> { Zbjbjzz 7&VQVVVVVjjj8~Tj&f(...%%%%%%%$'2*L%V.....%VV4%(((.VV%(.%((V#@$Kj]0"#%%0& $x~*R~*$~*V$..(.....%%(...&....~*......... : 2. Properties of algebra and equality are used to solve linear equations and systems of
equationsb. Analyze and solve pairs of simultaneous linear equations.
i. Explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. I
ii. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. I
iii. Solve realworld and mathematical problems leading to two linear equations in two variables. II will analyze pairs of simultaneous linear equations.
I will solve pairs of simultaneous linear equations.
I will explain that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs.
I will explain that solutions to a system of two linear equations in two variables correspond to points of intersections satisfy both equations simultaneously.
I will solve systems of two linear equations in two variables algebraically.
I will estimate solutions of two linear equations by graphing the equations.
I will solve simple cases by inspection.
I will solve realworld and problems leading to two linear equations in two variables.
I will solve mathematicall problems leading to two linear equations in two variables
Anal
Appl
Synth
SynthHolt, Rinehart, and Winston
p. 540
p. 540542
System of
Equations
Analyze
Linear Equations
Variables
3. Graphs, tables and equations can be used to distinguish between linear and nonlinear
functionsa.Define, evaluate, and compare functions.
i. Define a function as a rule that assigns to each input exactly one output. I
ii. Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding
output. I
iii. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). I
iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. I
v. Give examples of functions that are not linear. II will define functions.
I wll evaluate functions.
I will compare functions.
I will define a function as a rule that assigns to each input exactly one output.
I will defend how that the graph of a function is the set of ordered pairs consisting of an input.
I will defend how that the graph of a function is the set of ordered pairs consisting of an output.
I will compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
I will interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.
I will give examples of functions that are not linear.
Know
Comp
Appl
Comp
Comp
Comp
Holt, Rinehart, and Winston
p. 608610
p. 608610
p. 608610
p. 39
p. 613
Functions
Function Rule
Input
Output
Set of Ordered
Pairs
Equation3. Graphs, tables and equations can be used to distinguish between linear and nonlinear
functionsb. Use functions to model relationships between quantities.I
i. Construct a function to model a linear relationship between two quantities.I
ii. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. I
iii. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a
table of values. I
iv. Describe qualitatively the functional relationship between two quantities by analyzing a graph. I
v. Sketch a graph that exhibits the qualitative features of a function
that has been described verbally. I
vi. Analyze how credit and debt impact personal financial goals (PFL) ?
I will use functions to model relationships between quantities.
I will construct a function to model a linear relationship between two quantities.
I will determine the rate of change of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
I will determine the rate of initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
I will interpret the rate of change of a linear function in terms of the situatin it models, and in terms of its graph or a table of values.
I will interpret the rate of initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
I will describe qualitatively the functional relationship between two quantities by analyzing a graph.
I will sketch a graph that exhibits the qualitative features of a function
that has been described verbally.
I will analyze how credit impacts personal financial goals (PFL).
I will analyze how debt impacts personal financial goals (PFL).
Appl
Appl
Comp
Comp
Appl
Analysis
Holt, Rinehart, and Winston
p. 39
p. 346347
p. 613614
p. 4344
Rate of change
Initial Value
Sketch
1. Transformations of objects can be used to define the concepts of congruence and similaritya. Verify experimentally the properties of rotations, reflections, and translations. I
I will verify experimentally the properties of rotations.
I will verify experimentally the properties of reflections.
I will verify experimentally the properties of translations.
KnowHolt, Rinehart, and Winston
p. 254255, 362Rotation
Reflection
Translation1. Transformations of objects can be used to define the concepts of congruence and similarityb. Describe the effect of dilations, translations,
rotations, and reflections
on twodimensional figures using coordinates. II will describe the effect of dilations on twodimensional figures using coordinates.
I will describe the effect of translations on twodimensional figures using coordinates.
I will describe the effect of rotations on twodimensional figures using coordinates.
.
I will describe the effect of reflections on twodimensional figures using coordinates.
