New Jersey Center for Teaching and Learning. Progressive Mathematics Initiative

Slide 1 / 126 New Jersey Center for Teaching and Learning Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. Click to go to website: www.njctl.org

Slide 2 / 126 4th Grade Geometry 2014-05-21 www.njctl.org

Slide 3 / 126 Geometry Unit Topics Area of Rectangles Perimeter of Rectangles Area and Perimeter Word Problems Protractor Lines, Line Segments & Rays Types of Lines Lines of Symmetry Click on the topic to go to that section

Slide 4 / 126 Rectangles Return to Table of Contents

Slide 5 / 126 Area - The number of square units (units 2 ) it takes to cover the surface of a figure. ALWAYS label units 2!!! 12 ft 6 ft

Slide 6 / 126 How many 1 ft 2 tiles does it take to cover the rectangle? Use the squares to find out! Look for a faster way than covering the whole figure. 12 ft 6 ft

Slide 7 / 126 The Area (A) of a rectangle is found by using the formula: A = length(width) A = lw The Area (A) of a square is found by using the formula: A = side(side) A = s 2

Slide 8 / 126 1 What is the Area (A) of the figure? 15 ft Pull for answer 6 ft

Slide 9 / 126 2 Find the area of the square. 7 Pull for answer

Slide 10 / 126 3 Find the area. 120 cm. Pull for answer 30 cm.

Slide 11 / 126 4 What is the area of a rectangular room with a length of 11 feet and a width of 14 feet? Pull for answer

Slide 12 / 126 5 Which figure has the greatest area? A B B A C C

Slide 13 / 126 6 Which of the following has the same area as this figure? A B C

Slide 14 / 126 7 Which figure has an area greater than Figure Y? Y Y B A C

Slide 15 / 126 The area formula can also be used to find an unknown length or width when the area is known. Example: The area of a rectangle is 48 m length is 8 m, what is the width? 2. If the w=? A=48m 2 A = lw 48 = 8w 6 = w do 48 8 to solve l=8 m The width is 6 meters.

Slide 16 / 126 8 The area of a rectangle is 45 cm 2. If the width is 3 cm, what is the length? Hint: Draw a picture first. Pull for answer

Slide 17 / 126 9 The area of the principal's office is 56 ft 2. If the length of one side of the office is 8 ft, what is the length of the other? Pull for answer

Slide 18 / 126 10 The hallway has 1,224 tiles that are one foot by one foot in size covering the floor. If the width of the hallway is 9 feet, what is the length? Pull for answer

Slide 19 / 126 11 A table top has an area of 81 square feet. If one of the sides has a length of 9 feet, what is the length of the other side? Pull for answer

Slide 20 / 126 12 What is the area of the shaded region? The shaded area is equal to 32 square units

Slide 21 / 126 Perimeter Return to Table of Contents

Slide 22 / 126 Perimeter- What word do you see in the middle of perimeter? click PERIMETER

Slide 23 / 126 The perimeter of a shape is the measurement around the outside of the shape.

Slide 24 / 126 Perimeter of a polygon is the sum of the lengths of the sides. 9 m. For example: 6 m. P = 9 + 10 + 7 + 6 P = 32 units 10 m. 7 m.

Slide 25 / 126 13 What is the perimeter of this polygon? 4 cm. 5 cm. 4 cm. Pull for answer 9 cm.

Slide 26 / 126 14 What is the perimeter of this polygon? 8 ft. 8 ft. Pull for answer 8 ft. 8 ft. 8 ft.

Slide 27 / 126 15 What is the perimeter of this polygon? 4 in. 10 in. 7 in. Pull for answer

Slide 28 / 126 Perimeter of Rectangles= l + l + w + w l w l w Can this be shown by a formula that would be true for all rectangles? Note: (l) represents the Length, or longer side of the rectangle. (w) represents the Width, or shorter side of the rectangle. If no units are given, use " u".

Slide 29 / 126 Perimeter (P) of a rectangle is found by solving the following formula: Click for formula. P = 2l + 2w w l

Slide 30 / 126 Example: What is the perimeter of the rectangle? P = 2 l + 2 w P = 2(20) + 2(8) P = 40 + 16 P = 56 in. l = 20 in. w = 8 in.

Slide 31 / 126 Perimeter (P) of a square is found by doing four (4) times Side (s): P = 4s S

Slide 32 / 126 Example: P = 4 s P = 4(32) P = 128 units s = 32

Slide 33 / 126 16 What is the Perimeter (P) of the following rectangle? 15 ft. Pull for answer 6 ft.

Slide 34 / 126 17 What is the Perimeter (P) of the square below? 7 units Pull for answer

Slide 35 / 126 18 What is the perimeter of figure A? D B A C

Slide 36 / 126 19 What is the perimeter of Figure B? D B A C

Slide 37 / 126 20 What is the perimeter of Figure C? D B A C

Slide 38 / 126 21 What is the perimeter of Figure D? D B A C

Slide 39 / 126 22 Ms. Santiago wants to put a fence around her vegetable garden. The garden is the shape of a rectangle and has a length of 7 feet and a width of 6 feet. How many feet of fencing does she need?

