1: Number, Number Sense and Operations

1.A: Represent and compare numbers less than 0 through familiar applications and extending the number line.

Comparing and Ordering Integers
Real Number Line - Activity A

1.B: Compare, order and convert among fractions, decimals and percents.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

1.C: Develop meaning for percents, including percents greater than 100 and less than 1.

1.C.4: Describe what it means to find a specific percent of a number, using real-life examples.

Percent of Change
Percents and Proportions
Polling: Neighborhood

1.C.5: Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.

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

1.D: Use models and pictures to relate concepts of ratio, proportion and percent.

1.D.5: Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.

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

1.D.9: Give examples of how ratios are used to represent comparisons; e.g., part-to-part, part-to-whole, whole-to-part.

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

1.E: Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

1.E.6: Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions.

Order of Operations

1.H: Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

1.H.8: Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take [2 2/3 divided by 1/6].

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

1.H.12: Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use.

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

1.I: Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

1.I.10: Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 [divided by] [1/2] = 12

Dividing Fractions
Dividing Mixed Numbers

1.I.11: Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning.

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

1.I.13: Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., [7/8 + 12/13] [approximation] and 4.23 x 5.8 [approximation] 25.

Estimating Sums and Differences

1.I.14: Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.

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

1.I.15: Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100.

Percent of Change
Percents and Proportions
Polling: Neighborhood

2: Measurement

2.C: Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.

2.C.2: Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., [1/2] circle, [2/3] circle, [1/3] circle, [1/4] circle.

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

2.C.3: Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by:

2.C.3.a: estimating lengths using string or links, areas using tiles or grid, and volumes using cubes;

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area

2.C.3.b: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area

2.D: Select a tool and measure accurately to a specified level of precision.

Triple Beam Balance

2.E: Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature.

2.E.4: Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room.

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

2.F: Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

2.F.1: Understand and describe the difference between surface area and volume.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.F.6: Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

2.G: Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

2.G.1: Understand and describe the difference between surface area and volume.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.G.5: Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.

Area of Parallelograms - Activity A
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

3: Geometry and Spatial Sense

3.B: Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.

Circle: Circumference and Area
Circles

3.C: Specify locations and plot ordered pairs on a coordinate plane.

Introduction to Functions
Points in the Coordinate Plane - Activity A

3.D: Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

3.D.1: Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides.

Classifying Quadrilaterals - Activity A
Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Triangle Angle Sum - Activity A

3.D.2: Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse, and other vocabulary as appropriate.

Classifying Quadrilaterals - Activity A
Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

3.G: Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.

3.G.3: Use multiple classification criteria to classify triangles; e.g., right scalene triangle.

Classifying Quadrilaterals - Activity A
Classifying Triangles

3.H: Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.

3.H.5: Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.

Rotations, Reflections and Translations

3.I: Identify and draw three-dimensional objects from different views (top, side, front and perspective).

3.I.7: Build three-dimensional objects with cubes, and sketch the two-dimensional representations of each side; i.e., projection sets.

3D and Orthographic Views - Activity A

4: Patterns, Functions and Algebra

4.A: Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

4.A.1: Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.

Introduction to Functions
Using Algebraic Equations
Using Tables, Rules and Graphs

4.A.2: Use words and symbols to describe numerical and geometric patterns, rules and functions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

4.B: Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

Introduction to Functions
Using Algebraic Equations
Using Tables, Rules and Graphs

4.C: Use variables to create and solve equations and inequalities representing problem situations.

4.C.5: Produce and interpret graphs that represent the relationship between two variables.

Distance-Time Graphs

4.E: Use rules and variables to describe patterns, functions and other relationships.

4.E.2: Use words and symbols to describe numerical and geometric patterns, rules and functions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

4.F: Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.

Introduction to Functions
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Using Algebraic Equations
Using Tables, Rules and Graphs

4.H: Solve linear equations and inequalities symbolically, graphically and numerically.

4.H.4: Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.

Inequalities Involving Absolute Values
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Using Tables, Rules and Graphs

4.I: Explain how inverse operations are used to solve linear equations.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

4.K: Graph linear equations and inequalities.

4.K.4: Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.

Inequalities Involving Absolute Values
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Using Tables, Rules and Graphs

4.K.5: Produce and interpret graphs that represent the relationship between two variables.

Distance-Time Graphs

4.L: Analyze functional relationships, and explain how a change in one quantity results in a change in the other.

4.L.7: Identify and describe situations with constant or varying rates of change, and compare them.

Distance-Time Graphs

5: Data Analysis and Probability

5.A: Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

5.A.1: Read, construct and interpret line graphs, circle graphs and histograms.

Histograms
Populations and Samples

5.B: Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.

5.B.5: Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers.

Describing Data Using Statistics
Histograms
Line Plots
Mean, Median and Mode
Populations and Samples

5.D: Compare increasingly complex displays of data, such as multiple sets of data on the same graph.

5.D.3: Compare representations of the same data in different types of graphs, such as a bar graph and circle graph.

Populations and Samples

5.E: Collect, organize, display and interpret data for a specific purpose or need.

5.E.2: Select, create and use graphical representations that are appropriate for the type of data collected.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

5.F: Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

5.F.4: Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).

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

5.H: Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.

Permutations and Combinations

5.I: Describe the probability of an event using ratios, including fractional notation.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.J: Compare experimental and theoretical results for a variety of simple experiments.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

5.K: Make and justify predictions based on experimental and theoretical probabilities.

5.K.7: Design an experiment to test a theoretical probability and explain how the results may vary.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability