# Increasing and Decreasing Quantities by a Percent

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## Description

- Overview:
- This lesson unit is intended to help teachers assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties: translating between percents, decimals, and fractions; representing percent increase and decrease as multiplication; and recognizing the relationship between increases and decreases.

- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- License:
- Creative Commons Attribution-NonCommercial-NoDerivs 3.0
- Media Format:
- Downloadable docs, Text/HTML

# Comments

## Standards

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: 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.

Degree of Alignment: 3 Superior (1 user)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: 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.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Degree of Alignment: Not Rated (0 users)

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Degree of Alignment: Not Rated (0 users)

Standard: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Degree of Alignment: Not Rated (0 users)

Standard: Apply properties of operations as strategies to multiply and divide rational numbers.

Degree of Alignment: Not Rated (0 users)

Standard: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

Standard: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grade 7,Ratios and Proportional RelationshipsStandard: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Standard: Apply properties of operations as strategies to add and subtract rational numbers.

Degree of Alignment: Not Rated (0 users)

Standard: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Degree of Alignment: Not Rated (0 users)

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Degree of Alignment: Not Rated (0 users)

Standard: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Indicator: Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Indicator: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Standard: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Indicator: Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Apply properties of operations as strategies to add and subtract rational numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Apply properties of operations as strategies to multiply and divide rational numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: The Number System

Indicator: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Solve multi-step real world and mathematical problems involving ratios and percentages.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Compute unit rates, including those involving complex fractions, with like or different units.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Decide whether two quantities in a table or graph are in a proportional relationship.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Represent proportional relationships with equations.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: 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.

Degree of Alignment: Not Rated (0 users)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)Degree of Alignment | 3 (1 user) |

Quality of Explanation of the Subject Matter | 3 (1 user) |

Utility of Materials Designed to Support Teaching | 3 (1 user) |

Quality of Assessments | N/A |

Quality of Technological Interactivity | N/A |

Quality of Instructional and Practice Exercises | N/A |

Opportunities for Deeper Learning | N/A |

# Tags (11)

- Mathematics
- Numbers and Operations
- CCSS
- Common Core Math
- Common Core PD
- Decimals
- Fractions
- Multiplication
- ODE Learning
- Percents
- Ratios and Proportions

This is a lesson and assessment tool. It has many teacher resources like a detailed lesson plan, ppt for students, and materials to do in class activity. It is addressing CCSS 7.RP.3. Students have to combine the card sets like a puzzle to make accurate statements about percent of increase and decrease.