Number sequence: Year 6: Planning tool

Expected level of development

Australian Curriculum Mathematics V9: AC9M6N01

Numeracy Progression: Number and place value: P9

At this level, students use horizontal and vertical number lines to find solutions to everyday problems involving locating and ordering integers around zero; for example, elevators above and below sea level. They explore integers in financial contexts, such as the concept of profit and loss for a planned event.

Pose problems where students can appreciate how the number line can be extended in the negative direction such as modelling the temperatures of different planets of the solar system or golf scores such as 2 below par. Multiple exposures to different contexts for negative numbers helps students see the symmetrical relationships of integers on either side of zero and become familiar with the function of the negative (–) sign.

Provide opportunities for students to reason about positive and negative numbers. Encourage them to explain the difference in in location between (–22) and (+22) and their relationship to zero as –2< 0< 22<0<2. Highlight efficient mental strategies for calculating difference between positive and negative numbers. Two-colour counters are a concrete material that can support reasoning as one side can represent positive numbers and the other can represent negative numbers. Three red counters (+) and three yellow counters (–) can represent 0. An additional yellow counter can indicate a quantity of –1.

Explicitly teach students how to distinguish location using the Cartesian plane. Digital technologies can provide engaging contexts for learning, for instance, challenge students to program a robot to move along a series of coordinates using all four quadrants of the Cartesian plane. Have them provide the series of points as x and y coordinates.

Provide meaningful contexts for students to use integers to represent quantities in financial contexts. For example, they might pitch an idea for a school fete stall and use a digital system to forecast/calculate profit and loss. They might look at their bank statement and consider the balance of incoming credits and outgoing debits.

Teaching and learning summary:

Extend the number line to represent negative numbers and their relationship to zero.
Introduce horizontal and vertical number lines to distinguish a location.
Explore integers in meaningful contexts including financial contexts.
Use digital technologies to augment learning.

Students:

recognise and describe the difference in location between negative and positive numbers
find and program coordinates using the Cartesian plane
use digital technologies to solve problems and communicate ideas.

Some students may:

only conceptualise numbers as things that can be counted, they are unable to solve problems such as 3 take away 7. To support learning, use a number line to help students conceptualise the relative size of the numbers.
have difficulty bridging through zero. Help students understand use of zero and an origin point that other numbers can be referenced by.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

We are learning to recognise and describe the difference in location between negative and positive numbers.

Why are we learning about this?

Have you ever played the game Tug-of-War? Tug Harder is a version of this game which reinforces negative numbers and their relationship to positive numbers.

What to do

Play the game with a family member or friend.
Set the game up according to instructions on the page. You will need to draw a number line from –13 to 13 on a piece of paper and find a counter (or any small object) and two 1–6 dice to use.
Once you have played the game once or twice, try the second version of The Game, which introduces other operations.

Success criteria

I can:

recognise and describe the difference in location between negative and positive numbers.

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