Artitects in Action - Lesson Plan for Scale and Ratio
This is a detailed lesson plan on teaching students scale, scale factor, and ratios. The plan uses real-life situations to teach using a map of the U.S. It includes an activity for the students as well as discussion questions and extentions of the lesson. It incorporates a take home activity too. Also included is a way to evaluate students' learning. It has a suggested reading list and needed vocabulary.
Standards & Objectives
- Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same...
- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to...
- Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and...
- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings...
- Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0, and use rate language in the context of a ratio relationship....
- Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,...
- Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a...
- Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different...
- Recognize and represent proportional relationships between quantities.
- Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and...
- GLE 0301.3.3
- Know and apply the steps of the writing process: prewriting, drafting, revising, editing, evaluating, and publishing.
- GLE 0606.2.1
- Understand and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals.
- GLE 0606.2.3
- Understand and use ratios, rates and percents.
- GLE 0606.3.6
- Understand and use the Cartesian coordinate system.
- GLE 0706.2.3
- Develop an understanding of and apply proportionality.
- GLE 0706.2.4
- Use ratios, rates and percents to solve single- and multi-step problems in various contexts.
- GLE 0706.3.5
- Understand and graph proportional relationships.
- GLE 0706.4.2
- Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
- GLE 0706.4.3
- Understand and use scale factor to describe the relationships between length, area, and volume.
- GLE 0706.4.4
- Understand and use ratios, derived quantities, and indirect measurements.
- SPI 0606.2.6
- Solve problems involving ratios, rates and percents.
- SPI 0606.2.7
- Locate positive rational numbers on the number line.
- SPI 0606.2.8
- Locate integers on the number line.
- SPI 0606.3.9
- Graph ordered pairs of integers in all four quadrants of the Cartesian coordinate system.
- SPI 0706.1.3
- Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.
- SPI 0706.1.4
- Use scales to read maps.
- SPI 0706.2.6
- Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
- SPI 0706.2.7
- Use ratios and proportions to solve problems.
- SPI 0706.3.4
- Interpret the slope of a line as a unit rate given the graph of a proportional relationship.
- SPI 0706.3.5
- Represent proportional relationships with equations, tables and graphs.
- SPI 0706.4.3
- Apply scale factor to solve problems involving area and volume.
- SPI 0806.1.1
- Solve problems involving rate/time/distance (i.e., d = rt).
- SPI 0806.1.3
- Calculates rates involving cost per unit to determine the best buy.
- SPI 0806.4.2
- Apply the Pythagorean theorem to find distances between points in the coordinate plane to measure lengths and analyze polygons and polyhedra.
- SPI 0806.4.4
- Convert between and within the U.S. Customary System and the metric system.
- Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side that joins two vertices (vertical or...
- Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent...
- Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value...
- Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, the ratio of wings to beaks...
- Understand the concept of a unit rate a/b associated with a ratio a:b with b != 0. Use rate language in the context of a ratio relationship.
- Use ratio and rate reasoning to solve real-world and mathematical problems.
- Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale...
- Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For...
- Recognize and represent proportional relationships between quantities.
- Use proportional relationships to solve multi-step ratio and percent problems.
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
- understand that ratios are used to create scale models of buildings and structures;
- understand the principles of ratio and apply these principles in the solution of problems; and
- understand how to calculate scale using ratio.
Using what you have learned about ratios, proportions, and scale models, create four word problems for other students in your class to solve. For example: A square carpet measures 8 feet ? 4 feet. Suppose the scale of a drawing containing the carpet is 1 foot to 1/4 inch. What are the dimensions of the carpet in the drawing? The answer: 2 inches ? 1 inch.
Is it possible to draw scale models that are completely accurate? Why is accuracy important in the creation of maps, blueprints, and other scale models?
Compare your classroom floor plan to that of another student. How are they similar and different? Which would be more useful to a construction worker trying to build a classroom in a new school? Why?
List other instances in which you use ratio to compare objects in your daily life. Why is it important to maintain the same scale for each measurement you record when making your model?
Debate the merits of using the metric system and the English system to measure lengths. Explain how to convert between the two systems.
Compare your classroom to a nearby classroom using scale models of each. Explain how you could use estimation to create a scale model. Would the model be more or less accurate?
- 0.25-inch graph paper
- map(s) of the United States
- ruler (metric or inches)
- tape measure
- Take-Home Activity Sheet: Home Measurements