Understanding Decimals

SYLLABUS DOT POINTS

• Place positive and negative fractions, mixed numerals and decimals on a number line to compare their relative values.
• Order fractions, decimals and percentages

WORKING MATHEMATICALLY INDICATORS

Students will:

• Interpret and identify where to place decimal numbers on a number line. (Problem Solving, Understanding)
• Explore and explain the role of place value in decimals. (Communicating, Understanding)

LEARNING GOALS

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

• Explain the value of each digit in a decimal number and the relationship between them.
• Demonstrate how to order decimals. For example realising that 0.205 is a smaller decimal that 0.21.

MATERIALS REQUIRED

• Worksheet on the place values of decimals
• Worksheet for the place value of whole numbers (in reserve)
• Spiral number plane game sheets
• Whiteboard markers and rubber

The main focus of this lesson would be on re-accustoming students to the idea of decimals and then subsequently expanding upon their prior knowledge. It would be stressed that there are numbers other than whole numbers. Links to real life would be emphasised to reinforce the point. For example asking the students how often items are bought at a shop for amounts that are just whole numbers.

Following on from this, the lesson would then involve exploring the concept of place value and making students aware that place value also entails tenths, hundredths and thousandths etc. This would allow students to get an idea of what decimals are and how they are represented. Furthermore, the lesson would then involve students being able to tell the difference between decimals of various magnitude and ordering them in ascending or descending order.

Assuming each lesson is 60 minutes long...

ORIENTATION (5 MINUTES)

Seeing that this is the first lesson in the unit of work an orientation would occur prior to the start of the actual lesson. In this orientation students would be re-informed on what decimal numbers are and where they are used.

A particular question the teacher could ask the students is 'How often are items bought at a shop for amounts that are just whole numbers?'

This would get students thinking about what purpose decimal numbers might serve in real life. The teacher could then ask students 'Can you think of any other examples where you might have seen a decimal number?'

Following on from this discussion, if there is enough time, the teacher could also bring up the history of decimals and where they have been used over the centuries. Some facts from the HOME page on this website could be raised. For example the ancient Indus Valley Civilisation and their weighing system.

INTRODUCTION (10 MINUTES)

Following on from the orientation, students should now have a good idea of the relevance of decimals and where they could be utilised in real life. Looking into the lesson introduction, students would now be informed on what this lesson will entail.

Firstly, the teacher will look at the idea of the place value of decimal numbers. This is to make sure there are not any gaps in the prior knowledge of students. In the explanation the teacher will write up a decimal number on the board. For example 653.147. Here the teacher would ask students questions in regards to place value. For example. 'What place value is the 1?' and 'Why is there no such thing as a oneth column?'

Next the teacher would then inform students of the idea of ordering decimals. For this explanation the teacher could draw a number line from 1 to 10 and ask students questions. For example 'Where would I put the decimal 0.5?' and 'Do you think it would be okay for me to put the decimal 1.1 right on the number 1?'

Following this explanation this would now bring us to the body of the lesson.

BODY (35 MINUTES)

The body of this lesson will comprise of students completing activities in regards to place value first and then ordering decimals.

(15 MINUTES)

To start the lesson the teacher could hand out the second worksheet in the resources section on this page. It looks at place value of decimal numbers. Students would then be instructed to complete the worksheet. (It is the 2nd Resource Down). Whilst students are doing the work the teacher would circulate the room and answer any questions the students may have in regards to any questions they may be having trouble with. Alternatively if there are students struggling with this worksheet the teacher could provide them with the worksheet in the resources section on this page that looks at the place value of whole numbers. (It is the 3rd Resource Down). When the teacher has looked at students and seen that they are almost complete the lesson would be stopped and the teacher would instruct students that they are going through the answers. This could be achieved on the board with the teacher calling a different volunteer to write up their answer for each question.

(20 MINUTES)

The next part of the lesson would involve students playing the spiral number plane game. (It is the 1st Resource Down). In this activity students would work in pairs. For the game each pair requires the game board so the teacher would now hand out one to each group. Students would then be instructed to start playing. They would also be encourage to communicate with each other and once they have made their moves, discuss why (Communicating). Whilst this is occurring the teacher would circulate the room to ensure that students are on task and know what to do in the game. Following the conclusion of the game the teacher would start a class discussion and ask students questions. For example 'Did anyone come up with any good strategies?' and "Can someone tell us what was on their game board' (Reasoning)

ASSESSMENT FOR LEARNING CONCLUSION (10 MINUTES)

The teacher would then conclude the lesson. Students should be confident with place values of decimals and the ordering of decimals. For example the teacher could write up a decimal number and ask students 'can you tell me which digit is in the oneths place value column?' Homework would also be allocated. For example the teacher could instruct students who did not complete the worksheets to finish them off at home. Alternatively if students have a textbook the teacher could ask students to complete a few carefully selected questions. Furthermore, for consolidation of what was learnt today, the teacher could also tell students to have a look at the online ordering game at home. (The 4th Resource Down).

The teacher would then hand out exit slips to the students (AFL). (The questions on them would be prepared before class). Students would have around five minutes to quickly complete the questions. The teacher would collect them at the end of class. This would allow the teacher assess the prior knowledge of students and their confidence with what was introduced today.

LESSON EVALUATION QUESTIONS

Were students able to master the idea of place value in decimals?

Did students work well in pairs?

Were they engaged in the game?

Here students are able to once again explore place value and the idea of tenths, hundredths and thousandths. Having a look over place value beforehand is a good strategy to prepare students for the upcoming game. Once students are satisfied with their knowledge of different decimals they can then begin a game which lets them order decimals. A screenshot of the game itself is displayed below: