Lesson 1
Find the Largest Product
Warmup: Notice and Wonder: Digits (10 minutes)
Narrative
The purpose of this warmup is for students to discuss the location of digits in the products, which will be useful when students try to find the greatest product in a later activity. While students may notice and wonder many things, the location of the digits 6, 4, 1, and 8 is the important discussion point.
Launch
 Groups of 2
 Display the image.
Activity
 “What do you notice? What do you wonder?”
 1 minute: quiet think time
 1 minute: partner discussion
 Share and record responses.
Student Facing
What do you notice? What do you wonder?
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 “Without finding the values, which product do you think will be greater? Explain your reasoning.” (I think \(841 \times 6\) will be greater because 841 is a lot more than 641. I think \(641 \times 8\) will be larger because there is 4,800 in each and the second product has more 41s.)
 “We are going to revisit these problems in the lesson synthesis.”
Activity 1: Talk About it (15 minutes)
Narrative
The purpose of this activity is for students to practice using the standard algorithm and explain how the placement of the digits in factors impacts the value of the product when multiplying a twodigit number by a onedigit number. Students multiply different factors which use the same 3 digits and determine which combination yields the greatest product. While the problems were intentionally structured to encourage students to use an efficient strategy, such as the algorithm, students should use whatever strategy makes sense to them when solving these problems.
Students critically analyze a claim about the largest product that can be made with 3 digits and discuss their reasoning with several partners (MP3).
Advances: Listening, Speaking
Supports accessibility for: Organization, Conceptual Processing, Language
Launch
 Groups of 2
 “You will discuss a talking point in 2 rounds. In the first round, read the statement and take turns explaining whether you agree, disagree, or are unsure. Then we will switch groups and complete Round 2.”
 Partner work time: 2–3 minutes
Activity
 After partner work time, rearrange students into groups of 4. New groups of 4 should be formed where partners are not in the same group.
 “Now, you will complete Round 2 in your new group. Each person in the group will be given time to restate their reasoning.”
 1–2 minutes: group discussion
 “Decide if you want to revise your thinking and be prepared to explain why you changed your thinking. Each person in the group will say whether or not they changed their answer and explain why or why not.”
 1–2 minutes: smallgroup discussion
 “Think about something new that you learned from your group or something that you are still wondering about.”
 1–2 minutes: independent work time
 12 minutes: partner discussion
 “Now, use what you learned to complete the second problem.”
 12 minutes: independent work time
Student Facing
 Consider the statement below. Decide whether you agree, disagree, or are unsure. Be prepared to explain your reasoning.
agree disagree unsure Given the digits 7, 5, and 2, the largest product you can make is \(75\times2\) because 75 is the largest number you can make. After round 1: Given the digits 7, 5, and 2, the largest product you can make is \(75\times2\) because 75 is the largest number you can make. Write about something new that you learned from your group or something you still wonder about:
 Use the digits 6, 3, and 1 to make the largest possible product. Be prepared to explain your reasoning.
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis

Display:
\(72\times 5 =(70\times 5)+(2\times5)\)
\(52\times 7 =(50\times 7)+(2\times 7)\)
 “Why is \(52\times 7\) greater than \(72\times5\)?” (The product of ones and tens is the same in these products but \(52 \times 7\) has a larger product of ones and ones.)
 “What did you learn about placement of digits when multiplying a twodigit number by a onedigit number?”
Activity 2: More Digits (20 minutes)
Narrative
Launch
 Groups of 2

Display:
7, 3, 2, 5
 “Using only these digits, what multiplication expressions could we write?” (\(723 \times 5\), \(32 \times 57\), \(7 \times 3 \times2 \times 5\), \(73 \times 5 \times 2\).)
 1 minute: quiet think time
 Record answers for all to see.
 “Which of these expressions do you think would make the greatest product? Be prepared to explain your reasoning.” (I think the threedigit by onedigit expression would make the greatest product because you can put the 7 in the hundreds place.)
 “Use the digits 7, 3, 2, and 5 to make the greatest product.”
Activity
 5–7 minutes: partner work time
Student Facing
 Use the digits 7, 3, 2, and 5 to make the greatest product.
 Explain or show how you know you have made the greatest product.
Student Response
For access, consult one of our IM Certified Partners.
Advancing Student Thinking
Activity Synthesis
 “Which multiplication expression will have the greatest product?”
 Poll the class.
 Record responses for all to see.
 Display or write these expressions for all to see:
 “Why does switching the placement of the 5 and the 7 increase the value of the product?” (Both products have 35 hundreds, but when 7 is the second factor, the product has 7 groups of 32 instead of 5 groups.)
 Display or write these expressions for all to see:
 “Why does switching the placement of the digits 2 and 3 increase the value of the product?” (Both products have partial products \(50 \times 70\) and \(2 \times 3\), but when we switch the digits 2 and 3, the partial products in \(72 \times 53\) are greater.)
Lesson Synthesis
Lesson Synthesis
Display or write these products for all to see.
“Here are the problems from the warmup. Does anyone want to revise their thinking about which one is the greater product?” (\(641 \times 8\) because both products will have 4,800, but there will be two more groups of 41 in \(641 \times 8\).)
“Today we explored ways to arrange digits to make the greatest product. We had to solve a lot of multiplication problems. What is something new that you learned about multiplication today?” (I never realized how many different problems you could create with the same digits. I was surprised by some of the largest products. I thought \(841 \times 6\) would be larger than \(641 \times 8\).)
Cooldown: Multiply 2 Digits by 2 Digits (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.