II: Number Sense, Computation, and Operations

II.A: Number Sense

II.A.1: Order and compare integers, fractions, decimals and mixed numbers with >, <, and =. Locate and compare positive and negative 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

II.B: Computation and Operation

II.B.1: Determine the prime factorization of positive integers.

Finding Factors with Area Models

II.B.3: Use addition, subtraction, multiplication and division of multi-digit whole and decimal numbers to solve multi-step real-world and mathematical problems.

Adding Real Numbers
Adding and Subtracting Integers
Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

II.B.4: Multiply and divide, without a calculator, numbers containing up to three digits by numbers containing up to two digits, such as 347 / 83 or 4.91 x 9.2.

Multiplying with Decimals

II.B.7: Add, subtract, multiply and divide common fractions and mixed numbers as well as fractions where the common denominator equals one of the denominators.

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

II.B.8: Find, represent and use percentages in real-world and mathematical problems, including percentages greater than 100% and less than 1%.

Percent of Change
Percents and Proportions
Polling: Neighborhood

II.B.9: Apply the correct order of operations and grouping symbols when using calculators and other technologies.

Order of Operations

II.B.11: Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

Biconditional Statement
Conditional Statement

III: Patterns, Functions, and Algebra

III.A: Patterns and Functions

III.A.1: Demonstrate understanding of the four quadrants in a rectangular coordinate system by writing and plotting ordered pairs.

Points in the Coordinate Plane - Activity A

III.B: Algebra (Algebraic Thinking)

III.B.1: Apply the correct order of operations including addition, subtraction, multiplication, division and grouping symbols to simplify and evaluate numeric expressions.

Order of Operations

IV: Data Analysis, Statistics, and Probability

IV.A: Data and Statistics

IV.A.1: Collect, organize and represent categorical and numerical data with tables and bar graphs.

Describing Data Using Statistics

IV.A.2: Understand the differences and appropriate use of mean, median and mode.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

IV.A.3: Find the median and possible outliers.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

IV.B: Probability

IV.B.1: Generate and display data in graphs and tables to estimate experimental probabilities.

Box-and-Whisker Plots
Compound Independent Events
Compound Independent and Dependent Events
Describing Data Using Statistics
Geometric Probability - Activity A
Histograms
Independent and Dependent Events
Line Plots
Polling: City
Probability Simulations
Scatter Plots - Activity A
Stem-and-Leaf Plots
Theoretical and Experimental Probability

IV.B.2: Represent all possible outcomes for a probability problem with tables, grids and tree diagrams to calculate probabilities and draw conclusions from the results.

Permutations and Combinations

V: Spatial Sense, Geometry, and Measurement

V.A: Spatial Sense

V.A.1: Create models of three-dimensional geometric shapes from two-dimensional representations.

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

V.A.2: Predict the position and orientation of simple geometric shapes under transformations such as reflections, rotations and translations.

Rotations, Reflections and Translations

V.A.3: Identify symmetries in three-dimensional shapes.

Holiday Snowflake Designer
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

V.B: Geometry

V.B.1: Use facts about angles including the relationship between complementary angles, supplementary angles and the angles within triangles to solve real-world and mathematical problems.

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

V.B.2: Classify triangles as equilateral, isosceles or scalene, and right, acute or obtuse.

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

V.B.3: Find the area and circumference of a circle given the radius or diameter using common approximations of pi where appropriate.

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

V.B.4: Measure, identify, and draw perpendicular and parallel lines, angles and rectangles by using appropriate tools such as straightedge, ruler, compass, protractor or software.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
Triple Beam Balance

V.C: Measurement

V.C.3: Find the area and perimeter of rectangles, squares, triangles and parallelograms by measuring, using a grid or using a formula.

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