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8-1: Integers Review (Lime Green)
Key vocabulary:
• absolute value • addend • difference • factors • integers • minuend • opposite • product • quotient • subtrahend • sum • zero pair
• absolute value • addend • difference • factors • integers • minuend • opposite • product • quotient • subtrahend • sum • zero pair
1.1 Integer Operations: PatternsStudents use patterns to revisit the rules for adding, subtracting, multiplying, and dividing integers.
Standards 6.NS.C, 7.NS.A |
1.2 Integer Operations: A Counter ModelStudents use a model to revisit the rules for adding, subtracting, multiplying, and dividing integers.
Standards 6.NS.C, 7.NS.A |
1.3 Order of OperationsStudents review the conventions for the order of operations and apply them to evaluate expressions.
Standards 6.EE.A, 7.NS.A |
8-2 Expressions & Equations 1 (Blue)
Key vocabulary:
• equality • equation • evaluate • expression • inequality • simplify • solve (an equation) • variable (unknown)
• equality • equation • evaluate • expression • inequality • simplify • solve (an equation) • variable (unknown)
2.1 Exploring ExpressionsStudents write expressions with numbers and variables. Students simplify numerical expressions using the conventions for order of operations.
Standards 6.EE.A |
2.2 Exploring EquationsStudents learn to interpret equations. Students review the difference between expressions and equations. Students find values of variables to make equations true.
Standards 6.EE.B |
2.3 Mental Equation & Inequality StrategiesStudents solve equations using mental math strategies. Students solve inequalities and graph their solutions.
Standards 7.EE.B |
8-3 Patterns & Linear Functions 1 (Yellow)
Key vocabulary:
• function • explicit rule • (input-output rule) • inductive reasoning • linear function • ordered pair • recursive rule • y-intercept
• function • explicit rule • (input-output rule) • inductive reasoning • linear function • ordered pair • recursive rule • y-intercept
3.1 Geometric PatternsStudents extend geometric “toothpick” patterns. Students use numbers, pictures, symbols, and words (“the fourfold way”) to describe these patterns.
Standards 8.F.A, 8.F.B |
3.2 Number PatternsStudents observe and extend number sequences. They find recursive and explicit rules for number patterns.
Standards 8.F.A |
3.3 Saving for a PurchaseStudents use input-output equations, tables, and graphs to find how much time is needed to save for purchases.
Standards 8.EE.C, 8.F.A, 8.F.B |
8-4 Patterns & Linear Functions 2 (Magenta)
Key vocabulary:
• explicit rule (or input-output rule) • fourfold way • inductive reasoning • linear function • point of intersection • rate • slope (of a line) • y-intercept
• explicit rule (or input-output rule) • fourfold way • inductive reasoning • linear function • point of intersection • rate • slope (of a line) • y-intercept
4.1 Growing ShapesStudents extend square and rectangle patterns. Students represent geometric measures in the patterns using input-output tables, graphs, symbols, and words (the “fourfold way”). Standards 8.F.A, 8.F.B
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4.2 Going to the ParkStudents analyze information about friends going to a park after school to understand time, distance, and rate of speed relationships using numbers, graphs, symbols, and words.
Standards 8.EE.B, 8.EE.C, 8.F.A, 8.F.B |
4.3 Stacking CupsStudents measure and record heights of stacked cups, and represent the data using numbers, graphs, and algebraic symbols. Students estimate a line that fits the data.
Standards 8.F.A, 8.F.B, 8.SP.A |
8-5 Expressions & Equations 2 (Green)
Key vocabulary:
• additive inverse property • expression • distributive property • simplify • equation • solve (an equation) • evaluate • substitution • additive inverse property • terms (like terms)
• additive inverse property • expression • distributive property • simplify • equation • solve (an equation) • evaluate • substitution • additive inverse property • terms (like terms)
5.1 Cups & Counters ExpressionsStudents write and simplify expressions in the context of a model.
Standards 6.EE.A, 6.EE.B, 7.EE.B |
5.2 Number TricksStudents perform mathematical number tricks and use algebraic expressions to show how the number tricks work.
Standards 6.EE.A, 6.EE.B |
5.3 Cups and Counters Equations 1Students solve linear equations with one variable using a visual model, and they record the steps with pictures and algebraic symbols.
Standards 7.EE.B, 8.EE.C |
8-6 Solving Equations (Purple)
Key vocabulary:
• equation • rational numbers • integers • numerical coefficient • solution to an equation • variable • equation • rational numbers • integers • numerical coefficient • solution to an equation • variable
• equation • rational numbers • integers • numerical coefficient • solution to an equation • variable • equation • rational numbers • integers • numerical coefficient • solution to an equation • variable
6.1 Cups and Counters Equations 2Students solve linear equations using a model and record the steps with pictures and algebraic symbols.
Standards 7.EE.A, 7.EE.B, 8.EE.C |
6.2 Solving Equations with Integer CoefficientsStudents begin to transition from solving equations with a model to using only algebraic notation.
