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Grade 7 Mathematics
Course Overview:
Students will develop mathematical knowledge and understanding in a setting where connection
to other disciplines is valued. Through the implementation of daily warm-ups and a thematic
approach focused on pre-algebra, students will apply the properties of decimals, integers and
exponents while solving real world problems.
Required Topics:
Equations and Formulas
Geometry: Transformations
Data Representation and Analysis
Negative Numbers, Integers and their properties
2 D Geometry: Basics
Exponents, Roots and Radicals
Polygons and Circles
Exponents and Orders of Magnitude
Perimeter, Area and Volume
Measurement Estimation and Errors
Relationship of Common Fractions, Decimals and Percentages
Properties of Common Decimal Fractions Constructions w/Straightedge & Compass
Proportionality Concepts
3-D Geometry
Proportionality Problems
Congruence & Similarity
2-D Coordinate Geometry
Patterns, Relations and Functions
Foundation Standard (MT Standard #1)
Competencies: students will…
1.
define and solve problems
2.
reason logically
3.
estimate, communicate, and model their thinking and
understanding
4.
connect mathematical ideas within mathematics and to
other subject areas
5.
use appropriate technology
6.
know and use appropriate math vocabulary
7.
use comprehension strategies
Standard #1: Students understand and apply the concepts and procedures from numbers
and operations (MT Standard #2).
Big Ideas: Proportionality, Exponents and Roots, Signed Numbers
Vocabulary: Difference, Doubling, Least Common Multiple, Powers, Savings Account, Tip
A. Decimals and mixed numbers
Competencies: students will
1.
add, subtract, multiply and divide and rename mixed numbers and
decimals (1.1B)
2.
convert between mixed numbers, fractions, decimals and percents
3.
identify terminating and repeating decimals and use in problem
Solving
Recognize and generate equivalent fractions, decimals and percent (1.1E)
B. Grouping
Competencies: students will…
1.
know and apply the rules of the order of operations, including
exponents and integers (1.3A)
2.
3.
create an expression using grouping symbols
change value of an expression by using grouping symbols
C. Powers
Competencies: students will…
1.
write numbers using exponents and radicals (1.1B)
2.
multiply and divide by powers of 10
3.
translate large numbers into scientific notation (1.1A)
D. Positive and Negative Numbers
Competencies: students will…
1.
represent integers and common fractions on a number line,
exhibiting knowledge of infinity
2.
add, subtract, multiply and divide positive and negative numbers
3.
distinguish between opposites and absolute value
4.
graph inequalities on a number line
E. Proportionality
Competencies: students will…
1.
represent integers and common fractions on a number line, exhibiting
knowledge of infinity
2.
add, subtract, multiply and divide positive and negative numbers (1.3B)
3.
distinguish between opposites and absolute value
4.
graph inequalities on a number line
5.
order rational numbers and square roots (1.1F)
6.
use positive and negative integers to represent real-life situations (1.1G)
7.
develop and use rates, ratios, proportions and percents to solve
problems including discounts, interest, taxes, tips, and percent change
(1.3C)
8.
interpret percents less than 1% and greater than 100% in real life situations
(1.1C).
F. Other
Competencies: students will…
1. reason with regard to multiples, factors, primes and divisibility (1.1H)
2. judge the effects of addition, subtraction, multiplication and division on
rational numbers as well as the effects of operations with square roots and
exponents (1.2A)
3. estimate based on the operations above (1.3D)
4. apply the commutative, associative, identity, inverse, and distributive
properties (1.2B).
Standard #2: Students understand and apply the concepts and procedures from algebra
(patterns, functions and relations). (MT Standards #3 and #7)
Big Ideas: Linear patterns, equations, graphs, and models
Vocabulary: Solution
A. Variables
Competencies: students will…
2
1.
2.
3.
4.
describe a linear pattern using variables in sequences, equations and
expressions (2.2A)
represent linear real life situations with algebraic expressions or equations
(2.2A)
evaluate expressions for given values (2.2C)
recognize the equivalence of expressions as they relate to the same
situation (2.2D)
B. Equalities and Inequalities
Competencies: students will…
1.
solve linear equations in one variable with non-negative integral solutions
using concrete, numerical, and algebraic methods (2.2B)
2.
create a table of values, make a graph, and write an equation
3.
recognize the relationship between linear equations and their graphs (2.2E)
4.
investigate inequalities and nonlinear relationships informally.
C. Models
Competencies: students will…
1. Draw conclusions and make predictions based on patterns and relationships,
both mathematical and real life (2.1B)
2. Recognize and create multiple representations (e.g.,words, charts, algebraic
expressions or equations, and graphs) of the same linear real life situation
(2.3A)
3. Match a situation involving a constant or variable rate of change to a graph
that best represents that situation (2.4A)
4. Determine in a real life situation involving a constant rate of change how a
change in one variable affects the other variable (2.4B).
D. Patterns and Functions
Competencies: students will…
1. Formulate and solve multi-step and nonroutine problems using a variety of
strategies. Generalize methods to new problem situations.
2. Select and apply appropriate estimation strategies throughout the problemsolving process.
3. Interpret and communicate mathematical ideas and logical arguments using
correct mathematical terms and notations.
4. Recognize and investigate the relevance and usefulness of mathematics
through applications, both in and out of school.
5. Select and use appropriate technology to enhance mathematical
understanding. Appropriate technology may include, but is not limited to,
paper and pencil, calculator, computer, and data collection devices.
Standard #3: Students understand and apply the concepts and procedures from geometry
(MT Standard #4).
Big Ideas: Geometric Terms, Similarity, Transformations
Vocabulary: Dimensions, Image, Opposite Corner, Regular Polygon, Sector, Similar
A. Two-Dimensional Figures
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Competencies: students will…
1. identify complementary, supplementary and vertical angles (3.1B)
2. recognize and name special quadrilaterals and triangles (subsets)
3. understand, write and apply the Triangle-Sum Property
4. determine similarity of geometric figures based on congruence of angles and
proportionality of sides (3.1C)
5. graph and identify ordered pairs in all four quadrants.
B. Three-Dimensional Figures
Competencies: students will…
1. recognize, understand and apply the term: face, edge and vertex
2. understand the attributes of pyramid, cube, prism, sphere, cone and cylinder
3. reason about geometric figures and the relationships among them based on
their definitions and properties (3.1A)
4. determine characteristics of and relationships among various types of triangles
and angles, including vertical, complementary, and supplementary angles
(3.1B)
5. determine similarity of geometric figures based on congruence of angles and
proportionality of sides (3.1C)
6. construct a net (pattern) for a common 3-dimensional figure such as a prism or
pyramid (3.4A)
7. identify views (e.g., front, top, etc.) of a 3-dimensional structure (3.4B)
C. Symmetry and Transformations
Competencies: students will…
1. describe in words the transformation (translation, reflection, or rotation) that
moves a figure from one position to another (3.3A)
2. Recognize the connections between transformations and congruence line
symmetry, and rotational symmetry (3.3C)
D. Coordinate Geometry
Competencies: students will…
1. understand the properties of the four quadrants of the coordinate plane and
their relationship (3.2A?)
2. identify and create reflections, rotations and translations on a coordinate plane
(3.3B)
3. make connections between properties of geometric figures and coordinate
geometry (e.g., given the coordinates of three vetices of a square find the
coordinates of the fourth vertex) (3.2B)
Standard #4: Students understand and apply the concepts and procedures from
measurement (MT Standard #5).
