p5 maths lesson plan on percentage

ContentsIntroduction –Converting More Fractions to Percentages.............................................................................................................2

Instructional Objectives................................................................................................................................................................. 3

Common Pupils’ Difficulties........................................................................................................................................................... 4

Lesson Plan...................................................................................................................................................................................6

INTRODUCTION........................................................................................................................................................................6

DEVELOPMENT 1: FRACTION AS PERCENTAGE WITH PICTORIAL REPRESENTATION.................................................8

DEVELOPMENT 2: FIND THE EQUIVALENT FRACTION WITH DENOMINATOR 100........................................................11

DEVELOPMENT 3: MULTIPLICATION METHOD...................................................................................................................12

DEVELOPMENT 4: CHANGING THE FRACTION INTO DECIMAL AND MULTIPLY BY 100................................................14

DEVELOPMENT 5: USING THE CALCULATOR....................................................................................................................16

CONSOLIDATION: ABILITY TO CHOOSE FROM THE THREE METHODS TO CHANGE FROM FRACTION TO PERCENTAGE........................................................................................................................................................................ 18

CLOSURE:............................................................................................................................................................................... 20

Bibliography................................................................................................................................................................................. 21

1

Introduction –Converting More Fractions to Percentages

Taken from “My Pals are here!”, this chapter focuses on converting fractions to percentage using three methods Equivalent Fraction Multiplication Method Unitary Method

The previous lesson focuses on expressing fractions where the denominator is 100. This is the first exposure to the concept of percentage with pictorial representation of hundreds and shaded parts as the percentage required to compute.

It aims

to show understanding that percent means ‘per hundred’ to practice expressing a part of a whole as a percentage to practice expressing each fraction as a percentage to practice expressing each decimal as a percentage

This unit’s learning is to change fractions that do not have a denominator 100 into percentage. choose among the three methods to solve the questions efficiently. use the calculator

o to check their manual calculation and o to calculate denominators that are big to simplify or cannot be simplify.

understand the word problem and having systematic ways to find the percentageo Express in fraction the subset out of the total number of itemo Simplify the fraction (if possible)o Decide from the three methods and express the fraction as percentage

2

Instructional Objectives

Topic: Percentage

Sub Topic: Expressing Fractions as Percentages

Level: Primary 5 Standard

Characteristics of Students:

Mixed AbilityActive and tactile learner

Total Duration: 60 min (2 periods)

Prerequisites:

Students should be able to:Multiply a decimal by 10 and 100Read and interpret a percentage of a wholeExpress a fraction with denominator 100 or 10 as a percentageExpress a percentage as a fraction in its simplest form

SIO:

At the end of the lesson, pupils should be able to: Express a fraction as a percentage using algorithm

Equivalent Fraction Method Multiplication Method

Express a fraction as a percentage using a calculator

3

Common Pupils’ DifficultiesPercentage is about using the base 100 for comparison. The students may not recognise the 1 whole mentioned in percentage is 100%. In the initial stage of introducing the lesson, it is important that students should recognize denominator with number other than 100 should not be taken literally as being expressed as out of 100.

I would create an A3 size pictorial and abstract chart on “Percentage” (Figure 1) to introduce the students the concept of percentage in relationship with fractions. The chart shall be pin onto the class display board.

As I introduced the second lesson on percentage, I would explain the rationale of this chart. This is to link their fraction unit to percentage.

The students will be pointed out the chart have different denominators. We cannot take the numerator literally and take it as the percentage shaded of out 100%. The first diagram has a denominator 100 and we can take the percentage shaded literally as 10%. The rest cannot be done so even though majority of them converted have similar percentage shaded.

As a rule of thumb, all fractions should be multiply by 100%. This is to assist students who are not able to visualize the concept in the initial stage of learning percentage. With the chart to assist them visually, the students can deduce with a denominator 100. At a later stage, they might realize there is no need to go through this process for the first diagram since it is already expressed 10 out of 100 while the rest requires so since the denominator are not express as 100.

The grid should help them in recognizing that we are finding the equivalent fractions with an objective to change the denominator to 100.

