Learning Targets/Success Criteria: Math 700
Module 1: Ratios and 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 ½ mile in 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 the 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.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
- Solve word problems leading to equations of the form 𝑝 + 𝑞 = 𝑟 and 𝑝(𝑥) + 𝑞 = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
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:
Rational numbers
Variables
Equivalent Equation
Solution
Unit Rate
Constant of Proportionality Equivalent
Ratio
Table
Proportion(set up/solve)
Coordinate plane
Graph
X-axis
Y-axis
Origin
Coordinate point
X-value
Y-value
Tax
Tip/Gratuity
Markup/markdown
Discount
Commission
Percent increase/decrease Percent error
Understand/Be able to do:
- Create and solve equations to represent real world problems
- Interpret solutions to equations
- Identify equivalent rates
- Set up and solve a proportion
- Calculate and compare unit rates
- Calculate the constant of proportionality from a table, graphed line and from a real world problem.
- Write an equation in y = kx form.
- Calculate the amount of tip and tax on a total bill.
- Calculate the amount of markup or markdown on the price of an item.
- Calculate the amount of commission made based on total sales.
- Calculate the percent increase and decrease on the price of an item.
- Calculate the percent error of a real world problem.
Topic:
Days: 1 & 2
Unit Rate/Reducing Ratios
Eureka Lessons: 1 & 2
Walt:
We are learning to find unit rate and reduce ratios
Success Criteria:
- I can compute unit rates associated with ratios of quantities measured in different units.
- I can recall the meaning of value of ratio, equivalent ratios, rate, and unit rate.
- I understand two quantities are proportional to each other when there exists a constant.
- I can recognize the first quantity (x) is proportional to the second quantity (y) if y = kx for some positive number k.
Topic:
Day: 3
Proportional Relationships/Unit Rates
Eureka Lesson: 3
Walt:
We are learning to solve proportional relationships and unit rates
Success Criteria:
- I can examine situations to decide whether two quantities are proportional to each other by checking for a constant multiple between measures of x and measures of y when given a table.
- I can examine examples of relationships that are not proportional in addition to those that are not.
Topic:
Day: 4
Find missing value on a table
Eureka Lesson: 4
Walt:
We are learning to find missing values on a table
Success Criteria:
- I can examine situations to decide whether two quantities are proportional to each other by checking for a constant multiple between measures of x and measures of y when given a table or when required to create a table.
- I can study examples of relationships that are not proportional in addition to those that are.
Topic:
Day: 6
Proportional Relationships on a graph
Eureka Lessons: 5 & 6
Walt:
We are learning to find proportional relationships on a graph
Success Criteria:
- I can determine whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- I can study examples of relationships that are not proportional in addition to those that are.
- I can examine situations carefully to decide whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether all the points would fall on a line that passes through the origin.
Topic:
Days: 7 & 8
Using proportional relationships to create graphs
Eureka Lessons: 5 & 6
Walt:
I can use proportional relationships to create a graph
Success Criteria:
- I can decide whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- I can observe examples of relationships that are not proportional in addition to those that are.
- I can examine situations carefully to decide whether two quantities are proportional to each other by graphing on a coordinate plane.
- I can observe whether all the points would fall on a line that passes through the origin.
Topic:
Days: 9 & 10
Finding constant of proportionality
Eureka Lessons: 7, 8, 9, & 10
Walt:
We are learning to write an equation when finding constant of proportionality from a graph or table
Success Criteria:
- I can identify the same value relating the measure of x and the measures of y in a proportional relationship as the constant of proportionality and recognize it as the unit rate in the context of a given situation.
- I can find and interpret the constant of proportionality with the contexts of problems.
- I can use the constant of proportionality to represent proportional relationships by equations in real-world contexts as they relate the equations to a corresponding ratio table or graphical representation.
- I can consolidate understanding of equations representing proportional relationships as they interpret what points on the graphing of a proportional relationship mean in terms of the situation or context of the problem, including the point (0,0).
- I can identify and interpret in context the point (1,r) on the graph of a proportional relationship where r is the unit rate.
Topic:
Day: 11
Finding constant of proportionality
Eureka Lesson: 15
Walt:
We are learning to write an equation when finding constant of proportionality from a graph or table
Success Criteria:
- I can use equations and graphs to represent proportional relationships arising from ratios and rates involving fractions.
- I can interpret what points on the graph of the relationship mean in terms of the situation or context of the problem.
Topic:
Day: 15
Unit Rate/Better Buy (fractions)
Eureka Lessons: 11 & 12
Walt:
We are learning to calculate unit rate in order to determine the better buy.
