Learning Targets/Success Criteria: Math 700
Module 4: Percent & Proportional Relationships
Priority Standards:
7.RP.A.1 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 ¼ hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour.
7.RP.A.2 Recognize and represent proportional relationships between quantities.
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.
7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9¾ inches long in the center of a door that is 27 1⁄2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Overarching Skills:
Unit Rate
Equivalent ratio
Table
Proportion
Scale factor
Tax/Tip/Gratuity
Markup/markdown
Markdown
Discount
Commission
Percent increase/decrease
Percent error
Computation with rational numbers
Understand/Be able to do:
Topic:
Day: 1
Understanding Percents (Fraction/Decimal/Percents)
Eureka Lesson: 1
Walt:
We are learning to convert between fraction, decimal, and percent
Success Criteria:
Topic:
Day: 2
Part of a whole
Eureka Lesson: 2
Walt:
We are learning to find percent of a number
Success Criteria:
Topic:
Day: 3
Comparing quantities with percents
Eureka Lesson: 3
Walt:
We are learning to compare quantities with percents
Success Criteria:
Topic:
Day: 6
Percent Change
Eureka Lesson: 4
Walt:
We are learning to find percent increase and decrease
Success Criteria:
Topic:
Day: 7
Finding a whole
Eureka Lesson: 5
Walt:
We are learning to find the original amount
Success Criteria:
Topic:
Day: 8
Percent of a number
Eureka Lesson: 5
Walt:
We are learning to find percent of a number
Success Criteria:
Topic:
Day: 9
Fluency with Percents
Eureka Lesson: 6
Walt:
We are developing fluency with percents
Success Criteria:
Topic:
Day: 12
Mark-up/Mark-down
Eureka Lesson: 7
Walt:
We are learning to find markup and markdown
Success Criteria:
Topic:
Day: 13
Percent Error
Eureka Lesson: 8
Walt:
We are learning to find percent error
Topic:
Day: 14
Percent Change
Eureka Lesson: 9
Walt:
We are learning to find percent change
Success Criteria:
Topic:
Day: 15
Simple Interest
Eureka Lesson: 10
Walt:
We are learning to find simple interest
Success Criteria:
Topic:
Day: 16
Markup/Markdown Application
Eureka Lesson: 11
Walt:
We are learning to find tax, commission, and fees in real world problems
Success Criteria:
Topic:
Day: 20
Scale Factors as percents
Eureka Lessons: 12 & 13
Walt:
We are learning to find scale factors using percents
Success Criteria:
Topic:
Day: 21
Actual Lengths
Eureka Lessons: 14 & 15
Walt:
We are learning to find actual lengths
Success Criteria:
Topic:
Day: 22
Percents of Populations
Eureka Lesson: 16
Walt:
We are learning to find percents of populations
Success Criteria:
Topic:
Day: 23
Mixture Problems
Eureka Lesson: 17
Walt:
We are learning to solve mixture problems using expressions and equations
Success Criteria:
Topic:
Day: 24
Counting Problems
Eureka Lesson: 18
Walt:
We are learning to compute percents using probable outcomes
Success Criteria:
Module 4: Percent & Proportional Relationships
Priority Standards:
7.RP.A.1 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 ¼ hour, compute the unit rate as the complex fraction ½ / ¼ miles per hour, equivalently 2 miles per hour.
7.RP.A.2 Recognize and represent proportional relationships between quantities.
- 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.
- Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- 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 = 𝑝.
- 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.
7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9¾ inches long in the center of a door that is 27 1⁄2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Overarching Skills:
Unit Rate
Equivalent ratio
Table
Proportion
Scale factor
Tax/Tip/Gratuity
Markup/markdown
Markdown
Discount
Commission
Percent increase/decrease
Percent error
Computation with rational numbers
Understand/Be able to do:
- Add/subtract/multiply/divide positive and negative rational numbers in any form
- Fraction/Decimal/Percent conversions
- Identify equivalent rates.
