Lesson 4
Dive Back Into Division
Warmup: Notice and Wonder: Blank Spaces (10 minutes)
Narrative
The purpose of this warmup is to elicit the relationship between multiplication and division, which will be useful when students identify missing dividends and divisors in a later activity. While students may notice and wonder many things about this equation, possible numbers to fill in the blanks are the important discussion points.
Launch
 Groups of 2
 Display the equation.
 “What do you notice? What do you wonder?”
Activity
 1 minute: quiet think time
 1 minute: partner discussion
 Share and record responses.
Student Facing
What do you notice? What do you wonder?
\(\underline{\hspace{1 cm}} \div \underline{\hspace{1 cm}} = 136\)
Student Response
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Activity Synthesis
 “What numbers could go in the blanks? How do you know?” (I could put in 136 and 1 or 272 and 2. The first number has to be 136 times the second number.)
Activity 1: Reasonable Estimates (15 minutes)
Narrative
Launch
 Groups of 2
Activity
 5–10 minutes: independent work time
 5 minutes: partner discussion
Student Facing

Circle the most reasonable estimate. Show your reasoning.

\(364 \div 13\)
20
30
40

\(540 \div 12\)
40
50
60

\(1,\!008 \div 14\)
70
80
90


Find the value of each quotient.
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 “How did multiplication help you with your estimates?” (Multiplying by tens is easy to do in my head so I could find the product that was closest to the dividend.)
 “How did your estimates help you find the quotient?” (My estimates gave me a good idea what multiple of the divisor to subtract to begin my calculation. They helped me check that my answer was reasonable.)
Activity 2: Missing Dividends and Divisors (20 minutes)
Narrative
 multiply the quotient by friendly numbers such as 1, 2, or 5.
 multiply the quotient by powers of ten and use place value understanding.
 can explain the relationship between multiplication and division.
This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing
Supports accessibility for: Organization, Conceptual Processing, Language
Required Materials
Materials to Gather
Launch
 Groups of 2
Activity
 3–5 minutes: independent work time
 “Share your responses with your partner. If you have any equations that are the same, write a new equation that is different. Together, work to find 10 different equations.”
 3–5 minutes: partner discussion
 Give each group tools for creating a visual display.
MLR7 Compare and Connect
 “Work with your partner to create a visual display that shows your thinking about problems 1 and 2.”
 2–5 minutes: independent or group work
 3–5 minutes: gallery walk
Student Facing

Write different numbers in the blanks that make the equations true.
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 700\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 78\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 700\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 78\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 700\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 78\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 700\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 78\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 700\)
\(\underline{\hspace{1 cm}}\div\underline{\hspace{1 cm}}= 78\)
 What strategy did you use to choose numbers to write in the blanks?
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Display: \(\underline{\hspace{1cm}} \div \underline{\hspace{1cm}} = 700\)
 Invite students to share the numbers they used to make the equation true.
 “How did you find numbers that make the equation true?” (I multiplied 700 by different numbers. I chose simple quotients, like dividing by 1 or 2 or 10.)
 Display: \(\underline{\hspace{1cm}} \div \underline{\hspace{1cm}} = 78\)
 “Did the same strategies work to find numbers that make this equation true?” (Yes, but 78 is a more difficult number to multiply by in my head. So, 1 worked and 2 and 10, but it was harder to find a variety of numbers.)
Lesson Synthesis
Lesson Synthesis
Display or write for all to see.
\(\underline{\hspace{1cm}} \div \underline{\hspace{1cm}} = 25\)
“How can you use multiplication to find numbers that make the equation true?” (I know the number in the first blank has to be 25 times the number in the second blank.)
“What are some examples of numbers that make the equation true?” (25 and 1, 50 and 2, 100 and 4, 250 and 10)
“How did you choose the numbers?” (I looked for numbers that are easy to calculate in my head. I know lots of multiples of 25 that I can find in my head.)
Cooldown: Estimate and Evaluate (5 minutes)
CoolDown
For access, consult one of our IM Certified Partners.