Helping students turn a problem about GCF or LCM into a concrete model will help them understand what they are looking for and what steps they need to take to find the solution. The visual model helps them make sense of the situation so that they are not just relying on memorized steps.
A classic GCF problem has two quantities that need to be divided evenly into the greatest number of groups.
Example:
Mr. Gomez has 12 stickers and 18 gel pens. He wants to make the greatest number of packs possible with an equal number of stickers and an equal number of gel pens in each pack. How many packs can he make?
At this point, many students might confuse this with a LCM problem and say the answer is 36. Others will use a common factor such as 2 or 3 for their answer.
How can students use a model to solve GCF word problems?
GCF problems are all about equal groups. In order for a number to be a solution, we must be able to divide both numbers evenly into that number of groups.
It is good for students to act this out or draw this. Here we show you how students can make a drawing to model this situation. Notice the use of color in this model to represent stickers and pens.
Students can put all the stickers and pens into one bag but of course we can try making a few more bags – more fair to have more students getting fewer items than all goodies going to one student!!
First attempt
The model shows that we could have 2 bags or 3 bags, because 12 stickers and 18 gel pens can be divided so that there would be the same number in each bag.
But is this the greatest number of bags? Four bags will not work because 18 cannot be divided into 4 equal groups.
Second attempt
The strategy can continue until all possible groups have been tested. The solution is the greatest number of groups that work for both numbers. The model also provides an opportunity to describe the answer. There will be 6 bags. Each bag will have 2 stickers and 3 gel pens.
Third attempt
Drawing the groups can be time-consuming for larger numbers, but using counters works well too. Creating the arrays helps deepen the connection between factors, using arrays for multiplication, and area models.
Why should students use a model to solve GCF word problems?
By using a model, students have moved away from blindly applying GCF or LCM. They make sense of the situation. They try out different options. They don’t have to remember or guess what the concept is supposed to be.
We could give different pairs of students different situations, ask them to do a poster and then conduct a gallery walk. Students will notice that all factors work and that the greatest common factor is what ends up solving the problem. It also helps them to see what actually is happening inside of the groups – how many stickers and pens are in each group.
Also read: How To Solve LCM Problems
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Frequently Asked Questions on Solving GCF Word Problems
1. What is GCF?
It is the largest of all the factors that are common to two or more numbers.
Example: GCF of 12 and 18.
You can list all the factors of 12 and 18. Then find the greatest common factor.
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
GCF(12, 18) = 6
When using the model to solve GCF word problems, all the common factors like 1, 2, 3, 6 represent the number of groups that can be formed. 6 represents the largest number of groups that can be formed.
2. How can students use a model to solve GCF word problems?
Students should create a chart with two columns and multiple rows. The two columns stand for the items being split up. Each row represents the number of groups the item is split into. Students keep trying more and more groups till they have exhausted all options.
Students can work in pairs in different scenarios. Conduct a gallery walk with student work. Students will soon come to the conclusion that only common factors work for a number of groups and that the GCF is the largest number of groups you can make.
3. Why should students use a model to solve GCF word problems?
Solving GCF and LCM word problems is confusing. By using a model, students make sense of the situation. They do not need to memorize the steps.
4. Where can I find more worksheets on solving GCF word problems?
You can find math worksheets on GCF problems and other exclusive math resources, here.
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