Coordinate Plane

Level A:

1. Coordinate Plane: Intro

a. origin, quadrants, ordered pair, coordinates, x-axis, y-axis, horizontal, vertical

b. graphing points

2. Distance Between Two Points

a. Q1 only – horizontal and vertical

b. All 4 Q’s – horizontal and vertical

3. Drawing Polygons on a Coordinate Plane

a. Q1 only

b. All 4 Q’s

c. Calculate Perimeter and Area (Q1 only)

d. Calculate Perimeter and Area (Q1 to Q4)

4. Reflections Over One Axis

Level B:

1. Graphing Linear Equations

2. Graphing Non-Complex Quadratic and Cubic Equations

3. Reflections Over More Than One Axis

Level C:

1. Distance Between Two Points: Diagonals

a. Distance Formula/Pythagorean Theorem

2. Other Transformations:

a. Rotations, Translations, Dilations

Data: Graphs, Diagrams, Tables, Charts

See Also: “Coordinate Plane”

Level A:

1. Basic Review: Bar Graphs, Line Graphs, Circle Graphs

2. Evaluate Data: interpret and make predictions based on graphs, diagrams, tables, or charts

3. Venn Diagrams: interpret

4. Venn Diagrams: create

5. Coordinate Plane: read & interpret data

6. Connect circle graphs to percents

Level B:

1. Interpret data to solve multi-step word problems.

2. Solve percent problems based on data provided in graphs or tables.

Decimals

Level A:

1. Basic Review Topics For Level A:

a. Place Value

b. Read & Write up to thousandths

2. Locating & Plotting on a number line.

3. Comparing & Ordering to thousandths, including <, >, =

4. Rounding

5. Connecting Decimals & Fractions

6. Converting among/between fractions, decimals, percents

7. Add, Subtract, Multiply, Divide

Level B:

1. Terminating & Repeating Decimals

2. Using division to convert a fraction into a decimal.

Level C:

1. Negative Decimals

2. Scientific Notation

Elapsed Time

Level A:

1. Basic Review: Telling Time on an analog clock

2. Elapsed Time: Analog Clocks

3. Elapsed Time: Digital Clocks

4. Elapsed Time: Adding and Subtracting time intervals.

Level B:

1. Elapsed Time: Involving conversions of units

2. Elapsed Time: Spanning days, weeks, months, years

Exponents, Squares, Cubes, Square Roots, Cube Roots

Level A:

1. Basic Exponents & Powers of 10

2. Squared & Cubed

Level B:

1. Perfect Squares up to 225

2. Perfect Cubes up to 125

3. Square Roots of Perfect Squares

4. Cube Roots of Perfect Cubes

Level C:

1. Irrational Numbers: Introduction To

2. Square Roots of non-perfect squares (estimating)

3. Cube Roots of non-perfect cubes (estimating)

4. Cube Roots of negative numbers

5. Pythagorean Theorem/Distance Formula

6. Negative Bases

7. Negative Exponents

8. Scientific Notation

9. Laws of Exponents

Expressions & Equations

See Also: “Polynomials”

E&E: Intro to Algebra

Level A:

1. Order of Operations/PEMDAS

2. Variables, Constants, Coefficients

3. Terms, Monomials, Polynomials

4. Writing Simple Expressions

5. Expressions vs. Equations vs. Inequalities

E&E: Substitution of Variables

Level A:

1. Evaluating simple expressions

Level B:

1. Evaluating multi-variable expressions and nonlinear expressions

2. Evaluating expressions that involve fractions, decimals, mixed numbers, and negative integers

E&E: Equivalent Expressions

Level A:

1. Distributive Property

2. Combining Like Terms

3. Identify and Generate Equivalent Expressions (Basic)

Level B:

1. Factor One-Variable Expressions

2. Identify and Generate Equivalent Expressions (More Complex)

Level C:

1. Factor Multi-Variable Expressions

2. Identify and Generate Equivalent Expressions (Most Complex)

a. Negative Coefficients

b. Laws of Exponents

E&E: One-Variable Equations

Level A:

