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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Exploring the Area of a Circle

Grade 7 Unit 3: Measuring Circles Exploring the Area of a Circle

Warmup

Activity #1

Estimate the Area of a Circle.

  • Set the diameter of each circle to be 4, 6, 8, 10, and 12 using the slider, and use the applet to help estimate the area of the circle.
  • Record the diameter in column D and the corresponding area in column A for your circles.

In a previous lesson, you established the relationship between the diameter and circumference of a circle.

(1.) How is this graph the same?

(2.) How is it different?

Activity #2

Explore the Area of a Circle.

  • Drag the slider to the end to straighten the circumference of the circle.
  • Check the circumference box.
  • Click the dissect checkbox to dissect the circle.
  • Separate the dissected parts by moving the green slider half way through.

(1.) What shape does the figure look like when you rearrange the bisected parts?

  • Move the red slider back and forth to see how possible number of sectors.
  • Now, move the slider all the way to the end.

(2.) What does the figure begin to look like?

  • Move the red slider all the way to the right.

(3.) What are the dimensions of the new shape?

(4.) What is the formula for the area of that shape?

Activity #3

Explore the Area of a Circle in Relation to the Diameter.

  • Study the following two pictures and answer the questions that follow.

Here is a picture of two squares and a circle.

(1.) Use any tools in the applet above that can help you to explain why the area of the circle is more than 2 square units but less than 4 square units.

Here is another picture of two squares and a circle.

(2.) Use any tools in the applet above that can help you to explain why the area of this circle is more than 18 square units and less than 36 square units.

Challenge #1

Here is a square whose side length is the same as the radius of the circle.

How many of these squares do you think it would take to cover the circle exactly?

Challenge #2

Point A  is the center of the circle, and the length of  C D is 15 centimeters. Find the circumference of this circle.

Challenge #3

The x-axis of each graph has the diameter of a circle in meters. Label the y-axis on each graph with the appropriate measurement of a circle by dragging the labels.

Quiz Time

https://www.ixl.com/math/grade-7/area-of-semicircles-and-quarter-circles

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