Monday, February 24, 2014

Monday, February 24, 2014

Read Pages C16-C25 in your Science books and take Cornell style notes

POTD• Name a pair of complementary

angles.(two numbers)• Name a pair of supplementary

angles. (2 numbers)

Where do we see angles in our real life?Angles are used in daily life. •Engineers and architects use angles for designs, roads, buildings and sporting facilities. •Athletes use angles to enhance their performance. •Carpenters use angles to make chairs, tables and sofas. Everything in construction that is built is based on some point on a perpendicular 90 degree angle; walls, door frames, window frames.•Artists use their knowledge of angles to sketch portraits and paintings. •Look around the room, right angles (complementary) and straight angles (supplementary) are the basis for almost every structural design •Everything we build in the way of road construction, sidewalks, foundations, are at 180 degrees or some sort of variance because of the need.

FYI…

Area or Perimeter?That is the question!

Created by Danielle Miller, Hawk Ridge Math Facilitator

Area• The number of square units needed to cover

the flat surface inside a figure.

• Area is always measured in square units!

There are 40 squares covering the inside of the figure.


Area• To calculate the area of a regular figure use

the formula:Area = Length x Width

Area = 9m x 2mArea = 18 square meters

Area = 15 square feet

Lets find the area of this surface if each square is equal to one foot. Count the number of squares.

1 2

3

4 5 6 7 8

9 10 11 12 13 14

15

Two neighbors build swimming pools. This is what the pools look like.

Family A

Family B

Which family has the pool with the bigger swimming area?

Let’s do these problems together.


Perimeter• The distance around the outside edge of

figure.

• Perimeter is always measured in linear units.

The perimeter of this figure is51 inches.


Perimeter• To calculate the perimeter of a regular figure add the

lengths of all the sides!• Use this formula with rectangles P=2L + 2W

Perimeter = 9m + 2m + 9m + 2m orP= (9x2) + (2x2)= 22 m

Perimeter = 22 m

Take a walk around the edge!

The perimeter is…

32 cm !

This is a regular octagon with sides 4 cm

4

8

12 16

20

24

2832

Take a walk around the edge!

The perimeter is…

60 cm !

This shape has sides of 5 cm each

15

30

45

60

Perimeter = 24 feet

Let’s find the perimeter of this surface if each square is equal to one foot.Count the number of sides.

Count the number of sides to

determine the

perimeter of this flat object.

The perimeter is equal to

12.

Try this one!


Perimeter• Now you try…

The perimeter of this shape is____ units.


Perimeter

The perimeter of this shape is____ units.

Area and Perimeter Keywords

• Make a T-Chart in your notebook• Label one side Area and the other Perimeter• We will now guess whether clue words are

area or perimeter• Be sure to explain how you know

Area and Perimeter Keywords• Rim• perimeter• total space • area • tiles • area • edges • perimeter • carpet • area • trim • perimeter • fence • perimeter • border • perimeter

Area and Perimeter Keywords• around • perimeter • square units • area • outside • perimeter • distance around • perimeter • cover • area • paint • area • size of wall • area • total length • perimeter • face of an object • area


Area or Perimeter?• tiles for a bathroom floor• lace for the edge of a tablecloth• trim for the bulletin board in your classroom• paint for a wall• grass seed for your front yard• M&M candies for the outside edge of a cake top• carpet for the reading corner• fence for your backyard• mulch to cover the playground

area

areaarea

area

areaperimet

er

perimeter perimet

er

perimeter

Shape Estimated Area Estimated Perimeter Measured Area Measured Perimeter

A

B

C

D

E

F

Garden

•Explain your answers for the chart above.1. In your own words, explain what area means?2. In your own words, explain what perimeter means?3. Do all of your rectangles with 30 feet as their area have the same perimeter? Explain your answer.Which garden would you use? Why?

Rectangle Length (feet)

Width (feet)

Area (sq feet)equation

Perimeter (sq feet)equation

1234

Imagine that you are creating a garden for your mother as a surprise. Your total area foryour garden must equal 30 square units and be a rectangle. You may use your color tilesor graph paper.Find out how many different ways you can create your garden. List your answers in thetable below. List the length, width, area, and perimeter of each of your rectangles.

Multiplying 3 ways

• Distributive Property– Step 1 Break apart one factor– Step 2 multiply the other factor by both parts– Add your partial products

Multiplying 3 ways

• Box Method – Break apart the numbers by place values – Draw a rectangle and label the dimensions– Multiply– Then add the partial products

Multiplying 3 ways

• “Old Fashion Way”

Let’s ReviewCore Lesson

Multiply 512 x 46

512x 46

First, we need to multiply 512 by

6.

Then we need to multiply 512

by 40.


512x 46

2

1

7300

Adding a zero shows that we are

multiplying by 10’s.

8420+23,552

Next, we add the partial products.


405x 57

5

3

3280

Adding a zero shows that we are

multiplying by 10’s.

5220+23,085

Next, we add the partial products.

2

Tuesday, February 25, 2014

POTD1. Name a pair of complementary angles.2. Name a pair of supplementary angles3. Name a pair of vertical angles.

Homework Review

• http://www.worksheetworks.com/pdf/5df/09a21398afc9c/WorksheetWorks_Calculating_Area__Perimeter_1.pdf

Area and Perimeter Review

• http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html

Level 3 demonstrates area and perimeter of complex rectangles

http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html






Finding Missing Sides and Area and Perimeter of Complex Rectangles

• Video 1 http://www.youtube.com/watch?v=x1EZoifxmHE

– How to find the missing sides. Finding the area using subtraction method

• Video 2 http://www.youtube.com/watch?v=gXNum7RnQYo

– Finding the area using the addition method

http://www.youtube.com/watch?v=x1EZoifxmHE

http://www.youtube.com/watch?v=gXNum7RnQYo


Area of Irregular FiguresTo calculate the area of an irregular figure, follow thesesteps:

1. Divide the irregular figure into regular figures.

2. Look for missing measurements that you will need to find the area of each new regular figure.

3. Find the area of every regular figure.

4. Add the areas of each regular figure together to find the total area.


Step 1:Divide the irregular figure into regular figures.


Step 2:Look for missing measurements that you will need to find the area of each new

regular figure.

This side was 8mbut because you

split it to make tworegular rectangles,

look carefully atevery side of the

figure to see whatthe new measurements

will be!

Don’t forget the rule,opposite sides are

equal!

This will help you find themissing measurements!


Step 3: Find the area of every regular figure.

Find the area of rectangle “A”

A= L x WA = 4m x 4m

A = 16 square m

Find the area of rectangle “B”A= L x W

A = 10m x 4mA = 40 square m


Step 4: Add the areas of every regular figure.

Area of rectangle “A”A = 16 square m

Area of rectangle “B”A = 40 square m

40 square m

+ 16 square m 56 square m

The total area is 56 square m.

Subdivide this shape

This shape can be subdivided into two rectangles.

Use what you know about rectangles to help you figure out missing sides.

28 cm.

12 cm.

13 cm.

Since the side of this rectangle is 13; the other side has to be 13 also.

13 cm.

25 cm.

Since we know the entire side of the figure is 25, subtract 13 from 25 to figure out the width of the red rectangle. 25 -13 = 12

12 cm.

Figuring out the area of complex figures22 ft.

8ft.9 ft.

Step 1- Subdivide the figure into simple figures.

5 ft.

Step 3- Calculate the area of both rectangles.

4 ft.

Step 2- Figure out the missing measurements.

Area = l x w Area = 14 x 9

Area = 126

Area = l x w Area = 8 x 5 Area = 40

Step 4- Add the areas of the simple figures together. 126 + 40 = 166 ft. 2

14 ft.

Let’s Give it a Try

Figuring out the area of complex figures

15 in.

4 in.

5 in.


7 in.


4 in.



Area = 165


Area = 35

Step 4- Add the areas of the simple figures together. 165 + 35 = 200 in.2

11 in.


8 in.6 in.

2 in.


19 in.


5 in.Step 2- Figure out the missing measurements.


Area = 40


Area = 38

Step 4- Add the areas of the simple figures together. 40 + 38 = 78 in.2

24 in.


7 in.

11 in.

18 in.


24 in.

Step 3- Calculate the area of all the rectangles.

8 in.



Area = 144


Area = 168

Step 4- Add the areas of the simple figures together. 144 + 148 + 144 = 456 in.2

40 in.


Area = 144

8 in.

11 in.

Guided (glue in notebooks)

Independent

Wednesday, February 26, 2014

POTDFind the Missing Angles.1) A=2) B=3) C=4) D=

Homework Review

• http://eduplace.com/math/hmm/practice/4/practice/18_4.pdf

http://eduplace.com/math/hmm/practice/4/practice/18_4.pdf




Help me design my 1st floor Dimensions:

Room 1 _____

Room 2 _____

Room 3 _____

Room 4 _____

Area of entire 1st floor ______

Perimeter of entire 1st floor ______

Independent

Design one floor of your school/activity center/etc. You must have at least 4 rooms. Give each floor a name and list the dimensions. Create 3 Questions to go with your design. Remember to leave some dimensions missing!!

