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Using Multiplication to Count
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TweetMr Mattock
on 8 October 2016Transcript of Using Multiplication to Count
Using Multiplication to Count
Starter
Graham has a pack of 10 pens. 4 are black, 3 are blue and 3 are red.
Graham gives a random pen to Saskia and a random pen to Drew. List the possible combinations of pens that Saskia and Drew could have. The first has been done for you.
Activity
Complete the Multiplication and Counting Worksheet.
3 types of counting
L.O.  Understand the different ways of
multiplication to count possible outcomes.
Saskia Drew
Black Black
Starter
Graham has a pack of 10 pens. 4 are black, 3 are blue and 3 are red.
Graham gives a random pen to Saskia and a random pen to Drew. List the possible combinations of pens that Saskia and Drew could have. The first has been done for you.
Saskia Drew
Black Black
Black Blue
Black Red
Blue Black
Blue Blue
Blue Red
Red Black
Red Blue
Red Red
Plenary
Graham has a pack of 10 pens. 5 are black, 4 are blue and 1 is red.
Graham gives a random pen to Saskia and a random pen to Drew. How many possible combinations of pens are there.
Plenary
Graham has a pack of 10 pens. 5 are black, 4 are blue and 1 is red.
Graham gives a random pen to Saskia and a random pen to Drew. How many possible combinations of pens are there.
8
Using multiplication to count
Graham has a pack of 20 pens. 7 are black, 7 are blue and 6 are red.
Graham is going to give a pen to each of his friends. Work out the number of combinations possible if he has:
i) 1 friend
ii) 2 friends
iii) 3 friends
iv) 4 friends
v) 5 friends
vi) 6 friends
Using multiplication to count
Graham has a pack of 20 pens. 7 are black, 7 are blue and 6 are red.
Graham is going to give a pen to each of his friends. Work out the number of combinations possible if he has:
i) 1 friend
3
ii) 2 friends
9
iii) 3 friends
27
iv) 4 friends
81
v) 5 friends
243
vi) 6 friends
729
Powers
Graham has black, blue and red pens. He is giving a random pen to each of his 5 friends. Work out the possible number of combinations.
Multiplication
Graham a black, blue and red pen, an HB or 2H pencil, and a 30 cm and 15 cm ruler. Graham is going to give his friend a pen, pencil or ruler at random. Work out the number of possible combinations of pen, pencil and ruler that Graham's friend could have.
Graham a black, blue, red and green pen. He is going to arrange them in a line. Work out how many possible combinations of colours there are.
3 types of counting
Powers
Graham has black, blue and red pens. He is giving a random pen to each of his 5 friends. Work out the possible number of combinations.
Multiplication
Graham a black, blue and red pen, an HB or 2H pencil, and a 30 cm and 15 cm ruler. Graham is going to give his friend a pen, pencil or ruler at random. Work out the number of possible combinations of pen, pencil and ruler that Graham's friend could have.
Factorials
Graham a black, blue, red and green pen. He is going to arrange them in a line. Work out how many possible combinations of colours there are.
3 = 243
5
3 x 2 x 2 = 12
4 x 3 x 2 x 1 = 4! = 24
Activity
Consider the 4 numbers 2, 5, 7 and 15.
(a) How many different pairs of fractions can be made from the 4 numbers?
(b) Which pair gives the greatest sum?
(c) Which pair gives the greatest difference?
(d) Does this work for other sets of 4 numbers? Can you prove it?
Activity
Complete the Multiplication and Counting Worksheet.
1. 6! = 720
2. 2 = 16
3. 12! = 479001600
4. 20! = 2432902008000000000
5. 4 = 1024
6. 5! = 120
7. 26 x 25 x 10 x 9 x 8 x 7 = 3276000
8. 10 x 9 x 8 x 7 x 6 x 5 = 151200
9. Four digit numbers  3 x 4 x 3 x 2 = 72
Five digits numbers  5! = 120
Total  192.
4
5
Activity
Consider the 4 numbers 2, 5, 7 and 15.
(a) How many different pairs of fractions can be made from the 4 numbers?
3 x 2 x 2 = 12
(b) Which pair gives the greatest sum?
+
(c) Which pair gives the greatest difference?

(d) Does this work for other sets of 4 numbers? Can you prove it?
Yes, start with a < b < c < d and examine the sums and differences you can
make.
