N: Number and Operations

N.1: Understand numbers, ways of representing numbers, relationships among numbers and number systems

N.1.A: compare and order all positive rational numbers and find their approximate location on a number line

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

N.1.B: recognize and generate equivalent forms of fractions, decimals and percents

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

N.1.C: recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including exponential notation

Number Systems

N.2: Understand meanings of operations and how they relate to one another

N.2.B: describe the effects of all operations on rational numbers including integers

Adding Fractions (Fraction Tiles)
Fractions Greater than One (Fraction Tiles)

N.2.C: apply properties of operations (including order of operations) to positive rational numbers and integers

Order of Operations

N.2.D: approximate the value of square roots to the nearest whole number

Square Roots

N.3: Compute fluently and make reasonable estimates

N.3.C: apply all operations on rational numbers including integers

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 Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

N.3.D: estimate and justify the results of all operations on rational numbers

Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

N.3.E: solve problems involving proportions, such as scaling and finding equivalent ratios

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Percents and Proportions
Proportions and Common Multipliers

A: Algebraic Relationships

A.1: Understand patterns, relations and functions

A.1.B: analyze patterns represented graphically or numerically with words or symbolic rules, including recursive notation

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

A.1.D: identify functions as linear or nonlinear from tables, graphs or equations

Absolute Value with Linear Functions
Linear Functions

A.2: Represent and analyze mathematical situations and structures using algebraic symbols

A.2.A: use symbolic algebra to represent unknown quantities in expressions or equations and solve linear equations with one variable

Compound Interest
Modeling and Solving Two-Step Equations
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Using Algebraic Expressions

A.2.B: use properties to generate equivalent forms for simple algebraic expressions that include positive rationals and integers

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A.3: Use mathematical models to represent and understand quantitative relationships

A.3.A: model and solve problems, using multiple representations such as graphs, tables, expressions, and linear equations

Compound Interest
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

A.4: Analyze change in various contexts

A.4.A: compare situations with constant or varying rates of change

Compound Interest
Dilations

G: Geometric and Spatial Relationships

G.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

G.1.B: describe relationships between corresponding sides, corresponding angles and corresponding perimeters of similar polygons

Similar Figures

G.3: Apply transformations and use symmetry to analyze mathematical situations

G.3.B: describe the relationship between the scale factor and the perimeter of the image using a dilation (contractions-magnifications; stretching/shrinking)

Dilations

G.4: Use visualization, spatial reasoning and geometric modeling to solve problems

G.4.A: use spatial visualizations to identify various 2-dimensional views of isometric drawings

3D and Orthographic Views

M: Measurement

M.1: Understand measurable attributes of objects and the units, systems and processes of measurement

M.1.B: identify the equivalent area and volume measures within a system of measurement (e.g., sq ft. to sq in, m³ to c m³)

Unit Conversions

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

M.2.C: solve problems involving circumference and/or area of a circle and surface area/volume of a rectangular or triangular prism, or cylinder

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders

M.2.E: convert from one unit to another within a system of measurement (capacity) and convert square or cubic units within the same system of measurement

Unit Conversions

D: Data and Probability

D.1: Formulate questions that can be addressed with data and collect, organize and display relevant data to answer them

D.1.C: select, create and use appropriate graphical representation of data, including circle graphs, histograms

Distance-Time Graphs
Graphing Skills
Histograms
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

D.2: Select and use appropriate statistical methods to analyze data

D.2.A: find, use and interpret measures of center and spread, including ranges

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

D.3: Develop and evaluate inferences and predictions that are based on data

D.3.A: use observations about differences between samples to make conjectures about the populations from which the samples were taken

Polling: City
Polling: Neighborhood

D.4: Understand and apply basic concepts of probability

D.4.A: use models to compute the probability of an event and make conjectures (based on theoretical probability) about the results of experiments

Geometric Probability
Theoretical and Experimental Probability