Middle School Math Series: Course 1 - Carnegie Learning
Chapter
Lesson Title
Collection Connections 1.1 Factors and Multiples
Key Math Objective
CCSS
Physical Models of Factors and Multiples
Divisibility Rules! Investigating Divisibility Rules
Middle School Math Series: Course 1
• Determine factor pairs using arrays and area models. • Classify numbers using Venn diagrams.
4.OA.4 6.NS.4
• Area model • Set • Venn diagram
4.OA.4
• Prime numbers • Composite numbers • Multiplicative identity
4.OA.4
• Divisibility rules
• Formulate divisibility rules based on patterns seen in factors. • Use factors to help you develop divisibility rules.
Technology
Talk the Talk
4.OA.4
• Distinguish between prime and composite numbers. Investigating Prime and Composite • Identify and use the multiplicative identity. Numbers
1.4
• List factor pairs of numbers. • Relate factors, multiples, and divisibility.
Sifting for Prime Numbers 1.3
Key Terms
• Array • Factor pair • Factor • Commutative Property of Multiplication • Distinct factors • Perfect square • Multiple • Divisible
Models and More 1.2
Peer Analysis
Factors, Multiples, Primes, and This chapter reviews factors, multiples, primes, composites, and divisibility rules. Composites
Worked Examples
1
Modules
Middle School Math Series: Course 1
1
The Think Tank 2.1
Prime Factorization and Factor Trees
CCSS
Key Terms
• Determine the prime factorization of a number. • Understand the usefulness of prime factors. • Recognize that each whole number has exactly one prime factorization.
6.NS.4 6.EE.1
• Prime factorization • Associative Property of Multiplication • Factor tree • Power • Base • Exponent • Fundamental Theorem of Arithmetic
• Determine the least common multiple of two numbers.
6.NS.4
• Common multiple • Least common multiple (LCM)
• Determine the greatest common factor of two or more numbers.
6.NS.4
• Common factor • Greatest common factor (GCF) • Relatively prime numbers
• Recognize how to use common factors and common multiples to solve problems.
6.NS.4
N/A
Key Math Objective
Technology
Lesson Title
Talk the Talk
Chapter
This chapter demonstrates how least common multiples and greatest common factors are used to solve real-world problems.
Peer Analysis
Prime Factorization and the Fundamental Theorem of Arithmetic
Worked Examples
2
Modules
Middle School Math Series: Course 1
Together Again 2.2
Investigating Multiples and Least Common Multiples
Happenings at Harvest Day 2.3
Investigating Factors and Greatest Common Factors
Common Factors or Common Multiples? 2.4
Using GCF and LCM to Solve Problems
Middle School Math Series: Course 1
2
Flags and Fractions 3.1 Modeling Parts of a Whole
You Mean Three Can Be One? 3.2 Fractional Representations
Rocket Strips 3.3
Dividing a Whole into Fractional Parts
Getting Closer 3.4 Benchmark Fractions
Middle School Math Series: Course 1
• Determine equal parts of a whole. • Draw different representations of equal parts.
4.NF.1 6.NS.1
• Fraction • Numerator • Denominator
• Create different fractional representations using pattern blocks. • Write fractional statements for different representations given the whole. • Determine fractional representations given the whole. • Determine fractional representations given parts of the whole.
5.NF.1 6.NS.1
N/A
• Create equal parts of a whole. • Determine if fractions are equal. • Graph fractions on a number line.
4.NF.1 6.NS.1
• Unit fraction • Equivalent fractions
• Estimate fractions by using benchmark fractions. • Order fractions in ascending order. • Compare fractions.
4.NF.2 6.NS.1
• Benchmark fractions • Inequality
Key Math Objective
CCSS
Technology
Lesson Title
This chapter begins with a review of how to model parts of a whole and various fractional representations. Students create their own fraction strips and use them to model operations with fractions. The focus then shifts to the relationship between multiplication and division to understand the procedures for dividing fractions. An emphasis is placed on estimation skills throughout the chapter.
Talk the Talk
Chapter
Peer Analysis
Fractions
Worked Examples
3
Modules
Middle School Math Series: Course 1
Key Terms
3
Middle School Math Series: Course 1
What's My Cut? 3.5 Equivalent Fractions
• Determine equal portions of a whole. • Determine equivalent fractions. • Calculate equivalent fractions using a form of 1. • Simplify fractions. • Order fractions.
3.7
3.8
• Simplest form • Multiplicative Identity Property
• Write number sentences to represent 1. • Create models to represent addition and subtraction of fractions. Adding and Subtracting Fractions • Add and subtract fractions with common denominators. with Like and Unlike Denominators • Add and subtract fractions with unlike denominators.
4.NF.3b 4.NF.3d 5.NF.1 5.NF.2
• Common denominator • Least common denominator (LCD)
Trail Mix Extravaganza
• Create models to represent mixed numbers. • Write mixed numbers as improper fractions. • Write improper fractions as mixed numbers.
4.NF.3c 5.NF.1 6.NS.1
• Mixed number • Improper fraction
• Create models to represent parts of parts. • Analyze various methods for multiplying fractions. • Multiply fractions.
5.NF.4a 5.NF.4b 5.NF.6 6.NS.1
N/A
• Determine how many groups of a certain size are in a number. • Create a representation for division problems. • Divide fractions.
6.NS.1
• Reciprocal • Multiplicative Inverse Property • Multiplicative inverse
Trail Mix
3.6
4.NF.1
Improper Fractions and Mixed Numbers
Pizzas By the Slice—or the Rectangle! Parts of Parts
Yours is to Reason Why! 3.9 Parts in a Part
Middle School Math Series: Course 1
4
Middle School Math Series: Course 1
3.10
Divide Your Time Well, and Your Trail Mix, and Your ... Mixed Number Division
Middle School Math Series: Course 1
• Determine how many groups of a certain size are in a number. • Create a representation for division problems involving mixed numbers. • Divide fractions involving mixed numbers.
6.NS.1
N/A
5
Minty Fresh-Coins? 4.1 Introduction to Decimals
5.NBT.1 5.NBT.3.a
• Decimal
5.NBT.3.a 5.NBT.3.b 5.NBT.4
• Benchmark decimal • Round
• Write fractions as decimals.
4.NF.6
• Terminating decimal • Repeating decimal
• Estimate the sum and difference with decimals. • Add and subtract decimals.
6.NS.3
N/A
• Use hundredths and decimal grids to multiply two decimals. • Multiply decimals by whole numbers. • Multiply two decimals. • Use fractions to calculate the products of decimals. • Calculate the product of decimals using fractional forms. • Estimate the product of decimals.
6.NS.3
N/A
Key Math Objective
• Understand decimals as parts of wholes. • Represent decimals on a hundredths grid. • Write decimals. • Represent decimals on a number line.
• Compare decimal representations. • Order decimals. • Estimate sums and differences of decimals. Comparing, Ordering, Estimating, • Estimate decimals to benchmark numbers. and Rounding Decimals • Round decimals. You Be the Judge
4.2
4.3
The Ancient Spaniards Didn't Count the Thumbs!
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter begins with a comprehensive review of decimals. Models are used to develop the conceptual understanding of operations with decimals. Estimation is emphasized throughout.
Peer Analysis
Decimals
Worked Examples
4
Modules
Middle School Math Series: Course 1
Key Terms
Fraction-Decimal Equivalents
When Less is Better 4.4 Adding and Subtracting Decimals
4.5
I Just Spent One Week Going to Work! Multiplying Decimals
Middle School Math Series: Course 1
6
Middle School Math Series: Course 1
Organized Estimation 4.6 Long Division of Whole Numbers
4.7
Los Angeles Commute Didn't Top the List?
• Estimate quotients. • Develop an algorithm for dividing whole numbers.
6.NS.2 6.NS.3
• Dividend • Divisor • Quotient
• Estimate quotients of division of decimals. • Divide decimals.
6.NS.2 6.NS.3
N/A
Dividing Decimals
Middle School Math Series: Course 1
7
Mixing Paint 5.1 Introduction to Ratios
What's in a Name? 5.2 Ratio Representations
I'd Like to Solve the Puzzle ... 5.3 Writing Equivalent Ratios
5.4
The Most Important Meal of the Day
Key Math Objective
CCSS
6.RP.1
• Ratio
• Write comparisons using ratios. • Distinguish between part-to-part and part-to-whole ratios. • Write equivalent ratios.
