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### Title: PowerPoint Presentation Author: Shane Ulrich Last modified by: ClickOK Created Date: 4/11/2011 1:27:46 AM Document presentation format: On-screen Show (4:3) – PowerPoint PPT presentation

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Title: 21st Century Lessons

1
21st Century Lessons
Area of Right Triangles
Mrs. Thompson Level 1
2
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.
3
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
4
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.
5
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
6
Warm Up
OBJECTIVE SWBAT determine the area of any right
triangle and defend their method.
(Click to Return)
Agenda
7
Agenda
OBJECTIVE SWBAT determine the area of any right
triangle and defend their method.
1) Warm Up
3) Launch Strategies for Explore
4) Explore Problem Set (Partners Groups)
5) Summary Share Solutions Expand
6) Assessment Find the Area
8
1) How many rectangles can you find? What are
their areas?
Agenda
Hints
9
Here are a few solutions. Can you find ALL of
the rectangles?
Problem
Agenda
10
2) How many shapes can you find? Name them if
you can.
Agenda
Hints
11
Click Shape Name for Examples
Triangles
Squares
Rectangles
Parallelograms
Trapezoids
Octagon
Problem
Agenda
12
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?
1 square unit
Agenda
13
Launch
What is the area of the shaded region?
How do you know?
Agenda
14
Explore
Part 1 - (5 Min) Work with your PARTNER to find
the area of triangles. Make sure you can show or
1-Partners
2-Strategy Check
3-Groups
Agenda
15
Explore Check In
Part 2 - (5 Min) What strategies are you using
to find the areas of the right triangles? Show
1-Partners
2-Strategy Check
3-Groups
Agenda
To Summary
16
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
17
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
18
Summary (Part 1)
9)
10)
11)
1)
2)

4)
3)
12)
13)
14)

5)
6)
7)
8)
See All Solutions
Agenda
To Explore
19
Classwork Solution 1
The area is ½ cm2
Summary
20
Classwork Solution 2
The area is 1 cm2
Summary
21
Classwork Solution 3
The area is 2 cm2
Summary
22
Classwork Solution 4
The area is 2 cm2
Summary
23
Classwork Solution 5
The area is 1 ½ cm2
Summary
24
Classwork Solution 6
The area is 6 cm2
Summary
25
Classwork Solution 7
The area is 7 ½ cm2
Summary
26
Classwork Solution 8
The area is 5 cm2
Summary
27
Classwork Solution 9
The area is 2 cm2
Summary
Solution
28
Classwork Solution 10
The area is 4 cm2
Summary
Solution
29
Classwork Solution 14
The area is 5 cm2
Summary
Solution
30
Classwork Solution 11
The area is 3 cm2
Summary
Solution
31
Classwork Solution 12
The area is 3 cm2
Summary
Solution
32
Classwork Solution 13
The area is 6 ½ cm2
Summary
Solution
33
Summary
34
Classwork Solutions
• ½ cm2
• 1 cm2
• 2 cm2
• 2 cm2
1. 1 ½ cm2
2. 6 cm2
• 7 ½ cm2
• 5 cm2
• 2 cm2
• 4 cm2
• 3 cm2
• 3 cm2
• 6 ½ cm2
• 5 cm2

Summary
35
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
36
Summary (Part 2)
Expand your Thinking Does this strategy work
when there are no grid lines?
Agenda
37
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
38
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
39
Summary (Part 2) Independent Practice
40 ft2
48 m2
20 ft2
24 m2
Agenda
40
Exit Ticket
4 cm
1. What is the area of the Surrounding Rectangle
for this Right Triangle?

9 cm
1. 13 cm2
1. 18 cm2
1. 36 cm2

d) 25 cm2
Agenda
41
Exit Ticket
4 cm
1. What is the area of the Triangle?

