I: Students will expand number sense to include operations with rational numbers.

I.1: Represent rational numbers in a variety of ways.

I.1.d: Express numbers in scientific notation using positive powers of ten.

Unit Conversions

I.2: Explain relationships and equivalencies among rational numbers.

I.2.a: Place rational numbers on the number line.

Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values

I.2.b: Compare and order rational numbers, including positive and negative mixed fractions and decimals, using a variety of methods and symbols, including the number line and finding common denominators.

Rational Numbers, Opposites, and Absolute Values

I.2.d: Relate percents less than 1% or greater than 100% to equivalent fractions, decimals, whole numbers, and mixed numbers.

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

I.2.e: Recognize that the sum of an integer and its additive inverse is zero.

Adding and Subtracting Integers
Adding on the Number Line

I.3: Use number theory concepts to find prime factorizations, least common multiples, and greatest common factors.

I.3.a: Determine whether whole numbers to 100 are prime, composite, or neither.

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

I.3.b: Find the prime factorization of composite numbers to 100.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

I.4: Model and illustrate meanings of operations and describe how they relate.

I.4.a: Relate fractions to multiplication and division and use this relationship to explain procedures for multiplying and dividing fractions.

Dividing Fractions
Dividing Mixed Numbers
Factor Trees (Factoring Numbers)
Fraction Artist 1 (Area Models of Fractions)
Multiplying Fractions
Multiplying Mixed Numbers
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Solving Algebraic Equations II

I.5: Solve problems involving multiple steps.

I.5.a: Select appropriate methods to solve a multi-step problem involving multiplication and division of fractions and decimals.

Multiplying Decimals (Area Model)

I.5.c: Use estimation or calculation to compute results, depending on the context and numbers involved in the problem.

Estimating Population Size
Estimating Sums and Differences
Multiplying Decimals (Area Model)

I.5.d: Solve problems involving ratios and proportions.

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

I.6: Demonstrate proficiency with the four operations, with positive rational numbers, and with addition and subtraction of integers.

I.6.a: Multiply and divide a multi-digit number by a two-digit number, including decimals.

Multiplying Decimals (Area Model)

I.6.b: Add, subtract, multiply, and divide fractions and mixed numbers.

Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Fractions
Multiplying Mixed Numbers

I.6.c: Add and subtract integers.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

II: Students will use patterns, relations, and algebraic expressions to represent and analyze mathematical problems and number relationships.

II.1: Analyze algebraic expressions, tables, and graphs to determine patterns, relations, and rules.

II.1.a: Describe simple relationships by creating and analyzing tables, equations, and expressions.

Graphing Skills

II.1.b: Draw a graph and write an equation from a table of values.

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

II.1.c: Draw a graph and create a table of values from an equation.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Points, Lines, and Equations
Solving Equations on the Number Line

II.2: Write, interpret, and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations.

II.2.a: Solve single variable linear equations using a variety of strategies.

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

II.2.b: Recognize that expressions in different forms can be equivalent and rewrite an expression to represent a quantity in a different way.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

II.2.c: Evaluate and simplify expressions and formulas, substituting given values for the variables (e.g., 2x + 4; x = 2; therefore, 2 (2) + 4 = 8).

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

III: Students will use spatial and logical reasoning to recognize, describe, and analyze geometric shapes and principles.

III.1: Identify and analyze attributes and properties of geometric shapes to solve problems.

III.1.a: Identify the midpoint of a line segment and the center and circumference of a circle.

Circles
Circumference and Area of Circles

III.1.b: Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

Investigating Angle Theorems
Triangle Angle Sum

IV: Students will understand and apply measurement tools and techniques and find the circumference and area of a circle.

IV.1: Describe and find the circumference and area of a circle.

IV.1.a: Explore the relationship between the radius and diameter of a circle to the circle?s circumference to develop the formula for circumference.

Circumference and Area of Circles

IV.1.b: Find the circumference of a circle using a formula.

Circumference and Area of Circles

IV.1.e: Find the area of a circle using a formula.

Circumference and Area of Circles

IV.2: Identify and describe measurable attributes of objects and units of measurement, and solve problems involving measurement.

IV.2.b: Convert units of measurement within the metric system and convert units of measurement within the customary system.

Unit Conversions

IV.2.d: Determine when it is appropriate to estimate or use precise measurement when solving problems.

Estimating Population Size

IV.2.e: Derive and use the formula to determine the surface area and volume of a cylinder.

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

V: Students will analyze, draw conclusions, and make predictions based upon data and apply basic concepts of probability.

V.1: Design investigations to reach conclusions using statistical methods to make inferences based on data.

V.1.a: Design investigations to answer questions.

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

V.1.b: Extend data display and comparisons to include scatter plots and circle graphs.

Graphing Skills
Trends in Scatter Plots

V.1.c: Compare two similar sets of data on the same graph and compare two graphs representing the same set of data.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

V.1.d: Recognize that changing the scale influences the appearance of a display of data.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Stem-and-Leaf Plots

V.1.e: Propose and justify inferences and predictions based on data.

Polling: City
Real-Time Histogram

V.2: Apply basic concepts of probability and justify outcomes.

V.2.a: Write the results of a probability experiment as a fraction between zero and one, or an equivalent percent.

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

V.2.b: Compare experimental results with theoretical results (e.g., experimental: 7 out of 10 tails; whereas, theoretical 5 out of 10 tails).

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

V.2.c: Compare individual, small group, and large group results of a probability experiment in order to more accurately estimate the actual probabilities.

Independent and Dependent Events