Numeracy in Geography


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 Geography 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

If the percentage of the earth covered in water is x%, what is the surface area of the globe?

If the rate of pollution is increasing by 15% per annum, how much is it increasing by each day? What impact does this have on the quality of the air? What percentage of the air is oxygen?

If population is increasing at a rate of 9.8% per day, what will the population of Australia be by the end of the day/week/month/year?

 

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

Find the area of different spaces (communities, states, countries, continents) and express this number as different units of measurements.

Find the volume of different bodies of water and express this number as different units of measurements. If the average person weighs 70kg and the population of Australia is 24 million, what is the mass of all of the people combined? Express this number using milligrams, grams, kilograms, tonnes. Which is the most appropriate and why?

Express populations using different units of measurement, e.g. Australia has a population of 24.13 million. What does that mean? (24 130 000 people) Express this using scientific notation (2.413 x 107).

 

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

If the area of New South Wales is 809,444km2 and it was a rectangle, what dimensions could it be?

Find the perimeter of NSW using Google Maps (find a distance function). If this is the perimeter, what could the area be?

If all of the lakes in Australia were combined, how much area would the take up as a portion of the total area of the country?

Round results to questions above to the nearest unit, ten, hundred, thousand, etc.

 

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

Overlay the Cartesian coordinate plane onto maps. Determine the location using coordinates of places of interest. Record these coordinates using appropriate notation.

Discuss the change of location of coordinates when moving 2 positions across and 3 positions down (etc.). What are the new coordinates? What would that journey have looked like in terms of the terrain?

 

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

SLR Angle Properties Stage 4 NAPLAN question

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

Consider the angles made by different features of terrain.

 

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