Stage 4 number – computation with integers – compare, order and subtract integers

Strategy

Students can:

  • Recognise and describe the ‘direction’ and ‘magnitude’ of integers
  • Construct a directed number sentence to represent a real-life situation
  • Recognise and place integers on a number line
  • Add and subtract integers using mental and written strategies

Activities to support the strategy

Students first need to be able to interpret the real-life situation and represent it on a number line. Placing integers on a number line allows them to clearly see the required mathematical operation to solve the problem. Initially, students should be encouraged to draw number lines and mark positions carefully. With practice, students can develop confidence in visualising the number line and be able to use mental strategies where appropriate.

Activity 1

A number of examples should be provided to students. The examples should include pairs of positive integers, pairs of negative integers, and combinations of positive and negative integers as well as zero. There should also be real-life situations to interpret. In all cases, students should be encouraged to draw a number line and mark the positions of the integers. Once the sketch is completed, the students should be able to decide on the required operation. A significant amount of practice may be required before students develop the level of confidence required to complete such problems without the need of a diagram. Examples are shown below.

1. What is the difference between 5 and 15?

From the diagram you can see that both integers are on the same side.

2. I borrow $100 from a friend and then borrow $40 more. How much money do I owe my friend?

  • Initially, I borrow $100.
  • This is shown as –100 on the number line.
  • Borrowing $40 more is a further jump of 40 in the negative direction as shown.
  • The correct answer can simply be read off calculated as −100−40=−140

3. The maximum temperature in a city is 8°C, whilst the minimum temperature is –4°C. How much hotter is the maximum temperature compared to the minimum temperature?

After placing the two integers on the number line it can be clearly seen that the difference in temperature is 4 + 8 = 12

Activity 2

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.

Activity 3

Students can practice integer addition and subtraction using Scootle - exploring integers. This resource allows students to calculate temperature change. For example, if the temperature is 17 °C one day and 14 °C the next day, then the temperature change is -3 °C. Watch a video showing how temperature is expressed using integers.

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

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.

  • Scootle - exploring integers -calculate the change in temperature between two days.
  • Integer cruncher: addition and subtraction

Use counters to model the addition and subtraction of integers. For example, (-2)+(+5)=(+3) or (-2)–(-5)=(+3). See the calculations represented in an alternate form on a number line. This learning object is one in a series of four objects.

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