6.RP.1
N/A
• Use double number lines and diagrams to solve problems involving ratios.
6.RP.1 6.RP.3.d
6.RP.1 6.RP.3
Key Terms
• Write ratios as part-to-part and part-to-whole relationships. • Represent ratios using models. • Use models to determine equivalent ratios.
• Write ratios. • Scale up and scale down ratios.
Technology
Lesson Title
Talk the Talk
Chapter
This chapter focuses on the concept of ratios and the ratio relationship between two quantities. Ratio reasoning is developed through the use of tables, double number lines, and graphs. Rate and ratio reasoning is used to solve various real-world problems.
Peer Analysis
Ratios
Worked Examples
5
Modules
Middle School Math Series: Course 1
• Rate • Scaling up • Scaling down
• Double number line
N/A
Modeling Ratios
A Trip to the Moon 5.5
Using Tables to Represent Equivalent Ratios
Middle School Math Series: Course 1
• Create tables of equivalent ratios. • Use known values in a table to determine equivalent ratios.
6.RP.1 6.RP.3 6.RP.3.a
8
Middle School Math Series: Course 1
Graphing Out Equivalence 5.6
Using Graphs to Represent Equivalent Ratios
• Graph a table of equivalent values. • Read equivalent ratios from graphs. • Use graphs to determine equivalent ratios. • Use graphs to compare different ratios.
6.RP.1 6.RP.3.a 6.RP.3.b
N/A
6.RP.1 6.RP.3.a
N/A
6.RP.1 6.RP.2 6.RP.3.a 6.RP.3.b
• Unit rate
Water is a Precious Resource
5.7
• Read and interpret ratios from graphs, double number lines, and tables. • Use multiple ratio models to solve problems. Using Multiple Ratio • Determine equivalent ratios using multiple representations. Representations to Solve Problems
What is the Better Buy? 5.8 Introduction to Unit Rates
Middle School Math Series: Course 1
• Use unit rates to solve problems. • Use unit rates to calculate the best buy. • Calculate unit rates.
9
Percents Can Make or Break You! 6.1 Introduction to Percents
Wacky Weather! 6.2 Estimating Percents
• Write fractions, decimals, and percents. • Model percents on a hundredths grid. • Explain the similarities and differences of percents, fractions, and decimals.
6.RP.1 6.RP.3.c
• Percent
• Estimate percents as fractions and decimals. • Write fractions as percents. • Identify equivalent forms of fractions, decimals, and percents. • Order fractions, decimals, and percents.
6.RP.1 6.RP.3.c
• Benchmark percents
• Determine the percent of a number. • Use double number lines.
6.RP.1 6.RP.3.c
N/A
This chapter extends ratio reasoning to include percents. Estimation and benchmark percents are emphasized to continue the development of number sense. Various strategies are presented to help students think about efficiency when solving problems.
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
Peer Analysis
Percents
Modules
6
Worked Examples
Middle School Math Series: Course 1
Key Terms
It's All in the Follow-through 6.3
Determining the Percent of a Number
Middle School Math Series: Course 1
10
Middle School Math Series: Course 1
Mi Mi Mi Mi Mi Mi Mi! 6.4
Determining the Part, Whole, or Percent of Percent Problems
Practical Percents Practice! 6.5
Using Percents in Real-World Situations
Middle School Math Series: Course 1
• Determine the percent given the part and the whole. • Determine the whole given a part and the percent. • Determine the part given the whole and the percent.
6.RP.1 6.RP.3.c
N/A
• Calculate the percent increase and decrease. • Calculate the discount of a base price. • Calculate additional discount on sales price. • Calculate gratuity on a bill. • Calculate sales tax.
6.RP.1 6.RP.3.c
• Commission • Gratuity
11
7.1
There's a Reason Behind the Rhyme Order of Operations
Getting to the Root of It 7.2
Exploring Squares, Cubes, and Roots
Things that Vary 7.3 Understanding Variables
Middle School Math Series: Course 1
Key Math Objective
• Evaluate numerical expressions with addition, subtraction, multiplication, and division. • Evaluate numerical expressions involving exponents and parentheses. • Justify the order of operations used to simplify numerical expressions.
CCSS
6.EE.1
Technology
Lesson Title
Talk the Talk
Chapter
This chapter reviews numerical expressions that lead to algebraic expressions. A variable is introduced as a representation of a quantity that varies. An emphasis is placed on writing and representing expressions in multiple ways.
Peer Analysis
Introduction to Expressions
Worked Examples
7
Modules
Middle School Math Series: Course 1
Key Terms
• Conventions • Numerical expression • Evaluate • Operations • Parentheses • Order of operations
• Determine the square of a number. • Calculate the square root of a number. • Determine the cube of a number. • Calculate the cube root of a number.
6.NS.3 6.EE.1 6.EE.2.c
• Square of a number • Perfect squares • Square root • Radical • Radicand • Perfect cube • Cube of a number • Cube root • Index
• Analyze problem situations. • Solve problems. • Define variables. • Write algebraic expressions. • Evaluate algebraic expressions. • Write equations.
6.NS.3 6.EE.2.a 6.EE.2.c 6.EE.6
• Variable • Algebraic expression • Equation
12
Middle School Math Series: Course 1
What's My Number? 7.4 Writing Algebraic Expressions
• Write expressions. • Write algebraic expressions to determine values for real world situations. • Determine the parts of an algebraic expression.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.6
• Numerical coefficient • Constant • Evaluate an algebraic expression
• Use verbal descriptions, diagrams, algebraic expressions, tables, and graphs to represent problem situations.
6.EE.2.a 6.EE.2.c 6.EE.6
• Multiple representations
• Use multiple representations to analyze and solve problems.
6.EE.2.a 6.EE.2.c 6.EE.6
N/A
Different Ways 7.5
Multiple Representations of Algebraic Expressions
There's More than One Way 7.6
Using Multiple Representations of Problems
Middle School Math Series: Course 1
13
The Parts of Cars You Don't See 8.1 Relationships between Quantities
Tile Work 8.2 Simplifying Algeraic Expressions
Blueprints to Floor Plans to Computers 8.3 Using the Distributive Property to Simplify Algebraic Expressions
Middle School Math Series: Course 1
• Predict the next term in a sequence. • Write numerical and algebraic expressions.
6.EE.2.a 6.EE.2.b 6.EE.6
• Sequence • Term
• Use the Associative and Commutative Properties of Addition and Multiplication to simplify expressions. • Use the Order of Operations. • Use algebra tiles to simplify algebraic expressions.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.3 6.EE.4 6.EE.6
• Commutative Property of Addition • Commutative Property of Multiplication • Associative Property of Addition • Associative Property of Multiplication • Simplify • Like terms
• Simplify algebraic expressions using the Distributive Property. • Write algebraic expressions using the Distributive Property. • Model the Distributive Property using algebra tiles.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.3 6.EE.4 6.EE.6
• Distributive Property of Multiplication over Addition • Distributive Property of Multiplication over Subtraction • Distributive Property of Division over Addition • Distributive Property of Division over Subtraction
This chapter develops an understanding of the Distributive Property through real-world situations, manipulatives, and analysis of student work. An emphasis is placed on extending and applying properties of operations to generate equivalent expressions, and to determine when two expressions are equivalent.
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
Peer Analysis
Algebraic Expressions
Worked Examples
8
Modules
Middle School Math Series: Course 1
Key Terms
14
Middle School Math Series: Course 1
Are They Saying the Same Thing? 8.4
Multiple Representations of Equivalent Expressions
Like and Unlike 8.5 Combining Like Terms
DVDs and Songs: Fun with Expressions 8.6 Using Algebraic Expressions to Analyze and Solve Problems
Middle School Math Series: Course 1
• Compare expressions using properties, tables, and graphs. • Graph expressions on a calculator. • Determine if two expressions are equivalent. • Write the corresponding expressions to problem situations.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.3 6.EE.4 6.EE.6
• Equivalent expressions
• Develop models for algebraic terms. • Use models to combine like terms in algebraic expressions. • Combine like terms in algebraic expressions.
