Lesson 52 : Expressing Ratios in their Simplest Forms



Lesson 52 : Expressing Ratios in their Simplest Forms

Week 9

Objective: Expresses ratios in their simplest forms

Prerequisite Concepts and Skills:

• Dividing Numbers

• Prime and Composite Numbers

• Finding the Greatest Common Factor (GCF)

Materials : flash cards, concrete objects, activity sheets, charts

References : K to 12 Grade 5 Curriculum, M5NSIIi-125, Lesson Guide Grade 5 pp. 222 - 226, MISOSA Grade 5 Module - Ratio in its Simplest Form, Mathematics for a Better Life Textbook p.198 - 199

Instructional Procedure

A. Preliminary Activities

1. Drill

Mental computation on reducing fractions to lowest terms.

2. Review

Do what each problem asked.

COLON FRACTION

a. Ellen has 2 chicken eggs and 3 quail eggs _______ __________

in a tray. What is the ratio of quail eggs

to chicken eggs?

b. There are 5 baskets of mangoes. Each basket _______ __________

contains 75 mangoes. What is the ratio of

5 baskets to the total number of mangoes?

c. Kris bought 3 pairs of shoes and 5 pairs of _______ __________

socks. What is the ratio of shoes to socks?

3. Motivation

a. Use patterns to help you complete the table below.

Recycling Campaign

Number of |Bottles (kg) |1 |2 | |7 |10 | |15 | | |points |5 |10 |15 | | |60 | | |

b. Describe the pattern of the numbers in the table.

c. Write the ratio in the lowest terms for 15 points; 10 kg; 15 points; 60 points

d. What benefits can be derived from the “recycling campaign” activity?

B. Developmental Activities

1. Presentation

Have the pupils read and understand the situation below.

Ask these questions:

• What did Joel and Josie picked in the park?

• What they re going to do with those things?

• Would you have done the same thing as what Joel and Josie did?

2. Performing the Activities

Group the pupils into six working teams.

To change 12 : 24 to lowest

Expected answer

Solution : Finding the GCF of the given ratio

a. by listing method

Factors of 12 : 1, 2, 3, 4, 6, 12

Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24

GCF : 12

b. By dividing the numerator and denominator by their GCF

12 12 12 1

24 24 12 2

c. By using prime factorization

12 1 x 2 x 2 x 3 1

24 1 x 2 x 2 x 2 x 3 2

3. Processing the Activities

As a follow up, request some pupils to show and discuss their answers.

Ask: How did you solve the problem?

How did you change 12 : 24 to lowest term?

4. Reinforcing the Concept and Skill

Ask pupils to answer A and B exercises under Get Moving, pages ____ LM Math Grade 5. After the given time, check the pupils’ answers.

Allow pupils to answer exercises A and B under Keep Moving, pages ___ LM Math Grade 5. Check the pupils’ answers.

5. Summarizing the Lesson

Lead the pupils to generalize as follows:

6. Applying to New and Other Situations

Let pupils answer the problems under Apply Your Skills, page ___, LM Math Grade 5.

C. Assessment

Express each ratio to its lowest term.

1) 8 : 10 2) 9 : 12 3) 6 : 15 4) 4 : 12 5) 3 : 18

D. Home Activity

Remediation

A. Reduce these ratios to lowest terms.

1) 10 : 5 4) 15 : 30

2) 3 : 12 5) 6 : 8

3) 20 : 4

B. Express these ratios in lowest term

1) 100 4) 4

10 4000

2) 120 5) 200

2 2

3) 50

500

Enrichment

Give the ratio of the following problems, then reduce to lowest term.

1. In a Grade V class there are 20 boys and 28 girls. Find the ratio of the numbers of girls to the number of boys.

2. In a school there are 60 teachers and 300 pupils. Find the ratio of the numbers of teachers to the number of pupils.

3. Ellen is 130 cm tall and Cecil is 150 cm tall. Find the ratio of Ellen’s height to Cecil’s height.

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Value Focus: Love for Mother Earth by recycling

Joel and Josie went to the park to help clean it up by picking discarded bottles of soft drinks to be recycled. Joel picked 24 bottles while Josie got 12 bottles. What is the ratio of the number of bottles gathered by Joel to the number of bottles gathered by Josie in lowest term?

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=

=

=

=

In reducing a ratio to its lowest terms, think of a common divisor for the given ratio.

If the ratio has no common divisor except 1, there is no need to reduce the ratio to its lowest term. It is in its simplest form already.

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