Lesson 18

The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. When students use the structure of the array to figure out how many objects are shown, they look for and make use of structure (MP7).

• Groups of 2
• “How many do you see? How do you see them?”  
• Flash the image.
• 30 seconds: quiet think time

• Display the image.
• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “How did seeing equal groups help you know how many triangles there were in the array?”
• Consider asking:
  • “Who can restate the way _____ saw the triangles in different words?”
  • “Did anyone see the triangles the same way but would explain it differently?”

The purpose of this activity is for students to represent multiplication situations with arrays and multiplication expressions. Students should have the option to use math tools, such as counters or connecting cubes, to create the arrays before they draw them. Connecting situations, arrays, and expressions reinforces the idea that multiplication can be used to express the total number of objects in equal groups (MP2).

• Each group of 2 will need 20 connecting cubes or counters.

• Groups of 2
• Give students access to connecting cubes or counters.
• Display the first situation.
• “Take a minute to represent this situation with an array. You can use drawings or objects.”
• 2 minutes: independent work time
• “Discuss your ideas with your partner.”
• 2 minutes: partner discussion
• Share responses. Emphasize ways students used equal groups to create their arrays.

• “Work with your partner to represent the next three situations with an array. Be prepared to share how you see equal groups in your array.”
• 5 minutes: partner work time
• Have students share an array for problems 2–4. Try to show both drawings and arrays made of objects.
• “How do you see equal groups in your arrays?” (The rows can show the number of groups, and then you put however many are in each group across the row.)
• Display the first situation again.
• “Let’s revisit the first situation. What multiplication expression would represent this situation?”
• 30 seconds: quiet think time
• Share responses. Emphasize how students use equal groups to write the expression.
• “Work with your partner to write multiplication expressions for the other three situations.”
• 2 minutes: partner work time

• “How did you use equal groups to write your multiplication expression?” (I thought about how many groups were in the situation and then how many things were in each group. For example, I know that 2 teams of 10 students is 2 groups of 10, so I can write \(2\times10\).)

The purpose of this activity is for students to apply their knowledge from previous activities to draw arrays to match multiplication expressions. Have connecting cubes or counters available for students who need them. In the launch, students use their bodies to make an array for the expression \(4\times6\). Feel free to adjust this expression to better fit the number of students in your class.

• Groups of 2
• Display \(4\times6\)
• “Work together as a class to use your bodies to create an array for this multiplication expression.”
• If the number of students does not exactly match the product, ask extra students to monitor the array and be prepared to explain where they see parts of the expression in the array.
• 3–5 minutes: whole-class work time

• “Work with your partner to draw an array for each multiplication expression. Be ready to share connections you notice between the multiplication expressions and arrays.”
• 2–3 minutes: partner work time

If students draw equal groups that are not arrays, consider asking:

• “How did you use the expression to create your drawing?”
• “How could we rearrange your drawing into an array?”

• Share an array or two for each expression.
• “What connections did you and your partner see between the multiplication expressions and arrays?” (The factors tell us how many things are in each row and column. For \(2\times3\), we drew an array with 2 columns that have 3 things in each column. For \(2\times3\), we drew an array with 2 rows that have 3 things in each row.)