Standard #: MA.7.A.1.1 (Archived Standard)


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Distinguish between situations that are proportional or not proportional, and use proportions to solve problems.


Remarks


Example 1: Two snakes, Moe and Joe, are each measured at two points in time. The first time, Moe is 3 inches long and Joe is 4 inches long. One year later, Moe is 5 inches long and Joe is 6 inches long. Which snake grew more? Maria believes that both snakes grew the same amount. Tom believes that Moe grew more. Explain under what circumstances either explanation could be correct. (In absolute terms they grew the same amount, which is not a proportional relationship; in relative terms one grew more than the other, which is a proportional relationship.)

 

Example 2: A recipe calls for 3 cups of flour and 2 eggs. If you wanted to increase the recipe and use 9 cups of flour, how many eggs would you need to use to keep the same ratio of flour to eggs?



General Information

Subject Area: X-Mathematics (former standards - 2008)
Grade: 7
Body of Knowledge: Algebra
Idea: Level 3: Strategic Thinking & Complex Reasoning
Big Idea: BIG IDEA 1 - Develop an understanding of and apply proportionality, including similarity.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Item Type(s): This benchmark may be assessed using: MC , GR item(s)
    N/A

    Clarification :
    Students will distinguish between proportional and non-proportional relationships.

    Students will identify possible scenarios that may or may not be proportional.

    Students will use proportions to solve problems.
    Content Limits :
    Items will not include discounts, simple interest, taxes, tips, percents of increase or decrease, inverse variation, scale drawing, or constant speed.

    Items will not include negative numbers.
    Stimulus Attributes :
    Items should be set in a real-world or mathematical context.


Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1 If x and y are related, which of the following is true for x and y to be proportional? N/A MC: Multiple Choice
Sample Item 2 Larry’s recipe for his chocolate fudge is shown below.
  • 3 cups semi-sweet chocolate chips
  • 14 ounces sweetened condensed milk
  • Dash of salt
  • 3/4 cup chopped nuts (optional)
  • 1 1/2 teaspoons vanilla extract

Larry is making a large batch of his fudge and will use 12 cups of semi-sweet chocolate chips. Based on this information, what is the total number of ounces of sweetened condensed milk he will need to use?

 N/A GR: Gridded-Response


Related Resources

Lesson Plans

Name Description
Developing a Sense of Scale

This lesson unit is intended to help you assess whether students recognize relationships of direct proportion and how well they solve problems that involve proportional reasoning. In particular, it is intended to help you identify those students who use inappropriate additive strategies in scaling problems, which have a multiplicative structure, rely on piecemeal and inefficient strategies such as doubling, halving, and decomposition, and have not developed a single multiplier strategy for solving proportionality problems and see multiplication as making numbers bigger, and division as making numbers smaller.

Recognizing Proportional Relationships to Develop Sense of Scale This 90-minute lesson (15-minute pre-lesson, 60-minute lesson and 15-minute follow up lesson or homework) asks students to analyze proportional relationships to solve real world and mathematical problems. The examples use recipes, paint, and buildings. Students begin by working individually, then in pairs or threes, and then as a whole class. Student will need calculators, large sheets of paper to make a poster and the lesson materials.
Scientific calculations from a distant planet

Students will act as mathematicians and scientists as they use models, observations and space science concepts to perform calculations and draw inferences regarding a fictional solar system with three planets in circular orbits around a sun. Among the calculations are estimates of the size of the home planet (using a method more than 2000 years old) and the relative distances of the planets from their sun.

Problem-Solving Task

Name Description
Lifting a Lion

"Students will work in groups to solve a real-world problem presented by the book: How Do You Lift A Lion? Using a toy lion and a lever, students will discover how much work is needed to raise the toy lion. They will use proportions to determine the force needed to lift a real lion" from TI World Math.

Teaching Idea

Name Description
Word Problems: Proportions

This resource demonstrates how to solve problems using proportions. It includes an instructional model, practice word problems, and an answer checking feature. The site also contains a glossary.

Tutorial

Name Description
Using the Proportion Method to Solve Percent Problems

This site explicitly outlines the steps for using the proportion method to solve three different kinds of percent problems. It also includes sample problems for practice determining the part, the whole or the percent.

Student Resources

Tutorial

Name Description
Using the Proportion Method to Solve Percent Problems:

This site explicitly outlines the steps for using the proportion method to solve three different kinds of percent problems. It also includes sample problems for practice determining the part, the whole or the percent.



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