Wayne County Public Schools Mathematics Pacing Guide: Grade 8 Mathematics

Major Instructional Resource: NC DPI’s Grade 8 Math Unpacking Document REVISED July 2015

Domain / First Quarter / Second Quarter / Third Quarter / Fourth Quarter
The Number System
(2% - 7%) / Use rational and irrational numbers.
8.NS.1; 8.NS.2 / Review all Standards in this Domain
Expressions and Equations
(27% - 32%) / Work with radicals and integer exponents.
8.EE.1; 8.EE.2; 8.EE.3; 8.EE.4
Analyze and solve linear equations in one variable.
8.EE.7 / Understand the connections between proportional relationships, lines, and linear equations.
8.EE.5; 8.EE.6
Analyze and solve pairs of simultaneous linear equations.
8.EE.8 / Review all Standards in this Domain
Functions
(22% - 27%) / Define, evaluate, and compare functions.
8.F.1; 8.F.2; 8.F.3
Use functions to model relationships between quantities.
8.F.4; 8.F.5 / Review all Standards in this Domain
Geometry
(20% - 25%) / Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.1; 8.G.2; 8.G.3; 8.G.4; 8.G.5
Understand and apply the Pythagorean Theorem.
8.G.6; 8.G.7; 8.G.8
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.9 / Review all Standards in this Domain
Statistics and Probability
(15% - 20%) / Investigate patterns of association in bivariate data.
8.SP.1; 8.SP.2; 8.SP.3; 8.SP.4
Textbook
Holt Middle School Math, Course 3, © 2004
Note: The textbook does not provide one-to-one coverage of the Grade 8 NC SCoS Math Standards. Always use NC DPI’s Grade 8 Math Unpacking Document and supplement with the textbook only as appropriate.
Be sure to omit Chapters & Chapter Sections that are not aligned to the Grade 8 NC SCoS Math Standards.
Note: The textbook does not provide complete, in-depth coverage of the Common Core State Standards for Math; supplement with additional resources that provide standards-based activities that align with the Grade 8 Content Standards and the Standards for Mathematical Practice. / Use DPI’s Grade 8 Math Unpacking Document
Supplement with Textbook as Appropriate
Concepts to cover:
·  Exponents
·  Solving Equations
·  Rational & Irrational Numbers
·  Squares & Square Roots
·  Scientific Notation
The following Chapters/Sections in the textbook correlate to 1st 9-weeks Standards:
·  Chapter 1: Sections 1-4; 6-9
Omit Section 5: Inequalities
·  Chapter 2: Sections 1-4; 6-9
Omit Section 5: Inequalities
·  Chapter 3: Sections 2-6; 8-10
Omit Section 1: Rational Numbers
Omit Section 7: Inequalities
·  Chapter 10: Sections 1, 2, 3
1, 2, & 3: Solving Linear Equations
Omit Section 4: Inequalities / Use DPI’s Grade 8 Math Unpacking Document
Supplement with Textbook as Appropriate
Concepts to cover:
·  Pythagorean Theorem
·  Geometry
The following Chapters/Sections in the textbook correlate to 2nd 9-weeks Standards:
·  Chapter 5: Sections 1-3; 5-7
Omit Section 4: Polygons
Omit Section 8: Symmetry
Omit Section 9: Tessellations
·  Chapter 6: Sections 3, 4, 6, 7, & 10
Omit Sections 1, 2, 5, 8, & 9
·  Chapter 7: Sections 2, 5, 6
Omit Sections 1, 3, 4, 7, 8, 9
Note: Omit Chapters 8 & 9
Big Ideas for Grade 8
● Linear Equations ---
Modeling, Solving, &
Systems
● Slope
● Functions / Use DPI’s Grade 8 Math Unpacking Document
Supplement with Textbook as Appropriate
Concepts to cover:
·  Equations of Lines
·  Functions
·  Systems of Equations
The following Chapter/Sections in the textbook correlate to 3rd 9-weeks Standards:
·  Chapter 10: Sections 5 & 6
5 6: Systems of Equations
·  Chapter 11: Sections 1-3; 5
Omit Sections 4 & 6
·  Chapter 12: Sections 4-8
Omit Sections 1, 2, & 3
______
Big Ideas for Grade 8
● Transformations
● Congruence
● Similarity
● Pythagorean Theorem
● Volume of Cylinders,
Spheres, Cones –
Must know formulas. / Use DPI’s Grade 8 Math Unpacking Document
Supplement with Textbook as Appropriate
Concepts to cover:
·  Scatter Plots
The following Chapter/Sections in the textbook correlate to 4th 9-weeks Standards:
·  Chapter 4: Sections 2, 6, 7, & Extension
2: Make Tables (not Stem & Leaf Plots)
6: Misleading Graphs & Statistics –
--- embedded throughout
7: Scatter Plots
Extension: Mean Absolute Deviation
--- needed for Algebra 1
Omit Sections 1, 3, 4, 5
·  Chapter 11: Section 7: Line of Best Fit
------
Big Ideas for Grade 8
● Rational & Irrational
Numbers
● Integer Exponents
● Scatter Plots
● Angles formed by parallel
lines

7/2015

Wayne County Public Schools

2010 NC Standard Course of Study for Mathematics

Grade 8

Textbook Resource: Holt Middle School Math, Course 3, North Carolina Edition, by Holt, Inc., © 2004.

