The 50 day challenge

Achievement objectives

GM4-2: Convert between metric units, using whole numbers and commonly used decimals.

NA4-7: Form and solve simple linear equations.

Required materials

See Materials that come with this resource to download:

• The 50 day challenge (.pdf)

Activity

A teacher has set her class the task of "walking the length" of State Highway 1 in 50 school days. They are allowed to count each step that each student takes if they walk to and from school and if they walk laps of the 400 m track on the school field at fitness time.

Use the data the class has collected below to work out how many laps of the track each student will need to walk on each of the 50 challenge days.

Eleven students walk to school and back home every day. Each walker used a GPS app on a smartphone to measure their walk to school. The results are:

250, 186, 373, 1256, 812, 280, 140, 203, 95, 413, 77

The class Googled the length of State Highway 1 and got 2047 km.

The following prompts illustrate how this activity can be structured around the phases of the mathematics investigation cycle.

Make sense

Introduce the problem. Allow students time to read it and discuss it in pairs or small groups.

• Do I understand the situation and the words? (Students may need support to understand that the students walk individually around the track to complete the equivalent of the length of SH1.)
• What are the important numbers in the problem? What do the numbers refer to? (The distances students walked are the distance to school and will need to be doubled to include the distance to home. The total of 2047 km and the track distance of 400 m are lengths, but the problem involves rates, such as distance per student per day.)
• What important ideas are involved? (Sharing the distance among 28 students, sharing the total distance among 50 days. Both require division.)
• Can I represent the problem using a diagram or equations?

Plan approach

Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.

• How will I know when I have solved the problem? What will my solution look like? (Students need to recognise that they will have a distance for each student to walk each day that can be justified by their working.)
• What strategies can I use to get started? (A diagram or ratio table will be a good starting representation.)
• What kinds of calculations will I need to do?
• What tools will be helpful? (Calculators are important for this problem.)

Take action

Allow students time to work through their strategy and find a solution to the problem.

• Have I shown my workings in a way that is easy to follow?
• Does my answer seem correct? Does it seem realistic for the situation? Is the distance per student reasonable?
• How could I make sure that I haven’t missed anything?
• How do my results look different or the same compared to others? Why could this be?
• Is there another possible answer or way to solve it?

Convince yourself and others

Allow students time to check their answers, and then either have them pair share with other groups or ask for volunteers to share their solution with the class.

• What is the solution?
• How would I convince someone else that I am correct?
• Could I have solved the problem in a more efficient way?
• Which ideas would convince others that my findings answer the investigation question?
• Which ideas or tools worked well in my investigation?
• How could these strategies be used for other problems?