- Set up a proportion.
- Compare and calculate unit rates.
- Calculate the amount of tip and tax on a total bill.
- Calculate the amount of markup/Markdown on the price of an item.
- Calculate the amount of commission made based on total sales.
- Calculate the percent of increase/decrease on price of an item.
- Calculate the percent error of a real world problem.
Topic:
Day: 1
Understanding Percents (Fraction/Decimal/Percents)
Eureka Lesson: 1
Walt:
We are learning to convert between fraction, decimal, and percent
Success Criteria:
- I understand that 𝑃 percent is the number P / 100 and that the symbol % means percent.
- I can convert between a fraction, decimal, and percent, including percents that are less than 1% or greater than 100%.
- I can write a non-whole number percent as a complex fraction.
Topic:
Day: 2
Part of a whole
Eureka Lesson: 2
Walt:
We are learning to find percent of a number
Success Criteria:
- I understand that the whole is 100% and use the formula Part = Percent × Whole to problem-solve when given two terms out of three from the part, whole, and percent.
- I can solve word problems involving percent using expressions, equations, and numeric and visual models.
Topic:
Day: 3
Comparing quantities with percents
Eureka Lesson: 3
Walt:
We are learning to compare quantities with percents
Success Criteria:
- I can use the context of a word problem to determine which of two quantities represents the whole.
- I understand that the whole is 100% and think of one quantity as a percent of another using the formula Quantity = Percent × Whole to problem-solve when given two terms out of three from a quantity, whole, and percent. When comparing two quantities, students compute percent more or percent less using algebraic, numeric, and visual models.
Topic:
Day: 6
Percent Change
Eureka Lesson: 4
Walt:
We are learning to find percent increase and decrease
Success Criteria:
- I can solve percent problems when one quantity is a certain percent more or less than another.
- I can solve percent problems involving a percent increase or decrease.
Topic:
Day: 7
Finding a whole
Eureka Lesson: 5
Walt:
We are learning to find the original amount
Success Criteria:
- I can find 100% of a quantity (the whole) when given a quantity that is a percent of the whole by using a variety of methods including finding 1%, equations, mental math using factors of 100, and double number line models.
- I can solve word problems involving finding 100% of a given quantity with and without using equations.
Topic:
Day: 8
Percent of a number
Eureka Lesson: 5
Walt:
We are learning to find percent of a number
Success Criteria:
- I can find 100% of a quantity (the whole) when given a quantity that is a percent of the whole by using a variety of methods including finding 1%, equations, mental math using factors of 100, and double number line models.
- I can solve word problems involving finding 100% of a given quantity with and without using equations.
Topic:
Day: 9
Fluency with Percents
Eureka Lesson: 6
Walt:
We are developing fluency with percents
Success Criteria:
- I can solve various types of percent problems by identifying the type of percent problem and applying appropriate strategies.
- I can extend mental math practices to mentally calculate the part, the percent, or the whole in percent word problems.
Topic:
Day: 12
Mark-up/Mark-down
Eureka Lesson: 7
Walt:
We are learning to find markup and markdown
Success Criteria:
- I understand the terms original price, selling price, markup, markdown, markup rate, and markdown rate.
- I can identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multi-step markup and markdown problems.
- I can understand equations for markup and markdown problems and use them to solve for unknown quantities in such scenarios.
Topic:
Day: 13
Percent Error
Eureka Lesson: 8
Walt:
We are learning to find percent error
- I understand the meaning of percent error as the percent the absolute error is of the exact value. Given the exact value, 𝑥, of a quantity and an approximate value, 𝑎, of the quantity, students use the absolute error, |𝑎 − 𝑥|, to compute the percent error by using the formula |𝑎−𝑥| / |𝑥| × 100%.
- I understand that when an exact value is not known, an estimate of the percent error can still be computed when given a range determined by two inclusive values (e.g., if there are known to be between 6,000 and 7,000 black bears in New York, but the exact number is not known, the percent error can be estimated to be (1,000 / 6,000) (100%) at most, which is 16 2 / 3 %).
