Read and discuss each problem with your group. Without solving, predict whether each problem involves finding common multiples or finding common factors. Circle one or more options to show your prediction.

Then your teacher will assign one problem to your group. Work with your group to solve the problem. Then create a visual display that explains your group’s mathematical thinking while solving the problem. Your display may include a diagram, lists, tables, equations, descriptions, and math vocabulary.

1. Soccer. Diego and Andre are both in a summer soccer league. During the month of August, Diego has a game every 3rd day, starting August 3rd, and Andre has a game every 4th day, starting August 4th.

   • common multiples
   • least common multiple

   • common factors
   • greatest common factor
   1. What is the first date that both Diego and Andre will have a game?
   2. How many of their games fall on the same date in the month of August?

2. Performances. During a performing arts festival, students from elementary and middle schools will be grouped together for various performances. There are 32 elementary students and 40 middle-school students. The arts director wants identical groups for the performances, with students from both schools in each group. Each student must be in a group and can be a part of only one group.

   • common multiples
   • least common multiple

   • common factors
   • greatest common factor
   1. Name all the possible groupings of elementary- and middle-school students.
   2. What is the largest number of groups that can be formed? How many elementary-school students and how many middle-school students will be in each group?

3. Lights. A string of lights has red, gold, and blue lights. The red lights are set to blink every 12 seconds, the gold lights are set to blink every 8 seconds, and the blue lights are set to blink every 6 seconds. The lights are on an automatic timer that starts each day at 7:00 p.m. and stops at midnight.

   • common multiples
   • least common multiple

   • common factors
   • greatest common factor
   1. How often will all 3 colors of lights blink at the exact same time?
   2. How many total times will this happen in one day?

4. Banners. Noah is making identical square banners for students to hold during the Opening Day game. He has two square pieces of cloth—one is 72 inches wide, and the other is 90 inches wide. He wants to use up all the cloth and make the largest square banners possible.

   • common multiples
   • least common multiple

   • common factors
   • greatest common factor
   1. How wide should he cut the banners?
   2. How many banners can he cut?

5. Dancers. Elena is part of a recital where 48 dancers perform in the dark. All the dancers enter the stage in a straight line wearing glow-in-the-dark accessories. Every 3rd dancer wears a glow-in-the-dark headband, every 5th dancer wears a glow-in-the-dark belt, and every 9th dancer wears a set of glow-in-the-dark gloves.

   • common multiples
   • least common multiple

   • common factors
   • greatest common factor
   1. If Elena is the 30th dancer, what accessories will she wear?
   2. Will any of the dancers wear all 3 accessories? If so, which one(s)?
   3. How many of each accessory will the dance teacher need to order?

Your teacher will explain the directions for a bingo game. 

• Share one bingo board and some bingo chips with a partner.
• Your teacher will read some statements out loud. Work with your partner to decide which numbers fit each statement. 
• For each number you cover with a chip, be prepared to identify which statement it corresponds to and to share your reasoning.