6.EE.2.a 6.EE.2.b 6.EE.3 6.EE.4 6.EE.6
N/A
• Represent problem situations with algebraic expressions. • Analyze and solve problems with algebraic expressions.
6.EE.2.a 6.EE.3 6.EE.6
N/A
15
• One-step equation • Properties of Equality for Addition and Subtraction • Solution • Inverse operations
• Use inverse operations to solve one-step equations. Solving One-Step Equations Using • Use models to represent one-step equations. Multiplication and Division
6.EE.5 6.EE.7
• Properties of Equality for Multiplication and Division
Chapter
Lesson Title
Call to Order 9.1 Inequalities
Opposites Attract to Maintain a Balance 9.2 Solving One-Step Equations Using Addition and Subtraction
This chapter introduces algebraic equations and inequalities. A pan balance model is used to develop the conceptual understanding of solving equations involving one step. Equations, tables, and graphs are used to represent and solve real-world problems.
Key Math Objective
• Use inequalities to order the number system. • Graph inequalities on the number line.
CCSS
6.NS.7.a 6.EE.5 6.EE.6 6.EE.8
Technology
6.EE.5 6.EE.7
Inequalities and Equations
Talk the Talk
Worked Examples
• Use inverse operations to solve one-step equations. • Use models to represent one-step equations.
9
Peer Analysis
Modules
Middle School Math Series: Course 1
Key Terms
• Inequality • Graph of an inequality • Solution set of an inequality • Ray
Statements of Equality Redux 9.3
Middle School Math Series: Course 1
16
Middle School Math Series: Course 1
There are Many Ways ... 9.4
6.NS.6.c 6.EE.5 6.EE.6 6.EE.7
N/A
• Use multiple representations (words, symbols, tables, and graphs) to solve problems.
6.RP.3.b 6.NS.6.c 6.EE.5 6.EE.6 6.EE.7
N/A
• Examine the many different uses of variables in mathematics.
6.RP.3.b 6.NS.6.c 6.EE.5 6.EE.7
• Homonyms
• Identify and define independent and dependent variables and quantities.
6.RP.3.b 6.RP.3.c 6.NS.6.c 6.EE.5 6.EE.6 6.EE.7 6.EE.9
• Dependent quantity • Independent quantity • Independent variable • Dependent variable
• Represent two quantities that change in words, symbols, tables, and graphs. Representing Situations in Multiple • Solve one-step equations. Ways
Measuring Short 9.5
Using Multiple Representations to Solve Problems
Variables and More Variables 9.6
The Many Uses of Variables in Mathematics
Quantities that Change 9.7
Independent and Dependent Variables
Middle School Math Series: Course 1
17
What, Me Negative? 10.1 Introduction to Negative Integers
Key Math Objective
6.NS.5 6.NS.6.a 6.NS.6.c 6.NS.7.b
• Negative numbers • Infinity • Negative sign • Positive sign • Integers • Ellipses
• Classify sets of numbers.
6.NS.6.a 6.NS.6.c
• Fractional numbers • Rational numbers • Density Property
• Order rational numbers. • Define the absolute value of a number. • Calculate the absolute value of a number.
6.NS.6.a 6.NS.6.c 6.NS.7.c 6.NS.7.d
• Absolute value
Number Systems
Ordering and Absolute Value 10.3 Ordering the Rational Numbers
Middle School Math Series: Course 1
Key Terms
• Plot integers on a number line. • Solve problems where quantities increase and decrease. • Calculate the differences between quantities. • Represent quantities using positive and negative numbers.
Number Sets 10.2
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter develops the concept of negative numbers and moves toward the broader understanding of the rational number system including order and absolute value.
Peer Analysis
Integers
Worked Examples
10
Modules
Middle School Math Series: Course 1
18
Middle School Math Series: Course 1 Elevators, Making Money Redux, and Water Level 10.4 Solving Problems with Rational Numbers
Middle School Math Series: Course 1
• Solve problems using rational numbers. • Use positive and negative numbers to represent quantities in real-world situations.
6.NS.5 6.NS.6.a 6.NS.6.c 6.NS.7.c 6.NS.7.d
N/A
19
Four Quadrants 11.1 Extending the Coordinate Plane
Geometry and Graphs 11.2 Graphing Geometric Figures
Key Math Objective
CCSS
• Extend the coordinate system to four quadrants. • Name points on the plane. • Graph ordered pairs on the Cartesian Coordinate Plane. • Calculate the distance between points on the coordinate plane which are on the same vertical or horizontal line.
6.NS.6.b 6.NS.7.c 6.NS.8
• x-axis • y-axis • Origin • Quadrant • Ordered pair • Cartesian Coordinate Plane
• Plot points to form geometric figures. • Identify points on the coordinate plane to form geometric figures. • Identify geometric figures plotted on the coordinate plane.
6.NS.6.b 6.NS.8 6.G.3
N/A
• Analyze and solve problems with multiple representations.
6.RP.3.b 6.NS.5 6.NS.6.b 6.NS.8 6.EE.9
N/A
6.EE.9
N/A
Water, Water Everywhere 11.3
Solving Problems with Multiple Representations
Every Graph Tells a Story! 11.4 Interpreting Graphs
Middle School Math Series: Course 1
• Interpret information about a situation from a graphical representation. • Identify the graphs of situations.
Technology
Lesson Title
Talk the Talk
Chapter
This chapter extends plotting points to four quadrants and includes an introduction to coordinate geometry. Representations of algebraic expressions and equations are used to solve real-world problems.
Peer Analysis
The Cartesian Coordinate Plane
Worked Examples
11
Modules
Middle School Math Series: Course 1
Key Terms
20
Customary to Whom? 12.1 Customary Measurement
It's All Based on Powers of 10! 12.2 Metric Measurement
They're Saying the Same Thing? 12.3
Moving Between Measurement Systems
Is That Appropriate? 12.4 Choosing Appropriate Measures
Middle School Math Series: Course 1
• Select appropriate types of customary measurement. • Select appropriate units for each type of customary measurement. • Convert from one unit of customary measurement to another.
6.RP.1 6.RP.3.d
• Standard units of measure • Measurement • Convert
• Select appropriate types of metric measurement. • Select appropriate units for each type of metric measurement. • Convert from one metric unit to another.
6.RP.1 6.RP.3.d
• Meter (m) • Gram (g) • Liter (L) • Prefix
• Select appropriate types of measurement between customary and metric measurement systems. • Select appropriate units for each type of measurement. • Convert from one unit to another in different systems.
6.RP.1 6.RP.3.d
N/A
• Select appropriate types of measurement. • Select appropriate units for each type of measurement. • Determine approximate measurement for a variety of objects. • Determine appropriate measures for area, perimeter, and volume.
6.RP.1 6.RP.3.d
N/A
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter extends ratio reasoning to convert measurement units within and between Customary and Metric systems.
Peer Analysis
Units of Measure
Worked Examples
12
Modules
Middle School Math Series: Course 1
Key Terms
21
The Language of Geometry 13.1
Sketching, Drawing, Naming, and Sorting Basic Geometric Figures
Weaving a Rug 13.2
Area and Perimeter of Rectangles and Squares
Middle School Math Series: Course 1
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter connects the knowledge related to the areas of rectangles and squares to determine the areas of triangles, parallelograms, trapezoids, and rhombi. Formulas are used to solve real-world problems.
Peer Analysis
Area
Worked Examples
13
Modules
Middle School Math Series: Course 1
Key Terms
• Classify geometric figures as polygons, triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, and decagons. • Define consecutive sides and opposite sides. • Sort polygons into categories.
6.G.4
• Protractor • Compass • Straightedge • Sketch • Draw • Construct • Triangle • Equilateral triangle • Isosceles triangle • Scalene triangle • Equiangular triangle • Acute triangle • Right triangle • Obtuse triangle • Quadrilateral • Opposite sides • Consecutive sides • Square • Rectangle • Rhombus • Parallelogram • Kite • Trapezoid • Isosceles
• Calculate the area of rectangles and squares. • Calculate the perimeter of rectangles and squares. • Write a formula for the perimeter and area of a rectangle and a square. • Determine the effect of altering the dimensions of a rectangle or a square on the perimeter and area. • Calculate the area of composite figures.
