Grade 7

Unit 1: Scale Drawings
12 Topics
What Are Scaled Copies?
Corresponding Parts and Scale Factors
Making Scaled Copies
Scaled Relationships
The Size of the Scale Factor
Scaling and Area
Scale Drawings
Scale Drawings and Maps
Creating Scale Drawings
Changing Scales in Scale Drawings
Scales without Units
Units in Scale Drawings
Unit 2: Introducing Proportional Relationships
14 Topics
One of These Things Is Not Like the Others
Introducing Proportional Relationships with Tables
More about Constant of Proportionality
Proportional Relationships and Equations
Two Equations for Each Relationship
Using Equations to Solve Problems
Comparing Relationships with Tables
Comparing Relationships with Equations
Solving Problems about Proportional Relationships
Introducing Graphs of Proportional Relationships
Interpreting Graphs of Proportional Relationships
Using Graphs to Compare Relationships
Two Graphs for Each Relationship
Four Representations
Unit 3: Measuring Circles
10 Topics
How Well Can You Measure?
Exploring Circles
Exploring Circumference
Applying Circumference
Circumference and Wheels
Estimating Areas
Exploring the Area of a Circle
Relating Area to Circumference
Applying Area of Circles
Distinguishing Circumference and Area
Unit 4: Proportional Relationships and Percentages
14 Topics
Ratios and Rates with Fractions
Revisiting Proportional Relationships
Half as Much Again
Say It with Decimals
Increasing and Decreasing
One Hundred Percent
Percentage Increase and Decrease with Equations
More and Less than 1%
Tax and Tip
Percentage Concepts
Finding the Percentage
Measurement Error
Percentage Error
Error Intervals
Unit 5: Rational Number Arithmetic
16 Topics
Interpreting Negative Numbers
Changing Temperatures
Changing Elevation
Money and Debts
Representing Subtraction
Subtracting Rational Numbers
Adding and Subtracting to Solve Problems
Position, Speed, and Direction
Multiplying Rational Numbers
Multiply
Dividing Rational Numbers
Negative Rates
Expressions with Rational Numbers
Solving Problems with Rational Numbers
Solving Equations with Rational Numbers
Representing Contexts with Equations
Unit 6: Expressions, Equations, and Inequalities
20 Topics
Relationships between Quantities
Reasoning about Contexts with Tape Diagrams
Reasoning about Equations with Tape Diagrams
Distinguishing between Two Types of Situations
Reasoning about Solving Equations (Part 1)
Reasoning about Solving Equations (Part 2)
Dealing with Negative Numbers
Different Options for Solving One Equation
Using Equations to Solve Problems
Solving Problems about Percent Increase or Decrease
Reintroducing Inequalities
Finding Solutions to Inequalities in Context
Efficiently Solving Inequalities
Interpreting Inequalities
Modeling with Inequalities
Subtraction in Equivalent Expressions
Expanding and Factoring
Combining Like Terms (Part 1)
Combining Like Terms (Part 2)
Combining Like Terms (Part 3)
Unit 7: Angles, Triangles, and Prisms
17 Topics
Relationships of Angles
Adjacent Angles
Nonadjacent Angles
Solving for Unknown Angles
Using Equations to Solve for Unknown Angles
Building Polygons (Part 1)
Building Polygons (Part 2)
Triangles with 3 Common Measures
Drawing Triangles (Part 1)
Drawing Triangles (Part 2)
Slicing Solids
Volume of Right Prisms
Decomposing Bases for Area
Surface Area of Right Prisms
Distinguishing Volume and Surface Area
Applying Volume and Surface Area
Building Prisms
Unit 8: Probability and Sampling
18 Topics
Mystery Bags
Chance Experiments
What Are Probabilities?
Estimating Probabilities Through Repeated Experiments
More Estimating Probabilities
Estimating Probabilities Using Simulation
Simulating Multi-step Experiments
Keeping Track of All Possible Outcomes
Multi-step Experiments
Designing Simulations
Comparing Groups
Larger Populations
What Makes a Good Sample?
Sampling in a Fair Way
Estimating Population Measures of Center
Estimating Population Proportions
Comparing Populations Using Samples
Memory Test
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Using Equations to Solve for Unknown Angles

Grade 7 Unit 7: Angles, Triangles, and Prisms Using Equations to Solve for Unknown Angles

Warmup

(1.) Notice when the sides of the angles are adjacent and the vertices meet at one point, they form a straight angle.

What is the measure of a straight angle?

(2.) Tyler thinks that the figure below has enough information to figure out the values of a and b.

Do you agree? Explain your reasoning.

Activity #1

Solve for Unknown Angles Between Intersecting Lines.

  • Study each diagram below carefully and answer the questions that follow.

Elena and Diego each wrote equations to represent these diagrams. For each diagram, decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.

(2.) Now solve for the missing angles, x and w.

(4.) Now solve for the missing angle, w.

(6.) Now solve for the missing angles, w.

(8.) Now solve for the missing angles, w .

(10.) Now solve for the missing angles, w and x.

Activity #2

Find Unknown angles between Intersecting Lines.

  • Study the diagrams below and find the missing angles.
  • Show your thinking. Organize it so it can be followed by others. Geometric tools can be found under in the applet.

Activity #3

Find Unknown angles between Intersecting Lines.

The right half of the figure below is representing the different angles on the left. The two bold lines are parallel.

  • Find the other 7 missing angle measures. When you enter a correct value (right side), this angle will appear in the diagram. Note: LARGE POINTS are moveable.
  • When you find the 7 missing angles, click to get another set of angles.

Challenge #1

Find the value of X:

Challenge #2

The diagram below contains three squares. Three additional segments have been drawn that connect corners of the squares. We want to find the exact value of a + b + c.

Use a protractor to measure the three angles.

(1.) Use your measurements to conjecture about the value of a + b + c.

(2.) Find the value of a + b + c by reasoning about the diagram.

Quiz Time

https://www.ixl.com/math/grade-7/write-and-solve-equations-using-angle-relationships

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