Stage 4 number – computation with integers – ordering decimals

Strategy

Students can:

  • Order integers
  • Order decimals

Activities to support the strategy

Students need to be able to order decimals on a number line. Students will need an understanding of positive and negative numbers and be confident with place value with decimals. Activities should include a review of place value focusing on decimal places and a review of positive and negative numbers on number lines.

Activity 1

A number of examples and teaching techniques are provided for developing an understanding of integers. Teachers should review the TIMES teacher guides on The Integer and Decimals and Percentages.

This is a guide for teachers containing an introduction to decimals and percentages - TIMES teacher guide – Decimals and percentages.

Activity 2

1. A key step when ordering decimals is to have students write the numbers in a list form one under the other so that the decimal points are all aligned. In this way students can quickly determine their order. Some examples, dealing only with positive numbers are shown below.

Put the following decimals in ascending (smallest to largest) order: 0.2, 0.02, 2, 0.002

 

0

.

2

  

0

.

0

2

 

2

.

   

0

.

0

0

2

Clearly, the ascending order is 0.02, 0.02, 0.2. 2.

2. Students also need to know that directed numbers have a direction (positive/negative) and a magnitude (size). One way to think of this is as a distance from zero. The number +2 is two units to the positive side of zero, the number –5 is five units to the negative side of zero. In this way the numbers +6 and –6 are the same distance (six units) from zero.

References

Australian curriculum reference: ACMNA280

Compare, order, add and subtract integers

NSW syllabus reference: MA4-4NA

Compares, orders and calculates with integers, applying a range of strategies to aid computation

NSW syllabus reference: MA4-4NA

Compares, orders and calculates with integers, applying a range of strategies to aid computation

Student resources

Teachers should review the TIMES teacher guide on The Integers. A number of examples and teaching techniques are provided for developing an understanding of integers.

This is a 21-page guide for teachers containing an introduction to decimals and percentages. It shows how place value is extended to describe positive numbers less than one. It also explores how to represent decimals on the number line, compare decimals, undertake the four basic arithmetic operations with decimals and change vulgar fractions to decimals and vice versa. The notation of percentages is introduced. A history of the development of decimals concludes the module.

Help the boy cross the dangerous swamp by making a path of stepping stones. Place the decimals in an ascending order to form the path. Compare the decimal fraction on each stepping stone to the others to see if it is larger or smaller. Look carefully at whole numbers and the tenths, hundredths or thousandths. Put the decimals in order from smallest to largest. Test the sequence by sending the boy across the swamp. This learning object is the sixth in a series of six objects that progressively increase in difficulty.

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