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Arizona STEM

Acceleration Project

Around About Pi

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Around About Pi

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A 7th grade STEM lesson

Josylyn Larson

5/12/2023

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Notes for Teachers

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  • This lesson takes place in a classroom for one or more hours.
  • Students may work in small groups of 2-3.
  • An emphasis on the exploration of circles.
  • Facilitate student reflection on ratios and commonalities.

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List of Materials:

  • Circles
    • jar lids
    • cookie cutters
    • paper towel roll
    • Paper plates
    • cups
  • String or Ribbon
  • Rulers

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Arizona Standards

Math Standards:

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7.G.B Solve mathematical problems and problems in real-world context involving angle measure, area, surface area, and volume.

7.G.B.4 Understand and use the formulas for the area and circumference of a circle to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.RP.A Analyze proportional relationships and use them to solve mathematical problems and problems in real-world context.

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Science and Engineering Practices

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  • ask questions and define problems
  • develop and use models
  • plan and carry out investigations
  • analyze and interpret data
  • use mathematical and computational thinking
  • construct explanations and design solutions
  • engage in argument from evidence
  • obtain, evaluate and communicate information

Arizona Technology Standards

Standard 5. Computational Thinker - Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.

6-8.5.c. Students break problems into component parts, identify key pieces, and use that information to solve problems.

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Objectives:

Today we will explain how the circumference of a circle is proportional to its diameter

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Today we will collaborate and communicate effectively with our peers to complete an engineering investigation.

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Today students will be able to break apart circle components and how they are related.

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Agenda (60 minutes)

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Where do we see circles?

Read Sir Cumference

Measure and investigate circles

Collaborate with peers and discuss findings.

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Where do we see circles?

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Circle Definition

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the centre). Any interval joining a point on the circle to the centre is called a radius. By the definition of a circle, any two radii have the same length.

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Read-Aloud

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Instructions

In a group of 2-3, use the string to measure the circumference of the circular objects we have collected. Record your data in a data table.

  • Use the string to measure around the objects
  • Lay the string flat to measure in centimeters the circumference.
  • Use the ruler to measure the diameter passing through the center.

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How do we assess our work?

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  • Divide circumference by the diameter.
  • You should see familiarity between all measurements.

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Assessment

Test your measurements:

  • Do all measurements seem reasonable?
  • Are all measurements using the same units? (centimeters)
  • Are circumferences proportional to diameters?
  • If so what is the rate of proportionality?

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Differentiation

One way to differentiate in this lesson is to provide the circumference measurement. They can measure the diameter or radius and explore that way.

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Remediation

Extension/Enrichment

Students who are successful right away can explore harder to measure circles such as tree trunks or find the diameter of poles and pipes around campus.