6.G.1
N/A
22
Middle School Math Series: Course 1
Boundary Lines 13.3
Area of Parallelograms and Triangles
The Keystone Effect 13.4 Area of Trapezoids
Go Fly a Kite 13.5 Area of Rhombi and Kites
Street Signs 13.6 Area of Regular Polygons
Middle School Math Series: Course 1
6.G.1
• Altitude of a parallelogram • Height of a parallelogram • Altitude of a triangle • Height of a triangle
• Calculate the area of trapezoids. • Write a formula for the area of a trapezoid. • Calculate the area of composite figures.
6.G.1
• Bases of a trapezoid • Legs of a trapezoid • Altitude of a trapezoid • Height of a trapezoid
• Calculate the area of rhombi and kites. • Use formulas to compute the area of rhombi and kites. • Calculate the area of composite figures.
6.G.1
N/A
• Calculate the area of regular polygons. • Write a formula for the area of a regular polygon. • Calculate the area of composite figures.
6.G.1
• Congruent polygons • Apothem
• Calculate the area of parallelograms and triangles. • Write a formula for the area of a parallelogram and a triangle. • Calculate the area of composite figures.
23
Cut, Fold, and Voila! 14.1 Nets
More Cans in a Cube 14.2 The Cube
Prisms Can Improve Your Vision! 14.3 Prisms
Outside and Inside a Prism 14.4
Surface Area and Volume of a Prism
Middle School Math Series: Course 1
6.G.4
• Geometric solids • Prototype • Edge • Face • Vertex • Net
6.G.2 6.G.4
• Point • Line segment • Polygon • Polyhedron • Regular polyhedron • Congruent • Cube • Unit cube • Diameter • Surface area • Volume
• Sketch a model of a right rectangular prism. • Create models of various prisms. • Determine the characteristics of various prisms.
6.G.4
• Prism • Bases of a prism • Lateral faces • Height of a prism • Rectangular prism • Right prism
• Use unit cubes to estimate the volume and surface area of a right rectangular prism. • Use nets to compute the volume and surface area of a right rectangular prism. • Use a formula to determine the volume of a right rectangular prism. • Use appropriate units of measure when computing the surface area and volume of a right rectangular prism.
6.G.2 6.G.4
N/A
Key Math Objective
• Sketch various views of a solid figure to provide a two-dimensional representation of a threedimensional figure. • Construct a net from a model of a geometric solid. • Construct a model of a geometric solid from a net. • Use nets to provide two-dimensional representations of a geometric solid.
• Create a model of a cube from a net. • Construct a model of a geometric solid from a net. • Use nets to provide two-dimensional representations of a cube. • Estimate the volume and surface area of a cube. • Use nets to compute the volume and surface area of a cube. • Use a formula to determine the volume of a cube. • Use unit cubes to estimate the surface area and volume of larger cubes. • Use appropriate units of measure when computing the sur- face area and volume of a cube. • Explore how doubling the dimensions of a cube affects the volume of the cube.
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter develops an understanding of three-dimensional figures using nets made up of rectangles and triangles. Nets are then used to determine surface area. Estimation is emphasized prior to calculations and real-world problems are solved using volume and surface area formulas.
Peer Analysis
Introduction to the Third Dimension
Worked Examples
14
Modules
Middle School Math Series: Course 1
Key Terms
24
Middle School Math Series: Course 1
14.5
The Egyptians Were on to Something—Or Was It the Mayans? Pyramids
And The Winning Prototype Is … ? 14.6
Identifying Geometric Solids in Everyday Occurrences
Middle School Math Series: Course 1
• Create a model of a pyramid from a net. • Use nets to provide two-dimensional representations of a pyramid. • Use nets to estimate the surface area of a pyramid. • Use appropriate units of measure when computing the surface area of a pyramid.
6.G.2 6.G.4
• Pyramid • Vertex of a pyramid • Height of a pyramid • Slant height of a pyramid
• Identify geometric solids. • Compare and contrast the surface area of geometric solids. • Apply the surface area concept to a real-world situation.
6.G.4
N/A
25
Why Do We Use Statistics? Designing Statistical Questions
Dealing with Data Collecting, Displaying, and Analyzing Data
At the Olympics 15.3 Line Plots and Stem-and-Leaf Plots
Middle School Math Series: Course 1
Key Math Objective
6.SP.1
• Data • Statistical question • Population • Sample • Data analysis • Parameter • Statistic • Survey • Experiment
• Learn about statistical questions. • Recognize statistical questions and anticipate variability in data related to the question. • Design statistical questions that can be answered by a given data set. • Differentiate between surveys and experiments.
6.SP.4
• Categorical data • Quantitative data • Discrete data • Continuous data • Bar graph • Frequency • Double bar graph • Key • Stacked bar graph • Circle graph
• Discuss the different types of data that can be collected, displayed, and analyzed. • Determine how to select an appropriate graph to display different types of data. • Organize data into single, double, or stacked bar graphs. • Analyze data and interpret results from single, double, or stacked bar graphs and circle graphs.
• Dot plot • Distribution • Symmetric • Skewed right • Skewed left • Clusters • Gaps • Stem-and-leaf plot • Side-by-side stem-and-leaf plot
• Organize data and interpret dot plots. • Organize data and interpret stem-and-leaf plots.
CCSS
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.d
Technology
Talk the Talk
Lesson Title
15.1
15.2
Peer Analysis
Chapter
Collecting and Displaying Data This chapter develops the understanding of statistics and variability. Various representations are used to summarize numerical data sets.
Modules
15
Worked Examples
Middle School Math Series: Course 1
Key Terms
26
Middle School Math Series: Course 1
Building Up 15.4 Using Histograms
• Organize data into a histogram. • Analyze data presented in a histogram.
6.SP.4 6.SP.5.a
• Hisotgram • Frequency table
• Analyze data recorded during an experiment and answer questions that were posed at the beginning of the experiment.
6.SP.4 6.SP.5.a 6.SP.5.d
N/A
Analyze This! 15.5
Designing and Implementing an Experiment
Middle School Math Series: Course 1
27
Lesson Title
Key Math Objective
CCSS
In the Middle 16.1
• Review the meaning of mean, median, and mode. Analyzing Data Using Measures of • Calculate and interpret the mean, the median, and the mode for a set of data. Center
Which Measure of Center Should I Use? 16.2 Determining When to Use the Mean, Median, or Mode
Picking a Player 16.3
Calculating and Interpreting the Mean Absolute Deviation
Five Number Summary 16.4
Analyzing Data Using the Five Number Summary
Box It Up! 16.5
Displaying and Analyzing Data Using Box-and-Whisker Plots
Middle School Math Series: Course 1
6.SP.3
Technology
Talk the Talk
Chapter
Peer Analysis
This chapter reviews the measures of center with an emphasis on which measure is the most appropriate to describe a data set. Box-andAnalyzing and Interpreting Data whisker plots are used to display numerical data and investigate variation. Graphing calculators and spreadsheets are used to determine mean absolute deviation and to construct box-and-whisker plots.
Worked Examples
16
Modules
Middle School Math Series: Course 1
Key Terms
• Measure of center • Mode • Median • Balance point • Mean
• Calculate the mean, median, and mode from a graphical display of data. • Determine when to use the mean, median, or mode to describe a data set.
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.c 6.SP.5.d
N/A
• Calculate the deviations of each data value from the mean of a data set. • Calculate the absolute deviations of each data value from the mean of a data set. • Calculate and interpret the mean absolute deviation for a data set.
6.SP.3 6.SP.4 6.SP.5.c 6.SP.5.d
• Measures of variation or variability • Deviation • Absolute deviation • Mean absolute deviation
• Calculate and interpret the range, quartiles, and interquartile range as measures of variability for a data set. • Calculate and interpret the five number summary as a measure of variability for a data set.
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.c 6.SP.5.d
• Range • Quartiles (Q) • Interquartile range (IQR) • Five number summary
• Construct and interpret a box-and-whisker plot for a data set. • Determine if a data set has outliers, and discuss how outliers affect the display and analysis of the data.
