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21st Century Lessons

Area of Right Triangles

Mrs. Thompson Level 1

Lesson Overview (1 of 3)

Lesson Objective Lesson Objective SWBAT determine the area of a right triangle by enclosing the triangle in a rectangle and taking half of the area of that rectangle. Student-Friendly Objective SWBAT determine the area of any right triangle and defend their method.

Lesson Description Overview This is a constructivist lesson that will help students connect their previous knowledge about the Area of Rectangles with the Area of Right Triangles. This lesson assumes that students are comfortable with the idea of Area and can efficiently find the Area of Rectangles. Getting Ready This activity is meant to stimulate student interest, as well as help students visualize shapes as being able to break down into other shapes. Launch The launch is a brief introduction to the activity and is meant to give the students a common language to work with during the explore section, and clarify directions. Explore Broken up into 3 sections, the explore is chunked to allow students time to make some connections independently, then communicate with partners, groups, and then the whole class and share their findings. Summary This is time for students to check their work, share their strategies, and communicate about what theyve done. In part 2, they will be asked to extend what they did to a less concrete format and do some calculations. Assessment Students will answer 2 multiple-choice questions using a body-language protocol which will give the instructor feedback about individual students learning.

Lesson Overview (2 of 3)

Lesson Vocabulary Base A side of a figure that a height can be drawn from. Height The distance of a line, perpendicular to the base, measured from the base to the opposite side or vertex. Area The number of Square Units that cover a closed figure Square Unit Units used to measure area (in2, cm2, ft2, etc.) Surrounding Rectangle (Informal) A rectangle that can be drawn around a shape as a reference for finding its area. Compose Combining shapes to construct new ones. Decompose Breaking shapes apart into familiar pieces.

Materials -Projector on Whiteboard -Photocopies of classwork and homework

Scaffolding Alternate Worksheet An additional worksheet has been created with matching problems at the end to replace the drawing problems. This will be helpful for students with motor skill problems as well as struggling learners

Enrichment Advanced Objective SWBAT determine the shaded area of a shape with a subtracted section (see problems 12-14). Meeting the Advanced Objective Have students turn in a written description of their strategies for problems 12-14 or have them teach their strategy to another group.

Online Resources for Absent Students http//www.youtube.com/watch?vX570fklcibE

Lesson Overview (3 of 3)

Common Core State Standard Geometry 6.G Solve real-world and mathematical problems involving area, surface area, and volume. 1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes apply these techniques in the context of solving real-world and mathematical problems.

Before and After Before Introduction to Concept of Area PK.MD.MA1 (pre-kindergarten) Composing Shapes 1.G.2 (first grade) Square units 3.MD.5 (third grade) Perpendicular and Parallel Lines 4.G.1 (fourth grade) After Solving real-life math problems with area, surface area, and volume 7.G.4 Shape orientation (transformations) 8.G.4 Solving equations with one variable 8.EE.7

Topic Background Ancient Egyptian mathematicians have had a significant influence on the development of geometric concepts. Sources such as the Rhind Papyrus and the Moscow Papyrus demonstrate that the Ancient Egyptians knew how to compute areas of several geometric shapes (triangles, rectangles, circles, etc.) and the volumes of cylinders and pyramids the pyramids being one of the worlds wonders for which they are famous. Greek mathematicians were also fundamental contributors to the development of geometric concepts. Euclid, often referred to as the Father of Geometry, produced Elements, a series of books that covered various geometry concepts (including area) as well as much of what is now known as algebra, trigonometry, and advanced arithmetic. The Pythagorean Theorem, one of the most famous geometric concepts, has been attributed to the Greek philosopher and mathematician Pythagoras. While the Theorem is not directly related to this lesson or unit, a strong understanding of triangles and special quadrilaterals will lay the foundation for later learning.

Warm Up

OBJECTIVE SWBAT determine the area of any right

triangle and defend their method.

1) What is the Area of the Parallelogram below?

A b x h A 25 x 8 A 200 ft2

10 ft

8 ft

height base

25 ft

Calculate

(Click for Detailed Solutions)

Agenda

Warm Up

OBJECTIVE SWBAT determine the area of any right

triangle and defend their method.

(Click to Return)

Agenda

Agenda

OBJECTIVE SWBAT determine the area of any right

triangle and defend their method.

1) Warm Up

2) Getting Ready Geometry Puzzles

3) Launch Strategies for Explore

4) Explore Problem Set (Partners Groups)

5) Summary Share Solutions Expand

6) Assessment Find the Area

Getting Ready Puzzle!

1) How many rectangles can you find? What are

their areas?

Agenda

Hints

Getting Ready Puzzle!

Here are a few solutions. Can you find ALL of

the rectangles?

Problem

Agenda

Getting Ready Puzzle!

2) How many shapes can you find? Name them if

you can.

Agenda

Hints

Getting Ready Puzzle!

Click Shape Name for Examples

Triangles

Squares

Rectangles

Parallelograms

Trapezoids

Octagon

Problem

Agenda

Launch

This is a right triangle.

What is a right triangle?

A right triangle is a triangle that has one 90

angle.

What is the area of this right triangle? How do

you know?

How can you show your work/prove your answer?

