standard_description: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
problem_activity: Narrative
The purpose of this activity is for students to subtract one-digit and two-digit numbers from a three-digit number using the methods that make sense to them. Each difference would require students to decompose a ten to subtract by place. They may count back or count on by place to find the difference. They may also use their understanding of place value and their experiences decomposing a ten when they subtracted within 100. In the synthesis, focus on connecting and comparing these different methods and making sense of representations that show decomposing a unit when subtracting by place.
When students use base-ten blocks, number lines, or equations to find the value of each difference they use appropriate tools strategically (MP5).
This activity uses
MLR7 Compare and Connect
. Advances: representing, conversing.
Engagement: Provide Access by Recruiting Interest.
Optimize meaning and value. Invite students to share ideas of items to sell (cupcakes, sports cards, video games, etc.) and use that as the context around the problems to solve. Discuss the action of selling to represent subtraction.
Supports accessibility for: Attention, Conceptual Processing
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.”
3–4 minutes: independent work time
3–4 minutes: partner discussion
Monitor for an expression that generates a variety of student methods or representations to share in the synthesis, such as:
using base-ten blocks
drawing a number line
writing their reasoning in words
writing equations
Student Facing
Find the value of each expression in any way that makes sense to you. Explain or show your reasoning.
\(354 - 7\)
\(354 - 36\)
\(354 - 48\)
Student Response
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Activity Synthesis
MLR7 Compare and Connect
Invite one previously identified student who used a method that did not explicitly show decomposing a ten to share.
Invite one previously identified student to show how they decomposed a ten to subtract with base-ten blocks or a base-ten diagram.
“What is the same and what is different about the ways _____ and _____ represented the problem?” (____ used base-ten blocks and showed decomposing a ten. _____ showed a number line and counting back 36. They used the same numbers. They found the same difference.)


aligns: no