Exploring New York State's Common Core Mathematics Curriculum: Lesson 18
Welcome to our comprehensive guide on New York State's Common Core Mathematics Curriculum, specifically focusing on Lesson 18. This lesson, designed for Grade 7 students, delves into the concept of proportionality and unit pricing. Let's break down this engaging topic, ensuring we cater to both educators and students seeking a deeper understanding.
Understanding Proportionality and Unit Pricing
Lesson 18 introduces students to the concept of proportionality, which is the relationship between two quantities where one changes in direct proportion to the other. This lesson also introduces unit pricing, a practical application of proportionality, helping students understand how to compare prices of different quantities of the same item.
Key Concepts and Objectives
- Understanding the concept of proportionality
- Recognizing when two quantities are in a proportional relationship
- Calculating unit prices to compare the cost of different quantities of the same item
Proportional Relationships: Explained
Proportional relationships are a fundamental concept in mathematics, representing a constant ratio between two quantities. In Lesson 18, students will explore this concept through real-world scenarios, such as comparing the lengths of different objects or the heights of growing plants.
Representing Proportional Relationships
Students will learn to represent proportional relationships using tables, graphs, and equations. They will also understand that a proportional relationship between two quantities can be represented by a linear equation, where one quantity is a constant multiple of the other.
Unit Pricing: A Practical Application
Unit pricing is a practical application of proportionality, helping students understand how to compare the cost of different quantities of the same item. By calculating the unit price, students can determine the cost per unit of measure, making it easier to compare prices.
Calculating Unit Price
To calculate the unit price, students will divide the total cost of an item by the number of units in that item. For example, if a pack of 12 pens costs $3.60, the unit price would be $3.60 ÷ 12 = $0.30 per pen.
Practical Examples and Activities
Lesson 18 includes various practical examples and activities to help students grasp these concepts. Some examples include comparing the lengths of different objects, calculating the cost per ounce of different brands of cereal, and creating graphs to represent proportional relationships.
Table: Comparing Unit Prices
| Item | Quantity | Total Cost | Unit Price |
|---|---|---|---|
| Cereal A | 12 oz | $3.00 | $0.25 |
| Cereal B | 18 oz | $4.50 | $0.25 |
In the table above, students can see that while Cereal A and Cereal B have different total costs and quantities, their unit prices are the same. This helps students understand the importance of comparing unit prices when shopping.
Assessment and Further Learning
To assess student understanding, educators can use a variety of methods, including worksheets, quizzes, and real-world scenarios. For further learning, students can explore other applications of proportionality, such as scale drawings, dilations, and similar triangles.
