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
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
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.
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.
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.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
6-8
Hands -On Standards Common Core
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
Teaching the Common Core Math Standards with Hands-On Activities )
6-8
pg.121-122
pg.122-123
Constructing Ideas About Geometry
6-8
pg. 80-85
Mathematics for Elementary Teachers with Activities (Fourth Edition)
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.
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.