Lesson plan

In this lesson, we’ll introduce `\text{GCF}` and `\text{LCM}` word problems for `6`th graders by reviewing how to find the `\text{GCF}` and `\text{LCM}` of two numbers. Then we’ll sort some keywords that could help us before trying some word problems as a class.

Grade 6

Number System

6.NS.B.4

Step-by-step help

ByteLearn gives students targeted feedback and hints based on their specific mistakes

Preview step-by-step-help

Students will be able to find the greatest common factor or least common multiple from a pair of whole numbers in a word problem.

- Teacher Slideshow
- Online Practice

Helping students turn a problem about `\text{GCF}` or `\text{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. A visual model helps them make sense of the situation so that they are not just relying on memorized steps or guessing whether it is a `\text{GCF}` or an `\text{LCM}` problem.

You will start the class without telling them that they are going to use `\text{GCF}` or `\text{LCM}` Give them a problem and ask them work in pairs to solve the problem.

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You will notice that we do not say whether this is a `\text{GCF}` or an `\text{LCM}` problem. In fact, we don’t even say that Mr. Gomez needs the greatest number of packs possible.

Give students manipulatives like tiles and counters. You can even give them stickers and pens if you have any. Student work in pairs to figure out what are the different number of packs Mr. Gomez can make. Some students might want to make drawings.

After giving them some time, ask students to come to the board and draw the packs they were able to make. Ask them to talk through the packs that they tried but could not make. Here are some possible drawings.

You can make `2` or `3` packs:

If you make `4` packs, there are some pens left over:

Unlike, any one would try `5` packs. You can make `6` packs:

If nobody talks about it, ask them if they can make `1` packs. Have a conversation about why you were able to make `1, 2, 3` and `6` packs but not `4` packs. Students will begin to see that you can make packs when they are factors of the total number.

You can ask them what is the greatest number of packs you can make - but that is completely optional. Ask them how many stickers and pens are in each pack. These questions are helpful for students to understand the entire context.

The two common types of `\text{GCF}`-related problems are:

- Find the greatest number of groups when each group is similar. This is the Mr.Gomez problem that we just saw.
- Mr. Gomez has `12` stickers and `18` gel pens. He wants to make packs with an equal number of stickers and an equal number of gel pens in each pack. How many packs can he make if he does not want any stickers or pens left over?

- Find the greatest number of groups when each group has the same kind of object.
- There are `24` rose bushes and `18` geraniums. Each row should have only rose or only geranium. Each row has the same number of plants. How many rows can you make without any leftovers?

Introduce a problem where student will eventually find the `\text{LCM}`. Start with small manageable numbers under `10`.

As students work in pairs, they will figure out ways to organize their work. They might make lists, tables, number lines.

Studnents might start listing the days on which Rachel will do personal training and separately the days she does spinning class and see when both happen on the same day.

__Personal Training__:

Day: `4, 8, 12, 16, 20, 24, 28…`

__Spinning class__:

Day: `5, 10, 15, 20, 25, 30…`

or they might do two number lines. You could have close number lines ready for those who need them but don’t offer them at the beginning - if they begin to use number lines, you can offer these.

Make sure to ask students to write an answer sentence (It will be `20` days before both classes happen again on the same day). This will help you give you inputs how much students have conceptually understood what they were just did.

Some students might say that these are multiples and that the answer is the `\text{LCM}`.

I would not do any more practice problems as a class. Give them a few more problems to work through in pairs. Do not mention whether these are `\text{GCF}`-related or `\text{LCM}`-related problems.

After students have completed their lesson, it’s time for some independent practice! ByteLearn gives you access to tons of `\text{GCF}` and `\text{LCM}` word problems. The help that they get mimics the work they would have in the classroom. Check out their online practice and assign them to your students for classwork and/or homework!

`\text{GCF}` and `\text{LCM}` Word Problem Practice

Problem 1 of 4

<p>At Southeast High School, the Key Club is making food baskets to take to senior citizens during the holiday season. Students brought in `70` cans of food and `42` bottles of juice. They want all the baskets to be identical with no food left over.</p><ul><li>What is the greatest number of identical baskets the Key Club can make? </li><li>How many cans of food will be in each basket? </li><li>How many juice bottles are in each basket?</li></ul>

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