Pre_Algebra & CAHSEE Lesson
Subject Area: Mathematics
Grade Level: Pre-Algebra & CAHSEE
Benchmark Period: 3
Duration of Lesson: 2 hours.
Standard(s): Measurement & Geometry 2.1(C) - Students compute the perimeter, area, & volume of
common geometric objects & use the results to find measures of less common objects. They know how
perimeter, area & volume are affected by changes of scale: Use formulas routinely for finding the
perimeter & area of basic two dimensional figures & the surface area & volume of basic three
dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, &
cylinders. (3 questions on CAHSEE)
Learning Objective(s): Students determine the circumference & area of a circle.
Big Ideas involved in the lesson: Circumference is the distance around a circle. Area is the space inside
a circle.
As a result of this lesson students will:
Know:
 Vocabulary:
Circumference – Distance around a circle.
Area - Space inside a circle.
A = (pi)(radius2)
Arc – Outside curve of a circle
Diameter – Distance from one side of a circle to another across the center.
Radius – Half of a diameter. A segment that has once endpoint at the center of a circle & another
endpoint on the circle.
Center – The middle of a circle
Chord – Distance across two points of a circle not through the center.
Understand:
 Circumference = Pi times Diameter or Pi times 2 radii.
 Area is the space inside a circle.
Be Able To Do:
 Use a formula to find the circumference & the area of a circle.
Assessments:
Formative:
CFU Questions:
What will be
ABWA
 Explain the difference between circumference & area.
evidence of
Student Logbook &
 Explain the distinction between circumference &
student
Your Turn worksheets
perimeter
knowledge,
Summative:
 What units are used for circumference?
understanding &
Refer to 7MG2.1
 What units are used for area?
ability?
summative file for the
 What is the relationship between the diameter & the
quiz
radius.
1
7th grade M&G 2.1 C circles
Pre_Algebra & CAHSEE Lesson
Anticipatory Set:
a. T. focuses students
b. T. states objectives
c. T. establishes purpose of
the lesson
d. T. activates prior
knowledge
Lesson Plan
In order to allow students to connect to their everyday life, teachers will
bring realia such as: plates, tires, cups, wheels, watches, CDs, DVDs, etc. In
short, just make sure that the shapes are circular.
Radius
Diameter
Chord
Arc
Students will identify the above terms.
Review Definitions:
What – Circumference – Distance around a circle. For instance, the
distance around a circular swimming pool.
Why is it important- Imagine you want to install a fence around a circular
swimming pool, how many feet of fencing would you need to buy? This
means you need to buy a length of fence that is at least equal to the
(3.14)(diameter).
What-Area Space inside a circle.
A = (pi)(radius2)
Why is it important – If you want to install carpet for a circular room, then
you will need to find the area of the floor, which is the amount of space you
will have to cover.
Use Power Point presentation anticipatory set.
CFU:
1) Ask students to distinguish between the radius & the diameter.
2) Ask students to explain the difference between perimeter & circumference
of a shape & give examples.
3) Ask students to explain the difference between circumference & area &
give examples.
4) If A= πr2, what is the area in terms of the diameter? Answer: A=π(d/2)2 or
π(d2/4).
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for
Understanding
 Pose key questions
 Ask students to
explain concepts,
definitions, attributes in
their own words
 Have students
discriminate between
examples & non-
2
Review formulas:
Circumference – Distance around a circle.
C = πd or
C = 2πr
CFU:
How come the above two formulas will lead to the same answer?
Allow students to discover/discuss the relationship between diameter &
radius.
Area - Space inside a circle
A = (pi)(radius2)
CFU
If the figure only has the measurement of a diameter, how would you apply
the diameter to the above formula?
A=π(d/2)2 or π(d2/4).
7th grade M&G 2.1 C circles
Pre_Algebra & CAHSEE Lesson
examples
 Encourage students
generate their own
examples
 Use participation
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step
along w/students at the
same time
b. Elicit overt responses
from students that
demonstrate behavior in
objectives
c. T. slowly releases
student to do more work
on their own (semiindependent)
d. Check for understanding
that students were
correct at each step
e. Provide specific
knowledge of results
f. Provide close monitoring
Closure:
a. Students prove that they
know how to do the
work
b. T. verifies that students
can describe the what &
3
Use accompanying PowerPoint presentation (2.1c Instruction) through the
guided instruction.
Refer to Power point notes for CFU.
Teachers will show students how to do the following problems:
a. Find the circumference of a circle
 A circle of a diameter 26 inches
 A tire has a radius of 12 inches.
CFU:
 What units are used for circumference?
 What is the relationship between the radius & the diameter?
Students will practice the following problems with partners:
b. Find the circumference of a circle
 A circle of a diameter 20 inches
 A plate has a radius of 7 inches.
CFU:
 If you have a choice of choosing either a diameter or a radius to find the
circumference of a circle, which one would you choose? Why? (Note:
This question should stir a discussion in class because it might depend on
the numbers. For example, if the diameter = 15 & the radius = 7.5, it
would be easier to use C=(pi)(d). However, if the diameter = 20 & the
radius = 10, then C=2(pi)(r) might be easier for some students because if
you multiplied (2)(3.14) you will immediately know that it equals 6.28.
& then you can multiply 6.28 by 10. The answer will be 62.8).
Teachers will show students how to do the following problems:
c. Find the area of a circle
 A large pizza has a diameter 22 inches
 A tortilla has a radius of 6 inches.
CFU:
 What units are used for area?
 What is the relationship between the radius & the diameter?
 Find the area and circumference of each of the pizza and tortilla above.
Students will practice the following problems with partners:
d. Find the area and circumference of the circle described below.
 A pie has a diameter 10 inches
 A cake has a radius of 8 inches.
CFU:
 When do you use C=(pi)(d)?
 When do you use C=(2)(pi)(r)?
 When do you use Area = (pi)(r2)?
. The radius of an oversized m&m is 6 inches. What is its diameter? What is
the circumference? What is the area? Show work.
7th grade M&G 2.1 C circles
Pre_Algebra & CAHSEE Lesson
why of the work
c. Have each student
perform behavior
Independent Practice:
a. Have students continue
to practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
Resources: materials
needed to complete the
lesson
4
Pirate Pizza sells a 12’’ circular pizza for $15.00. Gracialita Pizza sells a
10’’ by 12’’rectangular pizza for $15.00. Which is a better buy? Show your
work & write a short paragraph to explain why
-ABWA (Assessment By Walking Around)
-Riverdeep program—Student Log & Your Turn worksheets
-PowerPoint presentation
-Associated files
7th grade M&G 2.1 C circles