Connecting Fractions and Decimals

INTRODUCTION

SYLLABUS DOT POINTS

Convert fractions to decimals (terminating and recurring) and percentages
Convert terminating decimals to fractions and percentages
Evaluate the reasonableness of statements in the media that quote decimals

WORKING MATHEMATICALLY INDICATORS

Students will:

Identify the correct process for converting fractions to decimals. (Understanding)
Compare fractions, decimals and percentages representing an identical value. (Communicating, Reasoning)
Identify how to convert terminating decimals to fractions and percentages. (Understanding)
Recognise that calculators may show approximations to recurring decimals and explain why. (Communicating, Reasoning)

LEARNING GOALS

By the end of this lesson students will be able to:

Explain how to convert fractions to terminating decimals.
Explain how to convert terminating decimals to fractions.

MATERIALS REQUIRED

Rope with pegs on it for the fractions game
Fractions to decimals worksheet
Whiteboard markers and rubber
Instruction sheet for Rope game

TEACHING AND LEARNING STRATEGIES

The focus on this lesson would be on connecting the idea of decimals to fractions and percentages. This would initially be achieved through teaching students how to convert fractions to both terminating and recurring decimals. It would be emphasised that both fractions and decimals are correspondingly used to represent parts of a whole so that is why it is important to connect the notions together.

The later part of the lesson would then involve students learning how to convert terminating decimals to fractions. i.e emphasing different ways of representing the same number. The concepts in this class would then be related to real life with examples such as for example average number of cars per household.

LESSON PLAN

INTRODUCTION (15 MINUTES)

The lesson would start with the teacher asking students if they had any issues with the homework from the previous class. The teacher could also quickly recap the key ideas from last class as well to ensure that students have retained the ideas that were taught.

Following this, what will be focused on in the lesson will be revealed to students. Looking at changing fractions to decimals and then decimals to fractions. As an initial explanation that teacher would explain that both fractions and decimals are just different ways of expressing parts of a whole. To help the teacher would draw pizzas on the board. For example they could show that 1/2 is the same as 0.5. They could say 'if this whole pizza is equal to 1. 1 whole. Then what do you think half of this pizza is equal to?' and 'isn't this the same as 1/2?' The teacher would then write up some examples on how to convert fractions to decimals and then decimals to fractions.

BODY (40 MINUTES)

(25 MINUTES)

Continuing on the body of the lesson would occur. The first activity the teacher would get students to do would be the fractions to decimals game involving the rope. (It is the 1st Resource down). For this game students would split into around 4-5 groups (Depending on the size of the class). Students would then be instructed to divide their rope up into different fractions and then record the matching equivalent decimal. The fractions for students to look at would be written up on the board. The teacher would then instruct students to experiment with their ropes and engage in a discussion. Whilst students are working the teacher could ask 'how many times do you have to fold your rope to make 1/5?' and 'what decimal is this?'

(15 MINUTES)

Once students have had enough time to complete the first activity they would then be instructed to go back to their seats. Here they will be provided with a worksheet that looks at connecting fractions to decimals and even percentages. (It is the 2nd resource down). Students will then be instructed to complete the worksheet individually. Whilst this is happening the teacher could circulate the room and answer questions when needed. If there are students who finish the worksheet really quickly they could then be handed the worksheet that has a more visual emphasis to it that requires students to write a fraction and then its equivalent decimal. (It is the 3rd resource down). Once students have had enough time to complete the first worksheet, the teacher would then go through the solutions on the board. Questions they could ask whilst doing this could include 'can the fraction 84/100 be simplified?' and 'we had the fraction 20/100 and simplified it to 1/5 right? Is 1/5 still equal to the decimal 0.2?'

ASSESSMENT FOR LEARNING AND CONCLUSION (5 MINUTES)

The key ideas from today would be reinforced. This could involve the teacher asking a few quick questions on the content that was looked at today (AFL). For example, 'before you leave class today just tell me again, is 1/2 equal to 0.5?' and then 'okay I can see that you are coming along really well with that. What about this question though. Do you think the fraction 3/2 is equal to the decimal 1.5?' If students are unable to answer the second question students would be instructed to have a think about it for homework. A few carefully selected suitable textbook questions would also be allocated so that students can consolidate what they learnt today.

LESSON EVALUATION QUESTIONS

Was there enough room in the classroom to complete the first activity?

Did students seem engaged with the rope exercise or were they not interested in experimenting with it?

Did the visual diagrams on the worksheets help students make connections between fractions and decimals?

RESOURCES

1) LIT

A rich task that could be implemented into the classroom, which looks at connecting decimals with fractions a game that was found on the maths300 website. The game is called "Fractions to Decimals (on a rope!)." It involves using a rope and pegs to represent a number line from 0-1. The pegs are divided into 10 parts to represent decimal numbers. For example 0.1-0.9. Students would then be instructed to make fractions such as one half by folding their rope. They could then repeat this for a fraction such as a third, so they would fold their rope three times. This is represented in the picture to the right. They could then be instructed to produce more fractions of their own.

The first part of this activity could also be particularly useful for addressing any gaps in prior knowledge. Students who may be struggling with decimals could be helped here with a visual demonstration of what decimals are.

Retrieved from: https://maths300.com/members/m300full/182lfrac.htm

2) LIT

The first included resource is worksheet that involves converting fractions to decimals and percentages. This worksheet is a good means of helping students understand the relationship between the three ideas and how they are all used to represent parts of a whole. The worksheet also has a visual component which could help students with the conversions required. The image is just a screenshot and involves more questions. Link to the worksheet: https://www.pinterest.com.au/pin/270708627582513342

3) ICT

The next resource is another one that utilises technology. It is a game called "Fruit Splat," that involves students matching fractions with their associated decimal. The game is quite engaging and is therefore suitable for helping students successfully learn the concept. It has multiple difficulty levels so it can also be effective for students wishing to challenge themselves more or others wanting to take a step back and try something easier.

Note: Adobe flash player needs to be enabled.

Link to the game:

http://www.sheppardsoftware.com/mathgames/fractions/FractionsToDecimals.htm

4) LIT (In Reserve)

This is another worksheet that could be good in reserve. It is quite easy so could be given to students who may be struggling to help them.

Retrieved from: https://www.tes.com/teaching-resource/tenths-fractions-and-decimals-6090788

This could also potentially prove very valuable for students who are more visual learners.

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