M8.A: Numbers and Operations

M8.A.1: Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.

M8.A.1.1: Represent numbers in equivalent forms.

M8.A.1.1.1: Represent numbers using scientific notation and/or exponential forms.

 Unit Conversions
 Unit Conversions 2 - Scientific Notation and Significant Digits

M8.A.1.1.2: Find the square or cube of a whole number (single digit) and/or the square root of a perfect square (without a calculator) and explain the relationship between the two (i.e. square and square root).

 Square Roots

M8.A.2: Understand the meanings of operations, use operations and understand how they relate to each other.

M8.A.2.1: Complete calculations by applying the order of operations.

M8.A.2.1.1: Simplify numeric expressions involving integers, using the order of operations. (May include all types of grouping symbols. No combining negatives with exponents [4 to the -3 power] or compound exponents.)

 Order of Operations

M8.A.2.2: Represent or solve problems using rates, ratios, proportions and/or percents.

M8.A.2.2.1: Solve problems involving percents (e.g., tax, discounts, etc) Do not include percent increase or decrease.

 Percent of Change
 Percents, Fractions, and Decimals
 Real-Time Histogram
 Time Estimation

M8.A.2.2.2: Represent or solve rate problems (e.g., unit rates, simple interest, distance, etc.) Students may be asked to solve for any term (formulas provided on the reference sheet for distance and interest).

 Compound Interest
 Household Energy Usage
 Road Trip (Problem Solving)

M8.A.3: Compute accurately and fluently and make reasonable estimates.

M8.A.3.1: Determine the appropriateness of overestimating, underestimating or calculating an exact answer in problem-solving situations.

M8.A.3.1.2: Identify, apply and/or explain when an exact answer is needed or when estimation is appropriate.

 Estimating Population Size
 Estimating Sums and Differences

M8.A.3.3: Compute and/or explain operations with integers, fractions and/or decimals.

M8.A.3.3.1: Add, subtract, multiply and/or divide integers, fractions and/or decimals with and without a calculator (straight computation or word problems).

 Adding Fractions (Fraction Tiles)
 Adding and Subtracting Integers
 Adding on the Number Line
 Addition of Polynomials
 Dividing Fractions
 Dividing Mixed Numbers
 Estimating Sums and Differences
 Fractions with Unlike Denominators
 Improper Fractions and Mixed Numbers
 Multiplying Fractions
 Multiplying Mixed Numbers
 Multiplying with Decimals
 Square Roots
 Sums and Differences with Decimals

M8.B: Measurement

M8.B.1: Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement.

M8.B.1.1: Convert measurements.

M8.B.1.1.1: Convert among metric measurements (milli, centi, kilo using meter, liter and gram) (table of equivalency provided on the reference sheet).

 Unit Conversions

M8.B.1.1.2: Convert customary measurements up to 2 units above or below the given unit (e.g., inches to yards, pints to gallons) (table of equivalency provided on the reference sheet).

 Unit Conversions

M8.B.1.1.3: Convert time up to 2 units above or below given unit (e.g., seconds to hours).

 Unit Conversions

M8.B.2: Apply appropriate techniques, tools and formulas to determine measurements.

M8.B.2.2: Use, describe and/or develop procedures to determine measures of perimeter, circumference, area, surface area and/or volume.

M8.B.2.2.1: Calculate the surface area of cubes and rectangular prisms (formula provided on the reference sheet).

 Surface and Lateral Areas of Prisms and Cylinders

M8B.2.2.2: Calculate the volume of cubes and rectangular prisms (formulas provided on the reference sheet).

 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders

M8.C: Geometry

M8.C.1: Analyze characteristics and properties of two- and three- dimensional geometric shapes and demonstrate understanding of geometric relationships.

M8.C.1.1: Identify, use, and/or describe properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.

M8.C.1.1.1: Match the three-dimensional figure with its net (cube, cylinder, cone, prism, pyramid). Any measurements used should be consistent in the stem and answer choices.

 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

M8.C.1.1.2: Define, identify and/or use properties of angles formed by intersecting lines (complementary, supplementary, adjacent and/or vertical angles).

 Triangle Angle Sum

M8.C.1.1.3: Define, identify and/or use properties of angles formed when two parallel lines are cut by a transversal (alternate interior, alternate exterior, vertical corresponding).

 Triangle Angle Sum

M8.C.1.2: Compute measures of sides of right triangles using the Pythagorean Theorem.

