Representing shared portions (Ratio and Percentage.) Strand: Numbers (Lesson 1)

 FOCUS QUESTION

How can I represent shared portions?

SPECIFIC OBJS.

1.       Use ratio to compare quantities.

2.       Write a ratio to compare the numbers of items in two sets or two parts of a single set.

3.       Write a ratio using the formats 1:5, 1 to 5, 1/5.

4.       Write equivalent ratios for a given ratio

CONTENT SUMMARY

ENGAGE

Students will be asked to differentiate between the concepts ‘Share” and “divide”

Share a group of 18 counters as instructed by teacher. That is, for every 1 counter Pete gets, Harry gets 2. Students will answer the questions:

(a)    How many did Harry get?

(b)   How many did Pete get?

EXPLORE

I want you to watch this video clip to glean information on RATIO.

 Youtube video (Introduction to ratios , ratios,rates and percentage) 

(Teacher will pause at intervals to highlight that ratios can be written in three different ways. Eg 2 to 3, 2:3, 2/3)

(Students will revisit the first activity done, and write how the counters were shared in ratio format. That is, 1:2.)

Let's review the concept "equivalent fraction". What do you recall about this?

 Ok, there can be equivalent ratios also. Let's read the following chart below. 

Now find a ratio equivalent to 1:2 = 6:12

We can also simplify given ratios. Look at the following.

EXPLAIN

Explain what ratio is and how it can be written.

Tell what is meant by equivalent ratios and provide examples.

EXTEND/ELABORATE

Work cooperatively to solve problems on ratio. Eg.

In a bag, there are 5 red marbles,  2 green and 7 black.

(a)    What is the ratio of green marbles to red marbles?

(b)   What is the ratio of red marbles to green marbles?

(c)    Green marbles to the total number of marbles?

EVALUATE

1. In a school, there are 60 boys and 40 girls. What is the ratio of girls to boy? What is the ratio of boys to the total number of students?

 2.  Simplify the following ratios.

(a)    14: 60  (b) 12: 50   (c) 20 : 25

3. Write two ratios that are equivalent to the ones below.

(a)    3:6   (b) 4:10   (c) 3:7

3.

 

4. 

Follow up Practice Exercise

Activity 1

Activity 2

Activity 3

Activity 4

Activity 5

Activity 6

Activity 7

Activity 8

Activity 9

Lesson Title: Understanding Ratio and Proportion

Grade Level: 6

Duration: 1 Hour

Focus Question: How can I represent shared portions?

Theme: Ratio and Proportion

STEM Integration: Technology (Virtual ratio models), Engineering (design challenge with ratios), Mathematics (core content)

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Objectives

By the end of the lesson, students should be able to:

1. Use ratio to compare quantities.

2. Write a ratio to compare the numbers of items in two sets or two parts of a single set.

3. Write a ratio using the formats: 1:5, 1 to 5, and 1/5.

4. Write equivalent ratios for a given ratio.

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Materials Needed

• Colored cubes or counters

• Chart paper

• Virtual ratio tools (optional: laptops)

• Juice powder and cups (real or pictures)

• Whiteboard/markers

• Projector

• Chromebooks

• Teacher's blogsite

🌀 5E Lesson Model

1. Engage (10 minutes)

Activity: Sharing Candy Challenge

• Display 2 bowls of candy: Bowl A with 10 red candies and 5 green candies.

• Ask: “If I wanted to compare how many red candies to green candies I have, how would I describe that?”

• Students discuss in pairs and then share out.

• Introduce the word ratio as a way to compare quantities.

• Connect to real-life situations (e.g., recipe ingredients, class girls to boys).

STEM Integration: Show a short video clip (1–2 mins) on how ratios are used in mixing paints or recipes using technology.

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2. Explore (15 minutes)

Activity: Ratio Sorting Stations

• Students rotate through 3 stations:

  1. Station 1: Use colored cubes to model ratios (e.g., 3 red to 2 blue cubes).

  2. Station 2: Picture cards showing grouped objects to write ratios.

  3. Station 3: Use a virtual manipulative site (e.g., Toy Theater Ratio Tool) to build and compare ratios.

Students will record the ratios in three formats:

• A:B,

• A to B,

• A/B

Differentiation:

• Tier 1: Use physical cubes.

• Tier 2: Add writing equivalent ratios.

• Tier 3: Predict missing values in ratio tables.

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3. Explain (10 minutes)

Teacher Input:

• Explicitly teach how to write ratios in different formats using examples from stations.

• Demonstrate how to write equivalent ratios using multiplication or division.
  Example: 2:3 → 4:6 → 6:9

• Discuss the meaning of part-to-part and part-to-whole ratios.

Students Record:

• Notes in their math journals with examples.

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4. Elaborate (15 minutes)

Activity: STEM Group Challenge – Juice Mixture

• Scenario: You are engineers creating a juice drink. The best taste comes from a ratio of 2 cups of water to 3 cups of juice.

• Task: In groups, scale the recipe to make enough for a party of 10 guests.

• Use measuring tools, cups, or visuals to demonstrate.

• Write at least two equivalent ratios and show the total mixture.

• Share findings with class.

Differentiation:

• Support groups: Use guided ratio tables.

• Advanced groups: Use ratio reasoning to determine missing quantities.

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5. Evaluate (10 minutes)

Three-Tiered Assessment:

Tier	Task
Tier 1 (Basic)	Write the ratio of 4 apples to 6 oranges in three formats.
Tier 2 (Intermediate)	Write two equivalent ratios for 3:4. Explain what makes them equivalent.
Tier 3 (Advanced)	Complete the ratio table and determine the missing number:
2:5 = ? : 15. Show your working.

Exit Ticket Prompt (optional):
“Describe a situation in real life where you’ve used or seen ratios. How were they helpful?”

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STEM Connection Summary

• Science/Engineering: Designing a drink mixture with precise proportions

• Technology: Using interactive digital tools to visualize and manipulate ratios

• Math: Writing, comparing, and explaining ratios and proportions

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Video Clip - Lattice way of multiplication