Math is…

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Goals for this Mini Unit:

Cultivate Grit and Perseverance

Notice, Describe and Generalize Patterns

Communicate

Create community

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Unit 0) Becoming a Mathematician

Big Ideas

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Unit 1) Scale Copies and Scale

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To be successful, I need to be able to:

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• Identify and find equivalent ratios and fractions
• Multiply with fractions
• Model fractions
• Create rate tables
• Calculate perimeter
• Calculate areas of squares, rectangles, and triangles

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Guiding Question:

How are shrinky dinks connected to scale?

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Outcomes for this Unit:

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Outcome 1: I can use scale factor to solve problems with scaled copies.^7.G.1

I can identify and define properties of scaled copies.^7.G.1

I can use a scale factor to compute lengths of a scaled copy.^7.G.1

I can find the scale factor between two scaled copies.^7.G.1

I can use scale factor to solve problems involving area.^7.G.1

HP: I can describe the relationship between the scale factors of two scaled copies.

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Outcome 2: I can use scale to solve problems with scale drawings.^7.G.1

I can identify scale when I know the corresponding scale dimensions and actual dimensions for a drawing.^7.G.1

I can apply scale to compute actual dimensions and scale drawing dimensions.^7.G.1

I can reproduce a scale drawing at a different scale from a given scale.^7.G.1

I can apply scale when solving problems involving area.^7.G.1

HP: I can describe how scale affects area differently than length.^7.G.1

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Vocabulary

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Unit 2) Proportional Relationships

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To be successful, I need to be able to:

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• Create rate tables
• Plot points in a coordinate grid
• Understand the relationship between multiplication and division

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Outcomes for this Unit:

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Outcome 3 : I can recognize and create proportional relationships in tables, graphs, and equations. ^7.RP.2

• I can decide if a proportional relationship exists between quantities.^7.RP.2
• I can calculate the unit rate (constant of proportionality) and interpret it in context. ^7.RP.2
• I can create a table to represent a proportional relationship.^7.RP.2
• I can write an equation in the form y=kx for a proportional relationship. ^7.RP
• I can create a graph to represent a proportional relationship.^7.RP.2

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Outcome 4 : I can use proportional relationships to solve problems. ^7.RP.2

• I can calculate the unit rate (constant of proportionality) that is most useful based on the context.^7.RP.2
• I can solve for unknowns in a proportional relationship using the unit rate (constant of proportionality). ^7.RP.2
• I can use tables, graphs, and equations to find missing values in proportional relationships. ^7.RP.2
• I can solve proportional relationships problems given in a verbal description. ^7.RP.2

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Outcome 5: I can use a graphical representation of a proportional relationship in context. ^7.RP.2

• I can explain the connection between a point on a graph (x, y) and the situation. ^7.RP.2
• I can explain the meaning of (0,0) in a proportional relationship. ^7.RP.2
• I can connect the meaning of the y coordinate in the ordered pair (1,r) to the unit rate. ^7.RP.2

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Outcome 6: I can compare two proportional relationships in context. ^7.RP.2

• I can explain the connections between different representations (table, graph, equation, words) of the same proportional relationship. ^7.RP.2
• I can compare two proportional relationships given in the same representation.^7.RP.2
• I can compare two proportional relationships given in different representations.^7.RP.2
• HP I can compare more than two proportional relationships with different representations

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Vocabulary

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Guiding Question:

What does it mean to be proportional?

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Unit 3) Rational Numbers

To be successful, I need to be able to:

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• Understand absolute value
• Add and subtract with numbers between 20 and 20
• All 4 operations with fractions and decimals

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Genetics

Guiding Question:

Outcomes for this Unit:

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1. Outcome 7: I can apply and extend previous understandings of division to positive rational numbers. ^7.NS.2

I can use the standard algorithm to divide fractions. ^7.NS.2

I can divide fractions and write the quotient (solution) in an appropriate form based on the realworld situation.^7.NS.2

