Lesson plan

In this lesson, we’ll introduce the concept of finding the greatest common factor for `6`th graders by listing all of the factors of the number and using a ladder diagram. Mastering how to find the `\text{GCF}` of two numbers is essential for students to efficiently simplify fractions. Listing factors from least to greatest helps students to organize their thinking. Using the ladder method allows students who do not have strong fluency to master this essential skill. It also helps when students are working with larger numbers - though this is not a requirement in `6`th grade.

Grade 6

Number System

6.NS.B.4

Step-by-step help

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Students will be able to find the greatest common factor of two whole numbers.

- Teacher Slideshow
- Partner Activity
- Online Practice

Start the lesson with a warm-up activity where students practice listing all the factors of different numbers. Remind students that factors are numbers that can be divided into the number, without leaving a remainder. Display slide `1` for students.

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Give students about `5` minutes to list off all of the factors of the following numbers. Once students are done, invite students to share the factors for each number. Then display slide `2` for students to see all of the factors. Student might share some ways in which they made sure that they captured all the factors - typically students will use a factor rainbow to find the factors.

or they might write the factor pairs separately: `1\times 24`, `2\times 12`, `3\times 8`, `6\times 4`

This will lead to the next activity of a notice and wonder on slide `2`.

Give students a few more minutes to jot down a few notices and a few wonders. Have them share with their tablemates or a partner. Some things students may notice:

- They all have a `1` in common and a `3` in common
- `15` has the smallest amount of factors
- `18` and `24` both have `1`, `2`, and `6` in common
- `24` has the most factors

Some things students may wonder:

- Why do they have numbers in common?
- Why does `15` have the smallest amount of factors/`24` the largest?

Transition into a class discussion about how they all have `1` and `3` in common. Explain to students that they will find the greatest common factor today using two different methods. The two methods are listing factors and the ladder method.

Use the list they have already generated to find all the common factors of `18` and `24` and then identify the greatest of these factors.

Share the process with students for their reference. Work together to find the `\text{GCF}` of `40` and `24`. Explain to them that often mathematicians use `\text{GCF}``(40, 24)` as a way to denote `\text{GCF}`.

Tell students that a fun way to find the greatest common factor is by using the ladder method. Walk through the next example with students to find the `\text{GCF}` of `40` and `24` again, using the ladder method.

Start by having students put the two numbers inside the ladder. Next, we need to identify any common factor between the two numbers. You can remind students of the divisibility rules, such as any even number is divisible by `2`. You’ll write the common factor outside the ladder, then divide `40` and `24` by that common factor, `2`.

You’ll continuously repeat to process and finding and dividing by a common factor until the last ring of the ladder contains two numbers that have `1` as a common factor.

Ask students how would you use the common factors outside to find the `\text{GCF}`. Since they already know that the `\text{GCF}` is `8`, they are likely to say that we need to multiply all the common factors. When they work on finding the `\text{GCF}` using the ladder method, you need to watch out for them by adding the factors instead of multiplying them.

Ask students if it would make a difference if they had started with a `4` instead of `2`. Try it out with students. They will love it that the answer stays the same.

There is one more example that you can work through as a class. Since the ladder method is likely more new and unfamiliar for students, you should use that method to find the `\text{GCF}`.

When you give larger numbers, students will see the usefulness of using the ladder method. It also allows them to move as fast or as slowly as they are comfortable with. For example, to find the `\text{GCF}` of `54` and `90`, they could factor out `2, 3, 3` or `9, 2` or `6, 3`.

For some additional practice, allow students to work in partners on the __Finding GCF activity__. Students are given `10` problems across three difficulty level and asked to work on any `5` problems.

It is good practice for students to see as they’re working with a partner that they might choose different common factors for their ladder, or they might choose the same factors, but in a different order. Students need to see that they will still get the same answer!

After students have completed their lesson, it’s time for some independent practice! ByteLearn gives you access to tons of greatest common factor problem activities. Check out the online practice and assign them to your students for classwork and/or homework!

Finding `\text{GCF}` Practice