Moving on
This is a level 4 algebra activity from the Figure It Out theme series. It is focused on using a formula to solve calculations and write a linear formula to express a linear relationship. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Use a formula to solve calculations.
- Write a linear formula to express a linear relationship.
Moving on
Achievement objectives
NA4-7: Form and solve simple linear equations.
Required materials
Figure It Out, Levels 3-4, Theme: Moving House, "Moving on", page 8
See Materials that come with this resource to download:
- Moving on activity (.pdf)
Activity
This activity requires the students to graph the costs for three removal firms. Each firm has a base charge and a rate per additional kilometre. If the students haven’t had experience with linear graphs, they may need to be taught the basics of plotting points and using them to determine a line.
There is no reason why they can’t work directly onto square grid paper. However, an alternative strategy is to ask them to make a table listing each of the three firms and their base charges, and the costs for the various distances, and to plot these results on the grid.
|
Base charge |
Rate per km |
Cost 10km |
20km |
25km |
100km |
|---|---|---|---|---|---|---|
Move it |
$350 |
>80km, $3 |
|
|
|
|
|
|
|
|
|
|
|
Tautoko |
|
|
$270 |
|
|
|
The graph can be drawn on paper, but if the students have access to a computer, they could enter the data into a spreadsheet program and use the program’s chart-making facility. The spreadsheet would look like this:
Choose the XY (Scatter) style of graph (straight line option) from the chart menu, not the line graph, to avoid problems with the horizontal axis and its scale.
It is important that the students learn to “read” graphs for their story instead of just looking at them.
- What does it mean if a line is horizontal?
- Uphill?
- Downhill?
- What does it mean if there is a bend in the line?
- What does it mean if two lines run parallel to each other?
- If one is steeper than another?
- If two lines intersect?
Do lines continue beyond the boundary of the graph? (Note that the students should not put arrowheads on lines to indicate that they continue beyond the edge of their graph.)
If a table has been created as above, writing formulae for question 4 should be straightforward: cost = base charge + (number of kilometres travelled × cost per kilometre). Be aware, however, that because of the way Move It charges, two formulae are required: one for up to 80 kilometres and one for >80 kilometres. Discuss with the students the advantages of graphs compared to those of formulae. (See the notes on Solar-powered Shower, page 27, for further discussion of this issue.)
1.
a. Tautoko Removals ($300)
b. For each of the three companies, take the base charge and add to this the additional charge per km (if any) for 25 km. The lowest result will indicate the cheapest company.
3.
Move It ($350)
4.
a. $250 + ($2 × km travelled)
b. km travelled <_ 80: $350
km travelled > 80: $350 + (3 × (km travelled – 80))
The quality of the images on this page may vary depending on the device you are using.