The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
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Subject(s) Grade/Course Unit of Study Unit Type(s) Pacing Mathematics 7th Ratios and Proportional Relationships ❑ Topical T Skills-­‐based ❑ Thematic Six Weeks Priority Pennsylvania Core Standards Supporting Standards PRIORITY PENNSYLVANIA CORE STANDARDS Numbers and Operations: CC.2.1.7.D.1: ANALYZE proportional relationships and USE them to MODEL and SOLVE real-­‐world and mathematical problems. UNWRAP CONCEPTS and ELIGIBLE CONTENT M07.A-­‐R.1.1.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. Example: If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. M07.A-­‐R.1.1.2: Determine whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin). M07.A-­‐R.1.1.3: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. M07.A-­‐R.1.1.4: Represent proportional relationships by equations. 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. M07.A-­‐R.1.1.5: 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. M07.A-­‐R.1.1.6: Use proportional relationships to solve multi-­‐step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease. “UNWRAPPED” Priority Pennsylvania Core Standards Supporting Standards Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. Permission needed to
duplicate.
The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
2
PRIORITY PENNSYLVANIA CORE STANDARDS Numbers and Operations: CC.2.1.7.D.1: ANALYZE proportional relationships and USE them to MODEL and SOLVE real-­‐world and mathematical problems. UNWRAP CONCEPTS and ELIGIBLE CONTENT M07.A-­‐R.1.1.1: COMPUTE unit rates associated with ratios of fractions, INCLUDING ratios of lengths, areas, and other quantities measured in like or different units. Example: If a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour. M07.A-­‐R.1.1.2: DETERMINE whether two quantities are proportionally related (e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin). M07.A-­‐R.1.1.3: IDENTIFY the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. M07.A-­‐R.1.1.4: REPRESENT proportional relationships by equations. 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. M07.A-­‐R.1.1.5: 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. M07.A-­‐R.1.1.6: USE proportional relationships to solve multi-­‐step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease. “Unwrapped” Concepts (students need to know) •
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“Unwrapped” Skills (students need to be able to do) proportional relationships •
problems problems problems unit rates ratios of lengths, areas, and other quantities whether two quantities are proportionally related •
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ANALYZE (proportional relationships) USE (real-­‐world and mathematical problems) MODEL (real-­‐world and mathematical problems) SOLVE(real-­‐world and mathematical problems) COMPUTE (unit rates associated with ratios of fractions) INCLUDE (ratios of lengths, areas, and other quantities measured in like or different units) DETERMINE (whether two quantities are proportionally related e.g., by testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin) IDENTIFY (the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships) Bloom’s Taxonomy Levels 4 2,3 3,4 3,4,5 3,4 2,3 4,5 2,3 Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. Permission needed to
duplicate.
The Chester Upland School District
Office of Curriculum & Instruction
Mathematics Curriculum Guide
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proportional relationships •
what a point on the graph of a proportional relationship means •
proportional relationships •
REPRESENT(proportional relationships by equations) 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) USE (proportional relationships to solve multi-­‐step ratio and percent problems) 3
4,5 6 3,4 Essential Questions 1. How do we determine whether two quantities are proportionally related? 2. How do students develop an understanding of and apply proportional reasoning? 3. What is the difference between unit rate and ratio? 4. What is a proportion? Corresponding Big Ideas 1. To determine whether two quantities are proportionally related you can use testing for equivalent ratios in a table, graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 2. Students extend their understanding of ratios and develop understanding of proportionality to solve single-­‐ and multi-­‐step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. Students will apply their understanding of proportional relationships to similar figures. 3. A ratio is the comparison between two numbers with the same unit. For example 3 oranges to two oranges. On the other hand, a rate is an indication of the measurements of different units per unit. For example, the statement 3 oranges/ person show the relationship between the measurements of oranges per person. the rate of something is the amount or speed of it, whereas the ratio is the proportion of one thing to another, like for example if there was 15 sweets in a bag; 10 red and 5 blue, so the ratio of red sweets to blue would be 2 to 1. 4. A proportion is a special form of an algebra equation. It is used to compare two ratios or make equivalent fractions. A ratio is a comparison between two values. Such as the following: 1 apple: 3 oranges. This ratio compares apples to oranges. It means for every apple there are 3 oranges. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. Permission needed to
duplicate.