I can describe the meaning of the quotient in a realworld situation.^7.NS.2

I can convert a fraction to a decimal using long division. ^7.NS.2

1. Outcome 8: I can solve realworld and mathematical problems with rational numbers. ^{7.NS.3, 7.NS.1}

I can add and subtract integers. ^7.NS.1

I can add and subtract rational numbers. ^7.NS.1

I can multiply and divide integers. ^7.NS.2

I can multiply and divide rational numbers.^7.NS.2

I can apply properties of the four operations to solve multistep realworld problems and mathematical problems. ^7.NS.3

Outcome 9: I can compute unit rates to solve realworld and mathematical problems. ^{7.RP. 1}

I can compute unit rates involving fractions. ^7.RP.1

I can rewrite any rate as a unit rate.^7.RP.1

I can find and describe the appropriate unit rate based on context.^7.RP.1

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Vocabulary

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Unit 4) Equations, Expressions and Inequalities

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To be successful, I need to be able to:

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• Add, subtract, multiply and divide with negative numbers
• Understand the relationship between multiplication and division
• Understand the relationship between addition and subtraction
• Use the order of operations
• Understand and use the symbols: < and >

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x + x + x = 1x + 1x + 1x = (1 + 1 + 1)x = 3x

Guiding Question: �

Outcomes for this Unit:

Outcome 17: I can solve realworld and mathematical problems using numerical and algebraic equations. ^7.EE.4

I can construct equations to solve realworld problems. ^7.EE.4

I can solve multistep equations with the variable on one side. ^7.EE.4

I can interpret the solution to an equation in context. ^7.EE.4

Outcome 18: I can solve realworld and mathematical problems using numerical and algebraic inequalities. ^7.EE.4

I can construct inequalities to solve realworld problems.

^7.EE.4

I can solve multistep inequalities with the variable on one side. ^7.EE.4

I can graph the solution set of an inequality. ^7.EE.4

I can interpret the solution set of an inequality in context. ^7.EE.4

Outcome 19: I can solve multistep realworld and mathematical problems posed with rational numbers in algebraic expressions. ^7.EE.3

I can apply properties of operations to calculate with positive and negative numbers in any form. ^7.EE.3

I can convert between different forms of a number and equivalent forms of the expression to solve problems. ^7.EE.3

Outcome 20: I can apply properties of operations to create equivalent expressions. ^{7.EE.1, 7.EE.2}

I can expand linear expressions with rational coefficients using the distributive property. ^7.EE.1

I can add, subtract, and expand linear expressions with rational coefficients.^7.EE.1

I can factor linear expressions with an integer GCF. ^7.EE.1

I can create equivalent expressions that can reveal realworld and mathematical relationships. ^7.EE.2

I can interpret the meaning of the parts of expressions in context. ^7.EE.2

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Vocabulary

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Unit 5) Circles and Composite Shapes

To be successful, I need to be able to:

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• Understand and be able to calculate area of quadrilaterals and triangles
• Understand and be able to calculate perimeter

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Guiding Question: �

Outcomes for this Unit:

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Outcome 11: I can solve real-world and mathematical problems involving area and circumference of a circle. ^7.G.4

I can apply the circumference formula to solve problems to find the circumference, radius or diameter.^7.G.4

I can apply the area formula of circles to solve problems to find the area.^7.G.4

I can solve real-world contextual problems that require circle formulas.^7.G.4

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HP: I can determine the radius or the diameter of a circle given the area. (Limit to radius to whole numbers)

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Vocabulary

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Cells and Microbiology

Guiding Question:

Outcomes for this Unit:

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Outcome 10: I can use proportional reasoning to solve ratio and percent problems ^{7.RP.3, 7.EE.2}

I can calculate the original amount or the new amount in realworld problems. ^7.RP.3

I can calculate the percent of change in realworld problems. ^7.RP.3

I can solve multistep percent problems about realworld situations. ^{7.RP.3, 7.EE.2}

I can convert both units of a rate to solve realworld problems.^7.RP.3

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Vocabulary

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Unit 7) Probability

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To be successful, I need to be able to:

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• Understand the relationship between fraction, decimal and percent
• Multiply with fractions and decimals
• Understand that a number can be written as a fraction, decimal and percent

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Guiding Question:

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Outcomes for this Unit:

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Outcome 12: I can use my understanding of probability models to predict the probability of simple events (or likelihood of a simple event occurring)?.^{7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8}

