standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
In this activity students compare two book sale scenarios in which there is a different base price of a book for the fundraiser. Students notice that when you increase the price by a lot, you make more profit per book, but you may also sell fewer books. On the other hand, if you increase the price by less money, you have to sell more books to make the same profit.
MLR6 Three Reads.
Keep books or devices closed. Display only the problem stem, without revealing the questions. “We are going to read this question 3 times.” After the 1st Read: “Tell your partner what this situation is about.” After the 2nd Read: “List the quantities. What can be counted or measured?” Reveal the question(s). After the 3rd Read: “What strategies can we use to solve this problem?”
Advances: Reading, Representing
Launch
Groups of 2
“When a school plans a book sale fundraiser, the school orders books from the publisher, or bookseller, for a certain price. Then the school sells it for a different price at the book fair.”
“Let’s imagine the school buys a book for \$10. Should they sell the book for more or less than \$10 at the book fair? Why?” (More if they want to make money from the sale.)
“This is called the mark-up price. For every book they sell, the bookseller will get \$10 and the school keeps the amount they added. The amount they add is called the profit.”
Activity
1 minute quiet think time
5 minutes: group work time
Monitor for students who consider the profit per book in their justifications.
Student Facing
Two schools buy science books for \$8 from a publisher to sell at their book sale. School A sells the books for \$12. School B sells the books for \$12.90.
Who do you think sells more science books? Why?
How much profit does each school make if they each sell 35 books?
School B sells 10 science books. How many science books does School A have to sell to raise about the same amount of money?
Student Response
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Activity Synthesis
“What is a reasonable mark-up price?”
“What do you need to consider when deciding a mark-up price?”


aligns: no