About this resource
In this lesson students will apply what they know about factors and multiples to solve a real world problem. When planning a party, camping trip, or other event for a variety of people it is important to have enough supplies (or food) for everyone coming. It is also important to know the different possibilities that may occur such as how many people will show up. In this problem students look at packing for a picnic and how many people they can invite with how much food they have.
Curriculum & Standards
Related General Curriculum / Common Core Area
MATH
Related Curriculum / Common Core Standard
CCSS.MATH.CONTENT.6.NS.B.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
What students will do
Students will be able to use common factors and multiples to solve real world problems.
Resources Needed
Classroom Resources Needed:
- Manipulatives (buttons, beads, small cups) **do not tell students what to use them for
- CMP: Prime Time book
- Paper
- Math Journal or scrap paper for warm-up
- Poster paper for each table group (3-4 students per group)
- Markers
Supplemental Resources:
- Khan Academy. "Greatest Common Factor Explained." YouTube, uploaded 17 Nov. 2006, https://youtu.be/jFd-6EPfnec
- Khan Academy. "Least Common Multiple Exercise." YouTube, uploaded 24 July 2013, https://youtu.be/znmPfDfsir8
- Michigan Council of Teachers of Mathematics offers resources such as Rich Math Tasks to address the CCSS Standards of Mathematical Practice while building content knowledge. See https://www.mictm.org/index.php/resources/rich-math-tasks
- NRICH Project of the University of Cambridge offers enrichment activities such as a Factors and Multiples Game. See https://nrich.maths.org/5468
Library Resources: The Middle School Librarian also makes supplemental book materials available to 6thgrade students for this unit by using MeLCat, the Michigan eLibrary resource sharing network.
Buxton, Marilynn L. R. Math Bafflers: Logic Puzzles That Use Real-World Math. Grades 6-8. Waco, TX: Prufrock Press, 2011. http://elibrary.mel.org/record=b21503141~S15
VandeCreek, Barbara. Math Rules!: 5th-6th Grade 25 Week Enrichment Challenge. Marion, Ill: Pieces of Learning, 2002. http://elibrary.mel.org/record=b22873891~S15
Zaccaro, Edward. Challenge Math: For the Elementary and Middle School Student. Bellevue, Iowa: Hickory Grove Press, 2000.http://elibrary.mel.org/record=b18865298~S15
Lesson sequence & procedures
Direct Instruction & Guided Practice (10 minutes):
Warm-Up: Students answer warm-up question in Math Notebooks. "Sally packed 8 sandwiches, 12 apples, and 4 juice boxes for her picnic. How many people can she invite to join her?"
After students are given time to answer this question, discuss all the possibilities as a class. Ask students how they came up with their answers, make sure that they use language such as factors and multiples.
Launch: Have students open their Prime Time books to pg. 33. Have students read through the Problem (individual or whole class). Ask students what their problem is asking for the day, then check to see if there are any general questions. Provide students with different manipulatives and work paper. Make sure along with how many people, students explain how much of each snack item each person will get. There can be no leftovers and everyone should have the same amount. Have students focus on A1 and 2, moving on from there if there is time.
Independent Practice (30 minutes):Allow students to come up with their own strategies to answer the Problem. Some may draw pictures, some may use a t-chart, and some may use the manipulatives with the buttons representing apples and trail mix bags. It is important not to give too much away, let the students work on their own and come up with their own ideas of how to show their thinking. After about 10-15 minutes of work time (depending on where students are at in their group thinking), provide each table group with poster board to show their thinking for A1 and A2.
Closing/Reflection (15 minutes): Have each group post their poster around the room. Give students time to do a Gallery Walk. During a Gallery Walk there is no discussing yet. Instead students walk around the room to examine each other's work for some independent think time. Before the walk starts remind students to be thinking "What strategy did they use? How is it similar to mine? How is it different from mine?" Then bring students together to discuss what they have seen through their work and others. There are a variety of things that may or may not come up depending on what the students discuss. Help to bring in vocabulary words if students do not. For example, it is possible to have 2 people go on the picnic and they would each get 12 apples and 18 bags of trail mix this is because 2 and 12 are a factor pair of 24..
Questions to ask during discussion:
- How did you come up with your numbers?
- How did you know how much each person would get?
- What is the greatest amount of snack packs we can make?
- How do you know that is the greatest?
How learning is assessed
Ticket Out the Door: Jake is shopping for his birthday party. He bought 20 pizza slices and a cake that will serve 30. How many people could he feed with everyone getting the same amount and no leftovers?
Extension: When packaging food items, corporations such as Nabisco are intentional about how many cookies they would include in a pack. In order for food to be shared equally amount a variety of people, a box of Oreos would be better having 30 cookies rather than 22. Why? Thirty cookies can be shared between 2, 3, 5, 6, 10 or fifteen people with everyone getting the same amount. Whereas 22 cookies could only be shared equally between 2 or eleven people (factors). If you were hired by Nabisco, what numbers (from 0 to 100) would you suggest to them when packaging items? Which numbers would you suggest against? Prove your reasoning. Students could also put together a presentation or packaging example with their numbers.