### EL Support Lesson

# Conversations About Prime and Composite Numbers

#### Objectives

##### Academic

Students will be able to find factor pairs for whole numbers and determine if they're prime or composite numbers.

##### Language

Students will be able to discuss prime and composite numbers using sentence starters and peer interaction.

#### Introduction

*(3 minutes)*

- Ask students the following question and have them discuss with a partner: How can we find the factors of a whole number?
- Define
**factors**as numbers that are multiplied together to get another number or a product. - Ask students to share key points from their discussion and record their responses on a piece of chart paper. Acknowledge their background knowledge and add on, using correct math terminology, if applicable.

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Introduce each vocabulary word to students by displaying the vocabulary card and reading the definition aloud.
- Have students turn to their partner and describe the image associated with the vocabulary word and discuss how it connects with the meaning of the word (e.g., "In the image for 'factor,' there is a number sentence
**2 x 3 = 6**with two arrows pointing to 2 and 3. This means that the numbers 2 and 3 are factors of 6 in this example."). - Have a few students share out their explanation of the image or example. Invite students to add on to the definition or provide a different example than the one given.
- Distribute a Glossary worksheet to each student. Have them write "More Information" in the title for the last column on the right. Give students time to write a synonym to the term in their home language (L1), or another example in this column, as they discussed with their partner. Then, ask students to paste the Glossary in their math journal for future reference.
- Explain to students that the number 0 and 1 are considered neither prime nor composite numbers. They are special and unique numbers that do not fit in either category.
- Remind students that there are some rules and patterns that will help them determine if some numbers are prime and composite. For example, all even numbers, except 2, are composite numbers because they are divisible by 2. All numbers that end in a 5 digit, except for 5, are also composite because they are divisible by 5. Tell students that they may discover more rules or patterns as they work on today's lesson.
- Place students into pairs and make sure they have their math journals with them. Ask students to consider the numbers 0–10 and work with a partner to determine whether each number is prime or composite. Encourage students to draw pictures or models to help them see if they are divisible by another number other than 1 and itself.
- Have students write out all the numbers between 0–10 in their math journals or scratch paper. Tell students to show their work of how they found the factors for these numbers and be prepared to explain their thinking.
- Have a few students share their process of determining whether the number is prime or composite using the sentence starter, "The number
**____**is prime/composite because..."

#### Guided Practice

*(10 minutes)*

- Put students into groups of 4. Tell them that they will play a game using a deck of cards. Explain that the ace card counts as one, the jack card is 11, the queen is 12, and the king is 13. Note: write these on the board to help students remember their values.
- Call on a few students to come up and model the game with you. Distribute the cards evenly amongst the four players. Tell students to hold their pile of cards face down. The game involves going around in a circle, with each student placing one card face up in the center pile. When a prime number appears, students are to put their hand on the pile. The first student to do this gets to keep the pile of cards. The game is won by the person that has the most cards.
- Tell students to play two to three rounds of the game. Circulate to monitor and assist students. Encourage students to engage in conversation with each other if there is a disagreement about a number (e.g., "The number
**____**is not a prime number because..."). - Inform students that now they should be familiar with prime and composite numbers up to 13. The goal for fourth graders is to become familiar with prime and composite numbers up to 100. Now they will learn some strategies for determining factor pairs for larger numbers.

#### Group work time

*(10 minutes)*

- Inform students that it is helpful to use models or visuals to help determine if a number is prime or composite. If we can form equal groups of the items, we know that the number is composite. If we cannot make equal groups, then we know it is only divisible by 1 and itself.
- Hand out the Prime Numbers vs. Composite Numbers worksheet to students and display a teacher copy on the document camera.
- Read aloud the directions and explain the first example of the 6 strawberries and how you can form 2 groups of 3 or 3 groups of 2 to know that it is a composite number because it has more than 2 factors (1, 2, 3, 6).
- Let students work on the rest of the worksheet with a partner. Review answers as a class when complete. Have students share their reasoning behind each example and record their reasoning on the chart paper. Make sure to write the student's name next to their reasoning.
- Tell students that there are different strategies to determine the type of number it is. Some people use the rainbow factor strategy while others use the factor tree method. Sometimes the factors can be found using mental math. On the document camera or board, show an example of factorization with both the rainbow and tree strategies for the same number, 24.
- Have students do the same process with a partner in their math journal or on scratch paper for the number 28. Check students' answers and have them compare the two strategies.
- Tell students to find all the factors, using the strategy of their choice, for the number 23.
- Ask students the following questions after they find the factors for each number:
- What are the factors of
**____**(*product*)? ("The factors of**____**are...") - Which strategy did you use to find the factors and why? ("We chose the
**____**strategy because..") - Is this number prime or composite? ("This number is prime/composite because...")

- What are the factors of
- Jot down students' responses on a piece of chart paper, using correct terminology and highlighting important vocabulary or ideas.

#### Additional EL adaptations

**Beginning**

- Have students repeat the directions in their home language (L1) or in English (L2) before beginning the work.
- Give students access to bilingual glossaries and online dictionaries for them to look up unfamiliar words throughout the lesson.
- Place students with more advanced ELs for partner work.
- Pull aside a small group of students as they work in groups and guide them through the process.
- Allow students to work on the formative assessment with a helpful partner.

**Advanced**

- Encourage students to speak and write their answers without using the sentence frames/stems.
- Allow students to be the first to share their ideas or rephrase their classmates' contributions to class discussions.
- Have students create and display a word/phrase bank with helpful terms from the lesson for reference purposes, with images if applicable.

#### Assessment

*(4 minutes)*

- Distribute an index card to each student. Have them complete the following sentence stems on their index card:
- "Prime numbers are... A few examples of prime numbers are..."
- "Composite numbers are... A few examples of composite numbers are..."

#### Review and closing

*(3 minutes)*

- Have a few students share their complete sentences from the index card. Congratulate students on correct definitions and examples; correct any misconceptions as needed. Collect the index cards to use them as a formative assessment.
- Direct students' attention to the chart papers with their ideas and math thinking that you documented throughout the lesson. Ask students to look at them and think if they would like to change any words or sentences, or add on to a particular thought. Explain that it is important to constantly reflect on our own math thinking because reflecting helps us to think critically.
- Tell students that knowing how to determine if a number is prime or composite will help them when they start working on more difficult math concepts such as algebra.