Unit 3, Lesson 6
Problems with Equal Groups of Fractions
Grade 4
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Learn how to use instructional routines to facilitate problem-based learning!
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The purpose of this True or False? is to elicit the strategies and understandings students have for finding products of a whole number and a fraction and for identifying equivalent expressions. This work helps students deepen their understanding of the properties of operations and will be helpful later when students solve problems with a whole number multiplied by a fraction.
In this activity, students have an opportunity to look for and make use of structure (MP7) as they consider how fractions are decomposed into various factors and multiplied in parts.
Decide whether each statement is true or false. Be prepared to explain your reasoning.
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Learn how to use instructional routines to facilitate problem-based learning!
None
The purpose of this activity is for students to use their understanding of multiplication of a unit fraction by a whole number to solve problems. Students use what they know to find the product when given the factors and to find the factors when given the product. This reinforces the idea that any fraction
Students may interpret quantities greater than 1 as a combination of whole numbers and fractions (for example,
A bakery makes banana bread. Here is the list of ingredients for 1 batch:
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Ingredients:
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The bakery makes 2 batches of banana bread on Monday. Complete the table to show how much of each ingredient is used.
Monday’s banana bread
| ingredient | expression | amount of ingredient |
|---|---|---|
| bananas | _______ | |
| butter | _______ cup(s) | |
| baking soda | _______ teaspoon(s) | |
| sugar | _______ cup(s) | |
| eggs | _______ | |
| flour | _______ cup(s) |
On Tuesday, the bakery needs
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Recipe:
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Based on the number of the batches made on Tuesday, complete the table for each ingredient.
Tuesday’s banana bread
| ingredient | expression | amount of ingredient |
|---|---|---|
| bananas | _______ | |
| butter |
|
|
| baking soda | _______ teaspoon(s) | |
| sugar | _______ cup(s) | |
| eggs | _______ | |
| flour | _______ cup(s) |
We learned to multiply a whole number and a fraction by thinking about equal-size groups, just as we did when multiplying two whole numbers.
We can think of
We also can think of
After looking at patterns closely, we noticed that when we multiply a whole number and a fraction, the whole number is multiplied only by the numerator of the fraction and the denominator stays the same.
Example:
We also learned that:
We can write different multiplication expressions for the same fraction. For example,
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The bakery that sells banana bread also sells fresh milkshakes. Each milkshake uses
Here are 5 descriptions of the milkshakes sold in a week and 5 expressions that represent the gallons of milk used.
Match each description to an expression that represents it.
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