5E Lesson

In this lesson, students explore concepts of perimeter, area, surface area, and volume while engaging in hands-on construction of origami boxes. Students collaborate to discover the formulas for volume and surface area. Then students listen to a civil engineer and learn how he uses volume and surface... Read more »

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Thinking Outside of the Box

Surface Area and Volume of Rectangular Prisms

- Individual Career Academic Plan (ICAP)

- Geometry

- Mathematics

- 9th - 10th

- G.3D.1.1

2-3 class periods

85-95 minutes

5E Lesson

In this lesson, students will learn the relationship between position, velocity, speed, and acceleration to solve real-world problems involving motion along a line. Students are expected to know the chain rule and how to find higher-order derivatives for both power and trigonometric functions before... Read more »

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Making Motion Matter

Connecting Position, Velocity, and Acceleration

- 12th Grade

- AP Calculus

- Mathematics

- CHA-3, CHA-3.B, CHA-3.B.1

2-3 class periods

95-110 minutes

5E Lesson

Students will create three-dimensional representations of volumes with known cross sections in order to better understand what the solids look like and to better calculate volume. Read more »

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What Does That Look Like?

Volumes With Known Cross Sections

- 11th - 12th

- AP Calculus

- Mathematics

- G.3D.1.1, G.3D.1.2

120 minutes

2-3 class period(s)

5E Lesson

Translations, Reflections, & Trapezoids

- 6th - 10th

In this lesson, students will create and explore mathematics found in hexaflexagons. This includes learning more about translations, rotations, and reflections of polygons, showing how these types of transformations preserve congruency, and learning to calculate area of trapezoids and composite figures. Read more »

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Things to Do with a Strip of Paper: Hexaflexagons

Translations, Reflections, & Trapezoids

- 6th - 10th

- Geometry, Middle School Mathematics

- Mathematics

- 6.GM.4.1, 6.GM.4.2, 7.GM.2.1

100 minutes

2-3 class period(s)

5E Lesson

In this lesson, students will look at phenomena using a weather simulation in order to learn more about descriptive statistics and measures of central tendency. The lesson focuses on extreme weather in different parts of the United States. Read more »

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That's Low, Fo' Drizzle

Measures of Central Tendency

- 6th - 8th

- Middle School Mathematics

- Mathematics

- 6.D.1.2, 7.D.1.1, 7.D.1.2, PA.D.1.2

90 minutes

2-3 class period(s)

5E Lesson

In this lesson, students will explore the puzzling ideas behind Grandi's series in order to construct an idea of how the sum of an infinite number of terms in a sequence can be evaluated. After exploring Grandi's series, students take a closer look at limits of rational functions as their values of... Read more »

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Take it to the Limit!

Limits Toward Infinity in Rational Functions

- 12th Grade

- AP Calculus

- Mathematics

- PK.S, M.1, M.2, M.3, M.4, M.5, M.6, K.PS2

100 minutes

2-3 class period(s)

5E Lesson

Students will explore what happens when one measures a "rough" object using different units of measure. This lesson is adapted from Benoit Mandelbrot's famous problem, "Measuring the Coastline of Britain." Students will learn about the concepts of convergent and divergent series and the paradoxical... Read more »

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Measuring Borders

Convergent and Divergent Series

- 10th - 12th

- AP Calculus, Algebra 2, Precalculus

- Mathematics

- LIM-7.A

60 minutes

1-2 class period(s)

5E Lesson

The goal of this lesson is to help students understand the relationships between a function and its first and second derivatives. Students will analyze graphs recalling their knowledge of sketching graphs by hand using the first and second derivatives and apply their graphical knowledge verbally through... Read more »

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Making Connections

Connecting Functions and Their Derivatives

- 12th Grade

- AP Calculus

- Mathematics

- FUN-4, FUN-4.A, FUN-4.A.11

2-3 class periods

95-135 minutes

5E Lesson

This lesson is a follow-up to I Sub, U-Sub, We All Sub. In the previous lesson, students worked with the teacher to create an anchor chart of what "worked" and what "didn't work" for anti-differentiating derivatives of functions. The goal of this lesson is to build on that knowledge in order for students... Read more »

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I Sub, U-Sub, We All Sub Again

Integration: U-Subsitution, Part 2

- 12th Grade

- AP Calculus

- Mathematics

- PK.S, M.1, M.2, M.3, M.4, M.5, M.6, K.PS2

2-3 class periods

75 minutes

5E Lesson

This lesson builds on students' prior knowledge of basic integration techniques in calculus. The purpose of this lesson is to allow students to explore how to "undo" a function's derivative that was found using the chain rule. The chain rule is a derivative technique that allows students to find derivatives... Read more »

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I Sub, U-Sub, We All Sub

Integration: U-Subtitution, Part 1

- 12th Grade

- AP Calculus

- Mathematics

- M.5, M.6

1-2 class period(s)

75 minutes