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

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

Following this, say, “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.Present the following numbers:

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

Prepare additional sets of number cards for students to discuss. You can create your own or use the number cards template (PDF 14.66KB)
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. Elicit 3-4 explanations for each card.

4. The line graph powerpoint (PPTX 86.38KB) can be used to display a line graph and then reveal labels of its features

Use the graph in the Ticket price and concert attendance PowerPoint (PPTX 271.88KB) for the next three activities.

Refer to the first point on the graph, write 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:

When the ticket price was _______ the number of people who attended the concert was _______.

Example solution:

When the ticket price was \$10 the number of people who attended the concert was 2,500.

Refer to the remaining points in sequence and elicit one sentence for each point. Write each sentence on the board as the students provide it.

Sample student responses:

When the ticket price was \$20 the number of people who attended the concert was 2,000.

When the ticket price was \$30 the number of people who attended the concert was 1,500.

When the ticket price was \$40 the number of people who attended the concert was 1,000.

When the ticket price was \$50 the number of people who attended the concert was 500.

Write definitions for the relationship between the two sets of numbers on the board. Students copy these onto device (or exercise books).

Direct relationship – When both sets of numbers go either up or down, the relationship is direct, for example, 3,6,8,11 and 6,15,20,22

Inverse relationship – When on set of numbers go up and the other set goes down, the relationship is inverse, for example, 3, 6, 8, 11 and 22, 20, 15, 6.

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

Students work in pairs to answer the questions in the Ticket price and attendance - controlled-vocabulary worksheet (PDF 150.81KB) referring to the graph. (The file contains the answers to assist the teacher)

#### Guided

1. Students complete a worksheet requiring them to arrange two sets of numbers according to instructions. Students complete the Arranging two sets of numbers (PDF 49.27KB) worksheet individually (includes contains sample solutions to assist the teacher).

2. Teacher displays the graph Ticket price and concert attendance (PDF 411.89KB) Prepare labels for the students to move into the correct positions on the graph.

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

3. Students complete Making a table from a graph worksheet (PDF150.18KB) individually. The main purpose is to create two sets of numbers which have an inverse relationship.

Extension: Discuss the relationship between the line's direction and the numbers, that is, 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.

4. Students complete the Line graph assignment (PDF 66.88KB) 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.

Use the last page of the assignment file to complete as feedback for each student.