Big Ideas: Perimeter, Area, Volume, Unites
Vocabulary: Mass, Miles per Gallon, Speed
Competencies: students will…
1. select the best measurement strategy to use relative to the purpose of the
measurement and its required accuracy (4.1A)
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2. given a measurement and error range, identify the possible “true” measurements
(4.1B)
3. use formulas to determine how a change in side length (radius) or height affects the
perimeter (circumference) and area in triangles, parallelograms and circles and the
volume in rectangular and triangular prisms (4.1C)
4. perform conversions among measurements of area and volume, e.g., 1 square
centimeter is equal to 100 square millimeters (4.1D)
5. predict how a change in one of the measurements of side length, perimeter and area
affect the other of these measurements in a triangle, square, or rectangle (4.1E)
6. estimate equivalent measures between customary and metric measures based on
benchmark equivalents (4.1F
7. make reasonable estimates of distance of height based on common benchmarks
(4.1G)
8. estimate perimeters and areas of irregular regions (4.2A)
9. solve problems involving rates (e.g., miles per gallon and cost per unit (4.2A, 4.2B)
10. use given formulas to find the circumferences of circles; areas of rectangles, triangles,
parallelograms, trapezoids, and circles; volumes of prisms, cylinders, cones, and
pyramids (4.2C, 4.2D, 4.2E)
11. solve problems involving scale factors (4.2F)
12. solve problems involving proportionality and geometric similarity (4.sG)
Standard #5: Students understand and apply the concepts and procedures from
probability and statistics (MT Standard #6).
Big Ideas: Constructing and Interpreting Graphical Representations, Probability
Vocabulary: Box-and-Whiskers Plot, Data, Probability, Random Sample, Survey
A. Probability
Competencies: students will…
1. understand and apply theoretical and experimental probability
2. use tree diagrams, the counting principle, factorials and histograms
3. make predictions based on probability.
B. Statistics
Competencies: students will…
1. determine appropriate data to collect for a given purpose and how to go about
collecting and analyzing that data (5.1A)
2. Select appropriate graphic representations for data sets (5.1B)
3. Interpret and construct bar graphs, pictographs, line graphs, line plots, stem-and-leaf
graphs, circle graphs, frequency charts, histograms and box-and-whisker graphs
(5.1C)
4. Recognize how different representations of the same data set can affect interpretation
(5.1D)
5. Calculate the mean, median, mode, and range of a data set and interpret their
meanings (5.2A)
6. Make judgments about the shape and spread of data sets, including consideration of
outliers and quartiles (5.2B)
7. Draw conclusions and make inferences and predictions based on data given in charts
and graphs (5.3A)
5
8. Determine all possible outcomes for an experiment, using a tree diagram, an
organized list, or, when appropriate, the fundamental counting principle (5.4A)
9. Find the theoretical probability of an event in experiment with equally likely
outcomes (5.4B)
10. Find theoretical probability involving simple independent events (5.4D)
11. Make predictions based on probability (5.4E).
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Grade 8 Mathematics
Course Overview:
Students will develop mathematical knowledge and understanding in a setting where connection
to other disciplines is valued. Through the implementation of daily warm ups and a thematic
approach focused on the transition from pre-algebra to algebra, students will apply the properties
of multi-step equations, 3-D geometry, exponents and radicals, slope, linear equations, the
Pythagorean Theorem and tangent.
Required Topics:
Equations and Formulas
Data Representation and Analysis
Exponents, Roots and Radicals
Polygons and Circles
Perimeter, Area and Volume
Proportionality Concepts
Proportionality Problems
2-D Coordinate Geometry
Rational Numbers and their properties
Negative Numbers, Integers and their properties
Slope and Trigonometry
Exponents and Orders of Magnitude
Constructions w/Straight edge & Compass
3-D Geometry
Congruence & Similarity
Patterns, Relations and Functions
Foundation Standard (MT Standard #1)
Competencies: students will…
1.
define and solve problems
2.
reason logically
3.
estimate, communicate, and model their thinking and
understanding
4.
connect mathematical ideas within mathematics and to other
subject areas
5.
use appropriate technology
6.
know and use appropriate math vocabulary
7.
use comprehension strategies
Standard #1: Students understand and apply the concepts and procedures from numbers
and operations (MT Standard #2).
Big Ideas: Compute with any type of number to solve real life problems
Vocabulary: Commission, Cost per Unit (Unit Rate), Percent, Prime Factorization, Proportion,
Value of an Expression, Calculate, Compute, Cube, Scale Factor, Numeric Expression
A. Operations
Competencies: students will…
1.
use order of operations to solve real-life problems involving integers,
rational numbers (including negative rationals), exponents and radicals
2.
estimate the results of operations using the above numbers
3.
recognize and generate equivalent fractions, decimals, and percents
4.
reason with regard to multiples, factors, primes and divisibility
B. Number Forms
Competencies: students will…
1.
recognize the effects of addition, subtraction, multiplication, and division
with rational numbers and roots (1.2A)
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2.
3.
4.
identify rational and irrational numbers in real life situations
convert between decimal notation and scientific notation
order rational numbers and square roots
C. Proportionality
Competencies: students will…
1. determine when to use ratios, rates, proportions and common fractions to
solve real-world problems and percents
2. compute with ratios, proportions, and percents(1.3C)
D. Properties and Rules
Competencies: students will…
1. use and identify properties of numbers, commutative, associative, distributive,
identities and inverses
2. apply the power rules and properties of positive and negative exponents
3. interpret integral exponents and roots (1.1C)
Standard #2: Students understand and apply the concepts and procedures from algebra
(patterns, functions and relations) (MT Standard 3 and #7).
Vocabulary: Equation of a Line, Intercepts: x-intercept and y-intercept, Linear Relationship,
Line of Best Fit (on a Scatterplot), Number Sequence, Rule for a Pattern, Scatterplot, Simplify an
Expression, Value of an Expression, Algebraic Expression
A. Variables
Competencies: students will…
1.
simplify expressions by combining like terms and applying the distributive
property
2.
differentiate between the use of a variable in expressions, in equations,
and in formulas
3.
evaluate expressions for given values
4.
recognize and write equivalent expressions
B. Equations and Inequalities
Competencies: students will…
1.
solve linear equations in one variable
2.
represent linear and simple quadratic real-life situations with algebraic
expressions, equations, or inequalities.
C. Linear Equations
Competencies: students will…
1.
graph linear equations and inequalities
2.
understand and apply slope as a rate of change
3.
recognize and transform simple equations into slope-intercept form
4.
write equations to represent linear graphs
5.
determine the slope and intercepts of a linear equation and interpret the
meaning of those values
6.
recognize and create multiple representations (e.g., words, charts,
algebraic expression or equations, and graphic representations) of the
same linear real life situations
8
D. Non-Linear Equations
Competencies: students will…
1.
recognize non-linear equations and graphs
1.
2.
3.
4.
5.
6.
E. Patterns, Relations, and Functions
Competencies: students will…
represent rules for real life and mathematical patterns using words, algebraic expressions,
or equations (2.1A)
draw conclusions and make predictions based on patterns and relationships, both
mathematical and from real life (2.1B)
recognize relationships represented by tables or graphs as linear or non-linear (2.1C)
recognize and create multiple representations (e.g., words, charts, algebraic expression or
equations, and graphs) of the same linear real life situation (2.1D)
match a situation involving a variable rate of change to a graphic representation that best
represents that situation (2.1E)
determine in a situation involving a constant or variable rate of change how a change in
one variable affects the other variable (2.1F).
Standard #3: Students understand and apply the concepts and procedures from geometry
(MT Standard #4).
Big Ideas: Geometric Reasoning, Symmetry
Vocabulary: Altitude (of a triangle), Central Angle, Diagonal (of a polygon), Formula, Line of
Best Fit (on a Scatterplot), midpoint, origin (on a coordinate Grid), Quadrant (on a coordinate
Grid), Radius, Scatterplot, Area, Circle, Radius, Diameter, Circumference, Congruent,
Coordinate Plane: Axes, Horizontal axis, Vertical Axis, Coordinates; Cube Diagonal of a
Polygon, Geometrically Similar, Grid, Image of a Transformation, Intersection, Scale on a
Coordinate Plane
1.
