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TEACHER WORKSHOP ACTIVITY - SHIRTS & PANTS
This workshop provides and models example activities designed to help teach mathematical problem solving for primary school years 2-6.
It models how teachers can transfer this activity direct into your own classroom with minimal effort and maximum effect.
The workshop is comprised of a short video and related, hands-on activities.
How To Run The Shirts & Pants Problem:
- STUDENTS: Problem solving
- TEACHERS: Strategies
- GENERAL: Documentation
In this workshop, students engage in solving a combinations problem.
This problem is from a branch of discrete mathematics called combinatorics- which is usually taught in high school or college as part of probability.
Getting Ready - Try the following activities for yourself in preparation for watching the workshop video.
REMINDER Students naturally develop their own strategies, with guidance from a facilitator who who shows that teachers should not need to suggest strategies or provide answers
SHIRTS & PANTS ACTIVITY
Record the date and the title 'Shirts and Pants' on a clean page in your journal (write your name at the top of the page if you are sharing or not using your own journal).
Solve the problem below for yourself and develop a way to convince others that your solution is correct.
Stephen has a white shirt, a blue shirt, and a yellow shirt. He has a pair of blue jeans and a pair of white jeans. How many different outfits can he make?
Write down your prediction of the number of outfits he can make which have no duplicates.
Keep a record of your solution, including your justifications/proof, to share during the next workshop (Workshop 2).
Share and compare your solution and justification with others in your group.
What did you used to think?
What do you think now?
EXAMPLE EXTENSION ACTIVITIES FOR STUDENTS
- Solve the following extensions to the Shirts and Pants problem. Share your solutions:
- Adding an Item - Remember that Stephen has a white shirt, a blue shirt, and a yellow shirt. He has a pair of blue jeans and a pair of white jeans. Stephen also has a brown belt and a black belt. How many different outfits can he make now?
- Reversibility - Mario has exactly 16 different outfits. Decide how this might be possible. Specify what pieces of clothing and how many of each he might have.
- Proportion - If Steven's mother were able to buy only one new item, what item should she buy? Which item would she buy to make the largest number of outfits?
TEACHER DISCUSSION
Imagine giving this problem to students that you teach. Do you think it is an appropriate problem for your students?
How do you think your students would solve and justify the problem?
TO SEE HOW SOME STUDENTS TACKLED THIS PROBLEM: Watch this example video.
Imagine giving this problem to students that you teach. Do you think it is an appropriate problem for your students?
How do you think your students would solve and justify the problem?
For most primary school mathematical assessment tasks, the numerical value of the answer is simply marked as right or wrong, and each student's mathematical ability is assessed accordingly.
For the Mathematical Thinking Project, the answers are of minor importance. Teachers can continue with their 'normal' mathematical teaching program. The Mathematical Thinking project is not intended to replace or be merged into the schools current day-to-day teaching of mathematics.
The Mathematical Thinking project was simply designed to discover how far children's natural curiosity and interest in mathematics takes them, whilst observing how students work towards a solution over time by devising their own way of representing and solving problems.
EXTENSION ACTIVITY FOR TEACHERS
REMINDER: NESA 2018 MATHEMATICS (All Stages): OUTCOMES
- Working Mathematically - Students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning
- Number & Algebra - Students develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation.
MATHS REASONING VERSUS COMPUTATION
This video should be de-contructed and re-packaged in ways suggested by Dan Meyer - How could this video be modified to make this excercises a useful 'Mathematical Thinking' classroom activity?
In real life, what problem that was worth solving, have you ever solved, where you knew all of the information in advance and can solve it by plugging values into a formula? No real problem is like that.
Here is an example video of the type often used in a conventional, explicit maths class.
How could this video be modified to make this a useful maths reasoning activity?
According to Dan Meyer these type of 'explicit' teaching resources/procedures need to be de-constructed and re-packaged. Here is his explanation and some examples:
- How can your students prove that they have found all possible outfits?
- Providing an answer such as '3 x 2 = 6' is NOT a proof! Why not?
- Why does adding an item of one type make more outfits than a different type of item?
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NESA Mathematics Outcomes - http://web1.bondibeach-p.schools.nsw.edu.au/doku.php?id=2018:mathematics:home