Topic:
Day: 14
Percent Change
Eureka Lesson: 9
Walt:
We are learning to find percent change
Success Criteria:
- I can solve percent problems where quantities and percents change.
- I can use a variety of methods to solve problems where quantities and percents change, including double number lines, visual models, and equations.
Topic:
Day: 15
Simple Interest
Eureka Lesson: 10
Walt:
We are learning to find simple interest
Success Criteria:
- I can solve simple interest problems using the formula 𝐼 = 𝑃rt, where 𝐼 represents interest, 𝑃 represents principal, 𝑟 represents interest rate, and 𝑡 represents time. When using the formula 𝐼 = 𝑃, students recognize that units for both interest rate and time must be compatible; students convert the units when necessary.
Topic:
Day: 16
Markup/Markdown Application
Eureka Lesson: 11
Walt:
We are learning to find tax, commission, and fees in real world problems
Success Criteria:
- I can solve real-world percent problems involving tax, gratuities, commissions, and fees.
- I can solve word problems involving percent using equations, tables, and graphs.
- I can identify the constant of proportionality (e.g., tax rate, commission rate) in graphs, equations, and tables, and in the context of the situation.
Topic:
Day: 20
Scale Factors as percents
Eureka Lessons: 12 & 13
Walt:
We are learning to find scale factors using percents
Success Criteria:
- I can make a scale drawing of a picture or geometric figure using that scale given a scale factor as a percent.
- I can recognize that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distances in the original picture.
- I understand scale factor to be the constant of proportionality.
- I can make scale drawings in which the horizontal and vertical scales are different.
- Given Drawing 1 and Drawing 2 (a scale model of Drawing 1 with scale factor), I understand that Drawing 1 is also a scale model of Drawing 2 and can compute the scale factor.
- Given three drawings that are scale drawings of each other and two scale factors, I can compute the other related scale factor.
Topic:
Day: 21
Actual Lengths
Eureka Lessons: 14 & 15
Walt:
We are learning to find actual lengths
Success Criteria:
- Given a scale drawing, I can compute the lengths in the actual picture using the scale factor.
- I can solve area problems related to scale drawings and percent by using the fact that an area, 𝐴′, of a scale drawing is 𝑘2 times the corresponding area, 𝐴, in the original drawing, where 𝑘 is the scale factor.
Topic:
Day: 22
Percents of Populations
Eureka Lesson: 16
Walt:
We are learning to find percents of populations
Success Criteria:
- I can write and use algebraic expressions and equations to solve percent word problems related to populations of people and compilations.
Topic:
Day: 23
Mixture Problems
Eureka Lesson: 17
Walt:
We are learning to solve mixture problems using expressions and equations
Success Criteria:
- I can write and use algebraic expressions and equations to solve percent word problems related to mixtures.
Topic:
Day: 24
Counting Problems
Eureka Lesson: 18
Walt:
We are learning to compute percents using probable outcomes
Success Criteria:
- I can solve counting problems related to computing percents.
What to Teach
Topic 1: Graphing on a Coordinate Plane
- I can identify a coordinate plane.
- I can identify the axis’ on a coordinate plane.
- I can identify a coordinate point.
- I can graph a coordinate point.
Topic 2: Unit Rates
- I know what the constant of proportionality is.
- I can identify the constant of proportionality in a table.
- I can calculate unit rate.
- I can use a proportion to calculate unit rate.
- I can identify equivalent unit rates.
- I can compare unit rates.
- I can apply rates to calculate new rates.
Topic 3: Graphing the Constant of Proportionality
- I can identify the constant of proportionality of a graphed line.
- I can calculate to find the constant of proportionality of a graphed line
vocabulary |
Unit ResourcesAssessmentPre Assessment
Real World Experience Post Assessment Formative Assessment Student Reflection and Goal Setting Sheet |
Learn the Math |