Thursday, February 27, 2014

POTD

Homework Review

Let’s get in groups of 4 and share our designs of the first floor of our homes. Are the dimensions correct?Are there missing measurements that I can solve?Can I answer my group members’ questions?

Guided/Independent1. A square has a perimeter of 36 inches. When you double the length of each side what is the new

perimeter? What is the new area? What if you triple the length of each side?

2. You want to fence in a garden that has been made of a large rectangle joined with a smaller square. The length of the rectangle and the side length of the square are both 8 yards. If the area of just the rectangle is 96 square yards what could the perimeter of the whole shape be? What could the area be?

3. An isosceles triangle has a perimeter of 28 inches. One side length is 16 inches. What are the lengths of the other two sides? Describe how you found your answer.

4. A trapezoid has 1 line of symmetry. One horizontal side is 5 inches. One horizontal side is 12 inches. If the total perimeter is 31 inches what are the side lengths of the two other sides?

Guided/Independent5. I triple the perimeter of a triangle and the new perimeter is 60 feet. In the original triangle, the longest side was at least 3 feet more than the other 2 sides. Find 3 possible combinations of the lengths of the original triangle.

6. A room in your house looks like a capital block letter T. The widest wall is 12 feet long. The opposite wall is 6 feet long. Two walls are 9 feet long. The other 4 walls have a combined length of 18 feet. Find 3 possible side lengths of the other 4 walls.

7. A regular hexagon has a perimeter of 30 yards. What is the side length of one side? If you connect 2 hexagons so that they share exactly one side what is the new perimeter? What about 3 connected hexagons? *Use pattern blocks if needed.

8. A rectangle that is 12 feet by 8 feet is doubled. Draw pictures of what the new rectangle might look like. What is the perimeter and area of the new rectangle?

Guided/Independent9. Four equilateral triangles have a combined perimeter between 58 and 98 inches. What are the possible side lengths of the triangle?

10. A playground is shaped like two combined rectangles. One has an area of 36 square yards. The other has an area of 72 square yards. What are the perimeter and area of the playground?

11. You want to put a garden up against your house. You have 24 yards of fencing for the three sides of the garden that you need to fence in. Which dimensions give you the largest garden?

12. An apartment is made of 2 large rectangular rooms that are the same size. Those rooms are connected by a smaller room. The length of the large room is 22 feet and the perimeter of the large room is 68 feet. The smaller room is a square with an area of 81 feet. What is the area of the entire apartment and the perimeter around the apartment?

Friday, February 28, 2014

POTD1)Name a pair of supplementary angles.2) Name a pair of complementary angles.3) Name a pair of vertical angles

Homework ReviewA rectangular field measures 10 ft by 3 ft. What is the area of this field? A ____ or P____

Solve:

A square-shaped room measures 6 ft on one side. What is the perimeter of this room? A ____ or P____

Solve:

Mary wants new carpeting for her dining room. Her dining room is a 5 yd by 10 yd rectangle. How much carpeting does she need to buy to cover her entire dining room? A ____ or P____

Solve:

Isabella is making a display board for the school elections. The display board is a 10 ft by 6 ft rectangle. She needs to add a ribbon border around the entire display board. What is the length of ribbon that she needs? A ____ or P____

Solve:

Jasmine is making a display board for the school talent show. The display board is a 10 ft by 9 ft rectangle. If ribbon costs $2 per foot, how much will it cost to add a ribbon border around the entire display board? A ___ or P___

Solve:

Danny has a rectangular rose garden that measures 8 m by 10 m. One bag of fertilizer can cover 16 m2. How many bags will he need to cover the entire garden? A __ or P__

Solve:

Guided/Independent1. You are putting new carpet in your bedroom. Your bedroom floor measures

11 ft. by 12 ft. How much carpet do you need to purchase? 2. You are painting a wall in your house. The wall is 12 ft. tall and 15 feet long. A. What is the area of the wall you are painting? B. Each can of paint covers 100 sq. ft. How many cans of paint do you need? 3. The area of a rectangle is 32 sq. ft. The length is twice the width. What are

the length and width of the rectangle? 4. The area of a square is 36 sq. cm. How long are the sides?

Guided/Independent5. The area of a rectangle is 75 sq. in. The length is 3 times the width. What are the length and width of the rectangle? 6. Your favorite blanket measures 45 inches by 60 inches. What is the area of your favorite blanket? 7. The area of a rectangle is 40 sq. m. The length is 3 more than the width. What are the length and width? 8. The area of a rectangle is 72 sq. in. The length is twice the width. What are the length and width?

Documents

Monday, February 24, 2014