1 square unit

Agenda

Launch

What is the area of the shaded region?

How do you know?

How can you show your work/prove your answer?

Agenda

Explore

Part 1 - (5 Min) Work with your PARTNER to find

the area of triangles. Make sure you can show or

explain your strategy!

1-Partners

2-Strategy Check

3-Groups

Agenda

Explore Check In

Part 2 - (5 Min) What strategies are you using

to find the areas of the right triangles? Show

examples and explain your reasoning!

1-Partners

2-Strategy Check

3-Groups

Agenda

To Summary

Explore Understanding the Strategy

- Angelas Strategy
- Draw a surrounding rectangle
- Determine the area of the rectangle
- The area of the triangle is half the area of the

rectangle!

Do you understand Angelas strategy?

Agenda

Explore - More

Part 3 - (10 Min) Finish the worksheet in

GROUPS Use Angelas Strategy to find the area of

the remaining triangles on the worksheet.

1-Partners

2-Strategy Check

3-Groups

Agenda

Summary (Part 1)

9)

10)

11)

1)

2)

4)

3)

12)

13)

14)

5)

6)

Create your own Click here

7)

8)

See All Solutions

Agenda

To Explore

Classwork Solution 1

The area is ½ cm2

Summary

Classwork Solution 2

The area is 1 cm2

Summary

Classwork Solution 3

The area is 2 cm2

Summary

Classwork Solution 4

The area is 2 cm2

Summary

Classwork Solution 5

The area is 1 ½ cm2

Summary

Classwork Solution 6

The area is 6 cm2

Summary

Classwork Solution 7

The area is 7 ½ cm2

Summary

Classwork Solution 8

The area is 5 cm2

Summary

Classwork Solution 9

The area is 2 cm2

Summary

Solution

Classwork Solution 10

The area is 4 cm2

Summary

Solution

Classwork Solution 14

The area is 5 cm2

Summary

Solution

Classwork Solution 11

The area is 3 cm2

Summary

Solution

Classwork Solution 12

The area is 3 cm2

Summary

Solution

Classwork Solution 13

The area is 6 ½ cm2

Summary

Solution

Classwork Solutions- Create Your Own

Summary

Classwork Solutions

- ½ cm2
- 1 cm2

- 2 cm2
- 2 cm2

- 1 ½ cm2
- 6 cm2

- 7 ½ cm2
- 5 cm2

- 2 cm2
- 4 cm2
- 3 cm2

- 3 cm2
- 6 ½ cm2
- 5 cm2

Summary

Summary (Part 2)

- Explain the Strategy
- Turn and Talk
- Lefty, tell Righty the strategy for finding the

area of ANY right triangle. - Righty, tell Lefty the strategy.
- Common Language
- Can you explain the strategy we learned that will

work for finding the area of ANY right triangle? - Why does this strategy work?

Agenda

Summary (Part 2)

Expand your Thinking Does this strategy work

when there are no grid lines?

Agenda

Summary (Part 2)

Try It (As a Class) Draw and label a triangle

with a base of 5 ft and a height of 10 ft. Then

find the area.

Area of Rectangle 5 ft x 10 ft 50 ft2 Area

of Triangle 50 ft2 2 25 ft2

10 ft

5 ft

Agenda

Summary (Part 2) Independent Practice

1) Draw and label a triangle with a base of 8

in and a height of 3 in. Then find the area.

Area of Rectangle 8 in x 3 in 24 in2 Area

of Triangle 24 in2 2 12 in2

3 in

8 in

Agenda

Summary (Part 2) Independent Practice

40 ft2

48 m2

20 ft2

24 m2

Agenda

Exit Ticket

4 cm

- What is the area of the Surrounding Rectangle

for this Right Triangle?

9 cm

- 13 cm2

- 18 cm2

- 36 cm2

d) 25 cm2

Agenda

Exit Ticket

4 cm

- What is the area of the Triangle?

9 cm

- 4 ½ cm2

- 18 cm2

- 36 cm2

d) 11 cm2

Agenda

1st Time Users of 21st Century Lessons

Description of 21st Century Lessons

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Standards for This Unit

The lesson that you are currently looking at is

part of a unit that teaches the following Common

Core Standards 6.G.1. Find the area of right

triangles, other triangles, special

quadrilaterals, and polygons by composing into

rectangles or decomposing into triangles and

other shapes apply these techniques in the

context of solving real-world and mathematical

problems. 6.G.4. Represent three-dimensional

figures using nets made up of rectangles and

triangles, and use the nets to find the surface

area of these figures. Apply these techniques in

the context of solving real-world and

mathematical problems. Note The state of

Massachusetts amended 6.G.1 to include the area

and circumference of circles, since we are a

Massachusetts based organization we included

these topics in our unit.

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Strongly Suggested to teach 21st Century Lessons

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df ) - Project onto a whiteboard so you or your

students can solve problems by hand. - (Lessons often have a digital option for showing

how to solve a problem, but - you may feel it is more effective to show the

work by hand on a whiteboard.) - Internet connectivity without the internet

you may not have full functionality for - some lessons.

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Lesson Preparation (Slide 1 of 2)

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Note All of our lessons are designed to be

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