1. Use the product rule for counting
Grade 7
Product Rule
Use the product rule for counting
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Use the product rule for counting
Grade 7
Prior Knowledge
Listing outcomes
Duration
20 minutes
Resources
Print slides:
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Difference between listing outcomes to find the number of possibilities and using the product rule
Show students the lengthy process of listing outcomes and contrast this to using the product rule using slide 4 and 5. Give students slide 12 printed. Students to complete ”demo” section with solution and a note of explanation. 5
Applying the product rule
Students to complete four practice questions and one further contextualised problem. Solutions on slide 7 and 9. 10
Use of product rule for counting in exam questions (from specimen papers)
Give students slide 13. This includes two exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated.
Next Steps
Assessment
PLC/Reformed Specification/Target7/Number/Product Rule

3. Key Vocabulary
Multiplicative counting Product rule Systematic listing

4. Choose a three course meal from 3 Appetizers, 4 mains and 3 desserts.
Listing Outcomes
Choose a three course meal from 3 Appetizers, 4 mains and 3 desserts.
Listing all the possible outcomes to find out how many different options:
A1 M1 D1
A1 M2 D1
A1 M3 D1
A1 M4 D1
A1 M1 D2
A1 M2 D2
A1 M3 D2
A1 M4 D2
A1 M1 D3
A1 M2 D3
A1 M3 D3
A1 M4 D3
A2 M1 D1
A2 M2 D1
A2 M3 D1
A2 M4 D1
A2 M1 D2
A2 M2 D2
A2 M3 D2
A2 M4 D2
A2 M1 D3
A2 M2 D3
A2 M3 D3
A2 M4 D3
A3 M1 D1
A3 M2 D1
A3 M3 D1
A3 M4 D1
A3 M1 D2
A3 M2 D2
A3 M3 D2
A3 M4 D2
A3 M1 D3
A3 M2 D3
A3 M3 D3
A3 M4 D3
There are 36 different options

5. The Product Rule
Alternatively we can use the product rule for counting. There are 3 appetizers, 4 mains and 3 deserts So x 4 x 3 = 36 different meals you can choose from.

6. Product rule – Practice
A football ground has 2 entrance turnstiles and 3 exit turnstiles. How many different ways are there to enter and exit the football ground?
Two coins are flipped. Use the product rule for counting to find the total number of possibilities.
If five coins are flipped. Use the product rule for counting to find the total number of possibilities.
A manicurist has three different nail polish colours Liz can pick from for each nail. The options are pink, orange and red. What is the total number of combinations Liz could have?

7. Product rule – Solutions
A football ground has 2 entrance turnstiles and 3 exit turnstiles. How many different ways are there to enter and exit the football ground?
Two coins are flipped. Use the product rule for counting to find the total number of possibilities.
If five coins are flipped. Use the product rule for counting to find the total number of possibilities.
A manicurist has three different nail polish colours Liz can pick from for each nail. The options are pink, orange and red. What is the total number of combinations Liz could have?
2 x 3 = 6
2 x 2 = 4
2 x 2 x 2 x 2 x 2= 32
310= 59049

8. Problem Solving and Reasoning
At a Pizzeria there are 8 different toppings. How many different combinations are there if Charlotte is going to choose three different fillings. Use the product rule for counting to find the answer...

9. Problem Solving and Reasoning
At a pizzeria there are 8 different toppings. How many different combinations are there if Charlotte is going to choose three different fillings. Use the product rule for counting to find the answer...
We could think of 8 different toppings and list them all to find the answer but this would take too long
If Charlotte is choosing 3 fillings...
1st choice at the beginning there are 8 different toppings to choose from
2nd choice - there are now 7 different toppings to choose from
3rd choice - there are now 6 different toppings to choose from
8 x 7 x 6= 336

10. Exam Question – Specimen Papers

11. Exam Question – Specimen Papers

12. Product rule Student Sheet 1 DEMO PRACTICE PROBLEM
Choose a three course meal from
3 Appetizers, 4 mains and 3 desserts.
DEMO
A football ground has 2 entrance turnstiles and 3 exit turnstiles. How many different ways are there to enter and exit the football ground?
Two coins are flipped. Use the product rule for counting to find the total number of possibilities.
If five coins are flipped. Use the product rule for counting to find the total number of possibilities.
A manicurist has three different nail polish colours Liz can pick from for each nail. The options are pink, orange and red. What is the total number of combinations Liz could have?
PRACTICE
At a Pizzeria there are 8 different toppings. How many different combinations are there if Charlotte is going to choose three different fillings. Use the product rule for counting to find the answer...
PROBLEM
Student Sheet 1

13. Exam Question – Specimen Papers
Student Sheet 2