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The purpose of this True or False? is to activate what students know about multiplying a fraction by a whole number (, in particular fractions with denominators 4, 8, and 12) and about fractions that are equivalent to whole numbers. The reasoning students do here will be helpful later when they solve problems involving fractional units of measurement in pounds, ounces, hours, and minutes.
The whole numbers and the denominators in the equations are multiples or factors of one another, so students have an opportunity to look for and make use of structure (MP7) to determine whether the equations are true.
Decide whether each statement is true or false. Be prepared to explain your reasoning.
The purpose of this activity is to introduce students to the structure of the MLR4 Information Gap routine. This routine facilitates meaningful interactions by positioning some students as holders of information that is needed by other students.
Tell students that first, a demonstration will be conducted, in which the whole class plays the role of the person with the problem card. Explain to students that it is the job of the person with the problem card (in this case, the whole class) to think about what information they need to answer the question.
For each question that is asked, students are expected to explain what they will do with the information, by responding to the question, “Why do you need to know _____ [that piece of information]?” If the problem card person asks for information that is not on the data card (including the answer), then the data card person must respond with, “I don’t have that information.”
Once students have enough information, they solve the problem independently.
The Info Gap routine requires students to make sense of problems by determining and then asking for the information needed to solve them. This may take several rounds of discussion if their first requests do not yield the information they need (MP1).
MLR4 Information Gap
Info Gap Noah's School Day Part 2 Cards
The Info Gap routine in this activity, prompts students to compare lengths of time given in different units. To make comparisons, students need to convert one unit into another or otherwise reason about equivalent amounts. They also need to relate quantities in multiplicative terms—to think of a quantity as a certain number of times as much as another quantity.
The Info Gap structure requires students to make sense of problems by determining, and then asking for, the information necessary to solve them. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows students to refine the language they use and to ask increasingly more precise questions until they get the information they need (MP6).
MLR4 Information Gap
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
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.
Optional
This optional activity invites students to apply their knowledge of pounds and ounces and multiplicative reasoning to solve a puzzle about the quantities of ingredients on a shopping list. To solve the puzzle, students need to express pounds as ounces and reason deductively.
As they work to eliminate possibilities, draw conclusions, and explain their thinking to others, students practice constructing logical arguments (MP3).
Here are 6 ingredients that a shopper bought and some clues about each quantity.
The items are listed in order of weight, from least to greatest.
| ingredient | pounds | ounces |
|---|---|---|
| rice noodles | ||
| shrimp | ||
| tapioca flour | ||
| tofu | ||
| carrots | ||
| brown rice |
Use the clues to find out the weight of each ingredient in both pounds and ounces.
“Today we solved measurement problems in which not all of the necessary information was provided.”
“How was that experience different from other problem-solving experiences you had so far?” (We had to think about what information was needed, and also about how to ask questions that would give what we needed.)
“What did you find interesting? What did you find challenging?” (We had to explain why we asked for certain pieces of information, which wasn’t always easy.)
We learned about various units for measuring length, distance, weight, capacity, and time. We saw how different units that measure the same property are related.
Here are the relationships we saw:
When given a measurement in one unit, we can find the value in another unit by reasoning and writing equations. For example, to express 5 kilograms in grams, we can write . To express 4 pounds in ounces, we can write .
Throughout the section, we used these relationships to convert measurements from one unit to another, to compare and order measurements, and to solve problems in different situations.