**Summary:**

This lesson involves students using a variety of strategies to solve an age old problem known as the “traffic jam.” This gives students the opportunity to work as a team and solve the problem as well as showing students that there is more than one way to solve a problem.

# Australian Curriculum Links:

- Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)
- Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

**Lesson:**

**Introduction:**

- Start of by introducing the problem through a bit of a story. “I was driving along the other when all of a sudden CRASH! (try make noise to scare too!) there was a traffic jam. Out of no where a policeman came and instructed the traffic through.
- Using Hula Hoops as circles, place 9 hoops in a row and pick out 8 students. Both team A and team B need to be facing each other as illustrated in the diagram below:
- Explain to the students that the cars labelled A need to make to the other side and same with B. However the cars can only move one space at a time only opposite cars can go around each other (illustrated below).
- NB* Only opposite cars can go around each other and the end result is to look like this.

- (This can be changed to suit your class needs). I asked for 8 volunteers (and i chose the ones who were more likely to solve it) to act as cars. Tell the cars they are not allowed to talk. Now the remainder of the class are the “policeman” and as a result need to instruct the cars through using the rules of one car forward and only opposites can go around each other.
- If you can, film the students using an ipad or video camera. Stop students half way and discuss what strategies are working an what aren’t. Tell students to try new ways as well as offer some cars to subituted in.
- Show students the video and discuss what they are doing well and what can be done better.
- Simulate a smaller problem with just 2 cars on each side and see if students can identify the pattern.
- Now that they know the pattern, students should be able to solve the problem of 4 and 4. Just for a bit of fun, i got the class complete it with 10 and 10 on each side.
- Next students will work in pairs to model the problem using counters. Get them to draw 9 dots in their maths book and simulate the problem using 2 different coloured counters.
- Please note: For extension, ask student to work out the algebraic formula for the patter that has occurred. Is there one…?

**Conclusion:**

- Upon solving the problem invite students to share how they solved the problem. Now discuss how we can solve problems using a variety of ways.
- Get them to describe what problem solving methods were used by articulating to others what they did. (Explaining in mathematics is so vital!)

# Resources:

- 9 hula hoops
- 2 different coloured counters
- Ipad or recording device of some sort