# Stage 4 - patterns and algebra – linear relationships

Interpret linear relationships created from simple number patterns and equations; understand and use appropriate terminology when reading linear graphs.

## Strategy

Students can:

• interpret linear relationships created from simple number patterns and equations
• understand and use appropriate terminology when reading linear graphs.

## Interpreting graphs

Interpreting graphs and making connections between the graph and real life experiences can be challenging for students learning English as an additional language or dialect (EAL/D). To understand graphs, students need to discriminate between the data presented to locate relevant information when solving problems and understand the terminology used.

EAL/D students require support in the development of specific English language skills needed for using mathematical concepts and strategies in a range of situations.

EAL/D students need to be able to:

• interpret and explain information from diagrams, graphs, charts and timetables
• transfer information from texts into given formats (5.5)
• extract and manipulate key ideas from text for problem solving (5.5)
• use a set of common specialised words (technical and non-technical terms appropriate to a topic area) (4.11)
• use simple phrases to express basic comparisons (3.11).

## Activities to support the strategy

The following teaching sequence will focus on exploring sets of numbers and interpreting data presented in graphs. Students will complete activities requiring them to:

• state whether a single set of numbers goes up or down
• determine whether the relationship between two sets of numbers is direct or inverse
• identify the two sets of numbers represented by points on a graph and determine how they are related
• learn the mathematical terms needed to discuss data presented graphically and
• explore situations in which specific sets of numbers might arise.

### Controlled

#### Vocabulary

• going up/going down
• increase/decrease
• ascending/descending

1. Teacher writes sets of numbers on the board and asks students to identify whether they are “going up”/“going down”. (Teacher extends language to “increase”/“ascending” and “decrease”/“descending”.)

2. Teacher writes the two headings “Ascending” and “Descending” on the board and then writes five unordered sets of numbers containing no repeated numbers. Teacher asks students to say out loud, the correctly ordered sequences of numbers. This provides students with practice saying negative and large numbers.

Following this, teacher says, “Now I want you to work in pairs, with one student reading out the numbers in ascending order and the other reading the numbers in descending order.”

Pair work encourages EAL/D students to contribute, which is important for the development of oral competency.

3. Teacher prepares an OHT or Interactive White Board (IWB) page containing the following numbers:

Teacher leads a class discussion about what experiences students have had that could result in this group of numbers. Possible experiences might be:

Teacher prepares additional sets of number cards (illustrated below) for students to discuss.
Teachers should photocopy onto cardboard enough for one copy between two students, cut out and place in individual envelopes.
(It is a good idea to use different coloured cardboard, so that sets can be kept separate for re-use.)
In pairs, students discuss each set of numbers. Each pair should think up a real life explanation for each card and note these down and then report back to the class. Teachers should elicit 3-4 explanations for each card.

View/print (PDF 14.66KB)

4. Teacher displays PowerPoint slide of a line graph and reveals labels of its features by following this procedure:

• open the PowerPoint
• click the tab called “slide show”
• click “from beginning”
• click the space bar to reveal each label.

If you do not have access to a computer, an OHT of the question can be prepared using the first slide, which is unlabelled, and annotations can be made with red pen.

View/print (PPTX 86.38KB)

5. Teacher displays PowerPoint slide or OHT of a different graph. The following three activities refer to this graph:

View/print (PPTX 271.88KB)

Teacher refers to the first point on the graph, writes the following sentence on the board and elicits the missing information from the class by running a finger down from the point to the horizontal axis and across to the vertical axis:

Teacher refers to the remaining points in sequence and elicits one sentence for each point. Teacher writes each sentence on the board as the students provide it:

Teacher writes definitions for the relationship between the two sets of numbers on the board and students either copy this onto their laptops or into their exercise books:

Teacher establishes that the relationship between the sets of numbers in the graph entitled “Ticket price and concert attendance” is inverse.

Teacher prepares an OHT and student handouts of questions about the same graph. Students work in pairs to answer the questions by referring to the graph. The file also contains the answers to assist the teacher.

View/print (PDF 150.81KB)

#### Guided

1. Students complete a worksheet requiring them to arrange two sets of numbers according to instructions. Teacher prints out worksheet for students to complete individually. The file also contains sample solutions to assist the teacher.

Arranging two sets of numbers (PDF 49.27KB)

2. Teacher displays the graph “Ticket price and concert attendance” on the IWB or on OHT. If using an IWB, the teacher can prepare labels for the students to move into the correct positions. If using an OHT, students can write the following labels on the graph.

• title
• vertical axis
• horizontal axis
• axis label
• number on axis
• axes
• point

Ticket price and concert attendance (PDF 411.89KB)

3. Students complete “Sets of Numbers Keyword Match” activity on the IWB, matching sets of numbers with situations.

If IWB is not available, teacher could give students the sets of numbers and situations on cards. Students match the sets of numbers with the situations they could relate to. Teachers should photocopy onto cardboard enough for one copy between two students, cut out and place in individual envelopes.

Number and situation matching cards

4. Teacher distributes worksheet on creating a table from a graph for the students to complete individually. The main purpose of this is to create two sets of numbers which have an inverse relationship.

Extension: Discuss the relationship between the line's direction and the numbers, i.e. a direct relationship would be represented by a line with a positive slope and an indirect relationship would be represented by a line that slopes negatively.

Making a table from a graph (PDF 150.18KB)

5. Teacher gives out an assignment for the students to complete individually. The assignment consists of four tasks requiring the students to:

• collect their own data and present it in a table
• create a line graph
• write questions about the graph
• present the graph and the questions to the class.

A marking matrix is included for students within the assignment instructions to provide them with the criteria on which their work will be judged. Teachers should use the last page of the assignment file to complete as feedback for each student.

Line graph assignment (PDF 66.88KB)

## References

### Australian curriculum

ACMSP170: Construct and compare a range of data displays including stem-and-leaf plots and dot plots.

### NSW syllabus

MA4-19SP: Collects, represents and interprets single sets of data, using appropriate statistical displays.