1: Students will acquire number sense and perform operations with rational numbers.

1.1: Represent whole numbers and decimals in a variety of ways.

1.1.e: Classify whole numbers to 100 as prime, composite, or neither.

Finding Factors with Area Models

1.2: Identify relationships among whole numbers, fractions (rational numbers), decimals, and percents.

1.2.b: Compare and order rational numbers, including mixed fractions, using a variety of methods and symbols.

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

1.2.c: Locate positive rational numbers 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

1.2.d: Convert common fractions, decimals, and percents from one form to another (e.g., 3/4= 0.75 = 75%).

Percents, Fractions and Decimals

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

1.3.b: Model addition, subtraction, multiplication, and division of fractions and decimals in a variety of ways (e.g., objects, a number line).

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Real Number Line - Activity A
Sums and Differences with Decimals

1.3.d: Select or write a number sentence that can be used to solve a multi-step problem and write a word problem when given a two-step expression or equation.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Using Algebraic Equations

1.4: Use fractions and percents to communicate parts of the whole.

1.4.c: Write a fraction or ratio in simplest form.

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

1.4.d: Name equivalent forms for fractions (halves, thirds, fourths, fifths, tenths), ratios, percents, and decimals, including repeating or terminating decimals.

Polling: Neighborhood

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

Improper Fractions and Mixed Numbers
Percents and Proportions

1.5: Solve problems using the four operations with whole numbers, decimals, and fractions.

1.5.c: Multiply up to a three-digit factor by a one- or two-digit factor including decimals.

Multiplying with Decimals

1.5.e: Add and subtract decimals to the thousandths place (e.g., 34.567+3.45; 65.3-5.987).

Sums and Differences with Decimals

1.5.f: Add, subtract, multiply, and divide fractions and mixed numbers.

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.5.g: Solve problems using ratios and proportions.

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

1.5.h: Simplify expressions, with exponents, using the order of operations.

Order of Operations

1.6: Model, illustrate, and perform the operations of addition and subtraction of integers.

1.6.a: Recognize that the sum of an integer and its opposite is zero.

Adding and Subtracting Integers

1.6.b: Model addition and subtraction of integers using manipulatives and a number line.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

1.6.c: Add and subtract integers.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Order of Operations

2: Students will use patterns, relations, and functions to represent and analyze mathematical situations using algebraic symbols.

2.1: Recognize, analyze, and use multiple representations of patterns and functions and describe their attributes.

2.1.a: Analyze patterns on graphs and tables and write a generalization to predict how the patterns will continue.

Arithmetic Sequences

2.1.b: Create tables and graphs to represent given patterns and algebraic expressions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Geometric Sequences
Introduction to Functions
Using Tables, Rules and Graphs

2.1.c: Write an algebraic expression from a graph or a table of values.

Distance-Time Graphs
Introduction to Functions
Using Tables, Rules and Graphs

2.1.d: Draw a graph from a table of values or to represent an equation.

Circles
Introduction to Functions
Solving Equations By Graphing Each Side
Using Tables, Rules and Graphs

2.2: Represent, solve, and analyze mathematical situations using algebraic symbols.

2.2.a: Recognize that a number in front of a variable indicates multiplication (e.g., 3y means 3 times the quantity y).

Using Algebraic Equations

2.2.b: Solve two-step equations involving whole numbers and a single variable (e.g., 3x+4=19).

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

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

3.1: Identify and analyze characteristics and properties of geometric shapes.

3.1.c: Identify the center, radius, diameter, and circumference of a circle.

Circle: Circumference and Area

3.1.d: Identify the number of faces, edges, and vertices of prisms and pyramids.

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

3.2: Specify locations and describe spatial relationships using coordinate geometry.

3.2.a: Graph points defined by ordered pairs in all four quadrants.

Points in the Coordinate Plane - Activity A

3.2.b: Write the ordered pair for a point in any quadrant.

Introduction to Functions
Points in the Coordinate Plane - Activity A

3.3: Visualize and identify geometric shapes after applying transformations.

3.3.a: Turn (rotate) a shape around a point and identify the location of the new vertices.

Rotations, Reflections and Translations

3.3.b: Slide (translate) a polygon either horizontally or vertically on a coordinate grid and identify the location of the new vertices.

Points in the Coordinate Plane - Activity A
Rotations, Reflections and Translations

3.3.c: Flip (reflect) a shape across either the x- or y-axis and identify the location of the new vertices.

Points in the Coordinate Plane - Activity A
Rotations, Reflections and Translations

4: Students will understand and apply measurement tools and techniques.

4.1: Identify and describe measurable attributes of objects and units of measurement.

4.1.c: Explain how the size of the unit used in measuring affects the precision.

Triple Beam Balance

4.2: Determine measurements using appropriate tools and formulas.

4.2.a: Measure length to the nearest one-sixteenth of an inch and to the nearest millimeter.

Triple Beam Balance

4.2.c: Calculate the circumference of a circle using a given formula.

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

4.2.d: Calculate elapsed time across a.m. and p.m. time periods.

Elapsed Time

4.2.e: Calculate the areas of triangles, rectangles, and parallelograms using given formulas.

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

4.2.f: Calculate the surface area and volume of right, rectangular prisms using given formulas.

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

5: Students will collect, analyze, and draw conclusions from data and apply basic concepts of probability.

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

5.1.a: Design investigations to answer questions by collecting and organizing data in a variety of ways (e.g., bar graphs, line graphs, frequency tables, stem and leaf plots).

Stem-and-Leaf Plots

5.1.b: Collect, compare, and display data using an appropriate format (i.e., bar graphs, line graphs, line plots, circle graphs, scatter plots).

Describing Data Using Statistics
Line Plots
Populations and Samples
Scatter Plots - Activity A

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

Box-and-Whisker Plots
Line Plots
Populations and Samples
Stem-and-Leaf Plots

5.2: Apply basic concepts of probability.

5.2.a: Write the results of a probability experiment as a fraction, ratio, or percent between zero and one.

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

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

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

5.2.c: Compare individual, small group, and large group results for a probability experiment.

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