M8.C.1.2.1: Use the Pythagorean Theorem to find the measure of a missing side of a right triangle (formula provided on the reference sheet - whole numbers only).

 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard

M8.C.3: Locate points or describe relationships using the coordinate plane.

M8.C.3.1: Plot and/or identify ordered pairs on a coordinate plane.

M8.C.3.1.1: Plot, locate or identify ordered pairs on a coordinate plane (the point may be a vertex of a polygon).

 City Tour (Coordinates)
 Linear Functions
 Point-Slope Form of a Line
 Points in the Coordinate Plane
 Points, Lines, and Equations
 Slope

M8.D: Algebraic Concepts

M8.D.1: Demonstrate an understanding of patterns, relations and functions.

M8.D.1.1: Analyze, extend or develop descriptions of patterns or functions.

M8.D.1.1.3: Determine the rule of a function (given elements in an input-output table, chart or list - limit to linear functions).

 Arithmetic Sequences
 Function Machines 1 (Functions and Tables)
 Geometric Sequences

M8.D.2: Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs.

M8.D.2.1: Select and/or use a strategy to simplify an expression, solve an equation or inequality and/or check the solution for accuracy.

M8.D.2.1.1: Solve one- or two-step equations and inequalities (should not include absolute values - one variable only).

 Compound Inequalities
 Exploring Linear Inequalities in One Variable
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations by Graphing Each Side
 Solving Equations on the Number Line
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

M8.D.2.1.3: Determine the value of an algebraic expression by simplifying and/or substituting a number for the variable.

 Dividing Exponential Expressions
 Equivalent Algebraic Expressions I
 Equivalent Algebraic Expressions II
 Multiplying Exponential Expressions
 Operations with Radical Expressions
 Order of Operations
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II

M8.D.2.2: Create and/or interpret expressions, equations or inequalities that model problem situations.

M8.D.2.2.1: Match a written situation to its numeric and/or algebraic expression, equation or inequality (up to two variables in equations or expressions - one variable with inequalities).

 Using Algebraic Expressions

M8.D.2.2.2: Write and/or solve an equation for a given problem situation (one variable only).

 Absolute Value Equations and Inequalities
 Arithmetic Sequences
 Geometric Sequences
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Equations on the Number Line
 Solving Two-Step Equations
 Using Algebraic Equations

M8.D.4: Describe or use models to represent quantitative relationships.

M8.D.4.1: Represent relationships with tables or graphs on the coordinate plane.

M8.D.4.1.1: Graph a linear function based on an x/y table (integers only).

 Points, Lines, and Equations

M8.D.4.1.2: Match the graph of a linear function to its x/y table (integers only).

 Points, Lines, and Equations

M8.D.4.1.3: Match the linear equation (y = mx + b form) to the x/y table (integers only in the table).

 Points, Lines, and Equations

M8.E: Data Analysis and Probability

M8.E.1: Formulate or answer questions that can be addressed with data and/or organize, display, interpret or analyze data.

M8.E.1.1: Choose, display or interpret data (tables, charts, graphs, etc.).

M8.E.1.1.1: Choose and/or explain the correct representation (graph) for a set of data.

 Box-and-Whisker Plots
 Correlation
 Stem-and-Leaf Plots

M8.E.1.1.2: Analyze data and/or answer questions pertaining to data shown in multiple line graphs, circle graphs or histograms.

 Histograms
 Polling: City
 Prairie Ecosystem
 Real-Time Histogram
 Sight vs. Sound Reactions

M8.E.1.1.3: Interpret data shown in stem-and-leaf or box-and-whisker plots.

 Box-and-Whisker Plots
 Stem-and-Leaf Plots

M8.E.3: Understand and/or apply basic concepts of probability or outcomes.

M8.E.3.2: Determine the number of combinations and/or permutations for an event.

M8.E.3.2.1: Determine/show the number of permutations and/or combinations for an event using up to four choices (e.g., organized list, etc.).

 Permutations and Combinations

M8.E.4: Develop and/or evaluate inferences and predictions or draw conclusions based on data or data displays.

M8.E.4.1: Draw conclusions, make inferences and/or evaluate hypotheses based on statistical and data displays.

M8.E.4.1.1: Fit a line to a scatter plot and/or describe any correlation between the two variables (positive, negative, strong, weak or none).

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

M8.E.4.1.2: Make predictions based on survey results or graphs (bar, line, circle, scatterplots, etc.).

 Correlation
 Polling: City
 Polling: Neighborhood

Correlation last revised: 5/23/2018

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