9 cm
1. 4 ½ cm2
1. 18 cm2
1. 36 cm2

d) 11 cm2
Agenda
42
1st Time Users of 21st Century Lessons
Description of 21st Century Lessons
Welcome to 21st Century Lessons! We are a
non-profit organization that is funded through an
AFT (American Federation of Teachers) Innovation
Grant. Our mission is to increase student
achievement by providing teachers with free
world-class lessons that can be taught via an LCD
projector and a computer. 21st Century Lessons
are extremely comprehensive we include
everything from warmups and assessments, to
scaffolding for English language learners and
special education students. The lessons are
designed into coherent units that are completely
aligned with the Common Core State Standards, and
Additionally, all of our lessons are completely
modifiable so you can adapt them if you like.
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43
1st Time Users of 21st Century Lessons
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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44
1st Time Users of 21st Century Lessons
Requirements to teach 21st Century Lessons
•  In order to properly use 21st Century Lessons
you will need to possess or arrange the following
things
•
• Required
• PowerPoint for P.C. (any version should work)
Note Certain capabilities in the
• PowerPoint Lessons are not compatible with
• some loss of functionality for Mac PowerPoint
users.
• An LCD projector
• Pre-arranged student groups of 2 (Many
lessons utilize student pairings. Pairs
• should be seated close by and be ready to work
together at a moments
• notice. Also, depending on which side of the
class they are sitting on, one
• partner should be identified as Lefty and one
as Righty.)
• Scissors at least 1 for every pair

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45
1st Time Users of 21st Century Lessons
Strongly Suggested to teach 21st Century Lessons
• Computer speakers that can amplify sound
throughout the entire class
• Calling Sticks a class set of popsicle
sticks with each students name on one
• A remote control or wireless presenter tool
to be able to advance the PowerPoint
• slides from anywhere in your classroom
• Personalize PowerPoints by substituting any
names and pictures of children we
• included in the PowerPoint with names and
• Since many lessons utilize short,
partner-processing activities, you will want a
pre-
• established technique for efficiently getting
• up, Count from 5 to 0 etc.)
• Have students reinforce the key questions of
the unit by creating, studying, and
• quizzing each other using flashcards. This
practice is further outlined below.
• (Research is clear that the active recall of
concepts, definitions, etc. helps
• students improve their memory. See
Recommendation 5 in
• ies.ed.gov/ncee/wwc/pdf/practiceguides/20072004.p
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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46
1st Time Users of 21st Century Lessons
Lesson Preparation (Slide 1 of 2)
We suggest spending 30-45 minutes reviewing a
lesson before teaching it. In order to review
the lesson run the PowerPoint in Slideshow -
Presenters View and advance to the Lesson
Overview slide. By clicking on the various tabs
this slide will provide you with a lot of
valuable information. (The table below gives a
brief explanation of each tab.) It is not
necessary to read through each tab in order to
teach the lesson, but we encourage you to figure
out which tabs are most useful for you.
Note All of our lessons are designed to be
taught during a 60-minute class, we allow for 5
minutes of transitions/non-productive time so the
lesson notes consider that you have only 55
minutes. If your class is shorter than 60
minutes you will have to decide which sections
to condense or remove. If your class is longer we
suggest incorporating some of the challenge
questions into your lesson as well as allowing
time for your students to quiz each other using
flashcards.
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47
1st Time Users of 21st Century Lessons
Lesson Preparation (Slide 2 of 2)
After reviewing the overview slide, click your
way through the PowerPoint. As you go, make sure
to read the presenter note section beneath each
slide. The note section is divided into two
sections In-Class Notes and Preparation
Notes. The In-Class Notes are designed to be
concise, bulleted information that you can use
on the fly as you teach the lesson. Included
in In-Class Notes are a) a suggested time frame
for a 55 minute lesson, so you can determine
whether you want to speed up, slow down, or skip
an activity, b) key questions and points that you
may want to bring up with your students to get at
the heart of the math, and c) answers to any
questions being presented on the slide. The
Preparation Notes use a narrative form to explain
how we envision the activity shown on the slide
to be delivered as well as the rationale for the
activity and any insight that we may have.
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48
1st Time Users of 21st Century Lessons
Features built into each PowerPoint lesson
There are several features which have been
incorporated into our PowerPoint lessons to help
make lessons run more smoothly as well as to give
lesson should you want them. These features
include   Wait Signal/Stars These symbols at
the bottom right of each slide indicate when the
teacher should wait for an animation (wait),
click for the next animation (yellow star), or
click to advance to the next slide (green
star).   Agenda Shortcuts On the agenda
slide, click on any section title and you will
advance to that section.   Action Buttons On
certain slides words will appear on the chalk or
erasers at the bottom of the chalkboard. These