This chart hopes to achieve a secondary objective that as they learn to attempt problem sum, they could recognise they are looking at part-whole relationship.

4

Percentage

100 squares

Fraction

Percentage

100% = 10%

50 squares

Fraction

Percentage

100% = 10%

25 squares

Fraction

Percentage

100 %= 20%

10 squares

Fraction

Percentage

100% = 10%

Figure 1

Lesson Plan

TEACHING AND LEARNING ACTIVITIES MATERIALS TIME

INTRODUCTION: PowerPoint Slide 5min

5


LINKING PRE-REQUISITES TO NEW TOPIC.

Teacher starts the PowerPoint slide 1. He will recap that the symbol for percent is %. He will move on the teaching and explain according to the slides until slide 5, and reminds the students that previous lesson gave them the idea of converting percentage to fractions and vice versa. They will see a summarized table in slide 6.

Percentage Fraction Decimal

60%60100

0.6

Teacher talk: A whole is 100%.

The teacher will show a transparency to show percentage from Part-Whole perspective.

Question:A student scores 20 out of 100 marks for his Math test. What is the percentage did he score?

The teacher will use a 10 by 10 Grid to represent the whole mark (100) and the shaded region represents the 20 marks.

1-6

6


The teacher shall ask how we can represent the pictorial grid to fraction (abstract). After a wait time, the teacher shall write the score into fraction on the whiteboard. The teacher will ask the students if it is correct to say the student score 20%. He shall write on the whiteboard.

= 20% Agree or disagree?

The students shall work in groups of four to discuss. They are to have a group representative to express their agreement or disagreement of the pictorial grid and express their understanding in one sentence. (Vygotsky’s Co-Operative Learning in their Zone of Proximal Development).The students will have a representative from the group to share out their conclusion (Mathematical Reasoning and Communication).

Key idea:The students are reminded that percentage is about using the base 100 for comparison.

7


DEVELOPMENT 1: FRACTION AS PERCENTAGE WITH PICTORIAL REPRESENTATION.

Using slide 7 to 9, the teacher shall show the students what they went through previously.The teacher will go to slide 10 to highlight the learning for the day. Next slide 11, he will read the question posted.

Question:The student scores 20 out of 50 marks for Science test. What was the percentage he scored?

The teacher shall click to go slide12. A 5 by 10 square grid appears.

Question:Are we able to represent the score on this square grid?Answer: Yes.

What is the reason that we can get this score represented easily?Answer: There are 50 squares and we need to shade 20 of them.

In terms of fraction, we get?Answer: 20 over 50 ( ).The teacher shall click to slide 12, showing 20 shaded squares and with the fraction and percentage representation.

Question:

PowerPoint Slide 7 - 14

5min

8


Can we use this grid directly and claim the student score 20% for science?Answer: No.What is the reason for not doing so?Answer; There are 50 squares not 100 squares.

If the grid is with 50 squares, how can we express the marks in percentage? The students are given wait time. (Thinking Skill: Analysing Parts and Whole)The students will share their ideas. Later, the teacher will scaffold their ideas.

Teacher talk:In order words, the percentage was not express as a whole of 100 squares.A 10 by 10 equivalent square grid is needed to represent 100 whole in order to find the percentage. (Conceptual understanding. Relating the whole (100) to percentage).

Question:We read the student scored 20 out of 50. If the 50 squares cannot be used to express percentage since it is not 100 squares, how shall we do to find the percentage using the grid?

The students shall work in groups of 2 to discuss the possibilities based on the grid. The teacher will close the discussion after they shared their methods. He will click the slide and show the solution.

Teacher talk:If we want to see the mark out of 100 marks, the denominator needs to express as 100.From the grid we need another similar grid (click the slide and will show a duplicated of 5 by10 square grid beside).

9


The teacher shall ask what they can deduce from the slide show.The students should be able to understand that the denominator is made 100. By counting the shaded part, they get the 40. They should derive the fraction as. Key Idea:From here, the teacher shall point out that the equivalent fraction with denominator 100 is the key to get the percentage (Bruner’s pictorial understanding).