CompHolt, Rinehart, and Winston
p. 254, 362Dilations
Translations
Reflections
Twodimensional
figures1. Transformations of objects can be used to define the concepts of congruence and similarityc. Demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. II will demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations.
I will demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of reflections.
I will demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of translations.
ApplHolt, Rinehart, and Winston
p. 254255, 362Congruent
Sequence1. Transformations of objects can be used to define the concepts of congruence and similarityd. Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. I
Given two congruent figures, I will describe a sequence of transformations that exhibits the congruence between them.
CompHolt, Rinehart, and Winston
p. 254255, 3621. Transformations of objects can be used to define the concepts of congruence and similaritye. Demonstrate that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations,
reflections, translations, and dilations. II will demonstrate that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations.
I will demonstrate that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of reflections.
I will demonstrate that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of translations.
I will demonstrate that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of dilations.
ApplHolt, Rinehart, and Winston
p. 254255, 362
1. Transformations of objects can be used to define the concepts of congruence and similarityf. Given two similar twodimensional figures, describe a sequence of
transformations that exhibits the similarity between them. I
Given two similar twodimensional figures, I will describe a sequence of
transformations that exhibits the similarity between them.Comp
Holt, Rinehart, and Winston
p. 254255, 3621. Transformations of objects can be used to define the concepts of congruence and similarityg. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. I
I will use informal arguments to establish facts about the angle sum and of triangles, about the angles created when parallel lines are cut by a transversal for similiarity of triangles.
I will use informal arguments to establish facts about the exterior angle of triangles, about the angles created when parallel lines are cut by the angleangle criterion for similarity of triangles.
I will use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal for similarity of triangles.
I will use informal arguments to establish facts about the exterior angle of triangles, about the angles created when parallel lines are cut by the angleangle criterion for similarity of triangles. ApplHolt, Rinehart, and Winston
p. 235236, 228229Parallel Lines
Transversal2. Direct and indirect measurement can be used to describe and make comparisonsd. State the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. I
Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (CCSS: 7.EE.4) S2B2
____________________________
Construct a function to model a linear relationship between two quantities. (CCSS: 8.F.4) S2B2
Represent and analyze quantitative relationships between dependent and independent variables. (CCSS: 6.EE) S2B3
Use variables to represent two quantities in a realworld problem that change in relationship to one another. (CCSS: 6.EE.9)
Write an equation to express one quantitiy, thought of as the dependent variable,interms of the other quantitiy, thought of as the independent variable. (CCSS.6.EE.9)
Analyze the relationship betweenthe dependent and independent variables using graphs and tables, and relate these to the equation. (CCSS:6.EE.9)
State the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. (CCSS: 8.G.9) S4B5
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. (CCSS: 8.G.7) S4B5
____________________________
Demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. (CCSS: 8.G.2) S4B6
Given two congruent figures,describe a sequence of transformations that exhibits the congruence between them. (CCSS: 8.G.2)S4B6
____________________________
Solve realworld and mathematical problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (CCSS: 7.G.6) S5B4
____________________________
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (CCSS: 7.RP.1)
State the formulas for the area and circumference of a circle and use them to solve problems. (CCSS: 7.G4) S5B5
__________________________
Analyze proportional relationships and use them to solve realworld and mathematical problems. (CCSS: 7.RP) S6B1
___________________________
Use proportional relationships to solve multistep ratio and percent problems. (CCSS:6.RP3) S6B1
____________________________
Use ratio reasoning to convert measurement units. (CCSS: 6.RP.3d) S6B1
Perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are not parentheses to specify a particular order (Order of Operations). (CCSS: 6.EE.2c) S6B2
____________________________
Apply the properties of integer exponents to generate equivalent numerical expressions. (CCSS:8.EE.1) S6B2
____________________________
Analyze proportional relatinships and use them to solve realworld and mathematical problems. (CCSS:7.RP) S6B4
____________________________
Use proportional relationships to solve multistep ratio and percent problems. (CCSS: 7.RP3) S6B4
Solve realworld and mathematical problems involving four operations with rational numbers. (CCSS: 7.NS.3) S6B4
___________________________
Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (CCSS: 7.EE.3) S6B4
I will state the formulas for the volumes of cones and use them to solve realworld and mathematical problems.
