Average

QCM 502

Average

Pre-requisite skills and knowledge required for this lesson Pupils should be able to:

1.

Add, multiply, subtract and divide numbers (up to 10 million) and decimals

2.

Use a calculator to divide whole numbers and decimals by a whole number

Specific Instructional Objectives (SIOs) for this lesson: At the end of the lesson, pupils should be able to:

1.

Interpret average as the sum of all quantities divided by the number of quantities in a group

2.

Find the average of a set of data

(a) through the “add-then-divide” approach (b) through the “evening-out” approach Key Concept

Level

Average is the arithmetic mean of a set of data.

Primary 5 Resources

Class Size

1.

3 Bags of Oranges or plainly visible objects (21)

40 Students

2.

Magnetic Cut-Outs of Oranges (45)

3.

Individual whiteboards

Class Ability

4.

Average Darts Activity Sheet (Appendix A)

Mixed

5.

Whistle

6.

Prizes (Such as pens)

Duration

7.

Magnetic Dart Boards (5)

2 Periods, 60 minutes

8.

Math Journals

9.

My Pals are Here Workbook 5B Part 1 (Appendix B)

10. Worksheet 9.1 (Appendix C)

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Prepared by: Lee Wei Loong

PRIMARY 5: AVERAGE

Engage (15 minutes) Time

Activities

Notes

Have students sit in groups of 4 (10 Groups of 4).

Key Terms Average

15 mins

Introducing Average

“Evening-Out” Approach

Teacher calls for 3 volunteers. Teacher hands one bag (containing 4 oranges, 9 oranges, and 8 oranges respectively) to each student.

“Add-then-divide” Approach

Teacher directs students to show items to class.

“If all the oranges are shared equally between the three of them, how many oranges would each of them get?”

Teacher allows students to average out the oranges on their own. If students used the “evening-out” approach, introduce the term “evening-out” approach and explain the approach using magnetic cutouts of oranges on the whiteboard. If the students used the “add-then-divide” approach, likewise explain the approach using magnetic cutouts of oranges on the whiteboard. Thereafter, teacher calls out another three students and encourages students to use the other method to average out the oranges and likewise explain the approach using magnetic cutouts on the board.

“Evening-out” Approach

Sum Quantities

Resource 21 Oranges (or plainly visible objects) 3 Bags 50 Magnetic Cut-outs of Oranges

Vocabulary Average: Sum of all quantities divided by number of quantities (for introduction) and Arithmetic mean of a set of data

“Add-then-divide” Approach

Teacher explains that 7 is the average of 4, 9 and 8.

Teacher explains that the average of 4,9 and 8 is the sum of 4, 9 and 8 (the quantities) divided by 3 (the number of quantities) Teacher explains that average is the arithmetic mean of a set of data.

Quantities 7

is the average of

Arithmetic Mean

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4, 8 and 9

The average of 4, 8 and 9 is the sum of the quantities

(4 + 8 + 9)

Set of Data divided by the number of quantities (3)

Prepared by: Lee Wei Loong

PRIMARY 5: AVERAGE

Elaborate (15 minutes) Time 15 mins

Activities

Notes

“Evening-out” vs “Add-then-divide”,

Key Terms

Teacher directs students to try finding the average of the following sets of data:

Set Data

Resource Individual Whiteboard (One per student)

Reminder The average of a set of data may not always be a whole number.

Teacher calls for 2 volunteers: one to demonstrate solving the first set using the “evening-out” approach and the second to solve the same set using the “add-thendivide” approach. Teacher directs the rest of the students to try using their individual whiteboard.

Teacher calls for another 2 volunteers, this time to solve the second set. Again, one is to demonstrate solving the set using the “evening-out” approach and the other to use the “add-then-divide” approach while the rest attempt the set on their individual whiteboards.

“Can we use the ‘evening-out’ approach all the time?”

“Which approach can be more easily applied?” (“Add-then-divide” approach) Finally, teacher calls for another two volunteers to attempt the third set similarly. By the end of the three examples, students should understand the difference between using the two approaches to find average and have a better idea of when to use each approach.

Teacher emphasizes that the add-then-divide approach can be used to get the average in all situations when the quantities in a set of data is known and can be found using the “add-then-divide” approach:

Average =

Sum of all quantities Number of quantities

Teacher also reminds students of the answer to the last set of data, that the average of a set of data may not always be a whole number.

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Prepared by: Lee Wei Loong

PRIMARY 5: AVERAGE

Explore (20 minutes) Time 20 mins

Activities

Notes

“Average Darts”,

Safety

Teacher to provide one magnetic dart board for every two groups.

Remind students to play the game safely and to not throw their darts at each other.

Conduct of “Average Darts” Game ‣Teacher distributes activity sheets (one per student) (Appendix A) ‣Teacher distributes magnetic dart boards to Teams 1, 3, 5, 7 and 9. ‣Teacher briefs students how the scoring takes place in the darts game

In each pair of groups, the groups will compete to get the highest score playing darts as they practise calculating average while completing the activity sheet. The groups will rotate four times.

‣If there are absentees, a player/players plays/ play twice in the team to fulfill four throws per game.

Resource 5 Magnetic Dart Boards Average Darts Activity Sheet (One per student) (Appendix A) Prizes (Small prizes such as pens) Whistle

‣Students record the scores in their activity sheets and calculate the average scores for both their own team and their opposing team ‣Students circle the result of their round, i.e. win/lose ‣Each game lasts for 3 minutes, before teacher blows a whistle and even-digit teams rotate to play with their next opponents based on the table on the left ‣After four rounds, students go back to their own seats and calculate the average for 4 rounds of scores based on individual scores and 4 average scores ‣Teacher distributes prizes to teams with the most wins

During each round, each group will record down the team highest individual score, and the average team score on their activity sheets.

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Prepared by: Lee Wei Loong

PRIMARY 5: AVERAGE

End (10 minutes) Time 10 mins

Activities

Notes

Resource

Summary,

Evaluation

Math Journal/

Teacher distributes homework (My Pals Are Here 5B, Workbook Part 1, Pages 49 to 52) and Worksheet 9.1 and jots down the deadline on the whiteboard.

Teacher to evaluate student responses during summary to decide whether it is necessary to revisit objectives set out in this lesson

Textbook

Teacher directs students to take out their Math Journals/Textbook.

Teacher directs students to jot down what they have learnt in their Math Journal/ Textbook.

Teacher gets volunteer students to share what they have written whilst ensuring that students present on the board: “Average = Total number or quantity/Total number of items” Example of “evening-out” approach

My Pals Are Here Workbook 5B, Part 1, Pages 49 to 52 (Appendix B)

Worksheet 9.1 (Appendix C)

Example of “add-then-divide” approach Teacher provides students with some questions to ponder on average: “If the average score of your class’s Math Test results is 15 out of 20, does that mean everyone scored 15 marks?” (No, not necessarily) “If your score is average, is that good or bad?” (It depends on the average score) To lead up to the next lesson (finding the sum given the average and number of items) “If each of you have an average of $5, how much money would all of you have?”

Lesson plan adapted from My Pals Are Here, Textbook 5B, and Teacher’s Guide, Math Works! Teacher’s Guide

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Prepared by: Lee Wei Loong