Proportion

Ämne / Topic

Creating and solving equations involving proportion.

Inlärningsmål / Learning Goals

Be able to write an equation involving proportion

Google Slides & Videos

Lektionssteg / Steps in the lesson:

1. Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson

Warm-up activity: What is proportion?

Material: Coloured straws

Participants: Pairs

This activity will help learners understand proportion better, through the use of using coloured straws.

Each pair will be given a different number of two different coloured straws.

Learners will need to identify how many of each colour straws they have and write this as a ratio eg. 4 green straws and 6 yellow straws

Learners will then need to simply the ration and Learners sharing and explaining their answers with the rest of the class. how they did this:

4 : 6 (can be simplified by dividing both numbers by two)

4 : 6

2 2

= 2 : 3

Learners can conclude that for every 2 green straws there will be 3 yellow.

2. Introduktion till lektionen / Introduction to the lesson content

The main activity of the lesson will start off with the learners watching a video on where proportion can be used in real world situations - this will help the learners see the relevance of proportion. After watching the video, the learners will work with a partner and come up with a real world proportional question, relative to their lives as teenagers.

3. Aktiviteter / Key Activities

After the introduction (watching the video and coming up with own questions) is complete, the teacher will continue the lesson, by going through different examples based on the equations.

Example 1: (Teacher led example)

In a school, the number of girls to boys is 7:9. Altogether there are 336 students at the school.

How many girls and how many boys are at the school?

Make the number we multiply by x.

1. Multiply the ratio of girls by x.

7x

2. Multiply the ratio of boys by x.

9x

3. Add the ratio of girls to the ratio of boys.

7x + 9x

4. Make the expression equal to the total number of students in the school.

7x + 9x = 336

5. Solve for x.

7x + 9x = 336

16x = 336

x = 21

6. Multiply the ratio of girls and the ratio of boys by the value for x.

Girls: 7 (21) = 147

Boys: 9 (21) = 189

So there are 147 girls and 189 girls in the school

Example 2: (Teacher and students complete together).

What is the ratio of the shortest side of the triangle to the longest side?

Express the answer in simplest form.

Side 1: 10 cm

Side 2: 8 cm

Side 3: 4 cm

1. What is the length of the shortest side?

4 cm

2. What is the length of the longest side?

10 cm

3.Write this as a ratio.

4 : 10

4.How do we simplify this ratio?

4 : 10

2 2

2 : 5

So, the proportion of the shortest side to the longest side is 2 : 5

Example 3: (Learners do on their own)

Three numbers are in the ratio 2 : 5 : 7.

The middle number is 75.

What are the other two numbers.

2x : 5x : 7x

5x = 75

5 5

x = 15

So, 2 (15) = 30

7 (15) = 105

So the other two numbers are 30 and 105

4. Kolla vad eleverna kan / Check for understanding / Exit ticket

Learner will complete three questions on the white boards that have been provided with. After a couple of minutes to complete the question, the teacher will say 'times up' and learners will need to hold up their boards with their answers.

1. What is the ratio of the number of red to the number of blue balls. Answer in simplest form.

2. The number of staples in box A is related to the number of staples in box B as 3 : 5.

If box B contains 25 staples, How many staples are there in box A?

3. Three numbers are in a ratio 3 : 5 : 8. The difference between the biggest number and the smallest number is 45. What are the tree numbers?

5. Stängning / Closure / Summary of lesson

Learners sharing and explaining their answers with the rest of the class.