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### Lesson plan

# Factors Over the Rainbow

#### Learning Objectives

Students will be able to find all factor pairs for a given number.

#### Introduction

*(5 minutes)*

- Write the number 12 on the board.
- Ask students to shout out factors (i.e., "What numbers go into 12?").
- Write the factors around the number and prompt students as needed to get all factors (1, 2, 3, 4, 6, 12).
- Explain, "These are all factors of 12.
**Factors**are numbers we can multiply together to get another number. For example,**3 x 4**is 12, so 3 and 4 are both factors of 12." - Write the definition of "factor" on the board (a whole number that divides exactly into another number).

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Tell students, "You helped me find the factors of 12. But when we list factors, we have to be sure we don't forget any. It can be easy to miss a factor if we just list them from memory."
- Explain, "One way to ensure that we have listed all the factors of a number is by finding
**factor pairs**: a set of two numbers that, when multiplied together, result in a given product." - Tell students that we can use
**factor rainbows**as a way to list factor pairs and find all the factors of a number, in order from least to greatest. - Make a rainbow with the factors of 12 (see related media for examples).
- Write another number, like 15, on the board.
- Remind students that 1 and the number itself are always factors of every number.
- Draw a factor rainbow for 15 starting with 1. Draw a big arch from 1 to 15, leaving room for other factors inside the first arch.
- Ask students, "Is 2 a factor? Is 3 a factor? What times 3 is 15?" Draw an arch from 3 to 5 to continue the rainbow.
- Tell students that when making a factor rainbow, they should keep counting up from 1 and adding factors until reaching a factor that is already listed (5 in this case). When they reach a factor that is already listed, the factor rainbow is complete.
- Guide students through an example of a square number, like 16, and demonstrate how to make a rainbow when a factor is used twice (i.e., write the factor once as the center number in the rainbow without an arch drawn above it).
- Optional extension: display factor rainbows for 12 and 16 side by side. Circle the common factors (1, 2, and 4) and explain, "When two numbers have factors in common, we call these
*common factors*. The term*greatest common factor*refers to the largest, or greatest, common factor between two or more numbers. In this case, 4 is the the greatest common factor."

#### Guided Practice

*(15 minutes)*

- Hand out the Factor Rainbows worksheet.
- Review the example problem, and complete the "try it" problem as a class.
- Have students complete the worksheet with their partner.
- Go over the worksheet with the class.

#### Independent working time

*(15 minutes)*

- Have students count off one through four and assign each number a different problem (i.e., if you are a number one, make a factor rainbow for 48; other numbers could be 56, 60, or 72).
- Hand out a sheet of paper to each student.
- Instruct students to use markers to make a factor rainbow for their assigned number.
- When students are finished, invite a few students up to share so that each of the four assigned numbers is represented.
- Optional extension: have students pair up with a partner whose assigned number was different than their own. Instruct partners to find the greatest common factor for their two numbers.

#### Differentiation

**Support:**

- Provide a multiplication table for students to refer to as needed.
- Provide partially completed factor rainbows for students to finish.
- Allow students to use a calculator to find factors during independent practice.

**Enrichment:**

- Have students make factor rainbows for larger numbers.
- Have students find the greatest common factor of two numbers (see optional resources).

#### Assessment

*(5 minutes)*

- In small groups, give students a number and ask them to tell you the factors. Create a factor rainbow as a small group.
- As an alternative assessment, hand out index cards to each student. Write a number, like 54, on the board and have students make a factor rainbow. Collect the cards and check for understanding.

#### Review and closing

*(5 minutes)*

- Ask and discuss, "Why are factors important? How can we use what we've learned about factors to help us in math?"