Reza Golkhandani

Lesson Overview

Title: Mathematics 7

Author: Mohammadreza Rahimiangolkhandani

Subject: Circumference and Area of Circles

Grade Level: 7

Lesson Description for Day: Taking this lesson comes after a study on circumferences. Additionally, students need to understand how circumference, pi, and the area of a circle relate to later topics, such as finding the surface area and volume of three-dimensional shapes (cylinder, cone). Students will be working individually in small groups to measure and calculate the area using the formula for area. A formula can be used to determine the area of a circle and point to a method that is non-equational. The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships.

Standards

Core Standards:

• CCSS.MATH.CONTENT.7.G.B.4: 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
• CCSS.MATH.CONTENT.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

BC Standards:

• 7.CC.3.1 Use mathematical vocabulary and language to contribute to mathematical discussions
• 7.CC.3.2 Explain and justify mathematical ideas and decisions
• 7.CC.3.3 Communicate mathematical thinking in many ways

Goals

Lesson Goals:

• Use reasoning and logic to explore, analyze, and apply mathematical ideas.
• Estimate reasonably.
• Demonstrate and apply mental math strategies.
• Model mathematics in contextualized experiences.

Students will be able to:

• Find the circumference of a circle given its radius or diameter, or vice versa.
• Find the area of a circle given its radius, diameter, or circumference, or vice versa.
• Find relationships between radius, diameter, circumference, and area to develop the C = π x d formula.
• Apply the A = π x r x r formula to find the area given radius or diameter.
• Solve real-life problems involving the areas and circumferences of circles.

Prerequisites

• Understanding what a circle is and identifying its radius and diameter.
• Familiarity with real numbers and operations on them.

Methods

Anticipatory Set:

• Name some circular shapes we usually find in natural environments.
• Name technologies and tools that are possible using circle-shaped pieces.
• Give students a G5 card with information related to circle calculations.
• Watch the video about the fun of circular movements: https://www.youtube.com/watch?v=snHKEpCv0Hk

Introduction to the formula for the area of a circle:

• Define essential elements: circle, radius, diameter, circumference
• Formula for Circumference: C = πd and C = 2πr
• Formula for Area: A = πr × r

Provide Guided Practice:

1. Draw a circle with a partner: one person as center, the other drawing the circle.
2. Measure the distance between them.
3. Use formula to calculate area.
4. Write measurements and results on the floor.

Provide Independent Practice:

Question: A goat is tethered by a 10-metre-long rope to the corner of a barn. What area of the field can the goat reach?

Answer: Calculate area of 3/4 circle (r=10) and 1/4 circle (r=5), then sum: Area = 3/4 π × 10² + 1/4 π × 5² = 75π + 6.25π = 81.25π.

Warmup

Students will count problems that can be solved using circle calculations. We will discuss planets' orbits as examples of circles and draw graphics using circles. Suggested Video: https://www.youtube.com/watch?v=ELetCV_wX_c

Assessment

Formative/Ongoing Assessment: Students will participate in an outdoor activity locating circular objects and calculating surface areas. They will create a map of the school using circles and calculate area based on their steps.

Summative Assessment:

1. Find the area of a circle of diameter d.
2. Find the area of a circle with diameter 4 cm.
3. Find the area of a given circle.
4. Calculate the area outside the bull’s eye in an archery target.

Rubric:

References

• CAST UDL Lesson Builder: http://lessonbuilder.cast.org/explore.php?op=static&pid=rocks_6
• Formative Assessment: Measurement | DREME TE: https://prek-math-te.stanford.edu/measurement-data/formative-assessment-measurement
• KNILT: https://knilt.arcc.albany.edu/images/7/71/Audio_Lesson.pdf
• Nagwa: https://www.nagwa.com/en/lessons/840181618052
• Scholastic: https://www.scholastic.com/teachers/teaching-tools/articles/lessons/perimeter-area-worksheets.html

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1. Equity and Digital Citizenry

• Intro
• Standard 1.a1
• Standard 1.a2
• Standard 1.a3
• Standard 1.a4
• Standard 1.b
• Standard 1.c
• Standard 1.d