standard_description: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
problem_activity: Narrative
The purpose of this activity is for students to find the value of quotients where the divisor is less than 1 and where the dividend is large enough that drawing a complete diagram is cumbersome. Instead, students are encouraged to use a diagram to find
how many divisor sized groups are in 1 whole and then multiply the dividend by that number to find the value of the quotient. When students use the value of
\(1 \div 0.2\)
and multiplication to find the value of
\(12 \div 0.2\)
they are using regularity in reasoning (MP8).
This activity uses
MLR1 Stronger and Clearer Each Time.
Advances: Conversing.
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, for finding the value of the expression. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Copy
Small Grids
Launch
Groups of 2
Give students access to blackline masters with hundredths grids.
Activity
3–5 minutes: independent work time
Monitor for students who use the following strategies for problem 1:
reason about how many divisor-sized groups are in 1 whole, possibly with a diagram, and then multiply by the dividend
use multiplication equations to find the value of the division expressions
Student Facing
Find the value of the expression. Use a diagram if it is helpful.
\(12 \div 0.2\)
[IMG]
This is the diagram and explanation Tyler used to justify why
\(12 \div 0.2 = 60\)
.
[IMG]
[IMG]
Explain how the expression
\(12 \times (1 \div 0.2)\)
relates to Tyler's reasoning.
Find the value of each expression.
\(14 \div 0.5\)
\(5 \div 0.25\)
Student Response
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Advancing Student Thinking
If a student is not sure how to explain Tyler’s reasoning in problem 2, ask them to read the expression to you and record the words they use. Then ask them how those words relate to the words Tyler used.
Activity Synthesis
Ask previously identified students to share their solutions and strategies for evaluating the expression in the first problem.
“How was multiplication useful to find the value of the expression in the first problem?” (I didn't have to draw 12 wholes because I knew there were five 0.2s in each one so that would be
\(12 \times 5\)
total.)
MLR1 Stronger and Clearer Each Time
“Share your response to problem 2 with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3-5 minutes: structured partner discussion
Repeat with 2 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2-3 minutes: independent work time


aligns: no