NC Common Core Middle School Math Compacted Curriculum
Model 2 Unit Overview (4:3)
In this model the compacting begins in the sixth grade.
· 6th Grade: 6th grade standards and some of 7th grade
· 7th Grade: Remaining 7th grade standards and some of 8th grade
· 8th Grade: Remaining 8th grade standards and Common Core Math I Standards for
Assessment
The purpose of this document is to give an overview of one possible way the standards for Compacting Model 2 (4:3) could be grouped into units. The units are not in a specific order nor are they numbered. The LEA should decide order and number of days per unit. Please note that some standards have been intentionally placed in multiple units.
The Standards for Mathematical Practice should be infused throughout all units:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning
1
Compacting Model 2 (4:3)
DRAFT
6th Grade /Unit Name / Clusters / Standards /
Understanding Ratios and Rates / Understand ratio concepts and use ratio reasoning to solve problems. / 6.RP.1
6.RP.2
6.RP.3a, b, d
Represent and analyze quantitative relationship between dependent and independent variables. / 6.EE.9
Analyze proportional relationships and use them to solve real-world and mathematical problems. / 7.RP.1
Reasoning Proportionally with Percents / Understand ratio concepts and use ratio reasoning to solve problems. / 6.RP.3c
Multi-digit Computation and Finding Common Factors / Compute fluently with multi-digit numbers and find common factors and multiples. / 6.NS.2
6.NS.3
6.NS.4
Apply and extend previous understandings of arithmetic to algebraic expressions. / 6.EE.3
Dividing Fractions / Apply and extend previous understandings of multiplication and division to divide fractions by fractions. / 6.NS.1
Extending the Number System / Apply and extend previous understandings of numbers to the system of rational numbers. / 6.NS.5
6.NS.6a, c
6.NS.7a, b, c, d
Relationships in the Coordinate Plane / Apply and extend previous understandings of numbers to the system of rational numbers. / 6.NS.6b, c
6.NS.8
Solve real-world and mathematical problems involving area, surface area and volume. / 6.G.3
Positive and Negative Rational Numbers / Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. / 7.NS.1a, b, c, d
7.NS.2a, b, c, d
7.NS.3
Algebraic Expressions / Apply and extend previous understandings of arithmetic to algebraic expressions. / 6.EE.1
6.EE.2a, b, c
6.EE.3
6.EE.4
Equations and Inequalities / Reason about and solve one-variable equations and inequalities. / 6.EE.5
6.EE.6
6.EE.7
6.EE.8
Problem Solving with Area in 2-Dimensional Shapes / Solve real-world and mathematical problems involving area, surface area, and volume. / 6.G.1
6.G.3
Draw construct, and describe geometrical figures and describe the relationships between them. / 7.G.2
7.G.3
Problem Solving with Volume and Surface Area / Solve real-world and mathematical problems involving area, surface area, and volume. / 6.G.2
6.G.4
Statistical Investigations and Sampling / Develop understanding of statistical variability. / 6.SP.1
6.SP.2
6.SP.3
Use random sampling to draw inferences about a population. / 7.SP.1
7.SP.2
Analyzing Data / Summarize and describe distributions. / 6.SP.4
6.SP.5a, b, c, d
Draw informal comparative inferences about two populations. / 7.SP.3
7.SP.4
7th Grade /
Unit Name / Clusters / Standards /
Proportional Reasoning and Relationships / Analyze proportional relationships and use them to solve real-world and mathematical problems. / 7.RP.2a, b, c, d
Draw, construct, and describe geometrical figures and describe the relationships between them. / 7.G.1
Understand the connections between proportional relationships, lines, and linear equations. / 8.EE.5
8.EE.6
Proportional Reasoning with Percents / Analyze proportional relationships and use them to solve real-world and mathematical problems. / 7.RP.3
Solve real-life and mathematical problems using numerical and algebraic expressions and equations. / 7.EE.3
Solving Inequalities / Use properties of operations to generate equivalent expressions. / 7.EE.1
7.EE.2
Solve real-life and mathematical problems using numerical and algebraic expressions and equations. / 7.EE.4b
Solving Equations / Use properties of operations to generate equivalent expressions. / 7.EE.1
7.EE2
Solve real-life and mathematical problems using numerical and algebraic expressions and equations. / 7.EE.3
7.EE.4a
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. / 7.G.5
Analyze and solve linear equations and pairs of simultaneous linear equations. / 8.EE.7a, b
Area and Volume / Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. / 7.G.4
7.G.6
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. / 8.G.9
Work with radicals and integer exponents. / 8.EE.2
Pythagorean Theorem / Know that there are numbers that are not rational, and approximate them by rational numbers. / 8.NS.1
8.NS.2
Understand and apply the Pythagorean Theorem. / 8.G.6
8.G.7
8.G.8
Work with radicals and integer exponents. / 8.EE.2
Use coordinates to prove simple geometric theorems algebraically. / G-GPE.6
G-GPE.7
Probability of Simple Events / Investigate chance processes and develop, use, and evaluate probability models. / 7.SP.5
7.SP.6
7.SP.7a, b
Probability of Compound Events / Investigate chance processes and develop, use, and evaluate probability models. / 7.SP.8a, b, c
Relationships in Geometric Figures / Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. / 7.G.5
Understand congruence and similarity using physical models, transparencies, or geometry software. / 8.G.5
Analyze and solve linear equations and pairs of simultaneous linear equations. / 8.EE.7b
Understanding Similarity through Transformations / Draw, construct, and describe geometrical figures and describe the relationships between them. / 7.G.1
7.G.2
