Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations


 Edwina Brown
 4 years ago
 Views:
Transcription
1 Math Buddies Grade Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane figures resulting from geometric transformations such as translation (slide), reflection (flip) and rotation (turn). Identify figures that are symmetric and lines of symmetry Vocabulary: Congruent figures have the same size and shape. The angles and line segments that make up the plane figure are exactly the same size and shape. Two shapes or solids are congruent if they are identical in every way except for their position; one can be turned into the other by rotation, reflection or translation. A figure or shape is Symmetrical when onehalf of the figure is the mirror image of the other half A Line of Symmetry divides a symmetrical figure, object, or arrangement of objects into two parts that are congruent if one part is reflected (flipped) over the line of symmetry Transformation is an operation that creates an image from an original figure or preimage. Translations, Reflections and Rotations are some of the transformations on the plane. Although there is a change in position for the original figure, there is no change to the shape or size of the original figure. Translation (Slide) is a transformation of an object that means to move the object without rotating or reflecting it. Every translation has a given direction and a given distance. Reflection (Flip) is a transformation of an object that means to produce its mirror image of the object on the opposite side of a line. Every reflection has a mirror line or a line of reflection. A reflection of an "R" is a backwards "R" Rotation (Turn) is a transformation of an object that means to turn it around a given point, called the center. Every rotation has a center of rotation, an angle of rotation, and a direction (counterclockwise and clockwise). Tessellations are patterns of shapes that cover a plane without gaps (holes) or overlaps are called tessellations. Related SOL: 4.17 The student will b) identify congruent and noncongruent shapes; and c) investigate congruence of plane figures after geometric transformations such as reflection (flip), translation (slide) and rotation (turn), using mirrors, paper folding, and tracing.
2 Math Buddies Grade Materials: 2 Mira Sheets of Patty Paper 50 assorted Pattern Block Pieces 1 set of colored pencils 2 Sets of Tangrams (7 piece Chinese puzzle) Translation, Reflection and Rotation Concentration Cards (20) Goal 1: Recognize congruent and noncongruent plane figures Activity 1.1: WarmUp: Congruent Object Search 1. Say: Look around the room. Can anyone identify two objects or figures that appear to be exactly alike? (Answers will vary) 2. Say: Lets look at these two objects (or figures). How many sides do the objects have? How many angles do the objects have? Are the shapes the same size? Do they have the same shape? 3. Say: Congruent figures have the same size and shape. Would you say these two objects (or figures) are congruent? 4. Say: To further explain congruence, think about going to your favorite mall and looking at dozens of copies of your favorite CD on sale. All of the CDs are exactly the same size and shape. In fact, you can probably think of many objects that are massproduced to be exactly the same size and shape. Congruent objects are exactly the same they are duplicates of one another. In Mathematics, if two figures are congruent and you cut one figure out with a pair of scissors, it would fit perfectly on top of the other figure. So, if two quadrilaterals (4 sided) are the same size and shape, they are congruent. If two pentagons (5 sided) are the same size and shape, they are congruent. 5. Say: Now, let s hear from you. Would you please describe what a pair of congruent objects or figures have in common? Students might suggest that congruent figures have the same size and shape. The angles and line segments that make up the congruent figures are exactly the same size and shape. Say: Yes, congruent figures have the same size and shape. 6. Say: Look around the room and see if you can identify two other objects in the classroom that are congruent. What did you find? Wait for answers. After the math buddies have chosen two objects, say: Can you explain to us why the objects are congruent? 7. Ask the following leading questions to guide the students in a discussion as to why the congruent figures are congruent. Depending on the objects, ask: How many sides do the shapes have? How many angles do the shapes have? How can you tell that the shapes the same size?