I can use the probability of an event to determine and describe the likelihood of the event happening.^7.SP.5

I can use a sample space to determine the probability of an event.^7.SP.7

I can use the results of a repeated experiment to estimate the probability of a simple event.^7.SP.6

I can determine and explain if experimental results are in agreement with the theoretical probability. ^7.SP.7

Outcome 13: I can use my understanding of probability models to predict the probability of compound events.^7.SP.8

I can identify and interpret an organized list, table, or treediagram that represents the sample space of a compound event.^7.SP.8

I can use a sample space to determine the probability of a compound event with or without replacement.^7.SP.8

I can predict the frequency of an outcome based on theoretical or experimental probability of a compound event.^7.SP.8

I can identify a simulation that can be used to estimate the probability of a realworld compound event. ^7.SP.8

I can use experimental results from a simulation to estimate the probability of a compound event. ^{7.SP.8, 7.SP.6}

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Vocabulary

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Unit 8) Sampling

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To be successful, I need to be able to:

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• Understand the relationship between fraction, decimal and percent
• Multiply with fractions and decimals
• Solve problems using percentages
• Be familiar with mean, median, mode and range

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Guiding Question:

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Outcomes for this Unit:

Outcome 14: I can calculate measures of center and measures of variability to draw inferences about a set of data. ^7.SP.3

I can calculate and interpret the mean (measure of center) of a set of data. ^7.SP.3

I can calculate and interpret the median (measure of center) of a set of data. ^7.SP.3

I can calculate and interpret the MAD (measure of variability) of a set of data. ^7.SP.3

I can calculate and interpret the range (measure of variability) of a set of data. ^7.SP.3

I can calculate and interpret the IQR (measure of variability) of a set of data. ^7.SP.3

Outcome 15: I can use random sampling to draw inferences about a population. ^{7.SP. 1, 7.SP.2}

I can determine a sample that is representative of a population interest.^7.SP.1

I can describe ways to get a representative random sample for a population of interest. ^7.SP.2

I can use sample statistics (means, medians, proportions) from a representative sample to make valid inferences about a population.^{7.SP.1, 7.SP.2}

I can determine a proportion that represents a given characteristic of interest for sample data.^7.SP.1

I can make estimates about a population using proportions from sample data.^7.SP.1

Outcome 16: I can use sample statistics to make inferences about a population of interest. ^{7.SP.4, 7.SP.2}

I can determine which measure of center and variability are appropriate to analyze data based on the shape and distribution of the data set.^7.SP.4

I can find the difference between measures of center to make inferences about two populations.^7.SP.4

I can find the difference between measures of variability to make inferences about two populations.^7.SP.4

I can use data from multiple random samples to estimate a characteristic of interest about a population.^7.SP.2

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Vocabulary

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Unit 9) Topics in Geometry

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To be successful, I need to be able to:

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• Find the area of rectangles, squares and triangles
• Estimate angle measurements
• Solve 2 step equations

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Angle Relationships

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Guiding Question:

Standards for this Unit:

Outcome 21: I can use facts about angle relationships to solve multistep problems. ^7.G.5

I can identify supplementary, complementary, vertical, and adjacent angles.^7.G.5

I can use angle relationships supplementary, complementary, vertical, and adjacent angles to find missing angle values. ^7.G.5

I can write and solve equations for an unknown angle in a figure. ^7.G.5

Outcome 22: I understand the characteristics of sides and angles that create a unique triangle, more than one triangle, or no triangle. ^7.G.2

I can determine if a triangle can be formed given three side lengths or three angle measures. ^7.G.2

I can determine if a triangle formed is unique.^7.G.2

I can determine possible side lengths that will form a triangle when given the measure of two sides. ^7.G.2

I can determine possible angle measures that will form a triangle when given the measure of two angles . ^7.G.2

Outcome 23: I can solve realworld and mathematical problems involving area, perimeter, volume, and surface area. ^7.G.6

I can find the perimeter of twodimensional objects composed of triangles, quadrilaterals, and polygons. ^7.G.6

I can find the area of twodimensional objects composed of triangles, quadrilaterals, and polygons. ^7.G.6