Success Criteria:
- I can use ratio tables and ratio reasoning to compute unit rates associated with ratios of fractions in the context of measured quantities such as recipes, lengths, areas, and speed.
- I can use unit rates to solve problems and analyze unit rates in the context of the problem.
Topic:
Day: 16
Unit Rate with Rational Numbers
Eureka Lessons: 11 & 12
Walt:
We are learning to calculate unit rate with rational numbers
Success Criteria:
- I can use ratio tables and ratio reasoning to compute unit rates associated with ratios of fractions in the context of measured quantities such as recipes, lengths, areas, and speed.
- I can use unit rates to solve problems and analyze unit rates in the context of the problem.
Topic:
Days: 17 & 18
Discount: finding price with fractional part off
Eureka Lessons:
Walt:
We are learning to find discount using rational numbers.
Success Criteria:
- I can multiply a decimal by a rational number.
- I can convert a percent into a decimal.
- I can identify when to find markdown.
- I can subtract a markdown amount to find the total.
Topic:
Day: 21
Scale Drawings
Eureka Lessons: 20 & 22
Walt:
We are learning to create scale drawings.
Success Criteria:
- I can create a scale drawing of the top-view of a furnished room or building.
- I can use a given scale drawing and can create a scale drawing with a different scale.
- I can recognize that the scale drawing of a different scale is a scale drawing of the original scale drawing
- I can use a scale drawing of a different scale, to compute the scale factor for the original scale drawing.
Topic:
Day: 22
Scale Factors
Eureka Lessons: 17, 18, & 19
Walt:
We are learning to find scale factors
Success Criteria:
- I can recognize that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distances in the original picture.
- I can recognize the scale factor to be the constant of proportionality
- I can use a given scale drawing, to compute the lengths in the actual picture using the scale.
- I can identify the scale factor in order to make intuitive comparisons of size and then devise a strategy for efficiently finding actual lengths using the scale.
- I can identify a scale factor
- I can use a given scale drawing, and compute the area in the actual picture.
Topic:
Day: 23
Actual Size
Eureka Lesson: 16
Walt:
We are learning to find actual size.
Success Criteria:
- I can understand that a scale drawing is either the reduction or the enlargement of a two-dimensional picture
- I can compare the scale drawing picture with the original picture and determine if the scale drawing is a reduction or an enlargement.
- I can match points and figures in one picture with points and figures in the other picture.
Topic:
Days: 24 & 25
Scale Drawing/Factors/& Actual Size
Eureka Lessons: 16, 17, 18, 19, 20, & 22
Walt:
We are learning to create and compare scale drawings or scale figures
Success Criteria:
- I can understand that a scale drawing is either the reduction or the enlargement of a two-dimensional picture
- I can compare the scale drawing picture with the original picture and determine if the scale drawing is a reduction or an enlargement.
- I can match points and figures in one picture with points and figures in the other picture.
- I can recognize that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distances in the original picture.
- I can recognize the scale factor to be the constant of proportionality
- I can use a given a scale drawing, to compute the lengths in the actual picture using the scale.
- I can identify the scale factor in order to make intuitive comparisons of size and then devise a strategy for efficiently finding actual lengths using the scale.
- I can identify a scale factor
- I can use a given scale drawing, and compute the area in the actual picture.
- I can create a scale drawing of the top-view of a furnished room or building.
- I can use a given scale drawing and can create a scale drawing with a different scale.
- I can recognize that the scale drawing of a different scale is a scale drawing of the original scale drawing
- I can use a scale drawing of a different scale to compute the scale factor for the original scale drawing.
What to Teach
Topic 1: Order of Operations
- I can simplify an algebraic expression.
Topic 2: Like and Unlike Terms
- I can identify like terms.
- I can combine like terms.
Topic 3: Using Properties
- I know the distributive property.
- I can identify when to use the distributive property.
- I can use the distributive property to simplify an expression.
- I can distribute a whole number, fraction, and decimal.
Topic 4: Using Expressions
- I can write an algebraic expression to represent a diagram.
- I can write an algebraic expression to represent a scenario.
- I can identify equivalent algebraic expressions.
- I can generate equivalent algebraic expressions..
vocabularyassociative property
combining like terms communitive property differnce distrubutive property expression factor integer product quotient sum variable |
Unit ResourcesAssessmentPre Assessment
Real World Experience Post Assessment Formative Assessment Studnet Reflection and Goal Setting |
Learn the MathGeorgia 7th overview
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