1. Write & Solve: one-step equations

Level B:

1. Write & Solve: two-step equations

2. Write & Solve: variables on both sides

3. Write & Solve: non-complex quadratic and cubic equations

Level C:

1. Write & Solve: more complex, multi-step equations

2. Write & Solve: absolute value equations

E&E: Two-Variable Relationships

Level C:

1. Two-Variable Equations: Intro To

2. Dependent and Independent Variables

3. Manipulating Equations: solving for a variable

4. Solutions of two-variable equations

5. Graphing two-variable linear equations

6. Slope

7. y = mx + b

8. Slope of parallel and perpendicular lines

9. Graphing non-linear equations: quadratic, cubic, absolute value

10. Solving systems of linear equations

Fractions & Mixed Numbers

Level A:

1. Basic Review Topics For Level A:

a. Benchmark Fractions & Mixed Numbers

b. Locating & Plotting on a number line.

c. Using line plots to add and subtract: halves, fourths, eighths

d. Equivalent Fractions

e. Simplifying Fractions

f. Mixed Numbers, Improper Fractions, Whole Numbers

g. Comparing & Ordering, including <, >, =

2. Connecting Fractions & Percents

3. Converting among/between: fractions, decimals, percents

4. Add, Subtract, Multiply, Divide

Level C:

1. Negative Mixed Numbers

Geometry

Level A – Basic Review:

Geometry: Angles

Level A:

1. Basic Review for Level A:

protractor, degrees, vertex, right, acute, obtuse, straight, circle = 360 degrees, parallel, perpendicular

2. Measuring Angles

3. Adjacent Angles: sum of measurements

4. Triangles: sum of angles equals 180 degrees

5. Supplementary and Complementary Angles

6. Reflex Angles

7. Angle Bisectors

Level C:

1. Vertical Angles

2. Transversals & Parallel Lines

a. interior angles, exterior angles, alternate angles, corresponding angles

b. angle measurements: parallel lines cut by a transversal

3. Solving for unknown angle measurements in complex diagrams

Geometry: Circles

Level A:

1. Basic Review: 360 degrees, center, radius, diameter, arc, chord

2. Central angles, sectors, tangents, secants

Level B:

1. Pi

2. Area

3. Circumference

4. Central Angle Measurements:

a. Calculate angle measurements based on data provided.

b. Create accurate circle graphs that represent data provided.

Geometry: Coordinate Plane

See: “Coordinate Plane”

Geometry: Perimeter, Area, Volume, Surface Area, Nets

Level A:

1. Perimeter & Area: triangles, squares, rectangles

2. Volume: cubes, rectangular prisms

3. Surface Area: cubes, rectangular prisms

4. Nets: comprised of squares, rectangles, triangles, circles

5. 3D Views: basic

Level B:

1. Perimeter & Area: other polygons, irregular shapes

2. Volume: other prisms, pyramids

3. Surface Area: other prisms, pyramids

4. Area: inscribed and circumscribed polygons

5. Perimeter, Area, Volume, Surface Area: fractional edge lengths

6. 3D Views: more complex

Level C:

1. Volume: cylinders, cones, spheres

2. Surface Area: cylinders, cones, spheres

3. Similar Shapes: calculate perimeter, area, and volume of actual shapes based on scale models or drawings.

Geometry: Similar Shapes & Scale Drawings

See: “Similar Figures & Scale Drawings”

Geometry: Transformations & Symmetry

See: “Transformations & Symmetry”

Geometry: Trigonometry

See: “Trigonometry”

point, line segment, line, ray, angle, acute, obtuse, straight, parallel, perpendicular, intersecting, circle, triangle, right triangle, equilateral triangle, isosceles triangle, scalene triangle, quadrilateral, square, rectangle, rhombus, parallelogram, trapezoid, pentagon, hexagon, octagon, polygon, cube, rectangular prism, triangular prism, pyramid, cylinder, cone, sphere, similar, congruent, line symmetry, perimeter, area, volume