I can find the volume of pyramids, prisms, or threedimensional objects composed of cubes, pyramids, and right prisms.^7.G.6

I can find the surface area of pyramids, prisms, or threedimensional objects composed of cubes, pyramids, and right prisms.^7.G.6

I can find missing dimensions given the area, perimeter, volume or surface area of an object.^7.G.6

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Vocabulary

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Skills for Success

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Skill Set 1: Ordering numbers

• I can compare positive and negative numbers
• I can make generalizations about how a negative affects adding and subtracting unknown numbers

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Skill Set 2: Operations with Rational Numbers (no calculator)

• I can change a mixed number to an improper fraction
• I can simplify fractions
• I can find a common denominator
• I can add fractions
• I can subtract fractions
• I can identify place value
• I can add decimals
• I can subtract decimals
• I can round numbers
• I can multiply two fractions
• I can divide two fractions
• I can multiply decimals
• I can divide decimals
• I can multiply a fraction and a whole number
• I can divide a fraction and a whole number
• I can add and subtract with negative whole numbers
• I can add and subtract with negative fractions and decimals
• I can multiply and divide with negative whole numbers
• I can multiply and divide with negative fractions and decimals

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Skill Set 3: Finding Unit Rate

• I can find a unit rate from a word problem
• I can find a unit rate with whole numbers
• I can find a unit rate with fractions and decimals
• I can find a unit rate from a table
• I can find a unit rate from a graph

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Skill Set 4: Reading a Graph

• I can identify a point on a graph
• I can write what the point represents in context
• I can plot a point on a graph
• I can interpret a point on a graph
• I can make a table to represent a graph

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Skill Set 5: Distributive Property

• I can distribute with positive numbers
• I can distribute with negative numbers
• I can distribute with fractions

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Skill Set 6: Interpreting and Evaluating Equations and Expressions

• I can evaluate an equation with points from a graph
• I can evaluate an expression
• I can check values to see if they are solutions to an equation
• I can solve one-step equations
• I can write an equation to represent a word problem
• I can write an equation from a graph

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Skill Set 7: Solving one-step Equations and Inequalities

• I can solve one-step equations
• I can solve one-step inequalities

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Skill Set 8: Topics in Geometry

• I can identify an angle given the name

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Skill Set 9: Topics in Geometry

• I can identify an angle given the name
• I can name an angle
• I can find a missing angle measurement
• I can find the area of a rectangle
• I can find the area of a triangle
• I can find the perimeter of simple shapes

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7th Grade Outcomes

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Outcome 1: I can use scale factor to solve problems with scaled copies.^7.G.1

• I can identify and define properties of scaled copies.^7.G.1
• I can use a scale factor to compute lengths of a scaled copy.^7.G.1
• I can find the scale factor between two scaled copies.^7.G.1
• I can use scale factor to solve problems involving area.^7.G.1
• HP: I can describe the relationship between the scale factors of two scaled copies.

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Outcome 2: I can use scale to solve problems with scale drawings.^7.G.1

• I can identify scale when I know the corresponding scale dimensions and actual dimensions for a drawing.^7.G.1
• I can apply scale to compute actual dimensions and scale drawing dimensions.^7.G.1
• I can reproduce a scale drawing at a different scale from a given scale.^7.G.1
• I can apply scale when solving problems involving area.^7.G.1
• I can describe how scale affects area differently than length.^7.G.1

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Outcome 3 : I can recognize and create proportional relationships in tables, graphs, and equations. ^7.RP.2

• I can decide if a proportional relationship exists between quantities.^7.RP.2
• I can calculate the unit rate (constant of proportionality) and interpret it in context. ^7.RP.2
• I can create a table to represent a proportional relationship.^7.RP.2
• I can write an equation in the form y=kx for a proportional relationship. ^7.RP
• I can create a graph to represent a proportional relationship.^7.RP.2

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Outcome 4 : I can use proportional relationships to solve problems. ^7.RP.2

• I can calculate the unit rate (constant of proportionality) that is most useful based on the context.^7.RP.2
• I can solve for unknowns in a proportional relationship using the unit rate (constant of proportionality). ^7.RP.2
• I can use tables, graphs, and equations to find missing values in proportional relationships. ^7.RP.2
• I can solve proportional relationships problems given in a verbal description. ^7.RP.2

