6th Grade Math Lesson

Comparing Rates: Grocery Prices and Fuel Efficiency

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6th GradeThinking ClassroomCCSS.MATH.CONTENT.6.RP.A.1, CCSS.MATH.CONTENT.6.RP.A.2, CCSS.MATH.CONTENT.6.RP.A.3b45 min

Learning Objective

Students will write ratios in multiple forms, compute unit rates by dividing quantities, and use unit rates to make optimal purchasing decisions in real-world contexts.

Lesson Overview

Students progress from writing ratios in multiple notations to computing and comparing unit rates in grocery and fuel contexts, culminating in a bulk-buying optimization challenge. Tasks are thin-sliced so only one variable changes between consecutive problems.

Materials

Vertical whiteboards or large chart paper posted on walls
Dry-erase markers (one per student or one per group)
Pencils and scratch paper at each board
Random grouping cards or a phone app to assign groups of 2-3
Basic calculator or phone calculator for Tasks 5-7

Scaffolded Task Progression

1Task 1

A grocery bag has

4

red apples and

6

green apples. Write the ratio of red apples to green apples in all THREE forms: using a colon, using the word 'to', and as a fraction. Then write the ratio of green apples to red apples in all three forms.

2Task 2

Same grocery bag:

4

red apples and

6

green apples. A student says: 'I can simplify this ratio by subtracting

2

from both numbers, so

4 : 6

simplifies to

2 : 4

.' Is this student correct? Show on your whiteboard why or why not using a diagram or a table of equivalent ratios.

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