LESSON PLANNING OF DEFINE RATIO OF TWO NUMBERS (UNITARY METHOD)

Subject Mathematics

Grade 5^{th}

Students` Learning Outcomes

- Define ratio of two numbers.

Information for Teachers

- Ratio shows the relative size of two or more numbers. Ratio is the comparison between two quantities, by expressing in same units.

- In the ratio a: b, “a” and “b” are called elements of the ration.

- Ratio can be shown in different ways:

Material / Resources

Writing board, chalk / marker, duster, textbook

Introduction

- Prior to class beginning, write RATIO in large letter in the center of the chalkboard.

- Ask students to tell what they think the term means. See how many students respond.

- Randomly select 10 or 15 students to come forward.
- Ask how many of you have more than 5-members in the family or more than 3 siblings. [Or any other question to differentiate]
- Those students who have more than five members in a family come on my right and those who have 5 or less come on the left side.
- Ask remaining class to count the students on your right and left. [7, 8]
- Tell the students that “Ratio shows the relative sizes of two or more values”
- On board, write the numbers above each group, separated by a colon. For example, 7:8

- Ratio can be shown in different ways:

- 7:8 using “:” to separate the values or 7 to 8 or 7/8, where denominator and numerator represent the elements of ratio.
- Write examples on the board and let students think and discuss.
- How many students have brown colour or black colour hair?
- Students who bring lunch daily?
- How many write with left hand and how many with right hand?
- Who wear glasses or those who don`t?

Development

Activity 1

- Tell students with the help of the examples that in ratio the order is very important workout following examples with the help of the students.
- Example 1: suppose there are thirty-five people, fifteen of whom are men. Then the ratio of men to women is 15 to 2.
- Tell students to notice that, in the expression “the ratio of men to women”, “men” came first. This order is very important, and must be respected: whichever word game first< its number must come first. If the expression had been “the ratio of women to men”, then the numbers would have been “20 to 15”. Expressing the ratio of men to women as “15 to 20” is expressing the ratio in words. There are two other notations for this “15 to 20” ratio:

Odds notation: 15:20

Fractional notation: 15/20

- Example 2: there are 16 ducks and 9 peacocks in a certain park. Express the ratio of ducks to peacocks as write on the board; 16 to 9 or 16 / 9, consider the above park. Express the ratio of peacocks to ducks in all three formats as such; 9 to 16 or 9:16 or 9/16. The numbers were the same in each of the above example, but the order in which they were listed differed, varying according to the order in which the elements of the ratio were expressed.

Activity 2

- Tell students that they must have seen construction of building. The material used in building is called concrete. Concrete is made by mixing cement, sand, stones and water.
- A typical mixer of cement, sand and stones are written as a ratio, such as 1:2:6 etc.
- You can multiply all values by the same amount and you will still have the same ratio.
- If you used 10 buckets of cement, you should use 20 of sand and 60 of stones.
- Explain further with the help of the following example.

- If you have just put 12 buckets of stones into a wheelbarrow then, how much cement and how much sand should you add to make a 1: 2:6 mixers?
- Let us lay it out in a table to make it clear:

- You can see that you have 12 buckets of stones but the ratio says 6.
- That is OK, you simply have twice as many stones as the number in the ratio….so you need twice as much of everything to keep the ratio.
- Here is solution:

- The ratio 2:4:12 is the same as 1:2:6[because they show the same relative sizes]
- Ask students why are they the same ratio?
- Tell them that in the 1:2:6 ratio there is 3 times more stones as sand, and in the 2:4:12 ratio there is also 3 times more stones as sand.
- Similarly there is twice amount as much sand as cement in both ratios.
- So the answer is: add 2 buckets of cement and 4 buckets of sand. [You will also need water and a lot of stirring]
- Refer students in pairs to textbook exercise questions to do in their notebooks.
- Keep roaming in the class while students are doing their work. Correct them if they make any mistake.

Sum up / Conclusion

- A ratio shows the relative sizes of two or more values.
- Ratio can be shown in different ways. A: B, or A to B or A/B etc.
- Order of ratio is very important and can`t be changed.
- Ratio means a relation between part to part or part to whole.

Assessment

- Ask following questions either by writing on board or making small work sheet.

Follow up

- Give following to simplify and write in all three formats.