7.G.4 - About the Math, Learning Targets, and Increasing Rigor
Grade 5 GT Geometry
7.G.4
Full Standard
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Learning Targets (I can)
- Describe the relationship between radius and diameter.
- Explain that the ratio of circumference to diameter is constant (pi).
- Prove that the ratio of circumference to diameter is constant with various models.
- Find the circumference of a circle.
- Find the area of a circle.
- Compare and contrast the area and circumference of a circle.
About the Math
Construction of circles with the us e of lines and points will allow students the opportunity to extend prior knowledge of circles. Practice constructing circles provides a geometric way to conceptually understand the measurement formula and why it is accurate to apply to the circle. This further deepens understanding of equivalence because circles are different from other two-dimensional shapes. They have a perimeter (circumference) and area similar to other two-dimensional shapes. The discovery of the relationship between the circumference and the area is provided through accurate work with the formulas. Essential vocabulary for this standard includes: circle, circumference, area, diameter, radius, pi, formula . Visit the online dictionary (Links to an external site.)
Links to an external site. or visual math dictionary (Links to an external site.)
Links to an external site. for vocabulary support.
Progression of Standard within Grade 5 G/T
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics
Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Progression of this Standard Across Grades
This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.
Grade | HS |
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TASKS
These tasks can be used with small group or whole group instruction.
- Find the circumference of all size pizzas at a pizza place of your choice and determine what item is priced lower based on size.
- Given several bike tires of various sizes have students determine which would be the optimal choice if participating in a road race and justify their reasoning.
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
Module 13 • Area, Volume, and Surface Area
Area and Circumference of a Circle:
- Lesson 3.1 How Well Can You Measure? Links to an external site.
- Lesson 3.2 Exploring Circles Links to an external site.
- Lesson 3.3 Exploring Circumference Links to an external site.
- Lesson 3.4 Applying Circumference Links to an external site.
- Lesson 3.5 Circumference and Wheels Links to an external site.
- Lesson 3.6 Estimating Area Links to an external site.
- Lesson 3.7 Exploring Area of a Circle Links to an external site.
- Lesson 3.8 Relating Area to Circumference Links to an external site.
Additional Tasks
These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]
- Designs (Illustrative Math) Links to an external site.
- Circumference of a Circle
Links to an external site.(Illustrative Math)
- Eight Circles Links to an external site. (Illustrative Math)
- Circles Links to an external site. (Illustrative Math)
- Wedges of a Circle Links to an external site. Links to an external site.(Illustrative Math)
- Frosting a Cake Download Frosting a Cake (R.Kimmel, Waverly ES)
- Pokémon Go Cheat Links to an external site. (Dan Meyer 3-Act Task, pictured)
- Applying Area to Circles: Lesson 3.9 Links to an external site.(Open-Up Resources - Illustrative Math)
- Distinguishing Circumference and Area: Lesson 3.10 Links to an external site. (Open-Up Resources - Illustrative Math)
- Stained Glass Windows: Lesson 3.11 Links to an external site. (Open-Up Resources - Illustrative Math)
- Which is Bigger? Links to an external site. (Inside Mathematics)
- The Giant Cookie Dilemma Links to an external site. (NCTM, Illuminations)
- Equations and Equalities to Solve Geometry Links to an external site. (Engage NY)
- Holes Links to an external site. (Dan Meyer, 3 Act Task)
- Coin Carpet Links to an external site. (Dan Meyer, 3 Act Task)
- Pizza Doubler Links to an external site. (Dan Meyer, 3 Act Task)
- Popcorn Picker Links to an external site.(Dan Meyer, 3 Act Task)
- Coffee Traveler Links to an external site. (Dan Meyer, 3 Act Task)
- Penny Circle Links to an external site. (Dan Meyer, 3 Act Task)
Tasks From Print Resources
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Book Thumbnail | Book Title | Grade | Pages |
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Teaching Student-Centered Mathematics | 6-8 | ||
Hands -On Standards Common Core
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7 | pg. 90-97 | |
Problem-Driven Math | 6-8 |
pg.100-101 pg.152-154 pg.155-157 pg.164-166 pg.221-223 pg.232-234 |
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Teaching the Common Core Math Standards with Hands-On Activities ) |
6-8 |
pg.121-122 pg.122-123 |
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Constructing Ideas About Geometry | 6-8 | pg. 80-85 | |
Mathematics for Elementary Teachers with Activities (Fourth Edition) | pg. CA-241 |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
- Relationship Between Radius and Diameter Links to an external site.
- Area of Circles Links to an external site.
- Area and Circumference Links to an external site.
- Area of Circles Links to an external site.
- Finding Circumference Links to an external site.
- Ratio of Circumference to Diameter Links to an external site.
- Apply Formulas for Area of Circle and Rectangle to Find Area of an Irregular Figure Links to an external site.
- Find Circumference of a Circle Links to an external site.
- Find Circumference of a Circle_2 Links to an external site.
- Reason About the Relationship Between Radius and Area of a Circle Links to an external site.
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Learning Targets
- Describe the relationship between radius and diameter.
- Explain that the ratio of circumference to diameter is constant (pi).
- Prove that the ratio of circumference to diameter is constant with various models.
- Find the circumference of a circle.
- Find the area of a circle.
- Compare and contrast the area and circumference of a circle.
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.
Rubric for Tasks Links to an external site.
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This course content is offered under a CC Attribution Non-Commercial Share Alike
Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.