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.c 6.SP.5.d
• Box-and-whisker plot • Outlier
28
Lesson Title
Collection Connections 1.1 Factors and Multiples
Key Math Objective
CCSS
Physical Models of Factors and Multiples
Divisibility Rules! Investigating Divisibility Rules
Middle School Math Series: Course 1
• Determine factor pairs using arrays and area models. • Classify numbers using Venn diagrams.
4.OA.4 6.NS.4
• Area model • Set • Venn diagram
4.OA.4
• Prime numbers • Composite numbers • Multiplicative identity
4.OA.4
• Divisibility rules
• Formulate divisibility rules based on patterns seen in factors. • Use factors to help you develop divisibility rules.
Technology
Talk the Talk
4.OA.4
• Distinguish between prime and composite numbers. Investigating Prime and Composite • Identify and use the multiplicative identity. Numbers
1.4
• List factor pairs of numbers. • Relate factors, multiples, and divisibility.
Sifting for Prime Numbers 1.3
Key Terms
• Array • Factor pair • Factor • Commutative Property of Multiplication • Distinct factors • Perfect square • Multiple • Divisible
Models and More 1.2
Peer Analysis
Factors, Multiples, Primes, and This chapter reviews factors, multiples, primes, composites, and divisibility rules. Composites
Worked Examples
1
Modules
Middle School Math Series: Course 1
1
The Think Tank 2.1
Prime Factorization and Factor Trees
CCSS
Key Terms
• Determine the prime factorization of a number. • Understand the usefulness of prime factors. • Recognize that each whole number has exactly one prime factorization.
6.NS.4 6.EE.1
• Prime factorization • Associative Property of Multiplication • Factor tree • Power • Base • Exponent • Fundamental Theorem of Arithmetic
• Determine the least common multiple of two numbers.
6.NS.4
• Common multiple • Least common multiple (LCM)
• Determine the greatest common factor of two or more numbers.
6.NS.4
• Common factor • Greatest common factor (GCF) • Relatively prime numbers
• Recognize how to use common factors and common multiples to solve problems.
6.NS.4
N/A
Key Math Objective
Technology
Lesson Title
Talk the Talk
Chapter
This chapter demonstrates how least common multiples and greatest common factors are used to solve real-world problems.
Peer Analysis
Prime Factorization and the Fundamental Theorem of Arithmetic
Worked Examples
2
Modules
Middle School Math Series: Course 1
Together Again 2.2
Investigating Multiples and Least Common Multiples
Happenings at Harvest Day 2.3
Investigating Factors and Greatest Common Factors
Common Factors or Common Multiples? 2.4
Using GCF and LCM to Solve Problems
Middle School Math Series: Course 1
2
Flags and Fractions 3.1 Modeling Parts of a Whole
You Mean Three Can Be One? 3.2 Fractional Representations
Rocket Strips 3.3
Dividing a Whole into Fractional Parts
Getting Closer 3.4 Benchmark Fractions
Middle School Math Series: Course 1
• Determine equal parts of a whole. • Draw different representations of equal parts.
4.NF.1 6.NS.1
• Fraction • Numerator • Denominator
• Create different fractional representations using pattern blocks. • Write fractional statements for different representations given the whole. • Determine fractional representations given the whole. • Determine fractional representations given parts of the whole.
5.NF.1 6.NS.1
N/A
• Create equal parts of a whole. • Determine if fractions are equal. • Graph fractions on a number line.
4.NF.1 6.NS.1
• Unit fraction • Equivalent fractions
• Estimate fractions by using benchmark fractions. • Order fractions in ascending order. • Compare fractions.
4.NF.2 6.NS.1
• Benchmark fractions • Inequality
Key Math Objective
CCSS
Technology
Lesson Title
This chapter begins with a review of how to model parts of a whole and various fractional representations. Students create their own fraction strips and use them to model operations with fractions. The focus then shifts to the relationship between multiplication and division to understand the procedures for dividing fractions. An emphasis is placed on estimation skills throughout the chapter.
Talk the Talk
Chapter
Peer Analysis
Fractions
Worked Examples
3
Modules
Middle School Math Series: Course 1
Key Terms
3
Middle School Math Series: Course 1
What's My Cut? 3.5 Equivalent Fractions
• Determine equal portions of a whole. • Determine equivalent fractions. • Calculate equivalent fractions using a form of 1. • Simplify fractions. • Order fractions.
3.7
3.8
• Simplest form • Multiplicative Identity Property
• Write number sentences to represent 1. • Create models to represent addition and subtraction of fractions. Adding and Subtracting Fractions • Add and subtract fractions with common denominators. with Like and Unlike Denominators • Add and subtract fractions with unlike denominators.
4.NF.3b 4.NF.3d 5.NF.1 5.NF.2
• Common denominator • Least common denominator (LCD)
Trail Mix Extravaganza
• Create models to represent mixed numbers. • Write mixed numbers as improper fractions. • Write improper fractions as mixed numbers.
4.NF.3c 5.NF.1 6.NS.1
• Mixed number • Improper fraction
• Create models to represent parts of parts. • Analyze various methods for multiplying fractions. • Multiply fractions.
5.NF.4a 5.NF.4b 5.NF.6 6.NS.1
N/A
• Determine how many groups of a certain size are in a number. • Create a representation for division problems. • Divide fractions.
6.NS.1
• Reciprocal • Multiplicative Inverse Property • Multiplicative inverse
Trail Mix
3.6
4.NF.1
Improper Fractions and Mixed Numbers
Pizzas By the Slice—or the Rectangle! Parts of Parts
Yours is to Reason Why! 3.9 Parts in a Part
Middle School Math Series: Course 1
4
Middle School Math Series: Course 1
3.10
Divide Your Time Well, and Your Trail Mix, and Your ... Mixed Number Division
Middle School Math Series: Course 1
• Determine how many groups of a certain size are in a number. • Create a representation for division problems involving mixed numbers. • Divide fractions involving mixed numbers.
6.NS.1
N/A
5
Minty Fresh-Coins? 4.1 Introduction to Decimals
5.NBT.1 5.NBT.3.a
• Decimal
5.NBT.3.a 5.NBT.3.b 5.NBT.4
• Benchmark decimal • Round
• Write fractions as decimals.
4.NF.6
• Terminating decimal • Repeating decimal
• Estimate the sum and difference with decimals. • Add and subtract decimals.
6.NS.3
N/A
• Use hundredths and decimal grids to multiply two decimals. • Multiply decimals by whole numbers. • Multiply two decimals. • Use fractions to calculate the products of decimals. • Calculate the product of decimals using fractional forms. • Estimate the product of decimals.
6.NS.3
N/A
Key Math Objective
• Understand decimals as parts of wholes. • Represent decimals on a hundredths grid. • Write decimals. • Represent decimals on a number line.
• Compare decimal representations. • Order decimals. • Estimate sums and differences of decimals. Comparing, Ordering, Estimating, • Estimate decimals to benchmark numbers. and Rounding Decimals • Round decimals. You Be the Judge
4.2
4.3
The Ancient Spaniards Didn't Count the Thumbs!
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter begins with a comprehensive review of decimals. Models are used to develop the conceptual understanding of operations with decimals. Estimation is emphasized throughout.
Peer Analysis
Decimals
Worked Examples
4
Modules
Middle School Math Series: Course 1
Key Terms
Fraction-Decimal Equivalents
When Less is Better 4.4 Adding and Subtracting Decimals
4.5
I Just Spent One Week Going to Work! Multiplying Decimals
Middle School Math Series: Course 1
6
Middle School Math Series: Course 1
Organized Estimation 4.6 Long Division of Whole Numbers
4.7
Los Angeles Commute Didn't Top the List?
• Estimate quotients. • Develop an algorithm for dividing whole numbers.
6.NS.2 6.NS.3
• Dividend • Divisor • Quotient
• Estimate quotients of division of decimals. • Divide decimals.
6.NS.2 6.NS.3
N/A
Dividing Decimals
Middle School Math Series: Course 1
7
Mixing Paint 5.1 Introduction to Ratios
What's in a Name? 5.2 Ratio Representations
I'd Like to Solve the Puzzle ... 5.3 Writing Equivalent Ratios
5.4
The Most Important Meal of the Day
Key Math Objective
CCSS
6.RP.1
• Ratio
• Write comparisons using ratios. • Distinguish between part-to-part and part-to-whole ratios. • Write equivalent ratios.