I will state the formulas for the volumes of cylinders and use them to solve realworld and mathematical problems.
I will state the formulas for the volumes spheres and use them to solve realworld and mathematical problems.
I will use variables to represent quantities in a realworld problem and construct simple equations to solve problems by reasoning about the quantities.
I will use variables to represent quantities in a mathematical problem, and construct simple equations to solve problems by reasoning about the quantities.
I will use variables to represent quantities in a realworld problem and construct simple inequalities to solve problems by reasoning about the quantities.
I will use variables to represent quantities in a mathematical problem, and construct simple inequalities to solve problems by reasoning about the quantities.
I will construct a function to model a linear relationship between two quantities.
I will represent quantitative relationships between dependent and independent variables.
I will analyze quantitative relationships between dependent and independent variables.
I will use variables to represent two quantities in a realworld problem that change in relationship to one another.
I will write an equation to express one quantitiy, thought of as the dependent variable,interms of the other quantitiy, thought of as the independent variable.
I will state the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld problems.
I will state the formulas for the volumes of cones, cylinders, and spheres and use them to mathematical problems.
I will apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld problems in two and three dimensions.
I will apply the Pythagorean Theorem to determine unknown side lengths in right triangles in mathematical problems in two and three dimensions.
______________________
I will demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations.
I will demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of reflections.
I will demonstrate that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence translations.
Given two congruent figures, I will describe a sequence of transformations that exhibits the congruence between them.
I will solve realworld problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
I will solve mathematical problems involving area, volume and surface area of two and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
I will compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
I will state the formulas for the area of a circle and use them to solve problems.
I will state the formulas for the circumference of a circle and use them to solve problems.
I will analyze proportional relationships and use them to solve realworld problems.
I will analyze proportional relationships and use them to solve mathematical problems.
I will use proportional relationships to solve multistep ratio problems.
I will use proportional relationships to solve multistep percent problems.
I will use ratio reasoning to convert measurement units.
I will perform arithmetic operations, including those involving wholenumber exponents, in the conventional order when there are not parentheses to specify a particular order (Order of Operations).
I will apply the properties of integer exponents to generate equivalent numerical expressions. ______________________ I will analyze proportional relationships and use them to solve realworld problems.
I will analyze proportional relationships and use them to solve mathematical problems.
I will use proportional relationships to solve multistep ratio problems.
.
I will use proportional relationships to solve multistep percent problems.
I will solve realworld problems involving four operations with rational numbers.
I will solve mathematical problems involving four operations with rational numbers.
I will apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation.
I will apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using estimation strategies. Know
APPL
APPL
ANAL
SYN
KNOWL
APPL
APPL
APPL
COMP
APPL
APPL
APPL
ANAL
APPL
APPL
APPL
APPL
ANAL
APPL
APPL
APPLHolt, Rinehart, and Winston
p. 312313, 307309, 324
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Holt, Rinehart, and Winston
Cones
Cylinder
Sphere
Function
Dependent Varibles
Independent Variables
Pythagorean Theorem
Right Triangles
Twodimensional figure
Rotation
Reflection
Translation
Transformations
Two dimensional object
Three dimensional object
Triangle
Quadrilateral
Polygon
Cube
Righ Prism
Ratio of fractions
Ratio of lengths
Ratio of area
Ratio of other quantities
Area of Circle
Area of Circumference
Proportional relationships
Proportional relationships
Percent problems
Exponents
Integer exponents
Rational Numbers
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math GRADE: 8 TIMELINE: 4th Quarter
Grade Level ExpectationEvidence OutcomeStudentFriendly
Learning ObjectiveLevel of
ThinkingResource Correlation
Academic Vocabulary
Learning Keys, 800.927.0478, HYPERLINK "http://www.learningkeys.org" www.learningkeys.org Page PAGE \* MERGEFORMAT 1
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