Standards 7.EE.A, 7.EE.B, 8.EE.C |
6.3 Solving Equations with Rational CoefficientsStudents solve more algebraic equations using algebraic notation. Students justify the steps used to solve equations. Some equations will involve noninteger values.
Standards 7.EE.A, 7.EE.B, 8.EE.C |
8-7 Exploring Functions (Orange)
Key vocabulary:
• direct proportion • function • graph of a function • input-output rule • linear function • rate • unit rate • variable
• direct proportion • function • graph of a function • input-output rule • linear function • rate • unit rate • variable
7.1 Introduction to FunctionsStudents explore the concept of a function. Students define the terms function and graph of a function. Students describe examples of functions and examples of non-functions.
Standards 8.F.A |
7.2 Rate GraphsStudents use words, pictures, tables of numbers, and graphs to represent rates. Students compare representations of functions.
Standards 8.F.A, 8.F.B |
7.3 Best Buy ProblemsStudents use numbers and graphs to help determine which choices are better buys, based on price. Students learn about a special linear function called a direct proportion.
Standards 6.RP.A, 7.RP.A, 8.EE.B, 8.F.A, 8.F.B |
8-8 Slope & Slope-Intercept Form of a Line (Pink)
Key vocabulary:
• congruent • slope (slope of a line) • input-output rule • x-intercept • linear function • y-intercept • slope-intercept form of a linear equation
• congruent • slope (slope of a line) • input-output rule • x-intercept • linear function • y-intercept • slope-intercept form of a linear equation
8.1 Introduction to SlopeStudents count distances and use slope definitions to find slopes of line segments on a grid and on a set of coordinate axes. Students explore the meaning of positive and negative slopes.
Standards 8.EE.B |
8.2 Input-Output InvestigationStudent will use input-output tables to help graph and find equations of lines.
Standards 8.F.A, 8.F.B, 8.EE.B |
8.3 Slope-Intercept FormStudents find equations of lines in slope-intercept form. Students extend the meaning of slope to horizontal and vertical lines. Students use properties of parallel lines and similar triangles to deepen our understanding of the meaning of slope of a line.
Standards 8.EE.B |
8-9 Systems of Linear Equations (Lime Green)
Key vocabulary:
• linear function • ordered pair • solution to a system of equations • slope of a line • system of equations • slope-intercept form of a linear equation • y-intercept
• linear function • ordered pair • solution to a system of equations • slope of a line • system of equations • slope-intercept form of a linear equation • y-intercept
9.1 Solving Linear Systems by GraphingStudents solve systems of linear equations by graphing. Students write linear equations in equivalent forms. Students create a mathematical model (equation) to solve “the rope problem.”
Standards 8.EE.C, 8.F.A, 8.F.B |
9.2 Solving Linear Systems by SubstitutionStudents solve systems of linear equations by the substitution method.
Standards 8.EE.C, 8.F.A, 8.F.B |
9.3 Solving Linear Systems by EliminationStudents solve systems of linear equations by the elimination method.
Standards 8.EE.C |
8-10 Bivariate Data (Blue)
Key vocabulary:
• association • bivariate data • categorical data • data displays • data set • frequency table • line of best fit • measurement data • numerical data • outlier • population • relative frequency table • scatter plot • two-way table
• association • bivariate data • categorical data • data displays • data set • frequency table • line of best fit • measurement data • numerical data • outlier • population • relative frequency table • scatter plot • two-way table
10.1 Categorical DataStudents use two-way tables to display the frequencies and relative frequencies of categorical data. Students examine patterns of association in bivariate categorical data. Students draw conclusions about possible associations. Standards 8.SP.A
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10.2 Numerical DataStudents construct scatter plots for bivariate numerical data. Students investigate various patterns of association in bivariate data. Students interpret scatter plots.
Standards 8.SP.A |
10.3 Lines of Best FitStudents construct linear models for measurement and other numerical data clustered around a straight line. Students draw lines of best fit. Students estimate an equation for the line of best fit. Students use the equation as a model to make predictions.
Standards 8.F.B, 8.SP.A |
8-11 Exponents & Roots (Yellow)
Key vocabulary:
• conjecture • exponential notation • factor • product • quotient • radical sign • radicand • scientific notation • square of a number • square root of a number
• conjecture • exponential notation • factor • product • quotient • radical sign • radicand • scientific notation • square of a number • square root of a number
11.1 Squares and Square RootsStudents find squares and square roots of numbers. Students approximate square roots, and they locate square roots on a number line. Standards 8.NS.A
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11.2 Conjectures About ExponentsStudents use patterns to make conjectures about rules for multiplying expressions involving exponents. Students explore rules for exponents, and they apply them to simplifying expressions. Standards 8.EE.
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11.3 Large and Small NumbersStudents write large and small numbers using a variety of notations, including scientific notation. Students problems involving large numbers. Standards 8.EE.A
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8-12 Lines, Angles & Triangles (Magenta)
Key vocabulary:
• adjacent angles • alternate exterior angles • alternate interior angles • complementary angles • converse of the Pythagorean Theorem • corresponding angles • deductive reasoning • exterior angle of a triangle • hypotenuse • inductive reasoning • legs • parallel lines • perpendicular lines • proof • Pythagorean Theorem • supplementary angles • transversal • vertical angles
• adjacent angles • alternate exterior angles • alternate interior angles • complementary angles • converse of the Pythagorean Theorem • corresponding angles • deductive reasoning • exterior angle of a triangle • hypotenuse • inductive reasoning • legs • parallel lines • perpendicular lines • proof • Pythagorean Theorem • supplementary angles • transversal • vertical angles
12.1 Angles & TrianglesStudents establish relationships among angles. Students establish facts about angle sums in triangles. Students solve problems involving angle measures.
Standards 8.G.A |
12.2 Parallel LinesStudents establish vocabulary and facts related to angles formed when parallel lines are crossed by a third line. Students use properties of parallel lines to solve problems.
Standards 8.G.A |
12.3 The Pythagorean TheoremStudents explore the relationship among the side lengths of right triangles and then understand a proof of the Pythagorean Theorem. Students use the Pythagorean Theorem to solve problems. Standards 8.EE.A, 8.G.B
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8-13 Translations, Rotations & Reflections (Green)
Key vocabulary:
• angle of rotation • center point of rotation • function • image • line of reflection • reflection • rotation • transformation • translation • vector
• angle of rotation • center point of rotation • function • image • line of reflection • reflection • rotation • transformation • translation • vector
13.1 TranslationsStudents perform a transformation experiment using patty paper. They define transformations of the plane and observe some properties of transformations. Students learn about a transformation called a translation.
Standards 8.F.A, 8.G.A |
13.2 RotationsStudents experiment with rotations and explore their properties. They make conjectures about rotations of coordinate pairs.
Standards 8.G.A |
13.3 ReflectionsStudents experiment with reflections and explore their properties. They will make conjectures about reflections of coordinate pairs. Students compare properties of translations, rotations, and reflections.
Standards 8.G.A |
8-14 Congruence & Similarity (Purple)
Key vocabulary:
• congruent figures • deductive reasoning • dilation • inductive reasoning • image • ratio of proportionality • proof • scale factor • similar figures • transformation
• congruent figures • deductive reasoning • dilation • inductive reasoning • image • ratio of proportionality • proof • scale factor • similar figures • transformation
14.1 CongruenceStudents define congruence and explore its properties.
Standards 8.G.A |
14.2 DilationsStudents experiment with dilations and explore properties of dilations.
Standards 8.G.A, 8.G.B |
14.3 SimilarityStudents define similarity and explore its properties. Students compare properties of similarity to properties of congruence.
Standards 8.G.A |
8-15 Geometry Discoveries (Orange)
Key vocabulary:
• area • base • circumference • cone • cylinder • diameter • height • hypotenuse • legs of a right triangle • parallel • pi • polyhedron • prism • Pythagorean Theorem • right rectangular prism • similar triangles • slope of a line • sphere • volume
• area • base • circumference • cone • cylinder • diameter • height • hypotenuse • legs of a right triangle • parallel • pi • polyhedron • prism • Pythagorean Theorem • right rectangular prism • similar triangles • slope of a line • sphere • volume
15.1 Similar TrianglesStudents establish and apply the angle-angle criterion for similarity of triangles. Students find missing side lengths of similar triangles. Students link properties of similarity to the slope of a line and to a famous theorem.
Standards 8.EE.B, 8.G.B |
15.2 Volume of CylindersStudents develop the formula for the volume of cylinders and apply it to solve problems. Standards 8.NS.A, 8.G.C
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15.3 Volume of Cones & SpheresStudents develop formulas for the volumes of cones and spheres and apply them to solve problems.
Standards 8.NS.A, 8.G.C |
8-16 The Real Number System (Pink)
Key vocabulary:
• cube of a number • cube root of a number • square of a number • square root of a number • integers • irrational numbers • natural numbers • rational numbers • real numbers • repeating decimal • terminating decimal • whole numbers
• cube of a number • cube root of a number • square of a number • square root of a number • integers • irrational numbers • natural numbers • rational numbers • real numbers • repeating decimal • terminating decimal • whole numbers
16.1 Exponents & Roots RevisitedStudents work with squares, square roots, cubes, and cube roots of rational numbers. Students review rules for exponents and roots. Students solve problems with large and small numbers written in multiple ways, including scientific notation.
Standards 8.EE.A |
16.2 Rational NumbersStudents deepen their understanding of rational numbers. Students learn why the decimal expansion of a rational number eventually repeats. Students learn how to express repeating decimals as quotients of integers. Students familiarize themselves with the decimal expansions of some common fractions by playing a game based on probability.
Standards 7.SP.C, 8.NS.A |
16.3 Irrational NumbersStudents practice locating decimal numbers on the real number line. Students learn that each real number has a decimal name (address) locating it on the real number line, that repeating decimals represent rational numbers, and that nonrepeating decimals represent irrational numbers. Students learn about two famous irrational numbers, pi and 2 .
Standards 8.NS.A |