Understand congruence and similarity using physical models, transparencies, or geometry software. / 8.G.3
8.G.4
8.G.5
Understanding Congruence through Transformations / Draw, construct, and describe geometrical figures and describe the relationships between them. / 7.G.2
Understand congruence and similarity using physical models, transparencies, or geometry software. / 8.G.1a, b, c
8.G.2
8.G.3
8th Grade /
Unit Name / Clusters / Standards /
Working with Exponents / Work with radicals and integer exponents. / 8.EE.1
8.EE.3
8.EE.4
Extend the properties of exponents to rational exponents. / N-RN.1
N-RN.2
One-Variable Equations and Inequalities / Create equations that describe numbers or relationships. / A-CED.1
A-CED.4
Understand solving equations as a process of reasoning and explain the reasoning. / A-REI .1
Solve equations and inequalities in one variable. / A-REI.3
Systems of Equations and Inequalities / Analyze and solve linear equations and pairs of simultaneous linear equations. / 8.EE.8a, b, c
Create equations that describe numbers or relationships / A-CED.3
Solve systems of equations. / A-REI.5
A-REI.6
Represent and solve equations and inequalities graphically. / A-REI.10
A-REI.11
A-REI.12
Area and Volume / Explain volume formulas and use them to solve problems. / G-GMD.1
Reason quantitatively and use units to solve problems. / G-GMD.3
Function Introduction / Define, evaluate, and compare functions. / 8.F.1
Use functions to model relationships between quantities. / 8.F.5
Understand the concept of a function and use function notation. / F-IF.1
F-IF.2
F-IF.3
Linear Functions / Define, evaluate, and compare functions. / 8.F.2
8.F.3
Use functions to model relationships between quantities. / 8.F.4
Interpret the structure of expressions.
/ A-SSE.1a, bCreate equations that describe numbers or relationships. / A-CED.2
Represent and solve equations and inequalities graphically. / A-REI.10
Build a function that models a relationship between two quantities. / F-BF.1a, b
F-BF.2
Build new functions from existing functions. / F-BF.3
Interpret functions that arise in applications in terms of the context. / F-IF.4
F-IF.5
F-IF.6
Analyze functions using different representations. / F-IF.7
F-IF.9
Construct and compare linear and exponential models and solve problems. / F-LE.1a, b
F-LE.2
Interpret expressions for functions in terms of the situation they model. / F-LE.5
Linear Relationship in Geometric Figures / Define, evaluate, and compare functions. / 8.F.3
Use functions to model relationships between quantities. / 8.F.4
Experiment with transformations in the plane. / G-CO.1
Use coordinates to prove simple geometric theorems algebraically. / G-GPE.4
G-GPE.5
Exponential Functions / Define, evaluate, and compare functions. / 8.F.2
Interpret the structure of expressions.
/ A-SSE.1a, bCreate equations that describe numbers or relationships. / A-CED.2
Represent and solve equations and inequalities graphically. / A-REI.10
Build a function that models a relationship between two quantities. / F-BF.1a, b
F-BF.2
Build new functions from existing functions. / F-BF.3
Interpret functions that arise in applications in terms of the context. / F-IF.4
F-IF.5
F-IF.6
Analyze functions using different representations. / F- IF.7e
F-IF.8a
F-IF.9
Construct and compare linear and exponential models and solve problems. / F-LE.1a, c
F-LE.2
F-LE.3
Interpret expressions for functions in terms of the situation they model. / F-LE.5
Working with Polynomials / Perform arithmetic operations on polynomials. / A-APR.1
Interpret the structure of expressions. / A-SSE.2
Quadratic Functions / Define, evaluate, and compare functions. / 8.F.2
Interpret the structure of expressions.
/ A-SSE.1a, bWrite expressions in equivalent forms to solve problems. / A-SSE.3a
Create equations that describe numbers or relationships. / A-CED.2
Construct and compare linear and exponential models and solve problems. / F-LE.3
Interpret functions that arise in applications in terms of the context. / F-IF.4
Analyze functions using different representations. / F-IF.7a
F-IF.8b
F-IF.9
Descriptive Statistics / Summarize, represent, and interpret data on a single count or measurement variable. / S-ID.1
S-ID.2
S-ID.3
Bivariate Data / Investigate patterns of association in bivariate data. / 8.SP.1
8.SP.2
8.SP.3
8.SP.4
Summarize, represent, and interpret data on two categorical and quantitative variables. / S-ID.5
S-ID.6a, b, c
Interpret linear models. / S-ID.7
S-ID.8
S-ID.9
NC Common Core Middle School Math Compacted Curriculum
6th Grade – Model 2 (4:3)
Understanding Ratios and RatesClusters / Common Core State Standards
Understand ratio concepts and use ratio reasoning to solve problems. / 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1
1 Expectations for unit rates in this grade are limited to non-complex fractions.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Represent and analyze quantitative relationships between dependent and independent variables. / 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Analyze proportional relationships and use them to solve real-world and mathematical problems. / 7.RP.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 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
Reasoning Proportionally with Percents
Clusters / Common Core State Standards
Understand ratio concepts and use ratio reasoning to solve problems. / 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Multi-digit Computation and Finding Common Factors
Clusters / Common Core State Standards
Compute fluently with multi-digit numbers and find common factors and multiples. / 6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Apply and extend previous understandings of arithmetic to algebraic expressions. / 6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Dividing Fractions
Clusters / Common Core State Standards