Students will be given the challenge of working backwards to find the pair of numbers that fulfills the given clues. (MP1) If they are struggling, I will suggest that they use a guess and check strategy.
What is the mystery number pair?
Clue 1: The GCF of the mystery pair is 7.
Clue 2: The LCM of the mystery pair is 70.
Clue 3: Both of the numbers in the mystery pair have two digits.
Clue 4: One of the numbers in the mystery pair is odd and the other is even.
Answer: 14 and 35
After about 10 minutes, I will randomly select students to share their strategy and answers with the class. Students may offer other strategies, such as listing the multiples of 7.
I will seat students in groups of 4. They will be grouped heterogeneously, with at least one high level math student at each group. This allows for groups to have at least one student who feels comfortable with the topic and problem. The high level math students have been determined by a baseline assessment and previous state math test scores.
Before beginning the project, I explain to students that their projects must have:
1. Your given problem
2. Work clearly shown
3. Answer (GCF/LCM) shown on a separate piece of paper
4. Group member names
I will explain to students that the project is a group grade. My expectations for each group are:
1. Work together
2. Respect each other
3. Stay on task
Each student will complete the work in their notebooks and then as a group agree on a strategy and answer. I will give each group a set of markers and they will show their work on chart paper. If a student or group is not meeting the expectations, we will discuss what needs to be improved and how to do so.
The second part of the project is the gallery walk, that will occur the following day. For this part, each group will view and answer another groups' project. Therefore, it is important that the work is correct, but they don't show their answer on the chart paper.
I will randomly assign each group their problem. As groups work I will circulate to ensure that they are following directions.
Group 1: Find the GCF and LCM of 42 and 24
Group 2: Find the GCF and LCM of 14 and 35
Group 3: Find the GCF and LCM of 32 and 56
Group 4: Find the GCF and LCM of 24 and 60
Group 5: Find the GCF and LCM of 36 and 42
Group 6: Find the GCF and LCM of 40 and 65
Group 7: Find the GCF and LCM of 30 and 48
Group 8: Find the GCF and LCM of 30 and 72
Students will work with their group until the end of the class period.