6.RP.1
N/A
• Use double number lines and diagrams to solve problems involving ratios.
6.RP.1 6.RP.3.d
6.RP.1 6.RP.3
Key Terms
• Write ratios as part-to-part and part-to-whole relationships. • Represent ratios using models. • Use models to determine equivalent ratios.
• Write ratios. • Scale up and scale down ratios.
Technology
Lesson Title
Talk the Talk
Chapter
This chapter focuses on the concept of ratios and the ratio relationship between two quantities. Ratio reasoning is developed through the use of tables, double number lines, and graphs. Rate and ratio reasoning is used to solve various real-world problems.
Peer Analysis
Ratios
Worked Examples
5
Modules
Middle School Math Series: Course 1
• Rate • Scaling up • Scaling down
• Double number line
N/A
Modeling Ratios
A Trip to the Moon 5.5
Using Tables to Represent Equivalent Ratios
Middle School Math Series: Course 1
• Create tables of equivalent ratios. • Use known values in a table to determine equivalent ratios.
6.RP.1 6.RP.3 6.RP.3.a
8
Middle School Math Series: Course 1
Graphing Out Equivalence 5.6
Using Graphs to Represent Equivalent Ratios
• Graph a table of equivalent values. • Read equivalent ratios from graphs. • Use graphs to determine equivalent ratios. • Use graphs to compare different ratios.
6.RP.1 6.RP.3.a 6.RP.3.b
N/A
6.RP.1 6.RP.3.a
N/A
6.RP.1 6.RP.2 6.RP.3.a 6.RP.3.b
• Unit rate
Water is a Precious Resource
5.7
• Read and interpret ratios from graphs, double number lines, and tables. • Use multiple ratio models to solve problems. Using Multiple Ratio • Determine equivalent ratios using multiple representations. Representations to Solve Problems
What is the Better Buy? 5.8 Introduction to Unit Rates
Middle School Math Series: Course 1
• Use unit rates to solve problems. • Use unit rates to calculate the best buy. • Calculate unit rates.
9
Percents Can Make or Break You! 6.1 Introduction to Percents
Wacky Weather! 6.2 Estimating Percents
• Write fractions, decimals, and percents. • Model percents on a hundredths grid. • Explain the similarities and differences of percents, fractions, and decimals.
6.RP.1 6.RP.3.c
• Percent
• Estimate percents as fractions and decimals. • Write fractions as percents. • Identify equivalent forms of fractions, decimals, and percents. • Order fractions, decimals, and percents.
6.RP.1 6.RP.3.c
• Benchmark percents
• Determine the percent of a number. • Use double number lines.
6.RP.1 6.RP.3.c
N/A
This chapter extends ratio reasoning to include percents. Estimation and benchmark percents are emphasized to continue the development of number sense. Various strategies are presented to help students think about efficiency when solving problems.
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
Peer Analysis
Percents
Modules
6
Worked Examples
Middle School Math Series: Course 1
Key Terms
It's All in the Follow-through 6.3
Determining the Percent of a Number
Middle School Math Series: Course 1
10
Middle School Math Series: Course 1
Mi Mi Mi Mi Mi Mi Mi! 6.4
Determining the Part, Whole, or Percent of Percent Problems
Practical Percents Practice! 6.5
Using Percents in Real-World Situations
Middle School Math Series: Course 1
• Determine the percent given the part and the whole. • Determine the whole given a part and the percent. • Determine the part given the whole and the percent.
6.RP.1 6.RP.3.c
N/A
• Calculate the percent increase and decrease. • Calculate the discount of a base price. • Calculate additional discount on sales price. • Calculate gratuity on a bill. • Calculate sales tax.
6.RP.1 6.RP.3.c
• Commission • Gratuity
11
7.1
There's a Reason Behind the Rhyme Order of Operations
Getting to the Root of It 7.2
Exploring Squares, Cubes, and Roots
Things that Vary 7.3 Understanding Variables
Middle School Math Series: Course 1
Key Math Objective
• Evaluate numerical expressions with addition, subtraction, multiplication, and division. • Evaluate numerical expressions involving exponents and parentheses. • Justify the order of operations used to simplify numerical expressions.
CCSS
6.EE.1
Technology
Lesson Title
Talk the Talk
Chapter
This chapter reviews numerical expressions that lead to algebraic expressions. A variable is introduced as a representation of a quantity that varies. An emphasis is placed on writing and representing expressions in multiple ways.
Peer Analysis
Introduction to Expressions
Worked Examples
7
Modules
Middle School Math Series: Course 1
Key Terms
• Conventions • Numerical expression • Evaluate • Operations • Parentheses • Order of operations
• Determine the square of a number. • Calculate the square root of a number. • Determine the cube of a number. • Calculate the cube root of a number.
6.NS.3 6.EE.1 6.EE.2.c
• Square of a number • Perfect squares • Square root • Radical • Radicand • Perfect cube • Cube of a number • Cube root • Index
• Analyze problem situations. • Solve problems. • Define variables. • Write algebraic expressions. • Evaluate algebraic expressions. • Write equations.
6.NS.3 6.EE.2.a 6.EE.2.c 6.EE.6
• Variable • Algebraic expression • Equation
12
Middle School Math Series: Course 1
What's My Number? 7.4 Writing Algebraic Expressions
• Write expressions. • Write algebraic expressions to determine values for real world situations. • Determine the parts of an algebraic expression.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.6
• Numerical coefficient • Constant • Evaluate an algebraic expression
• Use verbal descriptions, diagrams, algebraic expressions, tables, and graphs to represent problem situations.
6.EE.2.a 6.EE.2.c 6.EE.6
• Multiple representations
• Use multiple representations to analyze and solve problems.
6.EE.2.a 6.EE.2.c 6.EE.6
N/A
Different Ways 7.5
Multiple Representations of Algebraic Expressions
There's More than One Way 7.6
Using Multiple Representations of Problems
Middle School Math Series: Course 1
13
The Parts of Cars You Don't See 8.1 Relationships between Quantities
Tile Work 8.2 Simplifying Algeraic Expressions
Blueprints to Floor Plans to Computers 8.3 Using the Distributive Property to Simplify Algebraic Expressions
Middle School Math Series: Course 1
• Predict the next term in a sequence. • Write numerical and algebraic expressions.
6.EE.2.a 6.EE.2.b 6.EE.6
• Sequence • Term
• Use the Associative and Commutative Properties of Addition and Multiplication to simplify expressions. • Use the Order of Operations. • Use algebra tiles to simplify algebraic expressions.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.3 6.EE.4 6.EE.6
• Commutative Property of Addition • Commutative Property of Multiplication • Associative Property of Addition • Associative Property of Multiplication • Simplify • Like terms
• Simplify algebraic expressions using the Distributive Property. • Write algebraic expressions using the Distributive Property. • Model the Distributive Property using algebra tiles.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.3 6.EE.4 6.EE.6
• Distributive Property of Multiplication over Addition • Distributive Property of Multiplication over Subtraction • Distributive Property of Division over Addition • Distributive Property of Division over Subtraction
This chapter develops an understanding of the Distributive Property through real-world situations, manipulatives, and analysis of student work. An emphasis is placed on extending and applying properties of operations to generate equivalent expressions, and to determine when two expressions are equivalent.
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
Peer Analysis
Algebraic Expressions
Worked Examples
8
Modules
Middle School Math Series: Course 1
Key Terms
14
Middle School Math Series: Course 1
Are They Saying the Same Thing? 8.4
Multiple Representations of Equivalent Expressions
Like and Unlike 8.5 Combining Like Terms
DVDs and Songs: Fun with Expressions 8.6 Using Algebraic Expressions to Analyze and Solve Problems
Middle School Math Series: Course 1
• Compare expressions using properties, tables, and graphs. • Graph expressions on a calculator. • Determine if two expressions are equivalent. • Write the corresponding expressions to problem situations.
6.EE.2.a 6.EE.2.b 6.EE.2.c 6.EE.3 6.EE.4 6.EE.6
• Equivalent expressions
• Develop models for algebraic terms. • Use models to combine like terms in algebraic expressions. • Combine like terms in algebraic expressions.