Slide 40 / 126 Click for Geoboard Interactive National Library of Virtual Manipulatives When first open, close directions on the right, and click clear to remove the irregular shape.

Slide 41 / 126 Use geoboards to find how many rectangles you can make with an area of 12 units 2. Does the perimeter stay the same in each rectangle?

Slide 42 / 126 Areas of 12 square units. Perimeters are not the same.

Slide 43 / 126 Use geoboards to find two rectangles with an area of 16 square units. Draw a sketch. Label the sides. Record the area. Record the perimeter.

Slide 44 / 126 Use geoboards to find two rectangles with an area of 18 square units. Draw a sketch. Label the sides. Record the area. Record the perimeter.

Slide 45 / 126 Karen is going to buy 4 wooden boards to make a sandbox. She wants the area of the sandbox to be 36 square feet. What are all the different dimensions (length and width) that Karen's sandbox could be? Pull

Slide 46 / 126 23 If Karen's sandbox is 36 square feet, which dimensions will give her a perimeter of 26 feet? click for choices A 1 x 39 B 2 x 18 C 3 x 12 D 4 x 9 E 6 x 6

Slide 47 / 126 Troy is going to make a garden with an area of 24 square feet. What are the different dimensions that his garden can be?

Slide 48 / 126 24 If Troy's garden has an area of 24 square feet, and he has 20 feet of fencing to go around it. What are the dimensions of the garden he needs to make? A 1 x 24 B 2 x 12 C 3 x 8 D 4 x 6 click for choices

Slide 49 / 126 Area & Perimeter Word Problems Return to Table of Contents

Slide 50 / 126 A square measures 8 cm on each side. 8cm Perimeter = 4(8) = 32 cm. Area = 8(8) = 64 cm 2 You need to be careful when doing word problems, because area and perimeter are two different problems. Carefully read the problem to decide what is being asked.

Slide 51 / 126 25 Samuel is painting the outside of his garage door. The door is in the shape of a rectangle with a length of 20 feet and a height of 8 feet. How many square feet will Samuel paint? Is this an area or perimeter problem? A B area perimeter

Slide 52 / 126 26 Now solve. Samuel is painting the outside of his garage door. The door is in the shape of a rectangle with a length of 20 feet and a height of 8 feet. How many square feet will Samuel paint?

Slide 53 / 126 27 Michelle's bedroom floor is shaped like a rectangle. It is 10 feet long and 12 feet wide. How much carpeting would be needed for the floor? Is this an area or perimeter problem? A B area perimeter

Slide 54 / 126 28 Now solve. Michelle's bedroom floor is shaped like a rectangle. It is 10 feet long and 12 feet wide. How much carpeting would be needed for the floor?

Slide 55 / 126 29 Also in Michelle's bedroom she would like to have a border of paper around the room. Would she need to know the area or perimeter of the room to buy the border? A B area perimeter

Slide 56 / 126 30 Now solve. Michelle's room is a 10 ft. by 12 ft. rectangle. Border will not go where the window and the door are. Leaving out the border by the window that is 3 feet and door that is 4 feet, how much border will she buy?

Slide 57 / 126 31 Carl's bedroom is shaped like a square. The length of one side of his room is 11 feet. He wants to put new trim along the edge of the ceiling. How many feet of trim does he need? Is this an area or perimeter problem? A B area perimeter

Slide 58 / 126 32 Now solve. Carl's bedroom is shaped like a square. The length of one side of his room is 11 feet. He wants to put new trim along the edge of the ceiling. How many feet of trim does he need?

Slide 59 / 126 33 Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6 ft.? Is this an area or perimeter problem? A B area perimeter

Slide 60 / 126 34 Now solve. Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6 ft.?

Slide 61 / 126 Protractor Return to Table of Contents

Slide 62 / 126 An angle is formed when two rays meet at a point called the vertex. ray 55 o vertex ray

Slide 63 / 126 An angle is measured in units called degrees. 18 o 55 o 110 o 43 o 118 o

Slide 64 / 126 A protractor is an instrument used to measure angles. It has two scales, an inner scale and an outer scale. Each scale begins at 0 degrees and ends at 180 degrees.

Slide 65 / 126 The degrees come from the fact that there are 360 in a circle.

Slide 66 / 126 When using a protractor, you can extend the rays that form the sides of the angle. For this protractor, move the green circle to create the angle. Click on this green arrow to insert the angle on the page. Place the center of the base line of the protractor on the vertex of the angle.