3 Math Buddies Grade How do you know these are the same shapes? When we say two objects are congruent, does the color of the shape matter? (no) 8. Say: On paper, draw this symbol. Say: The mathematical symbol used to denote congruent is. The symbol is made up of two parts: ~ which means the same shape (similar) and = which means the same size (equal). Congruent Symbol Activity 1.2: Congruent or Not 1. Say: Open your book to Lesson #13: Student Activity Sheet #1:Congruent or Not. Look at the various shapes and determine whether they are congruent. Put a check under yes or no to indicate your answer. Then explain why they are or are not congruent. 2. Answers: 1. No, not the same size. 2. Yes, even though one is shaded. 3. No, different size and shaped triangles. 4. Yes, lines don t change the shape or size. 5. No, different size. 6. Yes, different position but the same shape and size. Activity 1.2: Tantalizing Triangles 1. Say: We can further refine our definition of congruent figure by saying that two shapes or solids are congruent if they are identical in every way except for their position; a figure can be moved by slides, flips or turns, and still be congruent. 2. Open the set of colored pencils for the Math Buddies to use and give each student one piece of patty paper to use as tracing paper. Say: Open your book to Lesson #13: Student Activity Sheet #2: Tantalizing Triangles. The objective of this activity is to find the tantalizing triangles that are congruent. To determine if they are congruent, carefully trace one of the triangles and then move the traced triangle around the page to find others that are congruent to it. Remember it does not matter what position the shape is in relative to another shape. Color any congruent triangles you find with the same color pencil. Then trace a second triangle and continue the same process. There are four different shaped triangles and all triangles should be colored. Good luck! Answers: Set #1: A, E, N, K are congruent Set #2: D, I, M, P are congruent Set #3: C, J, H, L are congruent Set #4: B, G, O, F are congruent Goal 2: Recognize the congruence of plane figures resulting from geometric transformations such as reflection (flip), translation (slide), and rotation (turn). Activity 2.1: WarmUp: Transformations with Tangrams 1. Describing figures and visualizing what they look like when they are transformed through translations (slides), reflections (flips), and rotations (turns), or when they are put together or
4 Math Buddies Grade taken apart in different ways are important aspects of the geometry program in elementary school. In this activity, students will use the seven tangram pieces to explore the transformation of shapes as they work to solve a few tangram puzzles. The potential for a highquality spatial visualization experiences provided this activity that involves the use of manipulatives should enhance student understanding of transformations. The manipulative to be used is Tangrams, which are an ancient Chinese moving piece puzzle, consisting of 7 geometric shapes. 2. Give each student a set of tangrams and say: This is a set of seven tangram pieces from the ancient Chinese puzzle. The Tangram shapes were used for recreational activity in China thousands of years ago. The word Tangram is derived from tan, meaning Chinese, and gram, meaning diagram or arrangement. Spread them out on the table and point to the pieces as I say them: the square, two small triangles, one medium triangle, two large triangles, and one parallelogram. 3. Say: Let s examine each of the five different Tangram pieces, and determine the area of each piece, assuming that the small triangle has an area of one unit. Answers Small Triangle 1 square unit Square 2 square units Parallelogram 2 square units Medium Triangle 2 square unit Large Triangle 4 square unit 4. Say: You can use all seven pieces to make a figure or your can use a given number to make a figure. We are going to make a square of different sizes using a defined number of pieces. Let s try these tasks together. Select one or more based upon time constraints. Possible solutions follow. Can you make a square using one piece? (use the square piece) Can you make a square using two pieces? (two small triangles or two large triangles) Can you make a square using three pieces? (two small triangles and one medium triangle) Can you make a square using four pieces? Can you make a square using five pieces? Note: Using six pieces can t be done Can you make a square using seven pieces? (see below)
5 Math Buddies Grade Say: Please use the seven tangram pieces to make one of the figures you select on Lesson#20: Student Activity Sheets #3A or #3B. You must use all seven pieces for each figure. I will check your answers once you inform me that you have completed a figure. 6. Answers: Activity 2.2: Transformations: Translations (Slides) 1. Say: You have been working with the Tangram pieces. While you worked to manipulate the shapes to create the different figures, often you were visualizing what they would look like once you had transformed them. You had a chance to move around the tangram pieces using a variety of transformations. 2. Say: Transformations is a word used to describe a category of movements that you can make with a shape. We will be studying three transformations: translations, rotations, and reflections. 3. Take out Lesson #13: Teacher Sheet #1. Refer to the top of the sheet as you describe translation transformations. Say: Translations are like slides, like sliding down a playground slide where you move from high to low but you are still sitting upright when you hit the bottom. A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction. [Note: The word "translate" in Latin means "carried across".] When you are sliding down a water slide, you are experiencing a translation. Your body is moving a given distance (the length of the slide) in a given direction. You do not change your size, shape or the direction in which you are facing. Translations can be seen in wallpaper designs, textile patterns, mosaics, and artwork. 4. Say: Open your student books to Lesson #13: Student Activity Sheet #4. Look at the pentagons (five sided figures) at the top left hand side of the page. In mathematics, the translation of an object is called its image. If the original object was labeled with letters, such as ABCDE, the image may be labeled with the same letters followed by a prime symbol (like an apostrophe), A'B'C'D'E'.
