The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.
Launch
Groups of 2
Display the image.
“What is an estimate that’s too high? Too low? About right?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Record responses.
Student Task Statement
Each regular pumpkin in this field weighs between 4 and 10 kilograms.
How many kilograms do you think the giant pumpkin weighs?
Record an estimate that is:
too low
about right
too high
Student Response
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Advancing Student Thinking
Activity Synthesis
“How did you use the image or what you know about pumpkins or other melons to help you make estimates?”
Consider asking:
“Is anyone’s estimate less than 100 kilograms? Is anyone’s estimate greater than 500 kilograms?”
“Based on this discussion, does anyone want to revise their estimate?”
Activity 1
20 mins
Info Gap: Pumpkin Weigh-Off
Standards Alignment
Building On
Addressing
3.MD.2
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
The Information Gap structure requires students to make sense of a problem by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). This process also allows students to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6). This Information Gap provides students an opportunity to solve multiplication and division problems involving weight.
Representation: Access for Perception. Begin by demonstrating one round of the Information Gap routine to support understanding of the context. Supports accessibility for: Conceptual Processing
Launch
Groups of 2
MLR4 Information Gap
Display the Task Statement, which shows a diagram of the Information Gap structure.
1–2 minutes: quiet think time
Read the steps of the routine aloud.
“I will give you either a Problem Card or a Data Card. Silently read your card. Do not read or show your card to your partner.”
Distribute cards.
1–2 minutes: quiet think time
Remind students that after the person with the Problem Card asks for a piece of information, the person with the Data Card should respond with “Why do you need to know _____ [that piece of information]?”
Activity
3–5 minutes: partner work time
After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.
Student Task Statement
Your teacher will give you either a Problem Card or a Data Card. Do not show or read your card to your partner.
Information Gap routine. Step 1, both students read the problem card. Cycle. Problem card student says, can you tell me, fill in the blank? Data card student says, why do you need to know, fill in the blank? Problem card student says, I need to know, fill in the blank, because dot, dot, dot. Data card student listens to partner's reason and answers with information from the data cards. Repeat cycle until the problem card student can state, I have enough information to solve this problem. Both solve the problem independently and continue to ask questions if more information is needed. Finally, share data card, then compare strategies and solutions.
Pause here so your teacher can review your work.
Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Activity Synthesis
“What parts of the problem helped you make sense of the situation?”
“Which quantities were important?”
“Did anyone solve the problem in a different way than their partner?”
Activity 2
20 mins
Info Gap: Pig Weigh-Off
Standards Alignment
Building On
Addressing
3.MD.2
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
In this activity, students solve addition and subtraction problems involving weight.
Launch
Groups of 2
MLR4 Information Gap
“Let’s use the same Information Gap routine to solve new problems about another weigh-off.”
“I will give you either a Problem Card or a Data Card. Silently read your card. Do not read or show your card to your partner.”
Distribute cards.
1–2 minutes: quiet think time
Remind students that after the person with the Problem Card asks for a piece of information, the person with the Data Card should respond with “Why do you need to know _____ [that piece of information]?”
Activity
3–5 minutes: partner work time
After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.
Student Task Statement
Your teacher will give you a new Problem Card or Data Card. Do not show or read your card to your partner.
Use the same Information Gap routine to solve the problem. Then pause so your teacher can review your work.
Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Student Response
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Advancing Student Thinking
Activity Synthesis
“What kinds of questions were the most useful to ask?”
“Were there any questions you weren't sure how to answer?”
“How did you represent your reasoning once you realized you needed to add (or subtract)?”
Lesson Synthesis
“We’ve been focusing on problem solving for the last two lessons. How would you describe your general approach to solving math problems to a friend? What are some important ideas you’d want to make sure to share with them?” (I start by thinking about the situation to see if I can imagine it to understand what is happening. I like to try to draw a representation like a number line or a diagram to make sense of the problem. I think about what the numbers mean and how they are related. I think about what information is given and what I want to know. I think about an equation I could write for the situation. I think about strategies I have for adding, subtracting, multiplying, or dividing depending on what is happening in the problem.)
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Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.