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Monday, February 24, 2014

Monday, February 24, 2014. Read Pages C16-C25 in your Science books and take Cornell style notes . FYI…. POTD. 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. 

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Monday, February 24, 2014

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  1. Monday, February 24, 2014 Read Pages C16-C25 in your Science books and take Cornell style notes 

  2. FYI… POTD • 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. • Name a pair of complementary angles.(two numbers) • Name a pair of supplementary angles. (2 numbers)

  3. Area or Perimeter? That is the question!

  4. 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. Created by Danielle Miller, Hawk Ridge Math Facilitator

  5. Area • To calculate the area of a regular figure use the formula: Area = Length x Width Area = 9m x 2mArea = 18 square meters Created by Danielle Miller, Hawk Ridge Math Facilitator

  6. Lets find the area of this surface if each square is equal to one foot. Count the number of squares. 1 2 Area = 15 square feet 3 4 5 6 7 8 9 10 11 12 13 14 15

  7. Family A Family B Let’s do these problems together. Two neighbors build swimming pools. This is what the pools look like. Which family has the pool with the bigger swimming area?

  8. Perimeter • The distance aroundthe outsideedge of figure. • Perimeter is always measured in linear units. The perimeter of this figure is 51 inches. Created by Danielle Miller, Hawk Ridge Math Facilitator

  9. 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 or P= (9x2) + (2x2)= 22 m Perimeter = 22 m Created by Danielle Miller, Hawk Ridge Math Facilitator

  10. 12 16 Take a walk around the edge! This is a regular octagon with sides 4 cm 20 8 The perimeter is… 4 32 cm ! 24 32 28

  11. 30 Take a walk around the edge! This shape has sides of 5 cm each The perimeter is… 15 60 cm ! 45 60

  12. Let’s find the perimeter of this surface if each square is equal to one foot. Count the number of sides. Perimeter = 24 feet

  13. Try this one! Count the number of sides to determine the perimeter of this flat object. The perimeter is equal to 12.

  14. Perimeter • Now you try… The perimeter of this shape is ____ units. Created by Danielle Miller, Hawk Ridge Math Facilitator

  15. Perimeter The perimeter of this shape is ____ units. Created by Danielle Miller, Hawk Ridge Math Facilitator

  16. 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 

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

  18. 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

  19. 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 or Perimeter? area perimeter perimeter area area perimeter area perimeter area Created by Danielle Miller, Hawk Ridge Math Facilitator

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

  21. Multiplying 3 ways • Distributive Property • Step 1 Break apart one factor • Step 2 multiply the other factor by both parts • Add your partial products

  22. 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

  23. Multiplying 3 ways • “Old Fashion Way” 

  24. Multiply 512 x 46 512 x 46 First, we need to multiply 512 by 6. Then we need to multiply 512 by 40.

  25. 1 512 x 46 Adding a zero shows that we are multiplying by 10’s. 2 30 7 + 4 20 0 8 23,552 Next, we add the partial products.

  26. 2 3 405 x 57 Adding a zero shows that we are multiplying by 10’s. 5 28 3 + 2 20 0 5 23,085 Next, we add the partial products.

  27. Tuesday, February 25, 2014

  28. POTD 1. Name a pair of complementary angles. 2. Name a pair of supplementary angles 3. Name a pair of vertical angles.

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

  30. 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

  31. 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

  32. Area of Irregular Figures To calculate the area of an irregular figure, follow these steps: • Divide the irregular figure into regular figures. • Look for missing measurements that you will need to find the area of each new regular figure. • Find the area of every regular figure. • Add the areas of each regular figure together to find the total area. Created by Danielle Miller, Hawk Ridge Math Facilitator

  33. Step 1:Divide the irregular figure into regular figures. Created by Danielle Miller, Hawk Ridge Math Facilitator

  34. This side was 8m but because you split it to make two regular rectangles, look carefully at every side of the figure to see what the new measurements will be! Don’t forget the rule, opposite sides are equal! This will help you find the missing measurements! Step 2:Look for missing measurements that you will need to find the area of each new regular figure. Created by Danielle Miller, Hawk Ridge Math Facilitator

  35. Find the area of rectangle “A”A= L x W A = 4m x 4m A = 16 square m Step 3:Find the area of every regular figure. Find the area of rectangle “B”A= L x W A = 10m x 4m A = 40 square m Created by Danielle Miller, Hawk Ridge Math Facilitator

  36. Area of rectangle “A”A = 16 square m Step 4:Add the areas of every regular figure. Area of rectangle “B”A = 40 square m 40 square m + 16 square m56 square m The total area is 56 square m. Created by Danielle Miller, Hawk Ridge Math Facilitator

  37. Subdivide this shape This shape can be subdivided into two rectangles.

  38. Use what you know about rectangles to help you figure out missing sides. 28 cm. 12 cm. 25 cm. 13 cm. 13 cm. 12 cm. Since the side of this rectangle is 13; the other side has to be 13 also. 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

  39. Figuring out the area of complex figures 22 ft. 5 ft. 9 ft. 8ft. 4 ft. 14 ft. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both rectangles. 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

  40. Let’s Give it a Try

  41. Figuring out the area of complex figures 7 in. 5 in. 4 in. 4 in. 11 in. 15 in. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both rectangles. Area = l x w Area = 15 x 11 Area = 165 Area = l x w Area = 7 x 5 Area = 35 Step 4- Add the areas of the simple figures together. 165 + 35 = 200 in.2

  42. Figuring out the area of complex figures 24 in. 2 in. 8 in. 19 in. 6 in. Step 1- Subdivide the figure into simple figures. 5 in. Step 2- Figure out the missing measurements. Step 3- Calculate the area of both rectangles. Area = l x w Area = 5 x 8 Area = 40 Area = l x w Area = 19 x 2 Area = 38 Step 4- Add the areas of the simple figures together. 40 + 38 = 78 in.2

  43. Figuring out the area of complex figures 40 in. 7 in. 18 in. 24 in. 11 in. 11 in. 8 in. 8 in. Step 1- Subdivide the figure into simple figures. Step 2- Figure out the missing measurements. Step 3- Calculate the area of all the rectangles. Area = l x w Area = 8 x 18 Area = 144 Area = l x w Area = 24 x 7 Area = 168 Area = l x w Area = 8 x 18 Area = 144 Step 4- Add the areas of the simple figures together. 144 + 148 + 144 = 456 in.2

  44. Guided (glue in notebooks)

  45. Independent

  46. Wednesday, February 26, 2014

  47. POTD Find the Missing Angles. • A= • B= • C= • D=

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

  49. 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 ______

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