6 Math Buddies Grade Think of polygon ABCDE as sliding two inches to the right and one inch down. Its new position is labeled A'B'C'D'E'. 5. Say: A translation moves an object without changing its size or shape and without turning it or flipping it. Take out the Pattern Blocks and say: Here are some pattern blocks. Take out a blue parallelogram, a green triangle and a red trapezoid. On the pattern block grid paper, draw the translations of each shape by first placing it on the original figure and then sliding the pattern blocks the distance and the direction indicated by the arrow. To simplify this process we have only labeled one vertex of the shape with a letter. The image of the shape should have the same letter followed by the prime symbol in its new position as it had in it s original position. Check for accuracy of drawing. Ask: Did your shapes look different as a result of your translations? (no they do not change size or shape, just position) 6. Say: Now look at Part B on Activity Sheet #4. For each of the four problems, check yes or no to indicate whether one figure is the translation of the other. 7. Answers: 1. yes 2. no (change in size) 3. yes (doesn t need a slide line) 4. yes Activity 2.3: Transformations: Rotations (Turns) 1. Again take out Lesson #13: Teacher Sheet #1. Refer to the middle of the sheet as you describe the rotation transformation. Say: Rotations are turns, like when a basketball player pivots on one foot, or when a Ferris wheel turns around the center of the wheel. Look at this picture on the teacher page. To rotate a shape, you need to identify three things. First you must identify the point around which you are turning the shape, called the center of rotation. Second, you need to know the direction of the turn, clockwise or counterclockwise. Third, you need to know the angle, the number of degrees of the turn, or the fractional part of 1 whole turn (e.g. turn, or turn). Notice that the picture displays a clockwise rotation of the R around a center point, and where the angle of the turn is 90 degrees, or a onequarter turn. 2. Say: Open your student books to Lesson #13: Student Activity Sheet #5: Discover Rotation. Notice the letter B being rotated four times around the center of the two intersecting lines. What is the direction of the rotation, clockwise or counterclockwise? (clockwise) What is the angle of the rotation for each turn? (90 degrees, or a onequarter turn) You might think of a rotation like putting an object on a plate or a Lazy
7 Math Buddies Grade Susan, and then spinning the plate (or Lazy Susan ) around while the plate's center (or Lazy Susan s center) stays in one place. The center of the object doesn't have to be at the center of rotation (i.e. the center of your plate). Any point can be used to mark the center of rotation. 3. Say: Now look at the pattern block arrangement. Using the pattern blocks, make this same arrangement on the left side of a piece of paper. Wait until made Now, move this pattern block arrangement in a clockwise direction for an angle of 90 degrees or of a turn. Did it move off the paper? (yes) Did you arrangement stay the same distance from the center of rotation which is the bottom left hand corner of the paper as it was when you first made it? (yes) 4. Say: Now open your student books to Lesson #13: Student Activity Sheet #6: Rotation and Reflection With Pattern Blocks. In Part A, I would like Math Buddy A to make a pattern block figure on line A. Once the pattern is complete, I would like Math Buddy B to make this same pattern block figure on line B showing the pattern after a onequarter rotation in a clockwise direction. Wait until this is complete. Ask: Take a look at your work. Do you think it represents a clockwise rotation of 90 degrees and that the figures are an equal distance from the center of rotation? If not, what must be changed? If yes, you have demonstrated a rotation. 5. Say: In Summary, how can a rotation of an object be described? (There are three essential parts: 1)the object must move in a direction, clockwise or counterclockwise; 2) the object must move around a point called the center of rotation; and the object must turn some number of degrees or a fractional part of 1 whole turn.) 6. Say: Now, go back to the bottom of Student Activity Sheet #5. Decide which of the four problems represent rotations and which are not. Answers: 1. yes (1/4 turn clockwise) 2. yes (3/4 turn clockwise, or turn counterclockwise) 3. No, a translation 4. Yes (1/2 turn clockwise, or turn counterclockwise) Activity 2.4: Transformations: Reflections (Flips) 1. Take out Lesson #13: Teacher Sheet #1. Refer to the third transformation called reflection. Say: Reflection is the third transformation we will study. Reflections are like flips: like the picture of a gymnast doing a handstand. Look at the happy face and the R on this page. Each has been reflected across a line of reflection. 2. Say: In the real world, a reflection can be seen in water, in a mirror, in glass, or in a shiny surface. An object and its reflection have the same shape and size, but the figures face in opposite directions. 3. Say: When you look in the mirror what do you notice that is the same and is different about your face? (Discuss answers) In a mirror, right and left are switched. Under a reflection in a mirror, the figure does not change size. It is simply flipped over the line of reflection. In mathematics, the reflection of an object is called its image.
8 Math Buddies Grade Say: Now open your student books to Lesson #13: Student Activity Sheet #6: Rotation and Reflection With Pattern Blocks. At the bottom of the page in Part B, I would like Math Buddy A to place a red trapezoid on the left side of the line, touching the line. Once the trapezoid is placed, say: Now, I would like Math Buddy B to place a red trapezoid on the right side of the line to show a reflection of this pattern block. Does everyone agree that this is the reflection image of the pattern block on the left. If not, make the corrections. This is one example; other placements of the trapezoid lead to other arrangements. Line of Reflection Reflection Image of Reflection 5. Say: Now let s try a more challenging task. At the bottom of the page in Part B, I would like Math Buddy A to make a pattern block design on the left side of the line so that the design touches the line. Once the pattern design is complete, I would like Math Buddy B to make the reflection of this pattern block design on the right side of the line to show the designs reflection. Once complete, say: Does everyone agree that this is the reflection of the pattern block design across the line of reflection? Do we need to make any corrections? 6. Say: Now, switch rolls, and Math Buddy B will create the design on the right side, and Math Buddy A will create it s reflection on the left side. Once complete, say: Does everyone agree that this is the reflection of the pattern block design across the line of reflection? Do we need to make any corrections? Activity 2.5: Rotation or Reflection? 1. Say: Now open your student books to Lesson #13: Student Activity Sheet #7: Rotation or Reflection? Here is a table of figures. Use your knowledge to decide whether the second figure, the image, is a rotation or a reflection of the first. Once you decide, check under the column heading of this transformation. Some images may represent a rotation and a reflection, so check both. 2. Answers: 1. Rotation (1/4 turn) 2. Reflection (across a horizontal line) or Rotation (1/2 turn) 3. Reflection (across a vertical line) 4. Rotation (3/4 turn clockwise; or turn counterclockwise) 5. Rotation (1/4 turn clockwise) 6. Reflection (across a horizontal line) 7. Reflection (across a horizontal line) 8. Reflection (across a vertical line) 9. Reflection (across a vertical line) 10. Rotation (3/4 turn clockwise; or turn counterclockwise) Activity 2.6: Is the Shape ReflectionCongruent? 1. Give each student a georeflector and introduce the students to its parts. Place the georeflector in front of the student so that the beveled edge is down (touching the desk) and the beveled edge is facing the student.
9 Math Buddies Grade Point to the parts of the georeflector as you describe them to the students. Say: This is a georeflector. Feel the top edge of the georeflector. It has square corners for edges. Feel the Bottom edge of the georeflector. Is it the same as the top edge? (No) Notice that it is not as thick as any other edge on the georeflector. It has a beveled edge on the front face of the georeflector and a square corner edge on the back face of the georeflector. When you are working, always keep the beveled edge of the georeflector facing you so that you are looking into the front face of the georeflector. 3. Then review the parts of the georeflector by asking: a. How can you tell the top from the bottom? (The beveled edge is on the bottom.) b. How is the beveled edge different from all the other edges of the georeflector? (It is a different thickness.) c. How can you tell which face is the front? (By finding the beveled edge that is on the front face.) 4. Say: Now, go back to the bottom of Student Activity Sheet #6. Place the GeoReflector on the line of reflection and rotate your book around so that the GeoReflector is sitting horizontally, parallel to the table s edge. 5. Say: Now take out a yellow pattern block and place it anywhere between you and the GeoReflector. Using a pencil draw the perimeter of the yellow hexagon. Now, making sure the hexagon stays in this same spot, look through the GeoReflector and what do you see? (reflection of the hexagon) Yes, you see the reflection of the hexagon. Now I would like you to draw the perimeter of the reflection of the hexagon free hand. Once this is done, say: Remove the GeoReflector and pattern block leaving the drawing of the original figure, the line of reflection, and the drawing of the figure s reflection, called the image of reflection. 6. Say: Now take out a few pattern blocks and place them in front of the GeoReflector and look through the GeoReflector at their reflection. 7. Say: Now we are going to check to see whether two shapes are congruent as a result of a reflection. Take out Lesson #13: Student Activity Sheet #8: Is the Shape Reflective Congruent. Place the GeoReflector between the two figures and move it around so that when you look into the GeoReflector you can see whether the one figure fits on top of the other. The figure between you and the GeoReflector, or what is in front of the GeoReflector is called the object. Notice that the object is outlined in black. The figure behind the GeoReflector is the image. What color is the image? (It is outlined in the color of the GeoReflector as a result of looking through the colored plastic.) 8. If the object and the image are congruent (e.g. same size and same shape), the pair of shapes are reflectivecongruent. Use the GeoReflector to determine whether the other pairs of figures are reflectivecongruent. Check Yes if they are and No if they are not. If they are congruent as a result of the reflection, draw the line of reflection by placing your pencil on the beveled edge and drawing along that edge when the object reflects onto the image.
10 Math Buddies Grade Answers: A.) Yes B.) No C.) No D.) Yes E). No F.) Yes G.) No H.) Yes Goal 3: Identify and Draw Lines of Symmetry Activity 3.1: Lines of Symmetry 1. Ask students: What is a line of symmetry? (A line of symmetry divides a symmetrical figure, object, or arrangement of objects into two parts that are congruent if one part is reflected (flipped) over the line of symmetry.) Symmetry is everywhere in nature, art, music, mathematics, and beyond. Can you think of anything that is symmetrical? (Answers might include a butterfly, the letter H, a pair of pants, etc.) 2. In this activity, students will enhance their understanding of symmetry, particularly, reflectional symmetry, using the GeoReflector. Say: In our last activity, when shapes were congruent as a result of a reflection, we were able to draw a line of reflection. This line represented the line across which the objects were flipped. In this activity we will use the GeoReflector on individual shapes as a line of symmetry. The reflection will produce the other congruent half of the shape. Consequently, we will learn that a line of symmetry is a line that divides a figure in to congruent halves, each of which is the reflection image of the other. 3. Say: Take out Lesson #13: Student Activity Sheet #9: Line of Symmetry. The dotted line on each shape is the line of symmetry. Place your GeoReflector on the dotted line and draw the other side of the shape by tracing its reflection. 4. Answers: Line of Symmetry Activity 3.2: Polygons: How Many Lines of Symmetry? 1. Say: Take out Lesson #13: Student Activity #10: Polygons: How Many Lines of Symmetry? The polygons on this page are regular polygons. Regular polygons are polygons that have congruent sides and congruent angles; that is sides of the same lengths and angles of the same angle measure. 2. Say: You are going to determine how many lines of symmetry each of these polygons has using the GeoReflector. Move your GeoReflector around on the shape to find
11 Math Buddies Grade lines of symmetry. When you find a line of symmetry, where one side can be reflected on the other, draw that line of symmetry by placing your pencil on the recessed (beveled) edge of the GeoReflector and drawing that line. As you complete each polygon, report the number of lines of symmetry for the identified shape in the table below. Work on this activity now and then we will summarize your findings in the table once you have finished. Lines of Symmetry: Triangle: 3 Square: 4 Pentagon: 5 Hexagon: 6 3. Say: Now, let s review the data you have collected in the table. How many lines of symmetry did you find for the equilateral triangle? (3) As you look back at these lines, notice that each line went through one vertex and through the midpoint of the side opposite the vertex. Now look at the five sided pentagon. How many lines of symmetry did you find for the pentagon? (5) How are these lines of symmetry similar to the lines of symmetry in the triangle? (Each line of symmetry went through one vertex and through the midpoint of the side opposite the vertex.) 4. Say: How many lines of symmetry did you find for the square? (4) As you look back at these lines, notice that two line went from one vertex through to the other vertex, and two line went from one midpoint through to the other midpoint on the opposite side. Now look at the six sided hexagon. How many lines of symmetry did you find for the hexagon? (6) How are these lines of symmetry similar in the hexagon similar to the lines of symmetry in the square? (Each line of symmetry went from one vertex to the opposite vertex, or from one midpoint to the opposite the midpoint.) 5. Say: Now, let s look at the numbers. Is there any relationship between the number of sides in a regular polygon and the number of lines of symmetry? (Yes, when finding lines of symmetry in regular polygons, the number of lines of symmetry equals the number of sides in the polygon.) Lesson #13: Assessment of Student Learning 1. Have students complete the thirteen multiplechoice assessment items independently by circling the correct answer. 2. Once complete, discuss the items that the students answered incorrectly, asking them to explain their thinking and reasoning about how they chose each answer. Answer Key: 1. B 2. C 3. A 4. C 5. B 6. A 7. C 8. B 9. C 10. J 11. G 12. A 13. J
12 Math Buddies Grade Lesson #13: Student Activity Sheet #1 Congruent or Not? Look at these figures and see if you can pick congruent figures. Check yes if the figures are congruent and no if the figures are not congruent. Congruent or Not? Yes No Congruent or Not? Yes No
13 Math Buddies Grade Lesson #13: Student Activity Sheet #2 Tantalizing Triangles Find out if the tantalizing triangles are congruent using tracing paper. Color any congruent triangles you find the same color. Hint: There are four congruent shapes for each of four different shapes! A B C D E H F G L I J K P M N O Four Congruent Triangles are: Four Congruent Triangles are: Four Congruent Triangles are: Four Congruent Triangles are:
14 Math Buddies Grade Lesson #13: Student Activity Sheet #3A Tangram Puzzles
15 Math Buddies Grade Lesson #13: Student Activity Sheet #3B Tangram Puzzles