Inequalities

Level A: One-Step Inequalities

1. Basic Review: <, >, <=, >=

2. Writing one-step inequalities with variables

3. Solving one-step inequalities

4. Graphing solutions on a number line

Level B: Multi-Step and Compound Inequalities (linear)

1. Writing & Solving two-step and multi-step inequalities

2. Writing & Solving inequalities with variables on both sides

3. Writing & Solving compound inequalities

4. Graphing solutions on a number line

Level C: Absolute Value and Systems of Inequalities

1. Writing & Solving inequalities that involve absolute value

2. Solving systems of two-variable linear inequalities

3. Graphing solutions on a number line or coordinate plane

Irrational Numbers

Level C:

1. Irrational Numbers: basic examples

2. Pi

3. Square Roots of non-perfect squares

4. Cube Roots of non-perfect cubes

Measurement

See Also: “Elapsed Time”

See Also: “Geometry: Perimeter, Area, Volume, Surface Area, Nets”

Level A:

1. Basic Review Topics For Level A:

a. Metric System vs. Customary System

b. Converting Units

i. Length/Distance: inches, feet, yards, miles, mm, cm, m, km

ii. Weight/Mass: ounces, pounds, tons, mg, g, kg

iii. Capacity: fluid ounces, cups, pints, quarts, gallons, ml, l

iv. Time: seconds, minutes, hours, days, weeks, months, years, decades, centuries, millenniums

Level B:

1. Converting Units:

a. Temperature: Fahrenheit, Celsius, Kelvin

Level C:

1. Pythagorean Theorem/Distance Formula

2. See Also: “Similar Figures and Scale Drawings”

Negative Numbers

Level A:

1. Number Lines & Coordinate Plane

2. Comparing & Ordering

3. Absolute Value

4. Opposite Numbers

5. Negative Temperatures

6. Below Sea Level

Level B:

1. Add, Subtract, Multiply, Divide

2. Evaluating expressions that contain negative integers

Level C:

1. Distributive Property: with negative coefficients

2. Combining Like Terms: with negative coefficients

3. Negative Mixed Numbers

4. Negative Decimals

5. Negative Exponents

Number System

Number System: Decimals

See: “Decimals”

Number System: Fractions

See: “Fractions & Mixed Numbers”

Number System: Exponents

See: “Exponents, Squares, Cubes, Square Roots, Cube Roots”

Number System: Negative Numbers

See: “Negative Numbers”

Number System: Irrational Numbers

See: “Irrational Numbers”

Level A:

1. Basic Review Topics For Level A:

a. Place Value

b. Reading & Writing: up to trillions

c. Comparing & Ordering: up to trillions

d. Rounding: up to trillions

e. Vocabulary: sum, difference, product, quotient

f. Add, Subtract, Multiply, Divide: multi-digit whole numbers

g. Patterns: numbers and shapes

h. Divisibility: including odd/even numbers and skip counting

i. Properties: Commutative, Associative

j. Prime & Composite Numbers

k. Prime Factorization

l. Factors & Multiples

m. GCF & LCM

2. Negative Numbers: number lines

3. Negative Numbers: compare & order

4. Absolute Value

5. Opposite Numbers

6. Exponents

7. Order of Operations

8. Distributive Property

Level B:

1. Add, Subtract, Multiply, Divide: Negative Numbers

Level C:

1. Negative Mixed Numbers

2. Negative Decimals

3. Negative Exponents

Percent

Level A:

1. Benchmark Percents

2. Estimating the percent of a number

3. Converting among fractions, decimals, percents

4. Basic Percent Problems:

-Calculating the percent, given the part and the whole.

-Calculating the whole, given the part and the percent.

-Calculating the part, given the whole and the percent.