10


DEVELOPMENT 2: FIND THE EQUIVALENT FRACTION WITH DENOMINATOR 100 The teacher shall ask the students to find the equivalent fraction with denominator 100 for without the help of the grid.The teacher will write the fraction on the whiteboard

=

The teacher shall ask the students to ponder how they can get to the denominator 100. (Framework of Mathematic Curriculum on Processes. Reasoning and Making connection to previous learnt unit, fraction).

After a wait time, the students are asked to volunteer to communicate their idea of getting the step to denominator 100. (Mathematical Communication).

The teacher concludes that the denominator 50 should be multiplied by A number to reach 100. That number should be used to multiply the numerator. He shall write on the whiteboard

=

Key Idea:The teacher shall point out this is the first method we can get the percentage, that is by equivalent fraction method. They are reminded equivalent fraction was mentioned in fraction unit and the rationale here is the same although we are in the percentage unit (Piaget’s process of adaptation).

5min

11


DEVELOPMENT 3: MULTIPLICATION METHODThe teacher shall move on with the same fraction multiplying by 100% to get the percentage.

The teacher shall write the on the whiteboard.

100%

He shall ask the student what they understand from this statement from fraction point of view. The students shall work in groups of two to discuss (Vygotsky’s Co-Operative Learning in their Zone of Proximal Development). They will be asked to pen it down what was written on the whiteboard in their journals.

After discussion they shall write down a sentence to explain the rationale of the written algorithm. (Mathematical reasoning and communication).

Key Idea:The teacher shall point out this is the same as fraction reasoning found in their Fraction Unit. of 100.

He will point out on the whiteboard that

1 whole is 100% = = 1.

of 100% = 100% = 40

The teacher shall point out this is the second method we can get the percentage, that is by multiplication method. A whole is 100% (Conceptual understanding. Metacongition).

The students complete My Pals are Here! Pupil’s Book 5B page 74, Question 1 and 2 to

My Pals are Here! Maths 2nd Edition Teacher’s Guide 5B,page 69, Practice 2 Question 1 and 2

10min

12


reinforce the two methods learnt. (Drill And Practice). The teacher will randomly pick up some questions to discuss and work on the whiteboard.

13


DEVELOPMENT 4: CHANGING THE FRACTION INTO DECIMAL AND MULTIPLY BY 100.

The teacher will convert into decimal.The teacher will ask the students if they can convert the fraction into decimal.After completing the conversion, the teacher will write down the steps of conversion on the whiteboard.

= = 2÷5 = 0.4

The teacher shall highlight to simplify the fraction before division.

Question :What is the reason for simplifying the fraction? (Mathematical reasoning)Answer:

(1) This is to reduce chances of error in our calculation. (2) It is easier to work with smaller number.

From the simplified fraction, the teacher shall ask the students to find the decimal number of .The teacher shall write on the board

2÷5 =

The students shall calculate and give the answer which is 0.4.

From the decimal, the teacher shall show the working to find the percentage0.4 100% = 40

Key Idea:

Worksheet “Change fraction into Percentage”(Appendix A)

5min

14


The teacher shall explain this is similar to multiplication method with the exception that the fraction is changed to decimal.

The students will be given a worksheet (Appendix 1) to complete on changing fraction into decimals and into percentage (Drill and Practice).They shall left the last column “Alternative method” for later part of the lesson.

15


DEVELOPMENT 5: USING THE CALCULATOR

The teacher shall ask the class to use their calculator to verify their answers for the worksheet.The teacher shall wait for their computation. Later, he shall ask the student how they key in the figures to the calculator.

From the question, He will show the fraction and ask the students to use the calculator to find the answer.He shall ask the students if they key in the calculator

2 ÷ 5 100 and the answer shown 40

He shall ask the students to key in

2 ÷ 5% and answer shown is 40

He will ask on how the calculator knows what to do.

Question: (1) When they key in %, what does the calculator interpret this %?Answer: The % symbol means multiply by 100%

(2) Which methods best describe the calculator’s % function?The teacher shall give hint that they should look into the three methods learnt and deduce which algorithm fits the best the calculator is doing (Thinking skill by comparing and identifying relationship. To achieve Conceptual understanding).The teacher will wait for the students’ response.

5min

16


They would find the multiplication method similar to the calculator. (Skemp’s Relational Understanding)The teacher shall mention to the use of calculator in this case.

The teacher shall ask the students What does the percentage symbol (%) represents? Answer: 100.

The students complete My Pals are Here! Pupil’s Book 5B page 75, Question 3 to reinforce the method learnt. (Drill And Practice).

Key Idea:After completion, the teacher will ask them when the appropriate time to use the calculator for computation. The student will realize besides using checking and verifying their worked out answers, the calculator is useful when they are dealing with big denominator or fraction that could not be easily resolved by the three methods learnt (Metacognition).

TSLN: The students would be challenged to use IT technology to find doing things with creativity and away from rote learning.

17


CONSOLIDATION: ABILITY TO CHOOSE FROM THE THREE METHODS TO CHANGE FROM FRACTION TO PERCENTAGE

The students shall get into groups of three and complete their worksheet (Appendix A) on the column “Alternative Method(s)”. They shall write down their all suggested answers in the column.

From Appendix A

Fraction Decimals Percentage Alternative method(s)?1÷2= 0.5 0.5100%=50% Equivalent fraction

… … …

The teacher will go through the questions and asking for their suggested alternative method used for the conversion from fraction to percentage their rationale for using the particular method chosen.

The teacher shall be assessing on their ability to perceive and reason out to use a less tedious method for deriving the answer. (Thinking skill by comparing and identifying relationship. To achieve Conceptual understanding). He shall participate and give suggest to their responses if need to help in their decision making when doing similar questions (Mathematical Attitude: creating interest and confidence. Metacognition).

The students will be given worksheet “Challenge Your Understanding” (Appendix B).They are to complete the questions with the use of calculator. From the three methods learnt, they are reminded to give alternative methods to solve the conversion of fraction to percentage. They are supposed to put “NIL” in the column and reason if they believe they could not find a plausible or simpler alternatives to derive the answer (Conceptual Understanding)

The teacher shall go through the worksheet with the students. They shall give their answers on the alternative methods.

Worksheet “Challenge Your Understanding”(Appendix B)

15min

18


Questions:Do you realize some of the denominators are big numbers and it is tedious to simplify them?Answer: Yes.Conclude: It would be helpful to use calculator for these kinds of question.

Questions:Do you realized there are some fractions that cannot be simplified or find equivalent fractions?Answer: Yes.Conclude: It would be easier to use multiplication method to find the answer.

This is to evaluate and reinforce their understanding by connecting the ideas of having three methods and use calculator taught in the lesson (Mathematical Attitude: creating Appreciation. Metacognition).

TSLN: The students would be challenged to seeking better ways of doing things through class participation that promotes learning from peers who may have creative idea of working out the problem. This is to move away from rote learning.

19


CLOSURE:

What have the students learnt in this lesson? The teacher shall ask the class get into groups of four. They are given an A4 size paper To list out the three methods of changing fractions into percentage.

(Suggested answer: Equivalent fractions, multiplication method and change to decimal) Gives reason why there are three methods they can to choose for the fraction to be change to

percentage (Suggested answer: It is dependent on the ease and ability of simplifying the steps to the percentage).

To reason the use of calculators (Suggested answer: it can be used to check computed answers it is to ease the computation of big denominator which is tedious).

They are to submit their work and write down their names on the paper. Their responses shall be check by the teacher and their work shall be pinned on the class display board (Vygotsky’s Co-Operative Learning in their Zone of Proximal Development and Mathematical Communication to the class through display).

For homework, the students will complete My Pals are Here! Workbook 5B page 69, Question 1 to 4 to reinforce the method learnt (Drill And Practice).

A4 paper 5min

20

BibliographyFong, H. K., Ramakrishnanm, C., & Choo, M. (2008). My Pals Are Here! : Maths 5B Teachers' Guide(2nd Edition). Singapore: Marshall Cavendish Education.

Lee, P. Y., & Lee, N. H. (2009). Teaching Primary School Mathemactics. A Resource Guide (2nd Edition). Singapore: McGraw-Hill Education(Asia).

21

p5 maths lesson plan on percentage

Documents