At this point, students should have a high level of understanding of factors, multiples, composite and prime numbers. I will give them the below problem to challenge their ability to use multiple concepts to problem solve.
What is my number?
Clue 1: My number is a multiple of 2 and 7.
Clue 2: My number is less than 100 but greater than 50.
Clue 3: My number is the product of three different prime numbers.
If a student is struggling with the problem, I will suggest that they look at each clue individually and then determine where the answers may overlap.
After about 10 minutes, I will reconvene the class and we will discuss the strategies they used to find the number. For students who aren't sure on how to approach this type of problem, it is helpful to hear others' strategies.
A common strategy is for students to list multiples of 7. They look for one that is divisible by 2, greater than 50, and then try to find the 3 prime numbers. Students who are better with their multiplication tables, may start with 56, knowing that it fulfills clues 1 and 2, but they will be unable to find three different prime numbers whose product is 56.
Students often have difficulty with word problems, so we will discuss how to approach GCF and LCM word problems. I will explain that it is important to look for key words or to think about the situation described in the word problem. I will give them the ideas and key words below as a guide to help them. However, I will explain to students that these tips are only meant as a guide and does not cover all situations that they may come across. It is helpful if students have these as notes for future reference.
GCF Ideas and Key Words
- splitting things into smaller sections
- arranging something into groups
- distributing equally
LCM Ideas and Key Words
- repeating an event
- a situation occurring again at the same time
After reviewing the key words we will work on an example as a class.
Since students are often intimidated by word problems because it's hard for them to decipher what the problem is asking of them and determine what's the important information. I use a KWL chart to help students organize the information given. (See GCF and LCM Word Problems KWL Chart) A KWL chart answers 3 questions: What do you know?, What do you want to know? What did you learn?
The KWL chart helps students focus on the important information.
Ex. 1 - Tameka has two pieces of cloth. One piece is 60 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?
We will start with the K. Students should write the important information, such as the lengths of the strips, 60 and 90.
Then the W. This is generally just restating the given question in their own words, to show understanding.
Next, students need to determine whether it's a GCF or LCM word problem and explain why. For this problem students should have identified it as a GCF problem because Tameka is splitting the cloth into smaller pieces.
Next, using their prior knowledge, they need to find the GCF.
Finally, they need to complete the L. This step is important to ensure that students have answered the original question and they understand what their answer represents.
Below the KWL chart, I've added a few questions to reinforce students' understanding of the problem. My goal for the second question is for students to really think about their answer and analyze the accuracy of it.
Students will work on a second example with their groups. Students are seated in heterogeneous groups of 4. Since there is a high level math student at each group, I will instruct students that they may help each other, but explain what that means. Students shouldn't be giving each other answers, but rather explaining how they arrived at their answer.
Task: Tameka has two pieces of cloth. One piece is 60 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?
After about 5 - 10 minutes, we will discuss the KWL chart and answer as a class.
I will hand out index cards to students. Students will be instructed to make up their own GCF or LCM word problem using a key words or idea from our discussion.
They are allowed to model their word problems after the examples, but they can't copy the problem.
I will have students exchange index cards with someone in their group. For homework they are to solve the word problem. I will explain that if students are unable to solve the word problem they need to explain why. For example, "I was unable to solve this problem because I didn't have enough information to figure out how many pieces of candy each student would receive."