Learning to drive

In this activity, the students are required to add combinations of the integers -100, 30, and -40 in order to arrive at the totals given in the questions. This is an excellent introduction to integers and is an appropriate activity for students working at level 3. (Integers are explored more fully in level 4.)

To introduce the activity to the students, ask them what buttons they would press to:

• travel back 200 years
• travel back 140 years

and then, as a slightly more complex option, to:

• travel back 10 years.

You could use a number line to model what is happening each time you press a button on the control panel. The students could then use number lines to work out their answers. For example, for question 1c:

Be aware that some students may not take into account that the buttons specify whether they move us forwards or backwards in time. They may only consider the absolute value for each number.

For example, some students may say that the answer to question 1a should be blue and yellow, having calculated 40 + 30 = 70. However, those students will not have taken into account the fact that one button is going back in time while the other is going forward in time. The net effect of pressing these two buttons is a trip back in time of only 10 years:

The order in which the buttons are pushed does not matter. Going backwards in time for 100 years and then moving forwards by 50 years takes you to exactly the same point as going forwards 50 years first and then backwards for 100 years. In numbers, this could be written as:

• -100 + 50 = -50, or
• 50 – 100 = -50.

Some students may have trouble with this concept. Have them walk it out. Draw a chalk timeline on the floor and mark a point as zero or the present. To one side, mark the years going backwards in time, and in the other direction, mark the years going forwards in time. Ask the students to pace out a combination of moves. Rearrange the same combination of moves and ask another student to pace this out.

For example:

• Student 1: forwards 10, backwards 20, forwards 40, and backwards 30
• Student 2: forwards 40, backwards 30, forwards 10, and backwards 20.
• Both students will arrive at the same destination (as long as they both start at the zero point).

As an extension, you could ask,

• How can you travel 20 years forward in time by using the blue and yellow buttons? (-40 + 30 + 30)
• How can you travel 20 years forward in time by using only the blue and red buttons? (-100 + 30 + 30 + 30 + 30)

You could also make up your own “control panel” and set questions accordingly, or you could add more “control buttons” to this panel and include larger numbers or numbers that are difficult to add and subtract.

1.

a. Press the red button and the blue button the same number of times (in any order).
b. Press the yellow button 3 times.
c. Press the red button twice as many times as the yellow button and the blue button (in any order).

2.

There are many ways. Three ways are:

• Press the red button twice.
• Press the yellow button 5 times.
• Press the red button 5 times and the blue button 10 times.

3.

No, because it doesn’t matter whether you move forward or backwards first; the answer is still the same.