Factorials
15 7
2 5
15 7
2 5
Activities
Activity
Answers
Key
Examples
Worked
Example
Worked
Example
Full transcriptStarter
Graham has a pack of 10 pens. 4 are black, 3 are blue and 3 are red.
Graham gives a random pen to Saskia and a random pen to Drew. List the possible combinations of pens that Saskia and Drew could have. The first has been done for you.
Activity
Complete the Multiplication and Counting Worksheet.
3 types of counting
L.O.  Understand the different ways of
multiplication to count possible outcomes.
Saskia Drew
Black Black
Starter
Graham has a pack of 10 pens. 4 are black, 3 are blue and 3 are red.
Graham gives a random pen to Saskia and a random pen to Drew. List the possible combinations of pens that Saskia and Drew could have. The first has been done for you.
Saskia Drew
Black Black
Black Blue
Black Red
Blue Black
Blue Blue
Blue Red
Red Black
Red Blue
Red Red
Plenary
Graham has a pack of 10 pens. 5 are black, 4 are blue and 1 is red.
Graham gives a random pen to Saskia and a random pen to Drew. How many possible combinations of pens are there.
Plenary
Graham has a pack of 10 pens. 5 are black, 4 are blue and 1 is red.
Graham gives a random pen to Saskia and a random pen to Drew. How many possible combinations of pens are there.
8
Using multiplication to count
Graham has a pack of 20 pens. 7 are black, 7 are blue and 6 are red.
Graham is going to give a pen to each of his friends. Work out the number of combinations possible if he has:
i) 1 friend
ii) 2 friends
iii) 3 friends
iv) 4 friends
v) 5 friends
vi) 6 friends
Using multiplication to count
Graham has a pack of 20 pens. 7 are black, 7 are blue and 6 are red.
Graham is going to give a pen to each of his friends. Work out the number of combinations possible if he has:
i) 1 friend
3
ii) 2 friends
9
iii) 3 friends
27
iv) 4 friends
81
v) 5 friends
243
vi) 6 friends
729
Powers
Graham has black, blue and red pens. He is giving a random pen to each of his 5 friends. Work out the possible number of combinations.
Multiplication
Graham a black, blue and red pen, an HB or 2H pencil, and a 30 cm and 15 cm ruler. Graham is going to give his friend a pen, pencil or ruler at random. Work out the number of possible combinations of pen, pencil and ruler that Graham's friend could have.
Graham a black, blue, red and green pen. He is going to arrange them in a line. Work out how many possible combinations of colours there are.
3 types of counting
Powers
Graham has black, blue and red pens. He is giving a random pen to each of his 5 friends. Work out the possible number of combinations.
Multiplication
Graham a black, blue and red pen, an HB or 2H pencil, and a 30 cm and 15 cm ruler. Graham is going to give his friend a pen, pencil or ruler at random. Work out the number of possible combinations of pen, pencil and ruler that Graham's friend could have.
Factorials
Graham a black, blue, red and green pen. He is going to arrange them in a line. Work out how many possible combinations of colours there are.
3 = 243
5
3 x 2 x 2 = 12
4 x 3 x 2 x 1 = 4! = 24
Activity
Consider the 4 numbers 2, 5, 7 and 15.
(a) How many different pairs of fractions can be made from the 4 numbers?
(b) Which pair gives the greatest sum?
(c) Which pair gives the greatest difference?
(d) Does this work for other sets of 4 numbers? Can you prove it?
Activity
Complete the Multiplication and Counting Worksheet.
1. 6! = 720
2. 2 = 16
3. 12! = 479001600
4. 20! = 2432902008000000000
5. 4 = 1024
6. 5! = 120
7. 26 x 25 x 10 x 9 x 8 x 7 = 3276000
8. 10 x 9 x 8 x 7 x 6 x 5 = 151200
9. Four digit numbers  3 x 4 x 3 x 2 = 72
Five digits numbers  5! = 120
Total  192.
4
5
Activity
Consider the 4 numbers 2, 5, 7 and 15.
(a) How many different pairs of fractions can be made from the 4 numbers?
3 x 2 x 2 = 12
(b) Which pair gives the greatest sum?
+
(c) Which pair gives the greatest difference?

(d) Does this work for other sets of 4 numbers? Can you prove it?
Yes, start with a < b < c < d and examine the sums and differences you can
make.
Factorials
15 7
2 5
15 7
2 5
Activities
Activity
Answers
Key
Examples
Worked
Example
Worked
Example