2.
3.
4.
A. Two- and Three Dimensional Shapes
Competencies: students will…
reason about geometric figures and relationships amond them based on their definitions
and properties
provide reasons that geometric statements are true and evaluate given reasons
provide counterexamples to show that certain geometric statements are false
determine similarity of geometric figures
B. Coordinate Geometry
1. make connections between properties of geometric figures and coordinate geometry (e.g.,
finding length of sides of polygons or coordinates of the midpoints of the sides
2. determine the image of a figure on the coordinate plane after a translations, reflection, or
rotation
C. Translations
Competencies: students will…
1.
describe the transformation(s) that transform a figure into its image
2.
recognize the connections between transformation and congruence,
line symmetry, and rotations symmetry.
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D. Spacial Reasoning
Competencies: students will…
1.
construct a net (pattern) for a common 3-dimensional figure
2.
identify views (e.g., top, right side) of a 3-dimentional structure
3.
solve problems involving simple networks
Standard #4: Students understand and apply the concepts and procedures from
measurement (MT Standard 5).
Big Ideas: Geometric Formulas, Pythagorean Theorem, Proportions and
Similarity
Vocabulary: Degrees Fahrenheit and Celsius), Geometrically Similar, Metric Units of Measure
(Capacity, Mass, Length), Standard Units of Measure
A. Measurement
Competencies: students will…
1.
select the best measurement strategy to use relative to the purpose of the
measurement and its required accuracy
2.
identify the possible error in a reported measurement
3.
use formulas to determine how a change in side length (radius) or height
affects the perimeter (circumference) and area in triangles, parallelograms
and circles, and the volume in rectangular or triangular prisms
4.
perform conversions among measurements of area and volume
5.
use tables to perform conversions among customary and metric units
6.
estimate equivalent measure between the customary and the metric systems
7.
solve problems involving rates and derived measurements, e.g., miles per
gallon (4.2A)
8.
estimate perimeters, areas, and volumes of irregular regions
9.
use given formulas to find the circumferences of circles and areas of
rectangles, triangles, parallelograms, trapezoids, and circles
10.
use given formulas to find the volumes of prisms, cylinders, cones, and
pyramids
11.
find surface areas of prisms and cylinders
12.
solve problems using a scale factor
13.
solve problems involving proportionality and geometric similarity
14.
solve problems involving the Pythagorean theorem
Standard #5: Students understand and apply the concepts and procedures from
probability and statistics (MT Standard #6).
Big Ideas: Graph and Interpret Data Sets, Make Predictions Using Data
Vocabulary: Equally Likely Events, Quartile, Display (Box-and-Whisker, Circle Graph, Bar
Graph, Stem-and-Leaf, Scatterplot), Median, Mean, Mode, Range
A. Graphs
Competencies: students will…
10
1. determine appropriate data to collect for a given purpose and how to go about
collecting and analyzing that data (5.1A)
2. construct, read and interpret appropriate displays: line graphs, box and
whisker, histograms, stem and leaf, and scatter plots
3. draw a line of bestfit for scatter plots and use it to make predictions
4. select appropriate graphical representations for a data set
5. recognize how different representations of the same data set can affect their
interpretation
6. calculate the mean, median, mode, and range of a data set and interpret them
7. make judgments regarding the shape and spread of a data set, including
consideration of outliers and quartiles
8. determine how a change in data points affects the mean and median of the
data set
9. draw conclusions and inferences and make predictions based on data given in
a chart or graph
B. Probability
Competencies: students will…
1.
predict theoretical probability for independent and dependent events
2.
find the theoretical probability of an event in an experiment with equally
likely outcomes (5.4B)
3.
find experimental/empirical probability from a set of data
4.
determine all possible outcomes of an experiment using a tree diagram, an
organized list, or the fundamental counting principle
11