Terminating and Recurring Decimals

SYLLABUS DOT POINTS

• Terminating and Recurring Decimals
• Use the notation for recurring (repeating) decimals
• Investigate 'irrational' numbers

WORKING MATHEMATICALLY INDICATORS

Students will:

• Explain the difference between terminating and recurring decimals. (Reasoning, Understanding)
• Identify terminating and recurring decimals. (Understanding)
• Describe, informally, the properties of irrational numbers. (Communicating)

LEARNING GOALS

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

• Identify how decimals can terminate or recur/repeat
• Explain how decimals can also continue without any pattern of numbers (irrational).

MATERIALS REQUIRED

• Terminating and recurring decimals worksheet
• Rational and irrational numbers worksheet
• Whiteboard markers and rubber
• Worksheet resource three

This lesson would initially introduce to the students the ideas of terminating and recurring decimals. Firstly, terminating decimals would be looked at, with students being made aware of what they are, i.e. a decimal with a set number decimal places. Then the idea of a recurring decimal would be introduced. An easy one to start with would be 1/3, whereby an example could be shown where 3 divides into 1, showing that the division does not end in decimal form. Notation would then be introduced to students for recurring decimals. Finally the class would end with the idea of irrational numbers being brought up to students.

INTRODUCTION (15 MINUTES)

Firstly, the teacher will ask students if they had any issues with the homework from last lesson. If there is a repeated question that multiple students struggled with the teacher will address this and complete the correct solution on the board step by step for each student to see.

Once this is completed the teacher will then inform students that in this lesson they will be looking at the idea of terminating and recurring decimals. The teacher will now undertake an explanation on the board. The first thing the teacher would talk about is the idea of terminating decimals. It would be outlined that a terminating decimal has a finite number of decimal places. Examples such as 0.5 and 0.725 would be written on the board. The teacher could ask 'Do you think 0.3 is a terminating decimal?' and 'What about if you were to rewrite the fraction 1/3 as a decimal. Do you think this is also a terminating decimal or do you think it might be something different?' The teacher would now explain to students that is in fact a recurring decimal. It would be said that a recurring decimal has an infinite number of decimal places, with a sequence of digits that are repeated.

The different types of notation used to represent recurring decimals would now also be shown. Following on from this the idea of rational and irrational numbers would also be referred to and connected. The teacher would say that rational numbers can be written as fractions whilst irrational numbers cannot. The teacher would then ask 'Do you think recurring decimals are rational and irrational?' and 'why?'

BODY (35 MINUTES)

(15 MINUTES)

Following the introduction the body of the lesson would now commence. The teacher would instruct students to undertake a worksheet on terminating and recurring decimals. (It is the 1st Resource down). Whilst students are working through the questions the teacher would circulate the room and ensure that all students are on task. The teacher could also ask, 'do you agree that all recurring decimals can be written as a fraction?' and 'Does recurring mean the same as repeating?' The teacher would also be ready to provide feedback and help students when needed. After about 10 minutes of allowing students to attempt the questions the solutions would now be worked through on the board. Here the teacher could write up a few answers themselves or even get volunteer students to come up to the board and write their own solutions. This would approximately take 10 minutes.

(20 MINUTES)

Following on from this for the next exercise the teacher would now ask students to break into small groups to complete the last two exercises. (The 2nd and 3rd Resources down). Here, different symbols for representing recurring decimals would be allocated as a discussion point for students to talk about (Reasoning, Communicating). For example to encourage discussion the teacher could ask 'Is the bar method or dot method a better way to represent recurring decimals?' Once students have had 15 minutes to work through the teacher would then open up the discussion to the entire class. Groups would then be asked one by one to outline the key points they talked about. Following on from this solutions would be provided with answers in the same manner as the worksheet that was completed earlier on.

ASSESSMENT FOR LEARNING AND CONCLUSION (10 MINUTES)

The teacher would summarise the key points from today. For example the teacher, 'Remember terminating and recurring decimals are both parts of our real number system, just like fractions, percentages, integers etc.' The teacher would then organise a quick quiz on the online program called Kahoot (AFL). The purpose of this would be to check if students coped well with the new content today. If students did not finish the questions than the rest would be allocated for homework. The teacher could also inform students on what they will be looking at tomorrow.

LESSON EVALUATION QUESTIONS

Were all students equally contributing in the group work?

Was it better getting students to break into groups to complete the worksheet rather than individually?

Was Kahoot a good way to implement assessment for learning this leason?