1: Square Roots and the Pythagorean Theorem

1.8N: Number

1.8N1: Demonstrate an understanding of perfect squares and square roots, concretely, pictorially and symbolically (limited to whole numbers).

1.8N1.1: Represent a given perfect square as a square region using materials, such as grid paper or square shapes.

Square Roots

1.8N1.3: Determine a square root of a given perfect square and record it symbolically.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

1.8N1.4: Determine the factors of a given perfect square, and explain why one of the factors is a square root and the others are not.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

1.8N1.5: Determine the square of a given number.

Square Roots

1.8N2: Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).

Square Roots

1.8N2.1: Estimate, or approximate, a square root of a given number that is not a perfect square using the roots of perfect squares as benchmarks.

Square Roots

1.8N2.2: Identify a whole number whose square root lies between two given numbers.

Square Roots

1.8N2.3: Approximate a square root of a given number that is not a perfect square using technology, e.g. calculator, computer.

Square Roots

1.8N2.4: Explain why the square root of a number shown on a calculator may be an approximation.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

1.8SS: Shape and Space

1.8SS1: Develop and apply the Pythagorean theorem to solve problems.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

1.8SS1.1: Model and explain the Pythagorean theorem concretely, pictorially or using technology.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

1.8SS1.2: Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

1.8SS1.3: Explain, using examples, that the Pythagorean theorem applies only to right triangles.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

1.8SS1.4: Determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

1.8SS1.5: Solve a given problem that involves Pythagorean triples, e.g. 3, 4, 5 or 5, 12, 13.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

2: Integers

2.8N: Number

2.8N7: Demonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically.

Adding and Subtracting Integers

2.8N7.1: Model the process of multiplying two integers using concrete materials or pictorial representations and record the process.

Adding and Subtracting Integers

2.8N7.11: Solve a given problem involving integers taking into consideration order of operations.

Order of Operations

3: Operations with Fractions

3.8N: Number

3.8N6: Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially and symbolically.

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions

3.8N6.2: Model multiplication of a positive fraction by a positive fraction concretely or pictorially using an area model and record the process.

Multiplying Fractions
Multiplying Mixed Numbers

3.8N6.3: Provide a context that requires the multiplication of two given positive fractions.

Multiplying Fractions
Multiplying Mixed Numbers

3.8N6.4: Estimate the product of two given positive proper fractions to determine if the product will be closer to 0, 1/2 , or 1.

Multiplying Mixed Numbers

3.8N6.5: Generalize and apply rules for multiplying positive proper fractions, including mixed numbers.

Multiplying Fractions
Multiplying Mixed Numbers

3.8N6.7: Model division of a positive proper fraction by a positive proper fraction pictorially and record the process.

Dividing Fractions
Dividing Mixed Numbers

3.8N6.9: Generalize and apply rules for dividing positive proper fractions.

Dividing Fractions
Dividing Mixed Numbers

3.8N6.10: Model, generalize and apply rules for dividing fractions with mixed numbers.

Dividing Mixed Numbers

3.8N6.11: Provide a context that requires the dividing of two given positive fractions.

Dividing Mixed Numbers

4: Measuring Prisms and Cylinders

4.8SS: Shape and Space (Measurement)

4.8SS2: Draw and construct nets for 3-D objects.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

4.8SS2.2: Draw nets for a given right circular cylinder, right rectangular prism, and verify by constructing the 3-D objects from the nets.

Surface and Lateral Areas of Prisms and Cylinders

4.8SS2.4: Construct a 3-D object from a given net.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

4.8SS3: Determine the surface area of:

4.8SS3.a: right rectangular prisms

Surface and Lateral Areas of Prisms and Cylinders

4.8SS3.b: right triangular prisms

Surface and Lateral Areas of Prisms and Cylinders

4.8SS3.c: right cylinders to solve problems.

Surface and Lateral Areas of Prisms and Cylinders

4.8SS3.2: Explain, using examples, the relationship between the area of a 2-D shape and the surface area of a given 3-D object.

Surface and Lateral Areas of Pyramids and Cones

4.8SS3.3: Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism.

Surface and Lateral Areas of Prisms and Cylinders

4.8SS3.4: Solve a given problem involving surface area.

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

4.8SS3.5: Describe and apply strategies for determining the surface area of a given right cylinder.

Surface and Lateral Areas of Prisms and Cylinders

4.8SS4: Develop and apply formulas for determining the volume of right prisms and right cylinders.

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

4.8SS4.1: Determine the volume of a given right prism, given the area of the base.

Prisms and Cylinders

4.8SS4.5: Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism.

Prisms and Cylinders

5: Percent, Ratio, and Rate

5.8N: Number

5.8N3: Demonstrate an understanding of percents greater than or equal to 0%.

