old hiked 15 miles each day until he crossed the mountains after 7 days. How many miles was his hike? Discuss which del of multiplication-set model (repeated addition), number-line (measurement), array, rectangular area, multiplication e, or Cartesian product-best fits the problem. w many miles did Harold hike?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Problem Solving: Multiplication Models

1. **Harold's Hiking Challenge**

   Harold hiked 15 miles each day until he crossed the mountains after 7 days. How many miles was his hike? Discuss which model of multiplication—set model (repeated addition), number-line (measurement), array, rectangular area, multiplication tree, or Cartesian product—best fits the problem.

   **Question:**
   How many miles did Harold hike?  
   ________ miles

   **Which model of multiplication best fits the problem?**

   - ⃝ Cartesian product model
   - ⃝ array model
   - ⃝ multiplication tree model
   - ⃝ set model
   - ⃝ rectangular area model
   - ⃝ number-line model

#### Explanation of Models:

- **Set Model (Repeated Addition):** This model visualizes multiplication as repeated addition. Example: 15 miles per day for 7 days means adding 15 repeatedly 7 times.

- **Number-Line Model (Measurement):** Visualizes multiplication by measuring intervals on a number line. Example: Each interval represents a day's hike.

- **Array Model:** Uses rows and columns to represent multiplication, ideal for calculations involving combinations.

- **Rectangular Area Model:** Visualizes multiplication as the area of a rectangle, where length and width are the factors.

- **Multiplication Tree Model:** Represents multiplication in a hierarchical structure, useful for breaking down complex problems.

- **Cartesian Product Model:** Represents all possible combinations of two sets, helpful in probability and statistics.
Transcribed Image Text:### Problem Solving: Multiplication Models 1. **Harold's Hiking Challenge** Harold hiked 15 miles each day until he crossed the mountains after 7 days. How many miles was his hike? Discuss which model of multiplication—set model (repeated addition), number-line (measurement), array, rectangular area, multiplication tree, or Cartesian product—best fits the problem. **Question:** How many miles did Harold hike? ________ miles **Which model of multiplication best fits the problem?** - ⃝ Cartesian product model - ⃝ array model - ⃝ multiplication tree model - ⃝ set model - ⃝ rectangular area model - ⃝ number-line model #### Explanation of Models: - **Set Model (Repeated Addition):** This model visualizes multiplication as repeated addition. Example: 15 miles per day for 7 days means adding 15 repeatedly 7 times. - **Number-Line Model (Measurement):** Visualizes multiplication by measuring intervals on a number line. Example: Each interval represents a day's hike. - **Array Model:** Uses rows and columns to represent multiplication, ideal for calculations involving combinations. - **Rectangular Area Model:** Visualizes multiplication as the area of a rectangle, where length and width are the factors. - **Multiplication Tree Model:** Represents multiplication in a hierarchical structure, useful for breaking down complex problems. - **Cartesian Product Model:** Represents all possible combinations of two sets, helpful in probability and statistics.
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