Grade 7 Online Math Tutorial5 (hrs)
Sep 19, 2020 20201124 13:06Grade 7 Online Math Tutorial5 (hrs)
Grade 7 Online Math Tutorial5 (hrs)
Students examine situations carefully to determine if they are describing a proportional relationship. Their analysis is applied to relationships given in tables, graphs, and verbal descriptions.
Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions and decimals serves as a significant foundation as well.
Consolidates and expands upon students’ understanding of equivalent expressions as they apply the properties of operations (associative, commutative, and distributive) to write expressions in both standard form (by expanding products into sums) and in factored form (by expanding sums into products). They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers.
Convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to represent and solve multistep percent scenarios. Students begin the module by solving problems without the use of a calculator to develop a greater fluency and deeper reasoning behind calculations with percent. Material in early lessons is designed to reinforce students’ understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students use visual models and equations, building on earlier work with these strategies.
Students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. The concept of probability provides a foundation for the thinking required to make inferential reasoning. Students delve further into several geometry topics they have been developing.

Ratios and Proportional Relationships
 An Experience in Relationships as Measuring Rate
 Proportional Relationships
 Identifying Proportional and NonProportional Relationships in Tables
 Identifying Proportional and NonProportional Relationships in Graphs
 Unit Rate as the Constant of Proportionality
 Interpreting Graphs of Proportional Relationships
 Ratios of Fractions and Their Unit Rates
 Finding Equivalent Ratios Given the Total Quantity
 MultiStep Ratio Problems
 Equations of Graphs of Proportional Relationships Involving Fractions
 Relating Scale Drawings to Ratios and Rates
 The Unit Rate as the Scale Factor
 Computing Actual Lengths from a Scale Drawing
 Computing Actual Areas from a Scale Drawing

Rational Numbers
 Opposite Quantities Combine to Make Zero
 Using the Number Line to Model the Addition of Integers
 Understanding Addition of Integers
 Efficiently Adding Integers and Other Rational Numbers
 Understanding Subtraction of Integers and Other Rational Numbers
 The Distance Between Two Rational Numbers
 Addition and Subtraction of Rational Numbers
 Applying the Properties of Operations to Add and Subtract Rational Numbers
 Understanding Multiplication of Integers
 Develop Rules for Multiplying Signed Numbers
 Division of Integers
 Converting Between Fractions and Decimals Using Equivalent Fractions
 Converting Rational Numbers to Decimals Using Long Division
 Multiplication and Division of Rational Numbers
 Applying the Properties of Operations to Multiply and Divide Rational Numbers
 Comparing Tape Diagram Solutions to Algebraic Solutions
 Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers
 Investments—Performing Operations with Rational Numbers

Expressions and Equations
 Generating Equivalent Expressions
 Writing Products as Sums and Sums as Products
 Using the Identity and Inverse to Write Equivalent Expressions
 Understanding Equations
 Using IfThen Moves in Solving Equations
 Angle Problems and Solving Equations
 Properties of Inequalities
 Solving Inequalities
 Graphing Solutions to Inequalities
 The Area of a Circle
 Unknown Area Problems on the Coordinate Plane
 The Volume of a Right Prism

Percent and Proportional Relationships
 Percent
 Comparing Quantities with Percent
 Percent Increase and Decrease
 Fluency with Percents
 Markup and Markdown Problems
 Percent Error Problems
 Simple Interest
 Tax, Commissions, Fees, and Other RealWorld Percent Applications
 The Scale Factor as a Percent for a Scale Drawing
 Changing Scales
 Computing Actual Lengths from a Scale Drawing
 Solving Area Problems Using Scale Drawings
 Population Problems
 Mixture Problems

Statistics and Probability
 Estimating Probabilities by Collecting Data
 The Difference Between Theoretical Probabilities and Estimated Probabilities
 Comparing Estimated Probabilities to Probabilities Predicted by a model
 Conducting a Simulation to Estimate the Probability of an Event
 Applying Probability to Make Informed Decisions
 Populations, Samples, and Generalizing from a Sample to a Population
 Methods for Selecting a Random Sample
 Sampling Variability and the Effect of Sample Size
 Understanding Variability When Estimating a Population Proportion

Geometry
 Complementary and Supplementary Angles
 Solving for Unknown Angles Using Equations
 Identical Triangles
 Drawing Geometric Shapes
 Drawing Parallelograms
 Drawing Triangles
 Conditions for a Unique Triangle―Three Sides and Two Sides and the Included Angle
 Conditions for a Unique Triangle—Two Angles and a Given Side
 Conditions on Measurements That Determine a Triangle
 Unique Triangles―Two Sides and a NonIncluded Angle
 Checking for Identical Triangles
 Slicing a Right Rectangular Prism with a Plane
 Slicing a Right Rectangular Pyramid with a Plane
 Slicing on an Angle
 Understanding ThreeDimensional Figures
 Problems Involving Area and Surface Area