16 Math Buddies Grade Lesson #13: Student Activity Sheet #4 Translation With Pattern Blocks Translation "slides" an object a fixed distance in a given direction. The original object (A) and its translation (A ) have the same shape and size, and they face in the same direction. Part A: Translate the pattern blocks the distance and the direction indicated by the arrows and draw the image of the translation. Part B: Check yes or no to indicate whether one figure is a translation of the other. Translation or Not? Yes No Translation or Not? Yes No
17 Math Buddies Grade Lesson #13: Student Activity Sheet #5 Discover Rotation Rotation B Center Center of Rotation OneFourth Turn or Rotation of 90 o Check the yes or no box to indicate whether one figure is a rotation of another. Rotation or Not? Yes No Rotation or Not? Yes No
18 Math Buddies Grade Lesson #13: Student Activity Sheet #6 Rotation and Reflection With Pattern Blocks Part A: Math Buddy A makes a pattern block figure on line A. Math Buddy B makes the onequarter rotation of Math Buddy A s pattern block figures on line B. Line A Center of Rotation Line B Part B: Math Buddy A makes a pattern block figure on one side of the line. Math Buddy B makes its reflection on the other side of the line. Line of Reflection
19 Math Buddies Grade Lesson #13: Student Activity Sheet #7 Rotation or Reflection? Check The Correct Transformation(s): Rotation Reflection
20 Math Buddies Grade Lesson #13: Student Activity Sheet #8 Is the Shape ReflectiveCongruent? Use your GeoReflector to check if the shapes are congruent as a result of a reflection. Check Yes if they are and draw the line of reflection; otherwise check No. A. Yes No E. Yes No B. Yes No F. Yes No C. Yes No G. Yes No D. Yes No H. Yes No
21 Math Buddies Grade Lesson #13: Student Activity Sheet #9 Line Of Symmetry Using the GeoReflector
22 Math Buddies Grade Lesson #13: Student Activity Sheet #10 Polygons: How Many Lines of Symmetry? Use the GeoReflector to draw as many lines of symmetry as you can find for each regular polygon. Complete the chart identifying the number of lines of symmetry. Shape Name of Shape Number of Sides Triangle 3 (Equilateral Triangle) Number of Lines of Symmetry Square 4 Pentagon (Regular Pentagon) Hexagon (Regular Hexagon) 5 6
23 Math Buddies Grade Lesson #13: Student Assessments 1. The arrow below moved 90 degrees clockwise or turn. 4. The example below is a demonstration of what? This is an example of what? A. Translation B. Rotation C. Reflection A. Translation B. Rotation C. Reflection 2. The example below is a demonstration of a. 5. In the example below, the triangles going from left to right is an illustration of a. A. Translation B. Rotation C. Reflection A. Translation B. Rotation C. Reflection 3. The change in the position of the triangles in Set A to the position of the triangles in Set B is an illustration of a. Set A Set B 6. What is it called when the arrow in picture A is moved up to the position in picture B? Picture A Picture B A. Translation B. Rotation C. Reflection A. Translation B. Rotation C. Reflection
24 Math Buddies Grade The arrow below in picture B is a mirror image of the arrow in picture A. This transformation is called a. 10. Picture A Picture B A. Translation B. Rotation C. Reflection 8. The example below is a demonstration of a. A. Translation B. Rotation C. Reflection 9. In which figure below is the line NOT a line of symmetry? Figure A Figure B Figure C 11. Which pair of figures does NOT show a translation? A. Figure A B. Figure B C. Figure C
25 Math Buddies Grade
26 Math Buddies Grade Lesson #13: Teacher Sheet #1 Transformations: Translations, Rotations and Reflections Translation: To translate an object means to move it a given distance in a given direction without rotating or reflecting it. Rotation To rotate an object means to turn it around. Every rotation has a center of rotation and an angle of rotation. 90 o angle is of a turn. Reflection To reflect an object means to flip it to produce its mirror image. Every reflection has a line of reflection along which it is flipped. Translation Slides a given distance in a given direction Rotation Turns around a center point of rotation, for a given angle or identified turn (example of turn ) reflection Flips across a line of reflection
27 Math Buddies Grade
Line Segments, Rays, and Lines
HOME LINK Line Segments, Rays, and Lines Family Note Help your child match each name below with the correct drawing of a line, ray, or line segment. Then observe as your child uses a straightedge to draw
More informationObjective To guide exploration of the connection between reflections and line symmetry. Assessment Management
Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family
More informationGrade 3 Core Standard III Assessment
Grade 3 Core Standard III Assessment Geometry and Measurement Name: Date: 3.3.1 Identify right angles in twodimensional shapes and determine if angles are greater than or less than a right angle (obtuse
More informationGrade 7/8 Math Circles November 3/4, 2015. M.C. Escher and Tessellations
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Tiling the Plane Grade 7/8 Math Circles November 3/4, 2015 M.C. Escher and Tessellations Do the following
More informationGrade 8 Mathematics Geometry: Lesson 2
Grade 8 Mathematics Geometry: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
More information2. If C is the midpoint of AB and B is the midpoint of AE, can you say that the measure of AC is 1/4 the measure of AE?