Level B:

1. More complex percent problems

2. Using equations to solve percent problems

3. Using proportions to solve percent problems

4. Percent Change/Percent Increase/ Percent Decrease

5. Sale Prices/Percent Discounts

6. Sales Tax Problems

7. Calculating Tips

8. Simple Interest (I = PRT)

Level C:

1. Percents greater than 100%

2. Percents less than 1%

3. Non-Integer Percents (ex: 6.25%)

4. Multiple Discount Problems

5. Compound Interest

6. Mortgages, Car Loans, Credit Cards

Polynomials

See Also: “Expressions & Equations”

Level A:

1. Variables, Constants, Coefficients, Terms

2. Monomials, Binomials, Trinomials, Polynomials

3. Distributive Property: basic ..... 6(2x + 5)

4. Combining Like Terms: positive coefficients

Level B:

1. Distributive Property: more complex ..... 3x(5y + 3x – 4)

2. Simplifying Polynomials: basic and multi-step

3. Factoring Polynomials: one-variable

Level C:

1. Multiplying Monomials, Binomials, Trinomials

2. Laws of Exponents

3. FOIL

4. Distributive Property: negative coefficients ..... -5x(-10xy - y + 2x)

5. Combining Like Terms: negative coefficients

6. Simplifying Polynomials: more complex

7. Factoring Polynomials: multi-variable

Probability & Statistics

Level A:

1. Mean, Median, Mode, Range, Outlier

2. Calculating the probability of simple events

3. Expressing probability as a fraction or a percent

4. Total Outcomes: tree diagrams and the counting principle

Level B:

1. Mutually Exclusive vs. Mutually Inclusive

2. Independent and Dependent Events

3. Calculating the probability of compound events

4. Probabilities involving: NOT, AND, OR

Level C:

1. Factorials

2. Permutations

3. Arrangements

4. Combinations

5. Experimental and Geometric Probability

6. Conditional Probability

Properties, Pythagorean Theorem, Laws of Exponents

Level A:

1. Associative and Commutative

2. Distributive

Level C:

1. Pythagorean Theorem/Distance Formula

a. See Also: "Coordinate Plane"

b. See Also: "Exponents, Squares, Cubes, Square Roots, Cube Roots"

c. See Also: "Measurement"

2. Laws of Exponents

a. See Also: "Exponents, Squares, Cubes, Square Roots, Cube Roots"

b. See Also: "Expressions & Equations: Equivalent Expressions"

c. See Also: "Polynomials"

Rates, Ratios, Proportions

See Also: “Percent"

See Also: “Measurement”

See Also: “Similar Figures & Scale Drawings”

Level A

1. Basic Ratios & Rates

2. Equivalent Ratios & Rates

3. Tables: explore ratios and rates

4. Unit Rates & Unit Prices: basic

Level B:

1. Ratios, Rates, Unit Rates, Unit Prices: more complex

2. Ratios & Unit Rates: involving fractions

3. Proportions & Equal Ratios

4. Solving Proportions Using Unit Rates

5. Cross Multiplication/Cross Products

6. Constant of Proportionality (Unit Rate)

7. Using equations to represent proportional relationships

8. Using proportions to solve multi-step ratio and percent problems

Level C:

1. See Also: "Similar Figures & Scale Drawings"

Similar Figures & Scale Drawings

Level A:

1. Basic Review: Similar and Congruent Shapes

Level B:

1. Using ratios to determine similarity

2. Calculating the missing dimensions of similar figures

Level C:

1. Scale: maps, drawings, models

2. Scale: calculating actual measurements based on scale

3. Scale: converting units and rates within scale problems

4. Area & Perimeter of actual figures based on scale, converting units when necessary

Transformations & Symmetry

Level A: Basic

Level B: More Complex

Level C: Most Complex

Topics For All Levels:

1. Transformations:

Translations (slides), Reflections (flips), Rotations (turns), Dilations (resizing)

2. Symmetry:

Line Symmetry, Rotational Symmetry, Point Symmetry

Transversals & Parallel Lines

See: “Geometry: Angles”

Trigonometry

Level C:

1. Sine, Cosine, Tangent

2. Indirect Measurement: using similarity ratios/proportions

3. Indirect Measurement: using trigonometric ratios

Variables

See: “Expressions & Equations”

See: “Polynomials”

Vertical Angles

See: “Geometry: Angles”