Lesson 1-1: Understanding Ratios

Scenario: Juice Mixing - Learn to mix the perfect juice using ratios!

Duration: 45-60 minutesScenario: Juice Mixing

Learning Objectives

Understand different ways to write ratios (1:3, 1/3, 1 to 3)
Distinguish between part-to-part and part-to-whole relationships
Use ratio tables to find equivalent ratios
Create and interpret tape diagrams

What is a Ratio?

Juice Mixing Scenario

Imagine you're making orange juice from concentrate. The recipe says to mix 1 cup of concentrate with 3 cups of water.

Ratio of concentrate to water: 1:3

This means for every 1 part concentrate, we need 3 parts water.

Different Ways to Write Ratios

Colon Notation

1:3

"1 to 3"

Fraction Form

1/3

"1 over 3"

Word Form

1 to 3

"1 to 3"

Part-to-Part vs Part-to-Whole

Part-to-Part

Concentrate to Water: 1:3

Compares one part to another part

Part-to-Whole

Concentrate to Total: 1:4

Compares one part to the whole mixture

Ratio Tables

Let's see how we can scale up our juice recipe using a ratio table:

Concentrate (cups)	Water (cups)	Total Juice (cups)
1	3	4
2	6	8
3	9	12
4	12	16

Key Pattern: When we multiply both parts of the ratio by the same number, the ratio stays the same!

1:3 = 2:6 = 3:9 = 4:12 (all equivalent ratios)

Tape Diagrams

Tape diagrams help us visualize ratios. Let's represent our 1:3 ratio:

Concentrate:

1 part

Water:

3 parts

Visual Tip: Each colored bar represents one part. Notice how water has 3 times as many bars as concentrate!

The tape diagram shows that water is 3 times as much as concentrate, maintaining our 1:3 ratio.

Practice Problems

Problem 1

A paint mixture uses 2 parts red paint to 5 parts white paint. Write this ratio in three different ways.

Your answer:

Colon:

Fraction:

Words:

Problem 2

Are the ratios 2:5 and 4:10 equivalent? Use a tape diagram to verify your answer.

Your reasoning:

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