5.8N3.1: Provide a context where a percent may be more than 100% or between 0% and 1%.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram

5.8N3.2: Represent a given fractional percent using grid paper.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

5.8N3.3: Represent a given percent greater than 100 using grid paper.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

5.8N3.4: Determine the percent represented by a given shaded region on a grid and record it in decimal, fractional and percent form.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

5.8N3.5: Express a given percent in decimal or fractional form.

Percents, Fractions, and Decimals

5.8N3.6: Express a given decimal in percent or fractional form.

Percents, Fractions, and Decimals

5.8N3.7: Express a given fraction in decimal or percent form.

Percents, Fractions, and Decimals

5.8N3.8: Solve a given problem involving percents.

Percent of Change
Percents, Fractions, and Decimals
Real-Time Histogram
Time Estimation

5.8N3.9: Solve a given problem involving combined percents.

Percent of Change
Percents, Fractions, and Decimals

5.8N3.10: Solve a given problem that involves finding the percent of a percent.

Percent of Change
Percents, Fractions, and Decimals

5.8N4: Demonstrate an understanding of ratio and rate.

5.8N4.1: Express a two-term ratio from a given context in the forms 3:5 or 3 to 5.

Beam to Moon (Ratios and Proportions) - Metric
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

5.8N4.2: Express a three-term ratio from a given context in the forms 4:7:3 or 4 to 7 to 3.

Beam to Moon (Ratios and Proportions) - Metric
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

5.8N4.4: Express a given ratio as a percent.

Beam to Moon (Ratios and Proportions) - Metric
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals

5.8N4.5: Identify and describe ratios from real life examples, and record them symbolically.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

5.8N4.8: Explain why a rate cannot be represented as a percent.

Percents and Proportions

5.8N5: Solve problems that involve rates, ratios and proportional reasoning.

5.8N5.1: Explain the meaning of a/b within a given context.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

5.8N5.2: Provide a context in which a/b represents a:

5.8N5.2.c: ratio

Part-to-part and Part-to-whole Ratios

5.8N5.3: Solve a given problem involving ratio.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

6: Linear Equations and Graphing

6.8PR: Patterns and Relations

6.8PR1: Graph and analyze two-variable linear relations.

6.8PR1.1: Create a table of values by substituting values for a variable in the equation of a given linear relation.

Direct and Inverse Variation
Points, Lines, and Equations

6.8PR1.3: Construct a graph from the equation of a given linear relation (limited to discrete data).

Absolute Value with Linear Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

6.8PR1.4: Describe the relationship between the variables in a given graph.

Absolute Value with Linear Functions

6.8PR2: Model and solve problems, concretely, pictorially and symbolically, using linear equations of the form:

6.8PR2.3: Verify the solution to a given linear equation using a variety of methods, including concrete materials, diagrams and substitution.

Modeling and Solving Two-Step Equations

6.8PR2.4: Solve a given linear equation symbolically.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

6.8PR2.5: Apply the distributive property to solve a given linear equation of the form a (x + b) = c.

Solving Algebraic Equations II
Solving Equations by Graphing Each Side

6.8PR2.7: Solve a given problem using a linear equation and record the process.

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

7: Data Analysis and Probability

7.8SP: Statistics and Probability (Data Analysis)

7.8SP1: Critique ways in which data is presented.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

7.8SP1.1: Compare the information that is provided for the same data set by a given set of graphs, including circle graphs, line graphs, bar graphs, double bar graphs and pictographs, to determine the strengths and limitations of each graph.

Forest Ecosystem
Reaction Time 1 (Graphs and Statistics)

7.8SP1.2: Identify the advantages and disadvantages of different graphs, including circle graphs, line graphs, bar graphs, double bar graphs and pictographs, in representing a specific given set of data.

Distance-Time Graphs - Metric
Forest Ecosystem
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

7.8SP1.3: Justify the choice of a graphical representation for a given situation and its corresponding data set.

Box-and-Whisker Plots
Stem-and-Leaf Plots

7.8SP1.6: Identify conclusions that are inconsistent with a given data set or graph and explain the misinterpretation.

Polling: City

7.8SP: Statistics and Probability (Chance and Uncertainty)

7.8SP2: Solve problems involving the probability of independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

7.8SP2.1: Determine the probability of two given independent events and verify the probability using a different strategy.

Independent and Dependent Events
Theoretical and Experimental Probability

7.8SP2.2: Generalize and apply a rule for determining the probability of independent events.

Independent and Dependent Events

7.8SP2.3: Solve a given problem that involves determining the probability of independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

7.8N5: Solve problems that involve rates, ratios and proportional reasoning.

7.8N5.2: Provide a context in which a/b represents a:

7.8N5.2.c: ratio

Part-to-part and Part-to-whole Ratios

8: Geometry

8.8SS: Shape and Space (3-D Objects and 2-D Shapes)

8.8SS5: Draw and interpret top, front and side views of 3-D objects composed of right rectangular prisms.

8.8SS5.1: Draw and label the top, front and side views for a given 3-D object on isometric dot paper.

3D and Orthographic Views