## Learning Across the Curriculum: Numeracy Strategies for Students

Students’ thinking in numeracy is guided by the explicit teaching of numeracy skills for reading and interpreting graphs. Students can successfully learn to unpack any table or graph information when they are provided with a checklist of strategies. The checklist should contain the steps students take in their thinking.

Numeracy Guides – Greystanes High School have developed a series of Numeracy Guides available on this site. Numeracy guides are for teachers, to ensure consistent terminology and similar methods of explaining. The intention is for teachers to include these guides in program folders or with lesson plans as a reference.

- What is the
**title**of the graph? What**type of graph**is it? - Look at the
**horizontal**axis- What is the
**label**on the axis?

- What is the

- Look at the
**vertical**axis- What is the
**label**on the axis? - What is the
**scale**on the axis? - What is the
**unit of measurement**?

- What is the
- How are the
**numbers**shown?

Thousands, hundreds, decimals or percentages. What do these numbers represent?

DISCUSS THE INFORMATION IN THE GRAPH:

- What does the information along the vertical axis tell us?
- What does each mark on the vertical axis represent?
- Would the graph look different if each marker along this axis represented $1?
- What does the information along the horizontal axis tell us?

**STRATEGY FOR CONSTRUCTING LINE GRAPHS**

- Create an appropriate scale on each axis.
- Label each axis, include the units of measurement.
- Choose an appropriate title for the graph.
- Plot each coordinate carefully on the graph.
- Join each point with a straight continuous line.
- Always use a ruler when constructing line graphs and be precise.

**STRATEGY FOR CONSTRUCTING COLUMN GRAPHS**

- Columns are equally spaced apart.
- Columns may be vertical or horizontal.
- The graph starts half of one column width into the horizontal axis.
- Each column has the same width.
- Label both the vertical and horizontal axes.
- Place the appropriate scale on both axes.
- Label the graph with an appropriate title.

**STRATEGY FOR READING AND INTERPRETING TABLES**

- What is the title of the table?
- What are the headings on each column?
- What are the headings on each row?
- What is the unit of measurement?
- What information can I extract from the table?

**STRATEGY FOR CONSTRUCTING SECTOR GRAPHS**

A sector graph is a data display that uses a circle divided proportionally into sectors to represent the parts of a total.

- Use a compass to draw a circle.
- Draw a radius – a line from the centre of the circle to the circumference as a reference line for measuring and creating each sector.
- Determine the size of each sector. If the size is given as a percentage, multiply the percentage by 360 this will give the required angle of each sector which can be measured with a protractor on the radius line.

For example:

A sector representing 50%,^{50}⁄_{100}x 360 = 180°

A sector representing 25%,^{25}⁄_{100}x 360 = 90°

A sector representing 10%,^{10}⁄_{100}x 360 = 36°

If the size is given as a number out of a total number, convert to a fraction and multiply by 360 to get the angle of each sector.

For example:

A sector representing 4 out of 20,^{4}⁄_{20}x 360 = 72°

A sector representing 6 out of 20,^{6}⁄_{20}x 360 = 108°

A sector representing 10 out of 20,^{10}⁄_{20}x 360 = 180° - To ensure you have not made a mistake check that all the sectors add to 360.
- Use a different colour to represent each sector, label each sector or create a key to represent each sector.
- Place a title at the top of the sector graph.

**STRATEGY FOR CONSTRUCTING DIVIDED BAR GRAPHS**

Divided bar graphs are used to show how a total is divided into parts. A divided bar graph uses a single bar divided proportionally into sections to represent the parts of a total.

- The proportion of the rectangle indicates the part of the ‘whole’ that each graphed amount represents.
- It is important to know the exact size of the whole, as each section of the bar represents a fraction of that amount.

- Draw a rectangle and divide accordingly. The length of each section should represent the percentages shown e.g. the orange bar should be 60% of the length of the rectangle.
- Label each section and include the percentage.
- Place an appropriate title for the divided bar graph.

**DOT PLOTS**

A Dot plot displays scores which are indicated by symbols such as dots drawn above a horizontal axis.

Each piece of data is represented by a single dot.

Dot plots can be used as an alternative to a column graph and are usually only for small data collections.

**STRATEGY FOR READING POPULATION PYRAMIDS**

Population Pyramids are graphical illustrations that show the distribution of various age groups in a population.

- They typically consist of two back-to-back graphs.
- The population plotted on the x-axis (horizontal) and age on the y-axis (vertical).
- One graph shows the number of males and one graph shows the number of females in a particular population. The age scale is in five-year age groups and are called cohorts.
- Males are conventionally shown on the left and females on the right.
- Amounts may be measured by raw numbers or as a percentage of the total population.
- Unpack each aspect of the population pyramid with students. Start with each axis and progress students to making general statements and conclusions about the data.

- Look at the vertical scale on the y-axis. What do the numbers represent?
- Look at the horizontal scale on the x-axis. What do the numbers represent? Are they in whole numbers or percentages?
- Look at the left hand side graph. What data is shown?
- Look at the right hand side graph. What data is shown?
- What does each column represent? Look at the size of the columns and the overall formation of the pyramid. What does the shape show?
- What is your age groups’ population?
- What can you say about the aging population?

**PICTURE GRAPHS**

A picture graph is a statistical graph for organising and displaying categorical data.

Students may begin by placing actual objects as data and group them in as display.

The pictures can represent one data value (one-to-one correspondence) or may represent more than one data value (many-to-one correspondence) as pictured in this example.

**STEM-AND-LEAF PLOTS**

A stem-and-leaf plot is a method of organising and displaying numerical data in which each data value is split into two parts, a ‘stem’ and a ‘leaf’. For example, the stem- and-leaf plot (at right) displays the resting pulse rates of 19 students. In this plot, the stem unit is ‘10’ and the leaf unit is ‘1’. Thus the top row in the plot 6 | 8 8 8 9 displays pulse rates of 68, 68, 68 and 69.

**BACK-TO-BACK STEM-AND-LEAF PLOTS**

A back-to-back stem-and-leaf plot is a method for comparing two data distributions by attaching two sets of ‘leaves’ to the same ‘stem’. For example, the stem-and-leaf plot (at right) displays the distribution of pulse rates of 19 students before and after gentle exercise.