MATH 206  Midterm Exam 2 Practice Exam Solutions 1. Show two rays in the same plane that intersect at more than one point. Rays AB and BA intersect at all points from A to B. 2. If C is the midpoint of
More informationDrawing Lines of Symmetry Grade Three
Ohio Standards Connection Geometry and Spatial Sense Benchmark H Identify and describe line and rotational symmetry in twodimensional shapes and designs. Indicator 4 Draw lines of symmetry to verify symmetrical
More informationGeometric Transformations Grade Four
Ohio Standards Connection Geometry and Spatial Sense Benchmark I Describe, identify and model reflections, rotations and translations, using physical materials. Indicator 7 Identify, describe and use reflections
More informationThird Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons
Third Grade Shapes Up! Grade Level: Third Grade Written by: Jill Pisman, St. Mary s School East Moline, Illinois Length of Unit: Eight Lessons I. ABSTRACT This unit contains lessons that focus on geometric
More informationTessellating with Regular Polygons
Tessellating with Regular Polygons You ve probably seen a floor tiled with square tiles. Squares make good tiles because they can cover a surface without any gaps or overlapping. This kind of tiling is
More informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationVolume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More information39 Symmetry of Plane Figures
39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that
More informationChapter 18 Symmetry. Symmetry of Shapes in a Plane 18.1. then unfold
Chapter 18 Symmetry Symmetry is of interest in many areas, for example, art, design in general, and even the study of molecules. This chapter begins with a look at two types of symmetry of twodimensional
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationExploring Tangrams. Goal. You will need scissors and a ruler. AtHome Help. 1. Trace and cut out the 7 tans.
HPTER 7 1 Exploring Tangrams Solve tangram puzzles. You will need scissors and a ruler. 1. Trace and cut out the 7 tans. thome Help tangram is an ancient hinese puzzle. It has the 7 shapes, or tans, shown
More informationElizabeth Evans Riverside Elementary 6 th Grade. Teaching Objectives To use tangrams to build figures that have symmetry. To identify line symmetry.
Elizabeth Evans Riverside Elementary 6 th Grade Teaching Objectives To use tangrams to build figures that have symmetry. To identify line symmetry. Instructional Activities (designed for groups of 4) 1.
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationE XPLORING QUADRILATERALS
E XPLORING QUADRILATERALS E 1 Geometry State Goal 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space. Statement of Purpose: The activities in this
More informationMaking tessellations combines the creativity of an art project with the challenge of solving a puzzle.
Activities Grades 6 8 www.exploratorium.edu/geometryplayground/activities EXPLORING TESSELLATIONS Background: What is a tessellation? A tessellation is any pattern made of repeating shapes that covers
More informationG333 Building Pyramids
G333 Building Pyramids Goal: Students will build skeletons of pyramids and describe properties of pyramids. Prior Knowledge Required: Polygons: triangles, quadrilaterals, pentagons, hexagons Vocabulary:
More informationAngle  a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees
Angle  a figure formed by two rays or two line segments with a common endpoint called the vertex of the angle; angles are measured in degrees Apex in a pyramid or cone, the vertex opposite the base; in
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationProblem of the Month: Cutting a Cube
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationGrade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge:
Grade 1 Geometric Shapes Conceptual Lessons Unit Outline Type of Knowledge & SBAC Claim Prerequisite Knowledge: Standards: Lesson Title and Objective/Description Shape names: square, rectangle, triangle,
More informationMathematics Materials for Tomorrow s Teachers
M2T2 E 1 Geometry Mathematics Materials for Tomorrow s Teachers STATE GOAL 9: Use geometric methods to analyze, categorize, and draw conclusions about points, lines, planes, and space. Statement of Purpose:
More informationTeaching Guidelines. Knowledge and Skills: Can specify defining characteristics of common polygons
CIRCLE FOLDING Teaching Guidelines Subject: Mathematics Topics: Geometry (Circles, Polygons) Grades: 46 Concepts: Property Diameter Radius Chord Perimeter Area Knowledge and Skills: Can specify defining
More informationDiscovering Math: Exploring Geometry Teacher s Guide
Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional
More informationWhich two rectangles fit together, without overlapping, to make a square?
SHAPE level 4 questions 1. Here are six rectangles on a grid. A B C D E F Which two rectangles fit together, without overlapping, to make a square?... and... International School of Madrid 1 2. Emily has
More information1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?
Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.
