Big Idea 1 : BIG IDEA 1 (Archived)



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Develop an understanding of and apply proportionality, including similarity.

General Information

Number: MA.7.A.1
Title: BIG IDEA 1
Type: Big Idea
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 7
Body of Knowledge: Algebra

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.7.A.1.1: Distinguish between situations that are proportional or not proportional, and use proportions to solve problems.
MA.7.A.1.2: Solve percent problems, including problems involving discounts, simple interest, taxes, tips, and percents of increase or decrease.
MA.7.A.1.3: Solve problems involving similar figures.
MA.7.A.1.4: Graph proportional relationships and identify the unit rate as the slope of the related linear function.
MA.7.A.1.5: Distinguish direct variation from other relationships, including inverse variation.
MA.7.A.1.6: Apply proportionality to measurement in multiple contexts, including scale drawings and constant speed.


Related Access Points

This cluster includes the following access points.

Independent

Access Point Number Access Point Title
MA.7.A.1.In.a: Solve real-world problems involving simple ratios, such as 2 to 1 or 1 to 3, using physical models, graphic representations, and charts.
MA.7.A.1.In.b: Identify that a higher percent represents a larger quantity or amount in real-world problems.
MA.7.A.1.In.c: Measure and describe how various kinds of models compare in size to real-life objects.

Supported

Access Point Number Access Point Title
MA.7.A.1.Su.a: Solve real-world problems involving simple ratios, such as 2 to 1, using objects or pictures.
MA.7.A.1.Su.b: Identify that percent discounts reduce the price of goods in real-world situations.
MA.7.A.1.Su.c: Compare the size of models to real-life objects using language, such as same, larger, and smaller.

Participatory

Access Point Number Access Point Title
MA.7.A.1.Pa.a: Solve a simple problem involving a 2 to 1 ratio using objects.
MA.7.A.1.Pa.b: Match objects to a model or picture that is a smaller version.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Educational Software / Tool

Name Description
Free Graph Paper: A variety of graph paper types for printing, including Cartesian, polar, engineering, isometric, logarithmic, hexagonal, probability, and Smith chart.

Lesson Plans

Name Description
Real Life Tax, Tip, and Discount!:

Students calculate the tax, tip, and discount in real-world situations.

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.

Pricing Twelve Days of Celebration:

Students will discover how much items would cost if they were to give gifts for 12 days. They will learn how to calculate and add sales tax to find a total.

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.
Making a Scale Drawing: Objective: Students will create a detailed scale drawing. Context: Students have used tools to measure length, solve proportions, and interpret scale drawings. They will continue to use ratio and proportion in the study of similar figures, percent, and probability.
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.

Here's a tip!:

Students will solve problems involving sales tax and tips; students will apply the properties of operations with numbers in decimal, percent, and fraction form. Students will convert between numbers in any form as appropriate.

Let's Go Shopping: Calculating Percents: In this lesson, students will participate in a simulated shopping experience where they choose items they would like to purchase from local sale advertisements. The students will be able to apply the percent formula and the percent of change formula to real world financial situations. Students will learn how to calculate percent discounts, their percent of savings, and tax. The students will analyze, compare, draw conclusions and explain in writing why specific types of discounts are the most advantageous given specific situations.

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 Ideas

Name Description
Packing For A L-o-o-o-ng Trip To Mars: In this engineering task, students will apply concepts of volume to decide what they will need to take on a 2-1/2 year journey to Mars. Then plan how to fit everything into a 1-cubic-meter box, using only a measuring tape, pencil and paper, and math.
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.

Calculating Sharks-SeaWorld Classroom Activity:
  • Given data about sharks and the amount of food they eat, students will be able to solve for the unknown in percentage problems.
  • Given information about a shark's growth, students will be able to graph coordinates and interpret a linear graph.
  • Given the conversion factor, students will be able to convert from metric to English units.

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.

Unit/Lesson Sequences

Name Description
Direct and Inverse Variation: "Lesson 1 of two lessons teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). Lesson 2 teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." from Insights into Algebra 1 - Annenberg Foundation.
Percents: What's the Use?:

This activity focuses on the use of percents in situations involving discounts and taxes. The students are assigned an interview to discover the use of percents in various careers. Working in pairs and using shopping catalogues, they will further their knowledge of percents by calculating discounts and taxes. To access their knowledge of percents, there is a writing activity and an assignment to create a menu with questions and an answer key.

Virtual Manipulatives

Name Description
Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Tutorial

Title 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.

Virtual Manipulatives

Title Description
Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.