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Outcome 5: I can use a graphical representation of a proportional relationship in context. ^7.RP.2

• I can explain the connection between a point on a graph (x, y) and the situation. ^7.RP.2
• I can explain the meaning of (0,0) in a proportional relationship. ^7.RP.2
• I can connect the meaning of the y coordinate in the ordered pair (1,r) to the unit rate. ^7.RP.2

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Outcome 6: I can compare two proportional relationships in context. ^7.RP.2

• I can explain the connections between different representations (table, graph, equation, words) of the same proportional relationship. ^7.RP.2
• I can compare two proportional relationships given in the same representation.^7.RP.2
• I can compare two proportional relationships given in different representations.^7.RP.2
• HP I can compare more than two proportional relationships with different representations

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• Outcome 7: I can apply and extend previous understandings of division to positive rational numbers. ^7.NS.2
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• I can use the standard algorithm to divide fractions. ^7.NS.2
• I can divide fractions and write the quotient (solution) in an appropriate form based on the real-world situation.^7.NS.2
• I can describe the meaning of the quotient in a real-world situation.^7.NS.2
• I can convert a fraction to a decimal using long division. ^7.NS.2
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• Outcome 8: I can solve real-world and mathematical problems with rational numbers. ^{7.NS.3, 7.NS.1}
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• I can add and subtract integers. ^7.NS.1
• I can add and subtract rational numbers. ^7.NS.1
• I can multiply and divide integers. ^7.NS.2
• I can multiply and divide rational numbers.^7.NS.2
• I can apply properties of the four operations to solve multi-step real-world problems and mathematical problems. ^7.NS.3

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Outcome 9: I can compute unit rates to solve real-world and mathematical problems. ^{7.RP. 1}

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• I can compute unit rates involving fractions. ^7.RP.1
• I can rewrite any rate as a unit rate.^7.RP.1
• I can find and describe the appropriate unit rate based on context.^7.RP.1

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Outcome 10: I can use proportional reasoning to solve ratio and percent problems ^{7.RP.3, 7.EE.2}

• I can calculate the original amount or the new amount in real-world problems. ^7.RP.3
• I can calculate the percent of change in real-world problems. ^7.RP.3
• I can solve multi-step percent problems about real-world situations. ^{7.RP.3, 7.EE.2}
• I can convert both units of a rate to solve real-world problems.^7.RP.3

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• Outcome 11: I can solve real-world and mathematical problems involving area and circumference of a circle. ^7.G.4
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• I can apply the circumference formula to solve problems to find the circumference, radius or diameter.^7.G.4
• I can apply the area formula of circles to solve problems to find the area.^7.G.4
• I can solve real-world contextual problems that require circle formulas.^7.G.4
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• HP: I can determine the radius or the diameter of a circle given the area. (Limit to radius to whole numbers)

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Outcome 12: I can use my understanding of probability models to predict the probability of simple events (or likelihood of a simple event occurring)?.^{7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8}

• I can use the probability of an event to determine and describe the likelihood of the event happening.^7.SP.5
• I can use a sample space to determine the probability of an event.^7.SP.7
• I can use the results of a repeated experiment to estimate the probability of a simple event.^7.SP.6
• I can determine and explain if experimental results are in agreement with the theoretical probability. ^7.SP.7

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Outcome 13: I can use my understanding of probability models to predict the probability of compound events.^7.SP.8

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• I can identify and interpret an organized list, table, or tree-diagram that represents the sample space of a compound event.^7.SP.8
• I can use a sample space to determine the probability of a compound event with or without replacement.^7.SP.8
• I can predict the frequency of an outcome based on theoretical or experimental probability of a compound event.^7.SP.8
• I can identify a simulation that can be used to estimate the probability of a real-world compound event. ^7.SP.8
• I can use experimental results from a simulation to estimate the probability of a compound event. ^{7.SP.8, 7.SP.6}

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Outcome 14: I can calculate measures of center and measures of variability to draw inferences about a set of data. ^7.SP.3

