Quite a Combo! Let's Talk Combinatorics
Explore combinations, permutations and why math is relevant in everyday life.
Little do we notice that combinations and permutations are used in our everyday life; whether it's pondering how many dishes we can make with a particular ingredient, to how many outfits this shirt can match with, to figuring out the combinations to a lock. Combinations and permutations are not only used in our everyday life or in math problems, but are also used all the time in every field of STEM!
What You Need
Activity 1: Sprint Quiz
- Handout (optional)
- Pencils
Activity 2: Egyptian Tomb Escape Room
- Computers with internet access
- Scientific calculators or calculator apps
- Scrap paper
- 4 toothpicks per person (optional)
- Pencils (optional)
Activity 3: Math in Everyday Life
- Printouts of activity sheet (or digital link)
- Scrap paper
- Pencils
Guide:
Presentation:
Physical Requirements
You will need a space that will allow you to comfortably lead/demonstrate activities. Check that you have all supplies necessary for the activity.
This kit can be done in-person or virtually. In either case, participants will need access to a computer with internet access for Activity 2 (Egyptian Tomb Escape Room).
This kit works best with a partner who can monitor the chat for questions, if being completed virtually.
Facilitators must complete the following PRIOR to the workshop.
- Print out the following:
- Sprint Quiz handout
- Egyptian Tomb answer key (has 2 pages)
- Functional Park activity sheet (has 2 pages)
- Tessellation Art activity sheet
- Let’s Budget activity sheet (has 2 pages)
- Cookie Recipe activity sheet (has 3 pages)
- Set up music for Egyptian Tomb Escape Room and play through any ads at the beginning
If running this workshop virtually:
- Upload the Let’s Talk Science and Egypt background photos to your video-conferencing software (optional)
What To Do
Activity 1: Sprint Quiz
-
CHOICE: You can run the quiz using a Zoom poll (make sure to upload questions before starting the meeting), using a separate quiz platform like Kahoot, or by printing copies of the handout from the PowerPoint presentation.
Activity 2: Egyptian Tomb Escape Room
- Share the link to the escape room with students.
- Once students open the link, they will be able to access the journal where they can input their answers as well as built-in hints and help documents. Most students will be able to work through the activity independently.
- Give students time warnings halfway through and when there are 5 minutes left.
- If students finish early, the escape room contains links to additional Let’s Talk Science web resources. You can also provide them with one or more of the Math in Everyday Life activity sheets.
- At the end of the activity are some slides about early combinatorics for historical context and to emphasize how useful this math is and has been.
Activity 3: Math in Everyday Life
- To transition into this activity, give students the opportunity to suggest ideas of where else combinatorics (combinations and permutations) could be used and where math is used in everyday life.
- If there is time, give students the opportunity to work through one or two of the activity sheets. They can also be provided as take-home activities and given to students who complete the Egyptian Tomb Escape Room activity early.
- Share the link to the career profiles on Let’s Talk Science’s website and provide an example of how math is used in a not-mathematics-based career.
Discovery
Combinatorics is a branch of math all about counting. Sounds simple, but it gets a bit more complicated than “1”, “2”, “3”! Two main topics in combinatorics are combinations and permutations. In everyday talk, these terms can be interchangeable, but they mean different things in math.
Combinations are groupings of items where the order doesn't matter. For example, ordering from a set menu where you can choose 1 main dish, 1 drink, and 1 dessert. There are many combinations of items you can choose and it doesn't matter what order you choose them in (i.e. drink first, main dish first, etc.)
Permutations are basically ordered combinations. They are groupings of items where the order does matter (which item is first, second, third, etc.). For example, code locks require numbers or letters to be entered in a particular order - 248 is not the same code as 824. They are different permutations, even though they are the same (mathematical) combination.
If items can repeat (e.g. can have 333), then the number of permutations is nr, where n is the number of items in the group and r is how many items you must choose. For example, the number of 3-digit permutations of the numbers {1, 2, 3, 4, 5}: n = 5 and r = 3, so the total number of permutations is 53 = 125
If items can’t repeat (e.g. CAN'T have 333) and ALL of the items in the group must be used, then the total number of permutations can be found using a factorial (symbol: !). A factorial is a multiplication function where the number you multiply by decreases by 1 each time. For example, 5! = 5x4x3x2x1. As long as the items can’t repeat and all of the items in the group are used, the number of permutations is equal to n!, where 'n' is the number of items in the group.
Mathematics is everywhere and it's part of our daily life, whether we notice it our not.
These are a few extension activities the students can continue to work on or try out after the Let’s Talk Science workshop.
- If there wasn’t time to play with the activity sheets during the workshop, they can be handed out afterwards for students to take home.
- Explore the career profiles on the Let’s Talk Science website.
- Solve the Hanoi Towers mathematical puzzle
What's Happening?
Combinatorics is a branch of math all about counting. Sounds simple, but it gets a bit more complicated than “1”, “2”, “3”! Two main topics in combinatorics are combinations and permutations. In everyday talk, these terms can be interchangeable, but they mean different things in math.
Combinations are groupings of items where the order doesn't matter. For example, ordering from a set menu where you can choose 1 main dish, 1 drink, and 1 dessert. There are many combinations of items you can choose and it doesn't matter what order you choose them in (i.e. drink first, main dish first, etc.)
Permutations are basically ordered combinations. They are groupings of items where the order does matter (which item is first, second, third, etc.). For example, code locks require numbers or letters to be entered in a particular order - 248 is not the same code as 824. They are different permutations, even though they are the same (mathematical) combination.
If items can repeat (e.g. can have 333), then the number of permutations is nr, where n is the number of items in the group and r is how many items you must choose. For example, the number of 3-digit permutations of the numbers {1, 2, 3, 4, 5}: n = 5 and r = 3, so the total number of permutations is 53 = 125
If items can’t repeat (e.g. CAN'T have 333) and ALL of the items in the group must be used, then the total number of permutations can be found using a factorial (symbol: !). A factorial is a multiplication function where the number you multiply by decreases by 1 each time. For example, 5! = 5x4x3x2x1. As long as the items can’t repeat and all of the items in the group are used, the number of permutations is equal to n!, where 'n' is the number of items in the group.
Why Does it Matter?
Mathematics is everywhere and it's part of our daily life, whether we notice it our not.
Investigate Further
These are a few extension activities the students can continue to work on or try out after the Let’s Talk Science workshop.
- If there wasn’t time to play with the activity sheets during the workshop, they can be handed out afterwards for students to take home.
- Explore the career profiles on the Let’s Talk Science website.
- Solve the Hanoi Towers mathematical puzzle