6.EE.2.a 6.EE.2.b 6.EE.3 6.EE.4 6.EE.6
N/A
• Represent problem situations with algebraic expressions. • Analyze and solve problems with algebraic expressions.
6.EE.2.a 6.EE.3 6.EE.6
N/A
15
• One-step equation • Properties of Equality for Addition and Subtraction • Solution • Inverse operations
• Use inverse operations to solve one-step equations. Solving One-Step Equations Using • Use models to represent one-step equations. Multiplication and Division
6.EE.5 6.EE.7
• Properties of Equality for Multiplication and Division
Chapter
Lesson Title
Call to Order 9.1 Inequalities
Opposites Attract to Maintain a Balance 9.2 Solving One-Step Equations Using Addition and Subtraction
This chapter introduces algebraic equations and inequalities. A pan balance model is used to develop the conceptual understanding of solving equations involving one step. Equations, tables, and graphs are used to represent and solve real-world problems.
Key Math Objective
• Use inequalities to order the number system. • Graph inequalities on the number line.
CCSS
6.NS.7.a 6.EE.5 6.EE.6 6.EE.8
Technology
6.EE.5 6.EE.7
Inequalities and Equations
Talk the Talk
Worked Examples
• Use inverse operations to solve one-step equations. • Use models to represent one-step equations.
9
Peer Analysis
Modules
Middle School Math Series: Course 1
Key Terms
• Inequality • Graph of an inequality • Solution set of an inequality • Ray
Statements of Equality Redux 9.3
Middle School Math Series: Course 1
16
Middle School Math Series: Course 1
There are Many Ways ... 9.4
6.NS.6.c 6.EE.5 6.EE.6 6.EE.7
N/A
• Use multiple representations (words, symbols, tables, and graphs) to solve problems.
6.RP.3.b 6.NS.6.c 6.EE.5 6.EE.6 6.EE.7
N/A
• Examine the many different uses of variables in mathematics.
6.RP.3.b 6.NS.6.c 6.EE.5 6.EE.7
• Homonyms
• Identify and define independent and dependent variables and quantities.
6.RP.3.b 6.RP.3.c 6.NS.6.c 6.EE.5 6.EE.6 6.EE.7 6.EE.9
• Dependent quantity • Independent quantity • Independent variable • Dependent variable
• Represent two quantities that change in words, symbols, tables, and graphs. Representing Situations in Multiple • Solve one-step equations. Ways
Measuring Short 9.5
Using Multiple Representations to Solve Problems
Variables and More Variables 9.6
The Many Uses of Variables in Mathematics
Quantities that Change 9.7
Independent and Dependent Variables
Middle School Math Series: Course 1
17
What, Me Negative? 10.1 Introduction to Negative Integers
Key Math Objective
6.NS.5 6.NS.6.a 6.NS.6.c 6.NS.7.b
• Negative numbers • Infinity • Negative sign • Positive sign • Integers • Ellipses
• Classify sets of numbers.
6.NS.6.a 6.NS.6.c
• Fractional numbers • Rational numbers • Density Property
• Order rational numbers. • Define the absolute value of a number. • Calculate the absolute value of a number.
6.NS.6.a 6.NS.6.c 6.NS.7.c 6.NS.7.d
• Absolute value
Number Systems
Ordering and Absolute Value 10.3 Ordering the Rational Numbers
Middle School Math Series: Course 1
Key Terms
• Plot integers on a number line. • Solve problems where quantities increase and decrease. • Calculate the differences between quantities. • Represent quantities using positive and negative numbers.
Number Sets 10.2
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter develops the concept of negative numbers and moves toward the broader understanding of the rational number system including order and absolute value.
Peer Analysis
Integers
Worked Examples
10
Modules
Middle School Math Series: Course 1
18
Middle School Math Series: Course 1 Elevators, Making Money Redux, and Water Level 10.4 Solving Problems with Rational Numbers
Middle School Math Series: Course 1
• Solve problems using rational numbers. • Use positive and negative numbers to represent quantities in real-world situations.
6.NS.5 6.NS.6.a 6.NS.6.c 6.NS.7.c 6.NS.7.d
N/A
19
Four Quadrants 11.1 Extending the Coordinate Plane
Geometry and Graphs 11.2 Graphing Geometric Figures
Key Math Objective
CCSS
• Extend the coordinate system to four quadrants. • Name points on the plane. • Graph ordered pairs on the Cartesian Coordinate Plane. • Calculate the distance between points on the coordinate plane which are on the same vertical or horizontal line.
6.NS.6.b 6.NS.7.c 6.NS.8
• x-axis • y-axis • Origin • Quadrant • Ordered pair • Cartesian Coordinate Plane
• Plot points to form geometric figures. • Identify points on the coordinate plane to form geometric figures. • Identify geometric figures plotted on the coordinate plane.
6.NS.6.b 6.NS.8 6.G.3
N/A
• Analyze and solve problems with multiple representations.
6.RP.3.b 6.NS.5 6.NS.6.b 6.NS.8 6.EE.9
N/A
6.EE.9
N/A
Water, Water Everywhere 11.3
Solving Problems with Multiple Representations
Every Graph Tells a Story! 11.4 Interpreting Graphs
Middle School Math Series: Course 1
• Interpret information about a situation from a graphical representation. • Identify the graphs of situations.
Technology
Lesson Title
Talk the Talk
Chapter
This chapter extends plotting points to four quadrants and includes an introduction to coordinate geometry. Representations of algebraic expressions and equations are used to solve real-world problems.
Peer Analysis
The Cartesian Coordinate Plane
Worked Examples
11
Modules
Middle School Math Series: Course 1
Key Terms
20
Customary to Whom? 12.1 Customary Measurement
It's All Based on Powers of 10! 12.2 Metric Measurement
They're Saying the Same Thing? 12.3
Moving Between Measurement Systems
Is That Appropriate? 12.4 Choosing Appropriate Measures
Middle School Math Series: Course 1
• Select appropriate types of customary measurement. • Select appropriate units for each type of customary measurement. • Convert from one unit of customary measurement to another.
6.RP.1 6.RP.3.d
• Standard units of measure • Measurement • Convert
• Select appropriate types of metric measurement. • Select appropriate units for each type of metric measurement. • Convert from one metric unit to another.
6.RP.1 6.RP.3.d
• Meter (m) • Gram (g) • Liter (L) • Prefix
• Select appropriate types of measurement between customary and metric measurement systems. • Select appropriate units for each type of measurement. • Convert from one unit to another in different systems.
6.RP.1 6.RP.3.d
N/A
• Select appropriate types of measurement. • Select appropriate units for each type of measurement. • Determine approximate measurement for a variety of objects. • Determine appropriate measures for area, perimeter, and volume.
6.RP.1 6.RP.3.d
N/A
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter extends ratio reasoning to convert measurement units within and between Customary and Metric systems.
Peer Analysis
Units of Measure
Worked Examples
12
Modules
Middle School Math Series: Course 1
Key Terms
21
The Language of Geometry 13.1
Sketching, Drawing, Naming, and Sorting Basic Geometric Figures
Weaving a Rug 13.2
Area and Perimeter of Rectangles and Squares
Middle School Math Series: Course 1
Key Math Objective
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter connects the knowledge related to the areas of rectangles and squares to determine the areas of triangles, parallelograms, trapezoids, and rhombi. Formulas are used to solve real-world problems.
Peer Analysis
Area
Worked Examples
13
Modules
Middle School Math Series: Course 1
Key Terms
• Classify geometric figures as polygons, triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, nonagons, and decagons. • Define consecutive sides and opposite sides. • Sort polygons into categories.
6.G.4
• Protractor • Compass • Straightedge • Sketch • Draw • Construct • Triangle • Equilateral triangle • Isosceles triangle • Scalene triangle • Equiangular triangle • Acute triangle • Right triangle • Obtuse triangle • Quadrilateral • Opposite sides • Consecutive sides • Square • Rectangle • Rhombus • Parallelogram • Kite • Trapezoid • Isosceles
• Calculate the area of rectangles and squares. • Calculate the perimeter of rectangles and squares. • Write a formula for the perimeter and area of a rectangle and a square. • Determine the effect of altering the dimensions of a rectangle or a square on the perimeter and area. • Calculate the area of composite figures.
