Author:
Subject:
Ratios and Proportions
Material Type:
Lesson Plan
Level:
Middle School
6
Provider:
Pearson
Tags:
6th Grade Mathematics, Comparison, Quantity, Values
Language:
English
Media Formats:
Text/HTML

Percents Greater than 100%

Overview

Students use percents greater than 100% to solve problems about rainfall, revenue, snowfall, and school attendance.

Key Concepts

Percents greater than 100% are useful in making comparisons between the values of a single quantity at two points in time. When a later value is more than 100% of an earlier value, it means the quantity has increased over time. This percent comparison can be used to find unknown values, whether the earlier or later value is unknown.

Goals and Learning Objectives

• Understand the meaning of a percent greater than 100% in real-world situations.
• Use percents greater than 100% to interpret situations and solve problems.

Lesson Guide

Have students read the prompt. Ask students to talk with a partner about whether the percent of normal rainfall is greater than or less than 100%. (Answer: It is greater than 100%. ) One possible way to find the answer is to divide 25 by 20.

SWD: Help students identify key information from the problems. One way is to have them underline key words and numbers that will help them solve the problem. Allow time for students to master this skill.

ELL: As with other oral instructions, ensure that the pace of your speech is appropriate for ELLs. Pause frequently to allow students to pose questions. Alternatively, ask questions as your explanation unfolds to monitor understanding.

Mathematics

The start of the lesson introduces the idea of a percent greater than 100% in the context of comparing rainfall between a normal year and the current year. There is a conceptual shift in this situation that students may need to make: instead of a percent representing a comparison between part of a quantity and the whole quantity, as in the previous lessons, the percent represents a comparison between an initial value, or “base,” and another value.

Too Much Rain

The city of Valley View normally gets 20 inches of rain per year.

Last year the city got 25 inches of rain.

Think of using percents to compare 25 inches of rain as a percent of the normal rainfall.

• Will this be greater than or less than 100%?
• What strategies can be used to solve this problem?

Lesson Guide

Discuss the Math Mission. Students will solve problems that involve percents greater than 100%.

Opening

Solve problems that involve percents greater than 100%.

Lesson Guide

Have students work in pairs on the problem.

SWD: Investigative work is intended to be a time for students to grapple with the mathematics, and it is crucial that you only help students understand the tasks, and not solve the problem.

Mathematical Practices

Students can draw on all of the resources they have developed so far in this unit (and before) to make sense of today’s problems. Some students may consider analogous problems as a way of getting started, some may make conjectures about values that would make sense before doing any calculations, and many will show perseverance in solving the problems—especially the problem about the company’s earnings (Task 4), which is less routine than the others.

Interventions

Student has difficulty setting up computations.

• Make a diagram to represent the situation.
• How much greater than 100% is the given value? (100% plus what?)
• Represent the percent in decimal form and write an equation to solve the problem. Use a letter to represent the unknown quantity.

• Last year’s rainfall is 125% of normal.

Rain

The city of Valley View normally gets 20 inches of rain per year.

Last year the city got 25 inches of rain.

• Calculate last year’s rainfall as a percent of normal.

To calculate the percent, would you divide 20 by 25 or divide 25 by 20?

Lesson Guide

Have students work in pairs on the problem.

Mathematical Practices

Mathematical Practice 1: Make sense of problems and persevere in solving them.

Students can draw on all of the resources they have developed so far in this unit (and before) to make sense of today’s problems. Some students may consider analogous problems as a way of getting started, some may make conjectures about values that would make sense before doing any calculations, and many will show perseverance in solving the problems.

Mathematical Practice 2: Reason abstractly and quantitatively.

This lesson also presents opportunities for students to shift back and forth between the computations needed to solve the problems and the meanings of the values as given by the context of each problem. Listen for students who are doing this explicitly in their work, whether it’s in verbal exchange with their partner, in labels for diagrams, in setting up equations, or otherwise.

Interventions

Student has difficulty setting up computations.

• Make a diagram to represent the situation.
• How much greater than 100% is the given value? (100% plus what?)
• Represent the percent in decimal form and write an equation to solve the problem. Use a letter to represent the unknown quantity.

Student has trouble interpreting the situation about the company’s earnings.

• Make a conjecture about the amount the waiter gave the busboy. Will it be less than or greater than $45? • Create a tape diagram showing a ratio of 5:2 to represent the quantities in this situation, and label each quantity and each unit of your diagram carefully. Student gets a correct answer, but does not create an explicit model or explain the solution. • How can you show that your answer is correct? Create a diagram that illustrates the relationship between quantities. • Create a tape diagram, a double number line, a table, or a graph to model the situation, and label your answer. Student creates an accurate and complete model, with the correct answer. • Use another tool to create a different kind of model to represent the relationship between quantities (e.g., a tape diagram, a double number line, a table, or a graph). • Explain how the parts of your first model relate to the parts of your second model. Possible Answers 1. The waiter gave the busboy$18.
2. The tape diagram shows a ratio of 5:2, with the 5 units in the upper tape representing the waiter’s $45 and the 2 units in the lower tape representing the busboy’s unknown amount. If the upper tape represents$45, then each unit represents $9, and the busboy’s amount is 2 ⋅$9 = $18. Formative Assessment Using Tools to Solve Ratio Problems Complete this Self Check by yourself. Use a tool such as the Ratio Table, Double Number Line, or a graph to solve the problem. A waiter at a restaurant shares his tips with the busboy in the ratio 5:2 (5 parts for himself, 2 for the busboy). • If the waiter had$45 after sharing his tips, how much did he give the busboy?

INTERACTIVE: Double Number Line Tool

INTERACTIVE: Ratio Table Tool