Ohio Resource Center
Lessons
Grid and Percent It
Discipline
Mathematics
6, 7, 8
Professional Commentary

In this lesson, students use a 10 x 10 grid to solve various types of percent problems. The grid model offers a means of visualizing the given information as well as suggesting different approaches to solving problems. Students begin with representing simple percents on the grid and then move to percents less than 1 and greater than 100. Solutions to the three standard kinds of percent problems are illustrated, as well as problems involving percent increase and percent decrease. A reproducible grid sheet is provided. This lesson plan was adapted from an article that appeared in the April 1994 issue of Mathematics Teaching in the Middle School. (author/sw)

Common Core State Standards for Mathematics
Ratios and Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
1. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
2. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
3. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Ratios and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.A.2
Recognize and represent proportional relationships between quantities.
1. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
2. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
3. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
4. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
Ohio Mathematics Academic Content Standards (2001)
Number, Number Sense and Operations Standard
Benchmarks (5–7)
C.
Develop meaning for percents, including percents greater than 100 and less than 1.
D.
Use models and pictures to relate concepts of ratio, proportion and percent.
I.
Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.
Benchmarks (8–10)
G.
Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.
1.
Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole.
4.
Describe what it means to find a specific percent of a number, using real-life examples.
5.
Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.
14.
Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.
15.
Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was \$140, and the sale price is \$100.
7.
Solve problems using the appropriate form of a rational number (fraction, decimal or percent).
8.
Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use.
6.
Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.
Mathematical Processes Standard
Benchmarks (5–7)
H.
Use representations to organize and communicate mathematical thinking and problem solutions.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Expectations (6–8)
work flexibly with fractions, decimals, and percents to solve problems;
develop meaning for percents greater than 100 and less than 1;
Representation Standard
Use representations to model and interpret physical, social, and mathematical phenomena