Lesson 13

Problems with Missing Information

Warm-up: Estimation Exploration: Giant Cantaloupe (10 minutes)

Narrative

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 Facing

A regular cantaloupe weighs between 1 and 5 kilograms.


This cantaloupe melon was a winner at the 2010 Alaska State Fair. How many kilograms do you think it weighs?

giant canteloupe

Record an estimate that is:

too low about right too high
\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

  • “How did you use the image or what you know about cantaloupe 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?”
  • Consider revealing that the actual weight of the giant cantaloupe is 344 kilograms.

Activity 1: Info Gap: Pumpkin Weigh-Off (20 minutes)

Narrative

This activity uses MLR4 Information Gap.

The Info Gap structure requires students to make sense of problems 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). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6). This Info Gap activity provides students an opportunity to solve multiplication and division problems involving weight.

Here is an image of the cards for reference:

Gap activity. Problem and data cards
Representation: Access for Perception. Begin by demonstrating one round of the info gap routine, to support understanding of the context.
Supports accessibility for: Conceptual Processing

Required Materials

Materials to Copy

  • Info Gap: Pumpkin Weigh-Off

Required Preparation

  • Create a set of cards from the blackline master for each group of 2. 
  • Keep set 1 separate from set 2.

Launch

  • Groups of 2
MLR4 Information Gap
  • Display the task statement, which shows a diagram of the info 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 (restate the information requested)?”

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 Facing

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 directions for problem card student and data card student.

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.

Student Response

For access, consult one of our IM Certified Partners.

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: Info Gap: Pig Weigh-Off (20 minutes)

Narrative

This activity uses MLR4 Information Gap.

In this activity, students solve addition and subtraction problems involving weight. Here is an image of the cards for reference:

Info gap problem cards.

Required Materials

Materials to Copy

  • Info Gap: Pig Weigh-Off

Required Preparation

  • Create a set of cards from the blackline master for each group of 2. 
  • Keep set 1 separate from set 2.

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 (restate the information requested)?”

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 Facing

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

For access, consult one of our IM Certified Partners.

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

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 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.)

Cool-down: Winner, Winner (5 minutes)

Cool-Down

For access, consult one of our IM Certified Partners.