Free Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 by Judith A. Muschla, Gary Robert Muschla, Erin Muschla-Berry

walked a mile the first day. She walked twice as far the second day. What is the total distance she walked?
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Operations and Algebraic Thinking: 4.OA.4
    “Gain familiarity with factors and multiples.”
4. “Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.”
    Background
    Every number except 1 has two or more factors. A number that has only two factors, 1 and the number, is a prime number. A number that has more than two factors is a composite number.
    Composite numbers can be expressed as the product of two or more pairs of factors. For example, 30 is a composite number. Its pairs of factors are , , , and . These pairs of factors can be rewritten as , , , and . The pairs are the same; only the order of the numbers is reversed.
    The prime numbers that are less than 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. (1 is neither prime nor composite.) All other numbers that are less than 100 are composite numbers.
Activity: The Prime Challenge
Working in small groups, students will play the game “The Prime Challenge,” in which they will identify prime and composite numbers.
Materials
Pens; one 4-inch-by-6-inch index card for each group of students; a dark marker for the teacher.
Preparation
Make a number card to easily identify groups. Fold the index cards in half, resembling a tent. Use a marker to label each card with Group 1, Group 2, and so on until each group has a number. On a sheet of paper, make a score sheet with group numbers labeled in each column, as shown below. ( Note: You may have more than six groups.)

Procedure
1. Distribute the group number cards, one to each group. Students should place the card on their desk so that you can easily see the group number to facilitate scoring.
2. Ask each group of students to use a pen to write any 10 numbers between 1 and 100 on a sheet of paper. ( Note: Using a pen prevents students from changing their numbers.)
3. Instruct each group to circle the prime numbers from the numbers they wrote. When called upon, they will read the prime numbers they circled.
4. Explain the rules. You will call on one group at a time. A group member will read the first prime number that the group circled. The other groups must agree or disagree if the number is a prime number. If a group disagrees, it must show a correct pair of factors. Following is an example of the scoring process, using Group 1:
     
If Group 1 is correct, and the other groups agree, Group 1 gets 10 points.
If Group 1 is correct, but a group feels that Group 1 is incorrect, the other group must offer a pair of factors to show why the number is not prime. If the first disagreeing group is incorrect, they lose 10 points. Likewise, if another group disagrees and is incorrect, they also lose 10 points. Group 1 gets 10 points.
If Group 1 is incorrect, the first group to disagree and state a correct pair of factors gains 10 points. Group 1 then loses 10 points.
If Group 1 is incorrect and no other groups disagree, or if disagreeing groups cannot provide a correct pair of factors, you provide the factors and all groups lose 10 points.
5. Offer this example: Suppose Group 1 said 29, and no other group disagreed. Group 1 gets 10 points. If Group 1 said 29 and another group disagrees, Group 1 gets 10 points for being correct. The group that disagreed loses 10 points. If Group 1 said 12 is prime, which is incorrect, the first team to disagree and show a correct pair of factors gains 10 points. Group 1 also loses 10 points. If Group 1 said 12 is prime and no other group disagrees, all teams lose 10 points.
6. Begin the