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 Science 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

What percentage of this solution is water?

If water takes 4 minutes to boil 100mls, what percentage does the time increase by when you add salt?

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

Measure liquids, gasses and solids using appropriate unit of measurement. Convert results into a series of different units of measurement. Discuss why it is appropriate to use certain units of measurement.

Teach scientific notation to express large or small numbers to express length, mass, volume, time or area using different units of measurement.

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

Calculate results of experiments rounding results to the nearest ten, unit, tenth, hundredth and thousandth.

Discuss the relationship between matter and transfer of heat energy. Connect this concept with surface area. Calculate the surface area of an object and work out the cooling rate based on the volume to surface area ratio.

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 graph results of experiments using Cartesian coordinate planes where results are both positive and negative.

Students graph more than one set of data on a Cartesian coordinate plane and discuss how the results have shifted (reflected, rotated, translated).

Students read data on experiments conducted from Cartesian coordinate planes, recording results using appropriate notation.

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

Discover the angle of trajectory of planets and stars in space. Discuss the impact of the angle of the earth from the sun and how that impacts the seasons.

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 Science teaching, visit the NESA Filter Syllabus page and select Syllabus (Science); Stage (4) and Learning Across the Curriculum (Numeracy) to find other potential numeracy learning experiences in the Science syllabus.