Numeracy involves using mathematical ideas effectively to participate in daily life and make sense of the world. It incorporates the use of numerical, spatial, graphical, statistical and algebraic concepts and skills in a variety of contexts and involves the critical evaluation, interpretation, application and communication of mathematical information in a range of practical situations.

Click the below strands of the Stage 4 Mathematics course to access the relevant section of the Stage 4 Statement, a corresponding NAPLAN questions where performance was not strong, and examples of PD/H/PE tasks that can integrate numeracy. 

PERCENTAGES

In 2017, Year 9 students were unable to do this below Stage 4 question, extracted from the exam the students sat. Students performed worse when compared with their peers across the state by more than 10%. 

The original price of a television is $2500. Micah buys the television at a sale for 15% off the original price. He has a discount voucher for an additional $75 off the sale price. What percentage of the original price does Micah pay for the television? 82%

Stage Statement (Stage 4)

Students use percentages, decimals and fractions to solve problems they are likely to encounter in their everyday lives. This involves:

• converting a percentage to a fraction or a decimal,
• finding a percentage of a given amount,
• increasing or decreasing an amount by a given percentage, and
• expressing one amount as a percentage of a whole.

Explicit teaching strategies should include exploring relationships using percentages and percentage calculations to answer harder questions. Questions should involve multiple steps utilising the skills mentioned above. Students develop mental strategies, recognise equivalences and explain their answers. 

EXAMPLEs OF INTEGRATION

Percentages of people who have a disease:

• If 1.2% of people have a disease,  which is 1,204,284 people, what was the population size at the time of collecting this data?
• What percentage of smokers die from/develop cancer?
• What percentage of people have this specific STD (aids, genital herpes, gonorrhoea)? How is this percentage increasing in specific communities? How accurate is this table? (e.g. how is it impacted by people who are undiagnosed?)

Consider the different blood types, if 38% of people have A+, how many people in the world are A+? How many are not? If this increased by 15%, how many people would then have A+?

METRIC CONVERSIONS

In 2017, Year 9 students were unable to do this below Stage 4 question, extracted from the exam the students sat. Students performed worse when compared with their peers across the state by more than 10%. 

A rectangular sheet of paper has an area of 302.5 square centimetres. What is the area of the paper in square millimetres?
a)      3.025 square millimetres
b)      30.25 square millimetres
c)      3 025 square millimetres
d)    30 250 square millimetres

Stage Statement (Stage 4)

Students use metric units to measure and convert to solve problems they are likely to encounter in their everyday lives. This involves:

• finding the size/length/volume/mass of objects using multiple units of measurement
• determining the most appropriate unit of measurement for a given circumstance
• expressing a length/area/volume/mass using a variety of units of measurement

Explicit teaching strategies should include exploring relationships between the tool used to measure and the units that the measurement is expressed in. Questions could involve multiple steps utilising the skills mentioned above. Students develop mental strategies, recognise equivalences and explain their answers.

EXAMPLES OF INTEGRATION

AREA 

In 2017, Year 9 students were unable to do this below Stage 4 question, extracted from the exam the students sat. Students performed worse when compared with their peers across the state by more than 10%. 

Thomas is making a rectangular yard for his sheep. He wants the yard to have an area of at least 500 square metres. He has two sides, each 33.6m in length.
What is the smallest possible length of each of the other two sides, rounded to one decimal place?

a)            14 metres
b)            14.8 metres
c)            14.9 metres
d)            15 metres

Stage Statement (Stage 4)

Students use multiplication, division, area formula and rounding to solve problems they are likely to encounter in their everyday lives. This involves:

• understanding practical applications of multiplication
• understanding division as the opposite to multiplication
• finding the area of rectangles
• finding the missing length of a rectangle when the area is provided with one other side length
• rounding decimals to the whole number; one and two decimal places

Explicit teaching strategies should include exploring relationships between area of rectangles and side length in conjunction with the connection between multiplication and division. Additional to this, teachers should explicitly teach students to round answers according to the circumstance requirements. Questions could involve multiple steps utilising the skills mentioned above. Students develop mental strategies, recognise equivalences and explain their answers. 

EXAMPLES OF INTEGRATION

Find the area of playing fields/courts for a variety of different sports.

Provide the area needed for a particular sporting game and then determine which dimensions would result in this area.

Time an activity. Round this to the nearest millisecond, second and minute.

COORDINATES

In 2017, Year 9 students were unable to do this below Stage 4 question, extracted from the exam the students sat. Students performed worse when compared with their peers across the state by more than 10%. 

David places a game piece at (-3,1). He moves the game piece down 3 units. What are the new coordinates of the game piece? 

a)    (-6,1 )
b)    (-3,-2)
c)    (-3,4)
d)     (0,1) 

Stage Statement (Stage 4)

Students locate, plot and transform points on the number plane. This involves:

• locating points on the Cartesian plane using positive and negative number combinations
• plotting points using positive and negative number combinations
• performing reflections, translations and rotations with and without a Cartesian plane.

Explicit teaching strategies should include exploring relationships between the x and y axis and plotting or locating points. Additionally, students should understand the metalanguage appropriate for transformations and how to apply them. Questions could involve multiple steps utilising the skills mentioned above. Students develop mental strategies, recognise equivalences and explain their answers. 

EXAMPLES OF INTEGRATION

Students perform activities where they are timed and graph the results using Cartesian coordinate planes and line graphs.

Students discuss the impact of all results shifting up or down by two seconds/minutes etc.

ANGLE PROPERTIES

In 2017, Year 9 students were unable to do this below Stage 4 question, extracted from the exam the students sat. Students performed worse when compared with their peers across the state by more than 10%. 

What is the size of the angle marked x in the diagram below? 80 degrees

Stage Statement (Stage 4)

Students use angle properties of triangles and quadrilaterals to find the size of unknown angles. This involves:

• knowing angle sum of triangles and quadrilaterals
• applying knowledge of angle sum of quadrilaterals or triangles to solve problems

Explicit teaching strategies should include exploring relationships between angle sum of a variety of different sided shapes and provide opportunities for problems solving to determine the size of angles in shapes that are irregular. Questions could involve multiple steps utilising the skills mentioned above.

Students develop mental strategies, recognise equivalences and explain their answers. 

EXAMPLES OF INTEGRATION

Calculate the different angles made when kicking or throwing a ball.

ORDER OF OPERATIONS

In 2017, Year 9 students were unable to do this below Stage 4 question, extracted from the exam the students sat. Students performed worse when compared with their peers across the state by more than 10%. 

6 + (15 - 6 x 2 + 1) = Z    What number does 'Z' represent?

a)      31
b)      25
c)      10
d)      8

Stage statement (Stage 4) 

Students use the operations and order of operations to solve problems they are likely to encounter in their everyday lives.

This involves using a combination of operations in any given problem utilising a specified order. The operations include:

• parenthesis
• exponentials
• multiplication
• division
• addition 
• subtraction

Explicit teaching strategies should include solve problems where multiple combinations of the above skills are mentioned to answer harder questions. Questions should involve multiple steps where increased difficulty is explored as students gain confidence. Students develop mental strategies, recognise equivalences and explain their answers.

For further information and examples around integrating numeracy into PD/H/PE teaching, visit the NESA Filter Syllabus page and select Syllabus (PD/H/PE); Stage (4) and Learning Across the Curriculum (Numeracy) to find other potential numeracy learning experiences in the PD/H/PE syllabus.