NOTE: Not all Chapters nor all sections of each Chapter of the textbook are aligned to the 2010 NC Math SCoS – be sure to use ONLY the sections that are aligned to the 2010 NC Math SCoS. The taught curriculum is the 2010 North Carolina Standard Course of Study for Mathematics; the textbook is only one of many instructional resources.

Chapter Topics

Chapter 1: Algebra Toolbox Sections: 1, 2, 3, 4, 6, 7, 8, 9

Chapter 2: Integers and Exponents Sections: 1, 2, 3, 4, 6, 7, 8, 9

Chapter 3: Rational and Real Numbers Sections: 2, 3, 4, 5, 6, 8, 9, 10

Chapter 4: Collecting, Displaying, and Analyzing Data Sections: 2, 6, 7, Extension

Chapter 5: Plane Geometry Sections: 1, 2, 3, 5, 6, 7

Chapter 6: Perimeter, Area, and Volume Sections: 3, 4, 6 (Cylinders), 7(Cones), 10 (Spheres)

Chapter 7: Ratios and Similarity Sections: 2, 5, 6

Chapter 8: Percents OMIT

Chapter 9: Probability OMIT

Chapter 10: More Equations and Inequalities Sections: 1, 2, 3, 5, 6

Chapter 11: Graphing Lines Sections: 1, 2, 3, 5, 7

Chapter 12: Sequences and Functions Sections: 4, 5, 6, 7, 8

7/2015

Grade 8 Mathematics

Holt Middle School Math: Course 3 (8th Grade), © 2004 Alignment to the 2010 NC Standard Course of Study

Textbook Section / Section Topic / 2010 NC Standard Course of Study
Grade 8 Mathematics
1-1 / Variables and Expressions / 8.EE.7
1-2 / Write Algebraic Expressions / 8.EE.7
1-3 / Solve Equations / 8.EE.7
1-4 / Solve Equations / 8.EE.7
1-5 / Inequalities / Not in 8th Grade
1-6 / Combine Like Terms / 8.EE.7
1-7 / Ordered Pairs / 8.F.1
1-8 / Graphing on the Coordinate Plane / 8.F.1
1-9 / Interpret Graphs and Tables / 8.F.5
2-1 / Adding Integers / Prerequisite for 8.EE.7 Calculator Inactive
2-2 / Subtracting Integers / Prerequisite for 8.EE.7 Calculator Inactive
2-3 / Multiplying and Dividing Integers / Prerequisite for 8.EE.7 Calculator Inactive
2-4 / Solving Equations with Integers / 8.EE.7
2-5 / Inequalities / Not in 8th Grade
2-6 / Exponents / 8.EE.1
2-7 / Properties of Exponents / 8.EE.1
2-8 / Patterns in Exponents / 8.EE.1
2-9 / Scientific Notation / 8.EE.3 8.EE.4
3-1 / Rational Numbers / Not in 8th Grade
3-2 / Adding and Subtracting Rational Numbers / Prerequisite for 8.EE.7 Calculator Inactive
3-3 / Multiplying Rational Numbers / Prerequisite for 8.EE.7 Calculator Inactive
3-4 / Dividing Rational Numbers / Prerequisite for 8.EE.7 Calculator Inactive
3-5 / Adding and Subtracting Fractions / Prerequisite for 8.EE.7 Calculator Inactive
3-6 / Solving Equations with Fractions / 8.EE.7
3-7 / Inequalities / Not in 8th Grade
3-8 / Squares and Square Roots / 8.EE.2
3-9 / Finding Square Roots / 8.EE.2
3-10 / The Real Numbers / 8.NS.1 & 8.NS.2
4-1 / Samples and Surveys / Not in 8th Grade
4-2 / Make Tables (not Stem & Leaf Plots) / 8.SP.4
4-3 / Measures of Central Tendency / Not in 8th Grade
4-4 / Box-and-Whisker Plots / Not in 8th Grade
4-5 / Displaying Data / Not in 8th Grade
4-6 / Misleading Graphs and Statistics / 8.F.5 (Embedded throughout)
4-7 / Scatterplots / 8.SP.1
Ch.4 Extension / Mean Absolute Deviation / Cover because it is new in 6th grade, and will be covered in Math One.
5-1 / Angles / 8.G.5
5-2 / Parallel and Perpendicular Lines / 8.G.5
5-3 / Triangles / 8.G.5
5-4 / Polygons / Not in 8th Grade
5-5 / Coordinate Geometry / 8.F.4
5-6 / Congruence / 8.G.2
5-7 / Transformations / 8.G.1 8.G.2 8.G.4
5-8 / Symmetry / Not in 8th Grade
5-9 / Tessellations / Not in 8th Grade
6-1 / Perimeter and Area (Parallelograms) / Not in 8th Grade
6-2 / Perimeter and Area (Triangles & Trapezoids) / Not in 8th Grade
6-3 / Pythagorean Theorem / 8.G.6 8.G.7 8.G.8
6-4 / Circles / Prerequisite for 8.G.9
6-5 / Drawing 3D Figures / Not in 8th Grade
6-6 / Volume of Cylinders (only) – Know Formula / 8.G.9
6-7 / Volume of Cones (only) – Know Formula / 8.G.9
6-8 / Surface Area / Not in 8th Grade
6-9 / Surface Area / Not in 8th Grade
6-10 / Volume of Spheres (only) / 8.G.9
7-1 / Ratios and Proportions / Not in 8th Grade
7-2 / Ratios, Rates & Unit Rates (as graphs) / 8.EE.5
7-3 / Analyze Units / Not in 8th Grade
7-4 / Solving Proportions / Not in 8th Grade
7-5 / Dilations / 8.G.3 8.G.4
7-6 / Similar Figures / 8.G.4
7-7 / Scale Drawings / Not in 8th Grade
7-8 / Scale Models / Not in 8th Grade
7-9 / Scaling 3D Figures / Not in 8th Grade
Chapter 8 / Not in 8th Grade
Chapter 9 / Not in 8th Grade
10-1 / Solving Two Step Equations / 8.EE.7
10-2 / Solve Multi-Step Equations / 8.EE.7
10-3 / Solve Equations with Variables on Both Sides / 8.EE.7
10-4 / Inequalities / Not in 8th Grade
10-5 / Solving for a variable (y) / 8.F.3
10-6 / Systems of Equations / 8.EE.8
11-1 / Graphing Linear Equations / 8.F.1 8.F.2
11-2 / Slope of a Line / 8.F.4
11-3 / Using Slopes and Intercepts / 8.F.4
11-4 / Point Slope Form / Not in 8th Grade
11-5 / Direct Variation / 8.F.3
11-6 / Inequalities / Not in 8th Grade
11-7 / Line of Best Fit / 8.SP.2 8.SP.3
12-1 / Arithmetic Sequences / Not in 8th Grade
12-2 / Geometric Sequences / Not in 8th Grade
12-3 / Other Sequences / Not in 8th Grade
12-4 / Functions / 8.F.1
12-5 / Linear Functions / 8.F.3
12-6 / Exponential Functions / 8.F.1
12-7 / Quadratic Functions / 8.F.1
12-8 / Inverse Variation / 8.F.1

