6.1: Number Sense and Computation

6.1.1: Compare, order and represent on a number line positive and negative integers, fractions, decimals to hundredths and mixed numbers.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Fraction Garden (Comparing Fractions)
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)
Modeling Fractions (Area Models)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A
Treasure Hunter (Decimals on the Number Line)

6.1.2: Interpret the absolute value of a number as the distance from zero on a number line. Find the absolute value of real numbers and know that the distance between two numbers on the number line is the absolute value of their difference.

Comparing and Ordering Integers
Real Number Line - Activity A

6.1.3: Use percents to represent parts of a whole. Find the percents part of a whole.

Percents and Proportions

6.1.4: Recognize commonly used fractions, decimals, percents and all of their equivalents and convert between any two representations of non-negative rational numbers without the use of a calculator.

Improper Fractions and Mixed Numbers
Percents and Proportions
Percents, Fractions and Decimals

6.1.5: Solve problems involving addition, subtraction, multiplication and division of integers and represent computation with integers on a number line. Describe the effect of operations with numbers less than zero.

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Comparing and Ordering Integers
Real Number Line - Activity A

6.1.6: Solve problems involving addition, subtraction, multiplication and division of positive fractions and decimals. Explain why a particular operation was used for a given situation.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Dividing Fractions
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying with Decimals
Subtracting Decimals (Base-10 Blocks)
Sums and Differences with Decimals

6.1.7: Interpret ratios, model ratios and use ratios to show the relative sizes of two quantities.

6.1.7.1: Use the notations: a/b, a to b and a:b.

Part:Part and Part:Whole Ratios
Polling: Neighborhood

6.1.7.2: Write equivalent ratios.

Part:Part and Part:Whole Ratios
Polling: Neighborhood

6.1.7.3: Express a ratio in its simplest form.

Part:Part and Part:Whole Ratios
Polling: Neighborhood

6.1.7.4: Find the ratio of two given quantities.

Adding Real Numbers
Part:Part and Part:Whole Ratios
Polling: Neighborhood

6.1.8: Recognize proportional relationships and solve problems involving proportional relationships. Find the missing term in a pair of equivalent ratios. Find one quantity given the other quantity and their ratio to each other.

Adding Real Numbers
Beam to Moon (Ratios and Proportions)
Estimating Population Size
Improper Fractions and Mixed Numbers
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

6.1.9: Solve simple percent, ratio and proportion problems, including problems involving discounts at sales, interest earned and tips.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Percent of Change
Percents and Proportions
Polling: Neighborhood
Proportions and Common Multipliers
Simple and Compound Interest

6.2: Algebra and Functions

6.2.1: Write and solve one-step linear equations and inequalities in one variable.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Using Algebraic Equations
Using Algebraic Expressions

6.2.2: Write and use formulas with up to three variables to solve problems.

Using Algebraic Equations
Using Algebraic Expressions

6.2.3: Apply the correct order of operations and the properties of real numbers (i.e., identity, inverse, commutative, associative and distributive properties) to evaluate numerical expressions, including those that use grouping symbols like parentheses. Justify each step in the process.

Chocomatic (Multiplication, Arrays, and Area)
Order of Operations

6.2.4: Identify and graph ordered pairs in all four quadrants of the coordinate plane.

City Tour (Coordinates)
Distance-Time Graphs
Elevator Operator (Line Graphs)
Points in the Coordinate Plane - Activity A

6.2.5: Solve problems involving linear functions with integer values. Create a table and graph the resulting ordered pairs of integers on a grid. Look for patterns in how a change in one variable relates to a change in the second variable and write an equation that models the relationship.

Distance-Time Graphs
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Using Tables, Rules and Graphs

6.3: Geometry and Measurement

6.3.1: Identify, draw and use the properties of vertical, adjacent, complementary and supplementary angles and the properties of triangles and quadrilaterals to solve problems involving the measure of an unknown angle.

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

6.3.2: Recognize that the sum of the interior angles of any triangle is 180º and that the sum of the interior angles of any quadrilateral is 360º. Use this information to solve problems.

Classifying Quadrilaterals - Activity A
Triangle Angle Sum - Activity A

6.3.3: Develop and use the formula for the circumference of a circle and the formula for the area of a circle.

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

6.3.4: Recognize that real-world measurements are approximations. Identify appropriate instruments and units for a given measurement situation, taking into account the precision of the measurement desired.

Measuring Motion
Triple Beam Balance

6.3.5: Develop and use the formula for the surface area of a cylinder and volume of a cylinder and find the surface area and volume of three-dimensional objects built from rectangular solids and cylinders.

Balancing Blocks (Volume)
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

6.4: Data Analysis and Probability

6.4.1: Construct and analyze circle graphs and stem-and-leaf plots.

Box-and-Whisker Plots
Describing Data Using Statistics
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 2 (Graphs and Statistics)
Scatter Plots - Activity A
Stem-and-Leaf Plots

6.4.2: Choose the appropriate display for a set of data from bar graphs, line graphs, circle graphs and stem-and-leaf plots. Justify the choice of data display.

Describing Data Using Statistics
Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

6.4.3: Compare the mean, median and mode for a set of data and explain which measure is most appropriate in a given context.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

6.4.4: Solve problems involving probability as a measure of chance and verify that the probabilities computed are reasonable.

Geometric Probability - Activity A
Spin the Big Wheel! (Probability)

6.4.5: Recognize and represent probabilities as ratios, measures of relative frequency, decimals between 0 and 1, and percents between 0 and 100.

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