Slide 67 / 126 Using this protractor measure the angles on the board, use your own to measure on your paper. 110 o 40 o

Slide 68 / 126 Using this protractor measure the angles on the board, use your own to measure on your paper. 30 o 80 o

Slide 69 / 126 35 Measure the angle using a protractor. What is the angle measurement? 55 o

Slide 70 / 126 36 Measure the angle using a protractor. What is the angle measurement? 100 o

Slide 71 / 126 37 Measure the angle using a protractor. What is the angle measurement? 63 o

Slide 72 / 126 38 Measure the angle using a protractor. What is the angle measurement? 162 o

Slide 73 / 126 39 Measure the angle using a protractor. What is the angle measurement? 42 o

Slide 74 / 126 Click for game to practice estimating angles

Slide 75 / 126 Click for Memory Game

Slide 76 / 126 Angles are classified according to their measures. A right angle measures 90 degrees A straight angle measures 180 degrees

Slide 77 / 126 Acute Angles 28 o An acute angle measures greater than 0 degrees and less than 90 degrees 87 o 52 o 6 o 56 o 67 o

Slide 78 / 126 Obtuse Angles 148 o A obtuse angle measures greater than 90 degrees and less than 180 degress 99 o 111 o 137 o 175 o

Slide 79 / 126 Sort the angles into the correct box. acute obtuse right straight 159 o 90 o 124 o 25 o 64 o 90 o 123 o 180 o 59 o 21 o

Slide 80 / 126 40 What is the correct name of this angle? A B C straight acute obtuse D right

Slide 81 / 126 41 What is the correct name of this angle? A B C straight acute obtuse D right

Slide 82 / 126 42 What is the correct name of this angle? A B C straight acute obtuse D right

Slide 83 / 126 43 What is the correct name of this angle? A B C straight acute obtuse D right

Slide 84 / 126 44 If you know the angle measures more than 90 degrees than it is called what type of angle? A B straight acute C obtuse D right

Slide 85 / 126 45 What kind of angle is shown in this picture? A straight B obtuse C acute D right

Slide 86 / 126 46 What kind of angle is shown in this picture? A straight B obtuse C acute D right

Slide 87 / 126 47 What kind of angle is shown in this picture? A straight B obtuse C acute D right

Slide 88 / 126 48 What kind of angle is shown in this picture? A straight B obtuse C acute D right

Slide 89 / 126 49 What kind of angle is shown in this picture? A straight B obtuse C acute D right

Slide 90 / 126 Lines, Line Segments & Rays Return to Table of Contents

Slide 91 / 126 Draw a Sketch Point A A point is an exact location in space. It has no length or width. A point is usually named with a capital letter.

Slide 92 / 126 Draw a Sketch Line A straight path of points that goes on forever in two directions. A B Click This is written as: AB

Slide 93 / 126 Draw a Sketch Line Segment A line with definite end points. C D Click This is written as: CD

Slide 94 / 126 Draw a Sketch Ray Part of a line that has one endpoint and extends forever in the other direction. E F This is written as: EF Click

Slide 95 / 126 Draw a Sketch Angle Figure formed by two rays with a common endpoint (vertex). Click

Slide 96 / 126 Match the label with the correct line, ray or line segment. R S x y g c d V h W GH WV RS VW XY RS ZY CD

Slide 97 / 126 50 Which of the following names a line? A B C AB BA AB D AB

Slide 98 / 126 51 Which of the following names a line segment? A AB B BA C AB D AB

Slide 99 / 126 52 Which of the following statements is not true? A A ray is part of a line B A line segment is part of a line C A line is made up of end points D A point is a location in space

Slide 100 / 126

Slide 101 / 126 Types of Lines Return to Table of Contents

Slide 102 / 126 Draw a Sketch Parallel Lines Lines in the same plane that do not intersect. Click

Slide 103 / 126 Move the lines to find the sets of parallel lines.

Slide 104 / 126 Draw a Sketch Perpendicular Lines Intersecting lines that form right angles. Click

Slide 105 / 126 Click for perpendicular lines applet

Slide 106 / 126 53 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 107 / 126 54 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 108 / 126 55 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 109 / 126 56 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 110 / 126 57 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 111 / 126 58 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 112 / 126 59 What type of lines are shown in this picture? A B C D parallel lines perpendicular lines both neither

Slide 113 / 126 Lines of Symmetry Return to Table of Contents

Slide 114 / 126 Draw a Sketch A figure has symmetry is one half of the figure is the mirror image of the other half. A line of symmetry is a line that can divide a figure into halves that are mirror images of each other. Move this line to see if each letter has a line of symmetry

Slide 115 / 126 When a shape is symmetrical, it is the same on both sides of a line of symmetry. A line of symmetry is a line where if the shape were folded, the two sides would be the same. Line of symmetry

Slide 116 / 126 Drag each object to the line of symmetry. Place each so that both sides would be the same if the shape was folded on that line. Line of Symmetry

Slide 117 / 126 Use the pen to draw the other side of this shape. What do you have to do to make sure both sides are the same? Line of Symmetry

Slide 118 / 126 These shapes have more than one line of symmetry. Draw the lines of symmetry.