1: Number and Operations

1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.A: Read, write and compare numbers

1.1.A.1: compare and order integers, positive rationals and percents, including finding their approximate location on a number line

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.1.B: Represent and use rational numbers

1.1.B.1: use fractions, decimals and percents to solve problems

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

1.1.C: Compose and decompose numbers

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

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

1.2: Understand meanings of operations and how they relate to one another

1.2.B: Describe effects of operations

1.2.B.1: describe the effects of multiplication and division on fractions and addition and subtraction on integers

Adding Real Numbers
Adding and Subtracting Integers
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers

1.2.C: Apply properties of operations

1.2.C.1: apply properties of operations (including order of operations) to positive rational numbers

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

1.2.D: Apply operations on real and complex numbers

1.2.D.1: approximate the value of square roots to the nearest whole number

Square Roots

1.3: Compute fluently and make reasonable estimates

1.3.C: Compute problems

1.3.C.1: multiply and divide positive rational numbers

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.3.D: Estimate and justify solutions

1.3.D.1: estimate and justify the results of multiplication and division of positive rational numbers

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.3.E: Use proportional reasoning

1.3.E.1: solve problems involving proportions, such as scaling and finding equivalent ratios

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2: Algebraic Relationships

2.1: Understand patterns, relations, and functions

2.1.B: Create and analyze patterns

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.1.D: Identify and compare functions

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

Introduction to Functions
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

2.2: Represent and analyze mathematical situations and structures using algebraic symbols

2.2.A: Represent mathematical situations

2.2.A.1: use variables to represent unknown quantities in equations and inequalities

Using Algebraic Equations

2.3: Use mathematical models to represent and understand quantitative relationships

2.3.A: Use mathematical models

2.3.A.1: model and solve problems, using multiple representations such as graphs, tables, expressions, equations or inequalities

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

2.4: Analyze change in various contexts

2.4.A: Analyze change

2.4.A.1: compare situations with constant or varying rates of change

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

3: Geometric and Spatial Relationships

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

3.1.A: Describe and use geometric relationships

3.1.A.1: classify 2- and 3- dimensional shapes based on their properties

Classifying Quadrilaterals - Activity A
Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals

3.1.B: Apply geometric relationships

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

Similar Figures - Activity A

3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

3.2.A: Use coordinate systems

3.2.A.1: given ordered pairs, identify geometric shapes in the coordinate plane using their properties

Points in the Coordinate Plane - Activity A

3.3: Apply transformations and use symmetry to analyze mathematical situations

3.3.A: Use transformations on objects

3.3.A.1: reposition shapes under informal transformations, such as reflection (flip), rotation (turn) and translation (slide)

Reflections
Rotations, Reflections and Translations

3.3.B: Use transformations on functions

3.3.B.1: describe the relationship between the scale factor and the perimeter of the image using a dilation (contractionsmagnifications) (stretching/shrin -king)

Dilations
Similar Figures - Activity A

3.3.C: Use symmetry

3.3.C.1: determine all lines of symmetry of polygons

Holiday Snowflake Designer

4: Measurement

4.1: Understand measurable attributes of objects and the units, systems and processes of measurement

4.1.A: Determine unit of measurement

4.1.A.1: identify and justify the unit of measure for volume (customary and metric)

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

4.1.C: Tell and use units of time

4.1.C.1: solve problems involving addition and subtraction of time (hours, minutes and seconds)

Elapsed Time

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

4.2.C: Apply geometric measurements

4.2.C.1: describe how to solve problems involving circumference and/or area of a circle

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

4.2.D: Analyze precision

4.2.D.1: analyze precision and accuracy in measurement situations

Triple Beam Balance

5: Data and Probability

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

5.1.C: Represent and interpret data

5.1.C.1: select, create and use appropriate graphical representation of data, including circle graphs, histograms and box plots (box and whiskers)

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A

5.2: Select and use appropriate statistical methods to analyze data

5.2.A: Describe and analyze data

5.2.A.1: find, use and interpret measures of center and spread, including ranges and interquartile range

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

5.2.B: Compare data representations

5.2.B.1: compare different representations of the same data and evaluate how well each representation shows important aspects of the data

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Populations and Samples
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.4: Understand and apply basic concepts of probability

5.4.A: Apply basic concepts of probability

5.4.A.1: use models to compute the probability of an event

Geometric Probability - Activity A