Download lesson 1.8

Susan Chaffee
Geometry Chapter 1
Spring 2009
Lesson 5 – Sections 1.8-1.9
Unit: Chapter 1 Tools of Geometry
Lesson: Section 1.8 The Coordinate Plane
Section 1.9 Perimeter, Area, Circumference
Lesson Goals: Understand distance in Coordinate plane and perimeter, area, circumference
Lesson Objectives:
Essential Geometry: Can you think of an application where perimeter, area, circumferences, or distance
might be useful to you in everyday life?
Materials and/or Special Notes:
 Graph paper
 SmartBoard
Write on the board: Section 1.8 the Coordinate Plane
(Definition) Coordinate Plane – Formed by x and y axis, points consist of (x,y) coordinates.
Motivation:
SB 1: Show map of Manhattan (smart board). What’s the shortest route? Why? Some student may
recall the Pythagorean theorem. We will cover PT in chapter 8, but this is where the distance formula
comes from.
Procedures (lesson outline):
INTO (Warm-up/Review/Connections: (5 minutes)
Review 1: Practice adding positive/negative numbers. Put problems on board and have students
work on these for a few minutes. Compare results with nbr. Give answers and ask for
questions.
SB 2: Review 2: Plot points A(-2,5),B(5,-2),C(0,6),D(-4,0),E(-4,-2). Have a student come to Smart
board to plot.
TEACHER and STUDENT ACTIVITIES :
1. Finding distance between 2 points.
Using SB 2: ask how we would find the distance between point A and B? or C and D?
On board: Distance Formula: √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Use parentheses on calculator!
Show x-distance & y-distance on SB.
Example: Plot the points R(-4,-1) and T(5,2). Highlight x1,x2 correspondence, emphasize order.
Examples: 6.
7. N(1, 0), P(3, 8) 8.
9. S(0, 5),T(0,-3)
2. Find midpoint of a segment.
Look back at SB 1 and SB 2. Show midpoint on each segment.
Susan Chaffee
Example: 12. A(6, 7), B(4, 3) 13.
Geometry Chapter 1
15.
Spring 2009
17.
Given one endpoint and the midpoint find the other endpoint.
For example. Suppose coordinate at Time Square is (2,6) and half way to Madison Square Park is at
(5,12). What is the coordinate of Madison Square Park?
Example: A(2,6), M(5,12) is midpoint of AB. Find coordinate of B.
Example D(4,12), M(4,11) is midpoint of CD. Find coordinate of C.
Section 1-9. Perimeter, Circumference, and Area
Careers video – Landscape architect. Look for use of angles, shapes, geometry of pathways, arc (straight
line slightly arced), parallel lines, 3-dim. “Geometry is one of the most powerful languages – it is the
backbone for explaining in words and drawing.”
http://www.thefutureschannel.com/dockets/hands-on_math/landscape_architects/
1. Finding Perimeter and Circumference
“Secure the perimeter”, action movies.
Perimeter of a polygon – distance around its sides
Circumference – distance around circle
Area – measure of the region enclosed by the figure. (number of square units)
Activity: Using grid paper, let 1 square grid represent a 1cm x 1cm square. For area you can simply add
up the number of square units enclosed.
 what are the units for perimeter? Area?
 Do rectangle with equal area have equal perimeters?
 How many different rectangles can you create with area 36. For example. B=36, h = 1,
Area=36.
Formulas for rectangles.
Rectangle, sides b and h. Perimeter = 2b + 2h, Area =b*h (Units: sq. in. or sq.ft.) or length*width
Square, side s. Perimeter = 4s, Area= s x s
Susan Chaffee
Geometry Chapter 1
Spring 2009
Dimensional analysis.
Formulas for circles.
Circumference C = πd or 2πr. Area = πr2
Exercises, pay attention to whether answer is in terms of π or an approximation. Remember 𝜋 is a
number stored in your calculator (show on calculator). Memorize formula in terms of d or r.
Exercises: #4,5,6, 21 on WS 1-9
Exercise . You wish to frame an 8x10in. photo with a frame whose border is 1 ½ inches wide. What is
the perimeter of the photo frame?
Draw it. Perimeter = 48 in. Area=143 sq.in.
Could you find the area of the border? Area entire square=area inner + area outer. Solve for outer.
Postulate 1-9: If 2 figures are congruent, then their areas are equal
Postulate 1-10: The area of a region is the sum of its non-overlapping parts.
Exercise: Find area of an irregular shape. Separate into regions that we know how to compute.
WS #14,15.
Lesson Closure: The name geometry “earth measurement”, dates back to Egyptians who developed
measurement procedures to survey land after Nile flooding caused property owners to lose their survey
markings.
Learning Log:
Assignments: p. 56,#1-7(odd),15,19,21,25,31,33,35,42,
Assessment:
 Formative: Learning Log.
What is π?
Alternative Group activity: 4 people. The group roles are:
 Surveyor – 2 people will use a string to measure circumference and diameter and measure the
string on ruler.
Susan Chaffee
Geometry Chapter 1
Spring 2009
 Recorder – records the values
 “Calculater” – This person calculates the ratio and tells the value to the recorder.
Object
Circumference
Diameter
(Circumference)÷(Diameter)
1
2
3
4
What do you notice about the last column of values?