1: Number

1.1: Develop number sense.

1.1.1: Demonstrate an understanding of place value, including numbers that are:

1.1.1.a: greater than one million

Number Systems

1.1.1.b: less than one thousandth.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Treasure Hunter (Decimals on the Number Line)

1.1.2: Solve problems involving whole numbers and decimal numbers.

Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Multiplying Decimals (Area Model)
Multiplying with Decimals
Percents, Fractions, and Decimals
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Treasure Hunter (Decimals on the Number Line)

1.1.3: Demonstrate an understanding of factors and multiples by:

1.1.3.a: determining multiples and factors of numbers less than 100

Factor Trees (Factoring Numbers)

1.1.3.b: identifying prime and composite numbers

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models

1.1.3.c: solving problems using multiples and factors.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

1.1.4: Relate improper fractions to mixed numbers and mixed numbers to improper fractions.

Dividing Mixed Numbers
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers

1.1.5: Demonstrate an understanding of ratio, concretely, pictorially and symbolically.

Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

1.1.6: Demonstrate an understanding of percent (limited to whole numbers), concretely, pictorially and symbolically.

Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

1.1.8: Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit natural number divisors).

Multiplying Decimals (Area Model)

1.1.9: Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers).

Order of Operations

2: Patterns and Relations

2.1: Use patterns to describe the world and to solve problems.

2.1.1: Represent and describe patterns and relationships, using graphs and tables.

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences

2.1.2: Demonstrate an understanding of the relationships within tables of values to solve problems.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Points, Lines, and Equations

2.2: Represent algebraic expressions in multiple ways.

2.2.4: Express a given problem as an equation in which a letter variable is used to represent an unknown number.

Solving Equations on the Number Line
Using Algebraic Equations

2.2.5: Demonstrate and explain the meaning of preservation of equality, concretely and pictorially.

Modeling and Solving Two-Step Equations
Using Algebraic Equations

3: Shape and Space

3.1: Use direct and indirect measurement to solve problems.

3.1.1: Demonstrate an understanding of angles by:

3.1.1.b: classifying angles according to their measure

Triangle Angle Sum

3.1.1.d: determining angle measures in degrees

Triangle Angle Sum

3.1.2: Demonstrate that the sum of interior angles is:

3.1.2.a: 180° in a triangle

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

3.1.2.b: 360° in a quadrilateral.

Polygon Angle Sum

3.1.3: Develop and apply a formula for determining the:

3.1.3.a: perimeter of polygons

Perimeter and Area of Rectangles

3.1.3.b: area of rectangles

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

3.1.3.c: volume of right rectangular prisms.

Balancing Blocks (Volume)
Prisms and Cylinders

3.2: Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

3.2.4: Construct and compare triangles, including:

3.2.4.b: isosceles in different orientations.

Isosceles and Equilateral Triangles

3.2.4.c: equilateral in different orientations.

Isosceles and Equilateral Triangles

3.2.4.d: right in different orientations.

Pythagorean Theorem with a Geoboard
Similarity in Right Triangles

3.3: Describe and analyze position and motion of objects and shapes.

3.3.6: Perform a combination of translations, rotations and/or reflections on a single 2-D shape, with and without technology, and draw and describe the image.

Rock Art (Transformations)
Rotations, Reflections, and Translations

3.3.7: Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations.

Rock Art (Transformations)

3.3.8: Identify and plot points in the first quadrant of a Cartesian plane, using whole number ordered pairs.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points, Lines, and Equations

3.3.9: Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole number vertices).

Rotations, Reflections, and Translations

4: Statistics and Probability

4.1: Collect, display and analyze data to solve problems.

4.1.1: Create, label and interpret line graphs to draw conclusions.

Distance-Time Graphs - Metric
Graphing Skills

4.1.2: Select, justify and use appropriate methods of collecting data, including:

4.1.2.a: questionnaires

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Reaction Time 2 (Graphs and Statistics)

4.1.2.b: experiments

Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Time Estimation

4.1.2.c: databases

Describing Data Using Statistics
Polling: City
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram

4.1.2.d: electronic media.

Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)

4.1.3: Graph collected data, and analyze the graph to solve problems.

Describing Data Using Statistics
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)

4.2: Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

4.2.4: Demonstrate an understanding of probability by:

4.2.4.a: identifying all possible outcomes of a probability experiment

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.2.4.b: differentiating between experimental and theoretical probability

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.2.4.c: determining the theoretical probability of outcomes in a probability experiment

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.2.4.d: determining the experimental probability of outcomes in a probability experiment

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.2.4.e: comparing experimental results with the theoretical probability for an experiment.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability