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MATH UNIT 16 4TH GRADE line rhombus quadrilateral line segment triangle 1. A polygon with three sides is known as a ____ 2. A part of a line that has one endpoint is a ___ 3. A four-sided polygon in which opposite sides are parallel and all sides are the same length is a ____ 4. A _______ is a straight path of points that goes on without end in two directions. Find the area of each polygon. 13’ 8’ 2’ 5’ 5’ 9’ 16’ 3’ Find the perimeter of each 4” polygon. 4” 6” 9” 7” 5” 6” 3” 2” 2” 3” 2” 2” 2” How do you classify angles using benchmark angles? An angle is a figure formed by two rays that have the same endpoint. That endpoint is also known as the vertex of the angle. Angles are usually measured in units called degrees. The symbol indicates degrees. You can use benchmark angles to classify angles. Benchmark angles are STANDARDS. You use benchmark angles to figure out the degrees of other angles. 90 180 45 A 90 angle makes a square corner. A 45 angle is and angle that is open half as much as a 90 angle. A 180 angle is an angle that forms a straight line. You can use benchmark angles to estimate angle measures. a. b. Less than 45 45 c. less than 90 d. 90 Classify each angle. A roller coaster has a brace support that forms a square corner. What is the angle measure of the angle formed by the brace support? Classify each angle. Classify each angle. Classify each angle. Sonny drew a rectangle that has a length of 6 inches and a width of 4 inches. Describe a different rectangle with the same perimeter as Sonny’s. Now tell which rectangle has the greater area. The hands on a clock show that the time is 6:00 How can you classify the angle formed by the hands on the clock? Write an equation to represent: “three times a number is 15. Then solve for n. Ron drew an angle that is less than 45 degrees. Which of the following could NOT be its measure? a. 12 degrees b. 35 degrees c. 41 degrees d. 86 degrees A protractor is a tool that is used to measure and draw angles. Draw an angle with a measure of 360 degrees. Draw a ray and label the endpoint B and another point on the ray A. Place the protractor so the middle of the bottom edge is over the endpoint of the ray. Find the 0 mark on the protractor and place a point. Label it C. Draw ray BC. Draw an angle with a measure of 360 degrees. Draw a ray and label the endpoint B and another point on the ray A. Place the protractor so the middle of the bottom edge is over the endpoint of the ray. Find the 0 mark on the protractor and place a point. Label it C. Draw ray BC. Do the MATH 45 degrees 90 degrees 180 degrees 60 degrees 25 degrees 80 degrees 10 degrees 30 degrees 120 degrees 150 degrees 5 degrees 50 degrees 170 degrees 360 degrees Tina draws an angle that is a straight line. What is the measure of her angle? Draw it. Frederica made a 5 point star on her paper. Identify each angle she used. Brianna made 5 three-point shots in her first game and 3 three-point shots in her second game. She also made 4 two-point shots in each game and no one-point free throws in either game. How many total points did she score? Lottie is reading a book containing 3 chapters. The first chapter is 120 pages long. The second chapter is 136 pages long. There are 583 pages in the book. How many pages are in the third chapter? Look at the angles shown on the home plate used in baseball. Label each angle. The point where two streets cross each other forms four square corners. Draw a picture of the streets crossing each other and label each angle with the number of degrees. TRANSLATIONS What is one way to move a figure? A translation moves a figure up, down, left, or right. In this honeycomb, the hexagon is translated to the right. slide Which have been TRANSLATED? Which have translated? KITES kites sticks 1 2 2 4 3 6 How many sticks would you need to make 12 kites? If Alex made 2 kites and Kolby made 5 kites, how many sticks did they use in all? Which of the following best represents a translation? a. b. c. d. An ice cube melting A plant growing A windmill spinning A hockey puck sliding In this picture which shows a translation of the horse labeled X? V W Y X Z Translations are often called SLIDES…… Is this an example of a slide? REFLECTION What is another way to move a figure? A REFLECTION of a figure gives its mirror image. MIRROR IMAGE = REFLECTION Are these REFLECTIONS? When a figure is reflected, the size and shape of the figure DO NOT change! They are FLIPPED over. Which are examples of REFLECTIONS? Another name for a REFLECTION is a FLIP. Which are examples of Flips or Reflections? Flip - Flip - Flip Yes or No? Draw a REFLECTION. Draw a flip / reflection of each figure. G Z 3 6 P E 7 5 Q S 9 C J K 2 M B Y 4 L Sharon can run five miles in fifty minutes. If she keeps this pace, how many miles can she run in sixty minutes? The Hall of Mirrors in the Palace of Versailles in France is 73 meters long. A guide posted at one end of the room walks in a straight line to the mirror at the other end, and then back to his post. How far in all did he walk? SYMMETRY What is a line of symmetry? A figure is SYMMETRIC if it can be folded on a line to form two congruent halves that fit on top of each other. The fold line is called a LINE OF SYMMETRY. A figure can have many lines of symmetry. Which have lines of symmetry? How many lines of symmetry? How many lines of symmetry? Anya drew a figure and said that it had an infinite number of lines of symmetry. What figure did she draw? Florida’s Capitol in Tallahassee has one line of symmetry. Draw the line of symmetry. Draw the lines of symmetry for each isosceles triangle. Generalize to all isosceles triangles. Write capitol letters that have only 1 line of symmetry. Draw examples of quadrilaterals that do not have lines of symmetry. Generalize about lines of symmetry for scalene triangles. How many lines of symmetry does each have? ROTATIONS What is another way to move a figure? A rotation moves a figure around at a point. Rotations The figure does not change size or shape. 90 180 360 Miguel says that a 180 degree turn of any figure is the same as a reflection of a figure. Draw a picture to prove this it either true or false. What figure is formed when a triangle has rotated 90 degrees? ROTATIONAL SYMMETRY When a figure can rotate onto itself in less than 360 degrees, the figure has ROTATIONAL SYMMETRY. This figure has rotational symmetry because it can be rotated back to land on itself. Many figures rotational Which do rotational B M do not have symmetry. not have symmetry? ROTATIONAL SYMMETRY True or False - Explain Do they have Rotational Symmetry? Write YES or NO and give the least angle measure that will rotate the figure onto itself. L H X Y T N Ronnie has 16 yards of fencing material to build a fence around his garden. He wants to fence a rectangular area. List all possible ways he can fence his garden. SIDE A 1 YD 2 YD 3 YD 4 YD SIDE B AREA 7 SQ YD There are 48 boxes in a warehouse. If there are 24 packages of paper in each box, how many packages of paper are in the warehouse? Each pack holds 50 sheets. How many sheets of paper are in the warehouse? The Megaray Kite has an area of almost 1,500 square meters. Suppose the wind suddenly changed and the kite moved 25 meters east. Has the shape or size of the kite changed? What type of movement occurred? 25 Meters East TESSELLATIONS A tessellation is a repeating pattern of shapes without any gaps or overlays. How to make a Tessellation. Start with a square and an equilateral triangle. Use reflection to get adjacent figures. Rotate 180 degrees. Finally, use a translation to continue the pattern. v THINK Which of these shapes will TESSELLATE? Not all shapes can make a tessellation. Notice the gaps – there can be no gaps or overlays in a tessellation. 3-D 3 - Dimensional Shapes A solid figure has three dimensions: Length, width, and height. Solids can have curved surfaces. Some solids have all flat surfaces. They are named by referring to their faces. Vertex – point where 3 or more edges meet Face – flat surface of a solid Edge – line segment where 2 faces meet Identify faces, vertices, and edges of each. TRIANGULAR PRISM SQUARE Rectangular pyramid Flat surfaces of solids that have some curved surfaces are called bases. BASE BASE BASE Guess I have four triangular faces and one square face. What am I? I have six square faces. What am I? I have one rectangular face and four triangular faces. What am I? I have two triangular faces and three rectangular faces. What am I? Fill in the table. SOLID FACES EDGES RECTANGULAR PYRAMID SHAPES OF FACES 6 RECTANGULAR PRISM CUBE VERTICES RECTANGLES 6 8 Geometric Solids in the real world. Mitchell’s mom offered to drive members of the soccer team to their game. Her car can hold 4 players at a time. She drives 10 players from her home to the game. How many one-way trips must she make if she stays to watch the game? In one soccer season, the Cougars scored six times as many goals as Walter made all season. If Walter scored 12 goals, how many goals did the Cougars score throughout the season? NETS How can you use a two-dimensional shape to represent a three-dimensional solid? A NET is a pattern that can be used to make a solid. You can open up a threedimensional objects to show the net. If you peel the skin off of a can you have the NET or pattern to make the can. Name the solid that can be made from each NET. Name the solid that can be made from each NET. Name the solid that can be made from each NET. NETS A pattern that can be used to make a solid. Ralph made the net below by tracing around each face of a solid. What solid did he trace? Reggie traced the net below. What solid is he making? Seziel has baseball pennants hanging on all 4 walls of his bedroom. There are 9 pennants on each wall. How many pennants are there? Florida’s state insect is the zebra longwing butterfly. How many lines of symmetry does the butterfly have? Does it have rotational symmetry? ZEBRA LONGWING BUTTERFLY List possible ways to find the total area of this figure? Draw two different rectangles that have an area of 24 square units. What is the perimeter of each? Leslee says that the net for any prism will always include at least one rectangle. Is she correct? Explain why or why not. Think Instruments. I am a percussion instrument. I have a cylinder shape. What am I? I am a three sided figure named for my shape. You hit me with a metal wand. What am I? I am made of a long, narrow rectangular prism and a short cylinder. What am I? I am a long cylinder with holes in my side. What am I? Hope plays three instruments. The drum weighs 5 pounds more than the guitar. The trumpet weighs 5 pounds less that the guitar. The trumpet weighs 3 pounds. How many pounds does the drum weigh? PERSPECTIVES How can you get information about a solid from different perspectives? Think about the solid. What would the solid look like from the front? Side? Top? Front Right side Top view Draw all six views of this shape. Draw all six views. Draw all six views. Keith says that 1/2 is always the same amount as 2/4. Torrence says that 1/2 and 2/4 are equivalent fractions, but that they could be different amounts. Explain your thinking. Gwendolyn wants to cut a triangle into thirds. Her sister told her to cut it like this. What is your thinking? Karen and Arlene knit the same size scarves. Karen’s scarf is 3/5 yellow while Arlene’s scarf is 3/4 yellow. Draw a picture to show whose scarf has more yellow yarn. The school newspaper has a total of 18 articles and some ads. There are 6 more articles than ads. How many articles and ads are there? Kenneth gets $25 a week to buy lunch at school. He spends $3.50 each day and saves the rest. Write an expression that can be used to find how much money Kenneth will save at the end of 4 weeks. During recess, Kirstin played on the bars and slides. She spent 10 minutes on the bars and twice as long on the slides. Write an expression to find how much time she spent on the slides. Three streets intersect With one another. East Street runs horizontally, North street runs vertically, and Fourth Street runs diagonally and intersects both East and North Street. What geometric figure is formed by the intersection of these three streets? Look at the number sentences below. What numbers replace Explain your answer. + = 18 + = 20 + = 14 Look at the number sentences below. What numbers replace Explain your answer. + = 27 + = 23 + = 24 Look at the number sentences below. What numbers replace Explain your answer. + = 30 + = 22 + = 20 Look at the number sentences below. What numbers replace Explain your answer. + = 115 + = + = 200 95 Look at the number sentences below. What numbers replace Explain your answer. + = 4 + = 1 + = 5.5 Look at the number sentences below. What numbers replace Explain your answer. + = 1 + = + = 1 1/2 1/2 Turn Rotation Slide Translation size Flip Reflection