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Prime and Composite Numbers
Students will be able to find factor pairs for whole numbers and determine if they’re prime or composite numbers.
- Display the teaching component at the top of the Factor Rainbows worksheet. Ask students to turn and talk to their partners about how to complete the rainbow. Listen for key terms such as "factors" and "math expressions."
- Choose a student to share their answers and allow other students to add to their answers or offer corrections.
- Define factors as numbers we can multiply together to get another number and show how the rainbow has factors that, when multiplied, produce the whole number on the rainbow.
- Explain that today they'll expand their understanding of factors by determining if the factors are prime numbers or composite numbers.
- Define prime numbers as whole numbers that can only be made by multiplying the number one by itself. Tell them if they cannot divide a number by any other number than itself and one, it is prime. Define composite numbers as whole numbers that have factors in addition to 1 and itself. Tell students 1 and 0 are neither prime nor composite.
- Ask students to shout out which numbers they think are prime and write them on the board in a T-chart with "prime" and "composite" written on top. Correct any misconceptions with multiplication sentences and/or visuals, or allow other students to offer explanations.
Explicit Instruction/Teacher modeling(10 minutes)
- Display problem B on the Factor Rainbow worksheet and find the factors using the factor tree strategy. Model dividing the number by another number to find the two factors for the tree. Make some errors and allow students to correct your mistakes.
- Continue using problem B. Draw a factor tree for the number 48. Model finding the factors and checking your answer by multiplying all the factors to get the product again. List the various expressions and box the composite factors and circle the prime factors. (Note: feel free to color code the box and circle.)
- Compare the factor tree to the factor rainbow to specify which numbers are composite or prime and compare and contrast the processes.
- Choose another problem from the Factor Rainbows worksheet to model. Choose students to box and circle the correct numbers on the board while the other students have a thumbs up for agree and thumbs down for disagree.
Guided Practice(15 minutes)
- Ask a student to explain the process you used to create the factor tree before having students separate into groups of 4–5 students.
- Give each group enough index cards so they can have one whole number per card for each factor they need to complete their factor tree. Give a different color marker to each group.
- Assign students a two-digit whole number and ask them to create a tree with their index cards. Have them discuss the prime and composite numbers. Remind them to divide the initial number or subsequent factors if they need help finding more factors.
- Have groups switch cards with each other so they have new groups. When they get their new cards have them re-create the groups factor trees and justify their choice of prime and composite numbers.
- Circulate around the room and correct misconceptions. Ask students to think about potential substitutions for the factors they got from the other group.
Independent working time(12 minutes)
- Distribute the Factor Tree worksheet and read through the directions. Choose two students to define composite and prime numbers and to provide examples.
- Ask students to complete the Factor Tree worksheet. Use the worksheet as a formative assessment of their ability to find and classify factors as either prime or composite numbers.
- Allow students to view the "Prime and Composite Numbers" video to the four-minute mark after the Explicit Teach section and then discuss the difference between composite and prime numbers. Then, have them find prime and composite numbers and prove their answers (see related media).
- Allow students to use manipulatives (e.g., unifix cubes) or multiplication charts with different color writing instruments to color-code the prime numbers as they complete the group activities and independent practice. Emphasize expression creation (e.g., 3 x 8) after every factor you add to the tree.
- Allow them to pretend to be the factors with another group of students and place themselves in the correct location on the factor tree or rainbow. Have them practice their vocabulary multiplication, prime numbers, composite numbers, and multiples during the activity.
- Ask students to create factor trees with three-digit numbers and missing factors. Then, have them switch with partners and complete the factor tree. Have them circle the composite factors and box the prime factors.
- Ask students to decide if the number 7 is prime or composite. Have them hold up two fingers for composite and one finger for prime.
- Distribute an index card and ask them to write down their reasoning.
Review and closing(5 minutes)
- Ask students to consider some patterns they can think about when classifying factors as composite or prime. For instance, what are some numbers you know will always be composite (e.g., even numbers except 2, numbers that end in 5, etc.).
- Ask students to consider how knowing these patterns can help them save time on their factor trees.