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This unit uses one of the digital learning objects, Drive: easy problems, to support students as they investigate linear relationships. It includes a sequence of problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

Achievement Objectives:

Achievement Objective: NA4-9: Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
  • solve problems using linear relationships shown on tables and graphs
Description of mathematics: 

The context of driving illustrates the relationship between time, distance and speed. The students use the information from one situation to establish the relationship between the variables and apply it to new numbers. Information is given in a table and on a graph. The students’ answers are shown on the graph. It is suitable for students working at stage 7 of the number framework. It Relevant Stages of the Number Framework,

The strategy section of the New Zealand Number Framework consists of a sequence of global stages that students use to solve mental number problems. On this framework students working at different strategy stages use characteristic ways to solve problems. This unit of work and the associated learning object are useful for students at stage 7, Advanced Multiplicative, of the Number Framework. At stage 7 students encounter problems that involve simple proportions.

Key Vocabulary: 

 linear relationships, proportions, rates, ratios, variables, time, distance, constant rate, 


Prior to using the Drive Learning Objects

The unit This is to That helps students to solve problems involving proportions. It would be a useful unit to do in conjunction with this Drive unit..

Working with the learning object with students (Distance)

  1. Show students the learning object and explain that it provides a model for working out the relationship between time and distance variables.
  2. Choose Find Distance from the front page.
    screen shot.
  3. Discuss the first screen with the students and clarify with them what the problem is asking.
  4. Discuss with the students that the information about the time and distance is shown on both the table and the graph. Ask them to work out if the new distance is smaller or larger than the distance given.
  5. Discuss with the students ways to find the new distance from the information given. For example, what is the ratio between 60 minutes and 30 kilometres and then apply this ratio to find the distance travelled in 10 minutes, or find the ratio between 60 minutes and 10 minutes and then apply this ratio to the distance travelled.
  6. Ask for a volunteer to discuss their answer and enter the number in the box.
  7. If the answer is not correct a red graph will show the student’s response.
  8. Discuss with the students how to use the red graph to work out if the answer was too low or too high.

    Working with the object with students (Time)

  9. Choose Find Time from the front page.
    screen shot.
  10. The same strategies for solving the distance problems can be applied to the time problems. Discuss with students why the same strategies can be applied.

Notes regarding calculating proportions.

There are a number of ways of solving problems involving proportions. Explained below are two ways that students can practise.

  1. The students can explain the proportion as a ratio. For example, taking 20 minutes to travel 40 kilometers is a ratio of 2:4 or 1:2. The distance travelled is 10 kilometres so using the ratio the time taken is 5 minutes.
  2. The students can solve problems involving proportions by solving a simpler example. For example, if it takes 10 minutes to travel 40 kilometers then 20 kilometers will take 10 minutes, and 10 kilometers will take 5 minutes.

Students working independently with the learning object

Because this learning object generates problems for the user, once they are familiar with how it works you could allow individual students or pairs of students to work with the learning object independently. The learning object also has a Mixture section which contains both time and distance problems.

Students working independently without the learning object

Independent activities that develop the same concepts as the learning object include:

  • Solving problems similar to those in the learning object.
  • Trying different strategies for finding the missing time or distance value.
  • The Drive: hard problems learning object involves more complex proportions.