6.G.1
N/A
22
Middle School Math Series: Course 1
Boundary Lines 13.3
Area of Parallelograms and Triangles
The Keystone Effect 13.4 Area of Trapezoids
Go Fly a Kite 13.5 Area of Rhombi and Kites
Street Signs 13.6 Area of Regular Polygons
Middle School Math Series: Course 1
6.G.1
• Altitude of a parallelogram • Height of a parallelogram • Altitude of a triangle • Height of a triangle
• Calculate the area of trapezoids. • Write a formula for the area of a trapezoid. • Calculate the area of composite figures.
6.G.1
• Bases of a trapezoid • Legs of a trapezoid • Altitude of a trapezoid • Height of a trapezoid
• Calculate the area of rhombi and kites. • Use formulas to compute the area of rhombi and kites. • Calculate the area of composite figures.
6.G.1
N/A
• Calculate the area of regular polygons. • Write a formula for the area of a regular polygon. • Calculate the area of composite figures.
6.G.1
• Congruent polygons • Apothem
• Calculate the area of parallelograms and triangles. • Write a formula for the area of a parallelogram and a triangle. • Calculate the area of composite figures.
23
Cut, Fold, and Voila! 14.1 Nets
More Cans in a Cube 14.2 The Cube
Prisms Can Improve Your Vision! 14.3 Prisms
Outside and Inside a Prism 14.4
Surface Area and Volume of a Prism
Middle School Math Series: Course 1
6.G.4
• Geometric solids • Prototype • Edge • Face • Vertex • Net
6.G.2 6.G.4
• Point • Line segment • Polygon • Polyhedron • Regular polyhedron • Congruent • Cube • Unit cube • Diameter • Surface area • Volume
• Sketch a model of a right rectangular prism. • Create models of various prisms. • Determine the characteristics of various prisms.
6.G.4
• Prism • Bases of a prism • Lateral faces • Height of a prism • Rectangular prism • Right prism
• Use unit cubes to estimate the volume and surface area of a right rectangular prism. • Use nets to compute the volume and surface area of a right rectangular prism. • Use a formula to determine the volume of a right rectangular prism. • Use appropriate units of measure when computing the surface area and volume of a right rectangular prism.
6.G.2 6.G.4
N/A
Key Math Objective
• Sketch various views of a solid figure to provide a two-dimensional representation of a threedimensional figure. • Construct a net from a model of a geometric solid. • Construct a model of a geometric solid from a net. • Use nets to provide two-dimensional representations of a geometric solid.
• Create a model of a cube from a net. • Construct a model of a geometric solid from a net. • Use nets to provide two-dimensional representations of a cube. • Estimate the volume and surface area of a cube. • Use nets to compute the volume and surface area of a cube. • Use a formula to determine the volume of a cube. • Use unit cubes to estimate the surface area and volume of larger cubes. • Use appropriate units of measure when computing the sur- face area and volume of a cube. • Explore how doubling the dimensions of a cube affects the volume of the cube.
CCSS
Technology
Lesson Title
Talk the Talk
Chapter
This chapter develops an understanding of three-dimensional figures using nets made up of rectangles and triangles. Nets are then used to determine surface area. Estimation is emphasized prior to calculations and real-world problems are solved using volume and surface area formulas.
Peer Analysis
Introduction to the Third Dimension
Worked Examples
14
Modules
Middle School Math Series: Course 1
Key Terms
24
Middle School Math Series: Course 1
14.5
The Egyptians Were on to Something—Or Was It the Mayans? Pyramids
And The Winning Prototype Is … ? 14.6
Identifying Geometric Solids in Everyday Occurrences
Middle School Math Series: Course 1
• Create a model of a pyramid from a net. • Use nets to provide two-dimensional representations of a pyramid. • Use nets to estimate the surface area of a pyramid. • Use appropriate units of measure when computing the surface area of a pyramid.
6.G.2 6.G.4
• Pyramid • Vertex of a pyramid • Height of a pyramid • Slant height of a pyramid
• Identify geometric solids. • Compare and contrast the surface area of geometric solids. • Apply the surface area concept to a real-world situation.
6.G.4
N/A
25
Why Do We Use Statistics? Designing Statistical Questions
Dealing with Data Collecting, Displaying, and Analyzing Data
At the Olympics 15.3 Line Plots and Stem-and-Leaf Plots
Middle School Math Series: Course 1
Key Math Objective
6.SP.1
• Data • Statistical question • Population • Sample • Data analysis • Parameter • Statistic • Survey • Experiment
• Learn about statistical questions. • Recognize statistical questions and anticipate variability in data related to the question. • Design statistical questions that can be answered by a given data set. • Differentiate between surveys and experiments.
6.SP.4
• Categorical data • Quantitative data • Discrete data • Continuous data • Bar graph • Frequency • Double bar graph • Key • Stacked bar graph • Circle graph
• Discuss the different types of data that can be collected, displayed, and analyzed. • Determine how to select an appropriate graph to display different types of data. • Organize data into single, double, or stacked bar graphs. • Analyze data and interpret results from single, double, or stacked bar graphs and circle graphs.
• Dot plot • Distribution • Symmetric • Skewed right • Skewed left • Clusters • Gaps • Stem-and-leaf plot • Side-by-side stem-and-leaf plot
• Organize data and interpret dot plots. • Organize data and interpret stem-and-leaf plots.
CCSS
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.d
Technology
Talk the Talk
Lesson Title
15.1
15.2
Peer Analysis
Chapter
Collecting and Displaying Data This chapter develops the understanding of statistics and variability. Various representations are used to summarize numerical data sets.
Modules
15
Worked Examples
Middle School Math Series: Course 1
Key Terms
26
Middle School Math Series: Course 1
Building Up 15.4 Using Histograms
• Organize data into a histogram. • Analyze data presented in a histogram.
6.SP.4 6.SP.5.a
• Hisotgram • Frequency table
• Analyze data recorded during an experiment and answer questions that were posed at the beginning of the experiment.
6.SP.4 6.SP.5.a 6.SP.5.d
N/A
Analyze This! 15.5
Designing and Implementing an Experiment
Middle School Math Series: Course 1
27
Lesson Title
Key Math Objective
CCSS
In the Middle 16.1
• Review the meaning of mean, median, and mode. Analyzing Data Using Measures of • Calculate and interpret the mean, the median, and the mode for a set of data. Center
Which Measure of Center Should I Use? 16.2 Determining When to Use the Mean, Median, or Mode
Picking a Player 16.3
Calculating and Interpreting the Mean Absolute Deviation
Five Number Summary 16.4
Analyzing Data Using the Five Number Summary
Box It Up! 16.5
Displaying and Analyzing Data Using Box-and-Whisker Plots
Middle School Math Series: Course 1
6.SP.3
Technology
Talk the Talk
Chapter
Peer Analysis
This chapter reviews the measures of center with an emphasis on which measure is the most appropriate to describe a data set. Box-andAnalyzing and Interpreting Data whisker plots are used to display numerical data and investigate variation. Graphing calculators and spreadsheets are used to determine mean absolute deviation and to construct box-and-whisker plots.
Worked Examples
16
Modules
Middle School Math Series: Course 1
Key Terms
• Measure of center • Mode • Median • Balance point • Mean
• Calculate the mean, median, and mode from a graphical display of data. • Determine when to use the mean, median, or mode to describe a data set.
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.c 6.SP.5.d
N/A
• Calculate the deviations of each data value from the mean of a data set. • Calculate the absolute deviations of each data value from the mean of a data set. • Calculate and interpret the mean absolute deviation for a data set.
6.SP.3 6.SP.4 6.SP.5.c 6.SP.5.d
• Measures of variation or variability • Deviation • Absolute deviation • Mean absolute deviation
• Calculate and interpret the range, quartiles, and interquartile range as measures of variability for a data set. • Calculate and interpret the five number summary as a measure of variability for a data set.
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.c 6.SP.5.d
• Range • Quartiles (Q) • Interquartile range (IQR) • Five number summary
• Construct and interpret a box-and-whisker plot for a data set. • Determine if a data set has outliers, and discuss how outliers affect the display and analysis of the data.
6.SP.4 6.SP.5.a 6.SP.5.b 6.SP.5.c 6.SP.5.d
• Box-and-whisker plot • Outlier
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