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• I can calculate and interpret the mean (measure of center) of a set of data. ^7.SP.3
• I can calculate and interpret the median (measure of center) of a set of data. ^7.SP.3
• I can calculate and interpret the MAD (measure of variability) of a set of data. ^7.SP.3
• I can calculate and interpret the range (measure of variability) of a set of data. ^7.SP.3
• I can calculate and interpret the IQR (measure of variability) of a set of data. ^7.SP.3
• I can use the 5-Number Summary to create a boxplot
• I can interpret box plots
• I can compare different box plots

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Outcome 15: I can use random sampling to draw inferences about a population. ^{7.SP. 1, 7.SP.2}

• I can determine a sample that is representative of a population interest.^7.SP.1
• I can describe ways to get a representative random sample for a population of interest. ^7.SP.2
• I can use sample statistics (means, medians, proportions) from a representative sample to make valid inferences about a population.^{7.SP.1, 7.SP.2}
• I can determine a proportion that represents a given characteristic of interest for sample data.^7.SP.1
• I can make estimates about a population using proportions from sample data.^7.SP.1

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Outcome 16: I can use sample statistics to make inferences about a population of interest. ^{7.SP.4, 7.SP.2}

• I can determine which measure of center and variability are appropriate to analyze data based on the shape and distribution of the data set.^7.SP.4
• I can find the difference between measures of center to make inferences about two populations.^7.SP.4
• I can find the difference between measures of variability to make inferences about two populations.^7.SP.4
• I can use data from multiple random samples to estimate a characteristic of interest about a population.^7.SP.2

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Outcome 17: I can solve real-world and mathematical problems using numerical and algebraic equations. ^7.EE.4

• I can construct equations to solve real-world problems. ^7.EE.4
• I can solve multistep equations with the variable on one side. ^7.EE.4
• I can interpret the solution to an equation in context. ^7.EE.4

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Outcome 18: I can solve real-world and mathematical problems using numerical and algebraic inequalities. ^7.EE.4

• I can construct inequalities to solve real-world problems.
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• I can solve multi-step inequalities with the variable on one side. ^7.EE.4
• I can graph the solution set of an inequality. ^7.EE.4
• I can interpret the solution set of an inequality in context. ^7.EE.4

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Outcome 19: I can solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions. ^7.EE.3

• I can apply properties of operations to calculate with positive and negative numbers in any form. ^7.EE.3
• I can convert between different forms of a number and equivalent forms of the expression to solve problems. ^7.EE.3

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Outcome 20: I can apply properties of operations to create equivalent expressions. ^{7.EE.1, 7.EE.2}

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• I can expand linear expressions with rational coefficients using the distributive property. ^7.EE.1
• I can add, subtract, and expand linear expressions with rational coefficients.^7.EE.1
• I can factor linear expressions with an integer GCF. ^7.EE.1
• I can create equivalent expressions that can reveal real-world and mathematical relationships. ^7.EE.2
• I can interpret the meaning of the parts of expressions in context. ^7.EE.2

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Outcome 21: I can use facts about angle relationships to solve multistep problems. ^7.G.5

• I can identify supplementary, complementary, vertical, and adjacent angles.^7.G.5
• I can use angle relationships supplementary, complementary, vertical, and adjacent angles to find missing angle values. ^7.G.5
• I can write and solve equations for an unknown angle in a figure. ^7.G.5

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Outcome 22: I understand the characteristics of sides and angles that create a unique triangle, more than one triangle, or no triangle. ^7.G.2

• I can determine if a triangle can be formed given three side lengths or three angle measures. ^7.G.2
• I can determine if a triangle formed is unique.^7.G.2
• I can determine possible side lengths that will form a triangle when given the measure of two sides. ^7.G.2
• I can determine possible angle measures that will form a triangle when given the measure of two angles . ^7.G.2

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Outcome 23: I can solve real-world and mathematical problems involving area, perimeter, volume, and surface area. ^7.G.6

• I can find the perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons. ^7.G.6
• I can find the area of two-dimensional objects composed of triangles, quadrilaterals, and polygons. ^7.G.6
• I can find the volume of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.^7.G.6
• I can find the surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.^7.G.6
• I can find missing dimensions given the area, perimeter, volume or surface area of an object.^7.G.6

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