for 6, 12, and 18 pencils from Cart A, then find pencils per dollar and use a double number line to decide whether the rates match.

Lesson moves

Give pairs 12 red and 18 blue counters; have them build 2:3 and 4:6 groups, then record each group in a table.
Ask, 'If 4 tickets cost $6, will 10 tickets cost $12?' Have students explain using a table and a per-ticket price.
Play ratio match with cards showing 3:4, 6:8, 2:5, 4:10, and their unit rates; students explain each match.
Post store tags showing $3 for 12 ounces and $4 for 20 ounces; students find each cost per ounce and choose the better buy.

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