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01Magic Spells Unit
CMath Vo abulary common multiple: a number that is a multiple of two or more numbers
1 . Find all the common multiples of two numbers between 1 and 80. 1. Have students first find the multiples of two
numbers (1 - 80) and then find the common
a. 4 and 6 b. 6 and 9 multiples.
Multiples of 4: 4, 8, 12, 16, 20, 24 ... Multiples of 6: 6, 12, 18, 24, 30 ... 2. Have them use the problem solving
method to solve the problems.
Multiples of 6: 6, 12, 18, 24, 30 ... Multiples of 9: 9, 18, 27, 36, 45 ...
2a.
Common multiples of 4 and 6: Common multiples of 6 and 9: Understand the Question
Q: What do you need to find?
12, 24, 36, 48, 60, 72 18, 36, 54, 72 A: The second time that both Thomas and
Ann will meet.
2 . Use common multiples to solve each problem. Q: Read the problem again. What do you
already know?
a. It takes Thomas 4 minutes to ride his bike around the park. It takes Ann A: It takes Thomas 4 minutes to ride his
8 minutes to ride her bike around the park. If they start together, how many bike around the park. It takes Ann
minutes after that will they meet for the second time? (Only count the times 8 minutes to ride her bike around the
they meet after they start.) park.
Plan the Process
Times that Thomas is at the starting point: 4, 8, 12, 16, 20, 24 ... Q: How will you solve the problem?
Times that Ann is at the starting point: 8, 16, 24, 32, 40, 48 ... A: Find the second common multiple of the
Common multiples of 4 and 8: 8, 16 ... two numbers.
Solve the Problem
Thomas and Ann will meet for the second time after 16 minutes. Refer to 2a. in the textbook.
Look Back
b. Jessica goes to the library every 6 days, and Ricky goes to the same library Q: Does your answer make sense?
every 8 days. Jessica and Ricky meet at the library for the first time.
How many days after will they meet for the second time? (Only count the
times they meet after today.)
Days that Jessica goes to the library: 6, 12, 18, 24, 30, 36, 42, 48 ...
Days that Ricky goes to the library: 8, 16, 24, 32, 40, 48 ...
Common multiples of 6 and 8: 24, 48 ...
Jessica and Ricky will meet for the second time after 48 days.
1. Magic Spells 7
Explain how to use a hundred chart to students who are having a difficult time
finding common multiples.
Problem: Use a hundred chart to find the common multiples of 4 and 6.
Step1: Have students find multiples of 4 in the hundred chart and color the
numbers gray.
Step2: Have them find multiples of 6 and draw red boxes around the numbers red.
Step3: The numbers that are colored gray with the red boxes around them are the
common multiples of 4 and 6: 12, 24, 36, 48, 60, 72, 84, and 96.
5A Unit 01 009
CMath Vo abulary common multiple: a number that is a multiple of two or more numbers
1 . Find all the common multiples of two numbers between 1 and 80. 1. Have students first find the multiples of two
numbers (1 - 80) and then find the common
a. 4 and 6 b. 6 and 9 multiples.
Multiples of 4: 4, 8, 12, 16, 20, 24 ... Multiples of 6: 6, 12, 18, 24, 30 ... 2. Have them use the problem solving
method to solve the problems.
Multiples of 6: 6, 12, 18, 24, 30 ... Multiples of 9: 9, 18, 27, 36, 45 ...
2a.
Common multiples of 4 and 6: Common multiples of 6 and 9: Understand the Question
Q: What do you need to find?
12, 24, 36, 48, 60, 72 18, 36, 54, 72 A: The second time that both Thomas and
Ann will meet.
2 . Use common multiples to solve each problem. Q: Read the problem again. What do you
already know?
a. It takes Thomas 4 minutes to ride his bike around the park. It takes Ann A: It takes Thomas 4 minutes to ride his
8 minutes to ride her bike around the park. If they start together, how many bike around the park. It takes Ann
minutes after that will they meet for the second time? (Only count the times 8 minutes to ride her bike around the
they meet after they start.) park.
Plan the Process
Times that Thomas is at the starting point: 4, 8, 12, 16, 20, 24 ... Q: How will you solve the problem?
Times that Ann is at the starting point: 8, 16, 24, 32, 40, 48 ... A: Find the second common multiple of the
Common multiples of 4 and 8: 8, 16 ... two numbers.
Solve the Problem
Thomas and Ann will meet for the second time after 16 minutes. Refer to 2a. in the textbook.
Look Back
b. Jessica goes to the library every 6 days, and Ricky goes to the same library Q: Does your answer make sense?
every 8 days. Jessica and Ricky meet at the library for the first time.
How many days after will they meet for the second time? (Only count the
times they meet after today.)
Days that Jessica goes to the library: 6, 12, 18, 24, 30, 36, 42, 48 ...
Days that Ricky goes to the library: 8, 16, 24, 32, 40, 48 ...
Common multiples of 6 and 8: 24, 48 ...
Jessica and Ricky will meet for the second time after 48 days.
1. Magic Spells 7
Explain how to use a hundred chart to students who are having a difficult time
finding common multiples.
Problem: Use a hundred chart to find the common multiples of 4 and 6.
Step1: Have students find multiples of 4 in the hundred chart and color the
numbers gray.
Step2: Have them find multiples of 6 and draw red boxes around the numbers red.
Step3: The numbers that are colored gray with the red boxes around them are the
common multiples of 4 and 6: 12, 24, 36, 48, 60, 72, 84, and 96.
5A Unit 01 009