NOTE: The textbook does not provide complete, in-depth coverage of the 2010 NC Standard Course of Study for Mathematics. Teachers will need to supplement with additional resources that provide standards-based activities that align with the Content Standards and the Standards for Mathematical Practice.

By standards-based, we mean that students are learning mathematics by exploring mathematically-rich tasks and sharing strategies, ideas, and approaches with one another. During these activities, the teacher’s role is to truly facilitate learning by posing a task, asking questions that guide students’ understanding, and assessing students’ mathematical understanding.

The phases of a lesson that involves a rich tasks might include:

Engage- Students open the lesson by engaging in a brief activity to build upon students’ prior knowledge.

Explore- Students explore a mathematically rich task or activity that includes the main mathematical goals. During this phase, the teacher may model how to play a game or do an activity, but should not model or over teach strategies or procedures.

Explain- Students discuss strategies and mathematical ideas from the Explore phase. The teacher may teach content and emphasize concepts or strategies here.

Elaborate- Students complete a follow-up activity or task that extends their work from Explore and the discussion of concepts in Explain.

Evaluation of Students

-  Formative Assessment- How can the teacher assess students during the lesson?

-  Summative Assessment- How can the teacher assess students’ work after the lesson?

Sample lessons that involve mathematically-rich tasks will be available at http://maccss.ncdpi.wikispaces.net/home

Visit this site regularly.

7/2015

Eighth Grade – 2010 NC Standard Course of Study – MATH

Critical Areas

1. Formulating and reasoning about expressions and equations, including modeling an

association in bivariate data with a linear equation, and solving linear equations and

systems of linear equations – Students use linear equations and systems of linear equations

to represent, analyze, and solve a variety of problems. Students recognize equations for

proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that

the constant of proportionality (m) is the slope, and the graphs are lines through the origin.

They understand that the slope (m) of a line is a constant rate of change, so that if the input or

x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m·A.

Students also use a linear equation to describe the association between two quantities in

bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting

the model, and assessing its fit to the data are done informally. Interpreting the model in the

context of the data requires students to express a relationship between the two quantities in

question and to interpret components of the relationship (such as slope and y-intercept) in

terms of the situation. Students strategically choose and efficiently implement procedures to

solve linear equations in one variable, understanding that when they use the properties of

equality and the concept of logical equivalence, they maintain the solutions of the original

equation. Students solve systems of two linear equations in two variables and relate the

systems to pairs of lines in the plane; these intersect, are parallel, or are the same line.

Students use linear equations, systems of linear equations, linear functions, and their

understanding of slope of a line to analyze situations and solve problems.

2. Grasping the concept of a function and using functions to describe quantitative

relationships – Students grasp the concept of a function as a rule that assigns to each input

exactly one output. They understand that functions describe situations where one quantity

determines another. They can translate among representations and partial representations of