# Lesson 11

Multiplication Expressions

## Warm-up: Choral Count: Twos and Fives (10 minutes)

### Narrative

The purpose of this Choral Count is for students to practice counting by 5 and 2 and notice patterns in the count. These understandings help students begin to develop fluency and will be helpful later in this lesson when students write multiplication expressions.

When students notice patterns in the count, such as in the count by 5 that the ones place alternates between 0 and 5, they look for and express regularity in repeated reasoning (MP8).

### Launch

• “Count by 5, starting at 0.”
• Record as students count. See Student Responses for recording structure.
• Stop counting and recording at 50.

### Activity

• “What patterns do you see?”
• 1-2 minutes: quiet think time
• Record responses.
• Repeat activity. Count by 2, start at 0 and stop at 20.

### Activity Synthesis

• “How could some of the patterns help you with counting by these numbers?” (I know that the next count by 5 should end in 5. I know that the next count by 2 should have a 2 in the ones place.)
• “Who can restate the pattern in different words?”
• “Does anyone want to add an observation on why that pattern is happening here?”
• “Do you agree or disagree? Why?”

## Activity 1: Multiplication Expression Match (10 minutes)

### Narrative

The purpose of this activity is for students to match drawings, tape diagrams, and situations to multiplication expressions (MP2). Students build on their understanding of how the structure of drawings, tape diagrams, and multiplication situations show equal groups and connect this to the structure of a multiplication expression (MP7). This will be helpful later in the lesson when students create drawings or diagrams to match expressions and write expressions that represent drawings, diagrams, and situations.

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 1 card from the card sort in the previous lesson.
• Post these expressions around the room:
• $$3\times5$$
• $$4\times3$$
• $$3\times2$$
• $$2\times10$$
• $$3\times10$$

### Launch

• Groups of 2
• Give each group of 2 students 1 card from the blackline master.

### Activity

• “Work with your partner to find the expression that matches your card. Then discuss how you know the expression matches your card.”
• 2 minutes: partner work time

### Student Facing

Your teacher will give you a card showing a drawing, a diagram, or a situation.

Match it to one of the expressions posted around the room. Be prepared to explain your reasoning.

### Activity Synthesis

• Have students standing near each expression share how they know their card matches the expression.
• “Where do you see each number in the expression on your card?”

## Activity 2: Expressions to Drawings and Diagrams (15 minutes)

### Narrative

The purpose of this activity is for students to demonstrate a conceptual understanding of multiplication expressions by creating drawings of equal groups or tape diagrams that match expressions. Drawings of equal groups and tape diagrams are familiar representations to students from previous lessons and support students as they make sense of multiplication expressions.

Three expressions are given, but the focus of the synthesis is the second expression, $$3\times4$$. This provides an opportunity to support students on the first problem as you monitor and then let them try the second and third expressions on their own. To keep things simple and allow ideas about commutativity to develop over time, in this activity we suggest you display student responses that follow the convention of groups as the first factor and the size of the groups as the second factor.

If there is time, and you want to include more movement, this activity could be done as a gallery walk.

MLR2 Collect and Display. Collect the language students use to describe the diagrams for each of the expressions. Display words and phrases such as: “5 groups of 2”, “there are 5 groups, and 2 in each group”, and “there are 5 equal groups”. During the synthesis, invite students to suggest ways to update the display and to borrow language from the display as needed.
Action and Expression: Develop Expression and Communication. Provide access to a variety of tools: mini-whiteboards and counters.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

### Launch

• Groups of 2
• Review key understandings of multiplication:
• “Multiplication is how we express equal groups.”
• “We use the multiplication symbol to create an expression like $$5\times10$$ which represents the total number of objects in ‘5 groups of 10’ or ‘5 tens.’”
• Display expressions.
• “Think about the drawings or diagrams you could make for these expressions.”
• 30 seconds: quiet think time

### Activity

• “Work with your partner to create a drawing or diagram for each expression. Then, write your own expression and matching diagram. Explain your reasoning.”
• 5–7 minutes: partner work time
• Monitor for student-created drawings and tape diagrams to share during synthesis.

### Student Facing

1. Create a drawing or diagram for each expression. Explain your reasoning.

1. $$5\times2$$
2. $$3\times4$$
3. $$3\times10$$

### Activity Synthesis

• For the expression $$3\times4$$, display 2 different representations side by side (one drawing of equal groups and one tape diagram).
• “How are they the same? How are they different?”
• “How would the diagram change if the expression was $$5\times4$$?” (There would be 5 sections instead of 3.)
• “How would the diagram change if the expression was $$3\times5$$?” (Each section would be 5 instead of 4.)

## Activity 3: Write Multiplication Expressions (10 minutes)

### Narrative

The purpose of this activity is for students to write expressions to represent drawings of equal groups, tape diagrams, and multiplication situations. As students work, continually ask where each number in the expression is in the drawing, diagram, or situation.

If students finish early, ask them to find something in the room they can represent with a multiplication expression. Have them record what they represented and their expression.

### Launch

• Groups of 2
• “Now you are going to write multiplication expressions to represent a drawing, a diagram, and a situation. Take a minute to look them over before you begin working.”
• 1 minute: quiet think time

### Activity

• “Work with your partner to write a multiplication expression to match each representation. Explain your reasoning.”
• 3–5 minutes: partner work

### Student Facing

Write a multiplication expression to match each representation. Explain your reasoning.

3. There were 2 packs of water. Each pack had 6 bottles of water.

### Student Response

If a student writes a multiplication expression that doesn’t match the given representation, consider asking:

• “How could you describe the equal groups in this drawing/diagram/situation?”
• “How could you turn your statement into a multiplication expression?”

### Activity Synthesis

• Share responses.
• “Why does each of the representations show multiplication?” (They all show groups where there is the same number of things in each group.)

## Lesson Synthesis

### Lesson Synthesis

Display the drawing of equal groups, tape diagram, situation, and expression from Activity 2.

“We’ve learned about different ways to represent multiplication. Share something that you learned today about multiplication with your partner.” (Multiplication can be shown with drawings of equal groups or with diagrams. Multiplication can be real-world situations that involve equal groups. Multiplication can be expressed using the multiplication symbol ($$\times$$). An expression like $$4\times5$$ means the total number of objects in 4 groups of 5.)