More informationShapes & Designs Notes
Problem 1.1 Definitions: regular polygons  polygons in which all the side lengths and angles have the same measure edge  also referred to as the side of a figure tiling  covering a flat surface with
More informationKristen Kachurek. Circumference, Perimeter, and Area Grades 710 5 Day lesson plan. Technology and Manipulatives used:
Kristen Kachurek Circumference, Perimeter, and Area Grades 710 5 Day lesson plan Technology and Manipulatives used: TI83 Plus calculator Area Form application (for TI83 Plus calculator) Login application
More informationUnit 8 Angles, 2D and 3D shapes, perimeter and area
Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest
More informationMD526 Stacking Blocks Pages 115 116
MD526 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.
More informationGrade 3 Geometry and Spatial Sense. Name:
Grade 3 Geometry and Spatial Sense Name: Ontario Mathematics Curriculum Grades 1 to 8, 1997 Strand: Geometry and Spatial Sense Grade: 3 All rights reserved Developed by T. Tasker May be photocopied for
More informationGrade 3 FCAT 2.0 Mathematics Sample Answers
Grade FCAT 2.0 Mathematics Sample Answers This booklet contains the answers to the FCAT 2.0 Mathematics sample questions, as well as explanations for the answers. It also gives the Next Generation Sunshine
More informationangle attribute Figure 1 4 right angles opposite sides parallel Lesson 14 5 Lesson 14 4 Vocab
Vocab angle attribute 006_055_G4_VisV_101741.indd Page F46 2/13/10 11:27:36 PM us014 /Volumes/114/GO00403/GO00403_Natl_Visual_Voca_Cards_G4%0 Figure 1 4 right angles opposite sides parallel endpoint hexagon
More informationGeometry Progress Ladder
Geometry Progress Ladder Maths Makes Sense Foundation Endofyear objectives page 2 Maths Makes Sense 1 2 Endofblock objectives page 3 Maths Makes Sense 3 4 Endofblock objectives page 4 Maths Makes
More informationLevel 1  Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3
Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels
More informationThreeDimensional Figures or Space Figures. Rectangular Prism Cylinder Cone Sphere. TwoDimensional Figures or Plane Figures
SHAPE NAMES ThreeDimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere TwoDimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. [triangle] [cone]
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationInvestigating Quadrilaterals Grade Four
Ohio Standards Connection Geometry and Spatial Sense Benchmark A Provide rationale for groupings and comparisons of twodimensional figures and threedimensional objects. Indicator 3 Identify similarities
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More information121 Representations of ThreeDimensional Figures
Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 121 Representations of ThreeDimensional Figures Use isometric dot paper to sketch each prism. 1. triangular
More informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More informationActivities Grades K 2 EXPLORING TESSELLATIONS. Background: What is a tessellation? Part One: Tessellating with One Shape
Activities Grades K 2 www.exploratorium.edu/geometryplayground/activities EXPLORING TESSELLATIONS Background: What is a tessellation? A tessellation is any pattern made of repeating shapes that covers
More informationDuplicating Segments and Angles
CONDENSED LESSON 3.1 Duplicating Segments and ngles In this lesson, you Learn what it means to create a geometric construction Duplicate a segment by using a straightedge and a compass and by using patty
More informationGeometry of Minerals
Geometry of Minerals Objectives Students will connect geometry and science Students will study 2 and 3 dimensional shapes Students will recognize numerical relationships and write algebraic expressions
More informationNumeracy Targets. I can count at least 20 objects
Targets 1c I can read numbers up to 10 I can count up to 10 objects I can say the number names in order up to 20 I can write at least 4 numbers up to 10. When someone gives me a small number of objects
More informationEVERY DAY COUNTS CALENDAR MATH 2005 correlated to
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 35 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:
More informationSGS4.3 Stage 4 Space & Geometry Part A Activity 24
SGS4.3 Stage 4 Space & Geometry Part A Activity 24 Exploring triangles Resources required: Each pair students will need: 1 container (eg. a rectangular plastic takeaway container) 5 long pipe cleaners
More informationBuilding a Bridge to Academic Vocabulary in Mathematics
Building a Bridge to Academic Vocabulary in Mathematics AISD Elementary Mathematics Department How Students Develop a Repertoire of Academic English in Mathematics Developed and researched by the AISD
More informationMATH STUDENT BOOK. 8th Grade Unit 6
MATH STUDENT BOOK 8th Grade Unit 6 Unit 6 Measurement Math 806 Measurement Introduction 3 1. Angle Measures and Circles 5 Classify and Measure Angles 5 Perpendicular and Parallel Lines, Part 1 12 Perpendicular
More informationGeometry of 2D Shapes
Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles
More information37 Basic Geometric Shapes and Figures
37 Basic Geometric Shapes and Figures In this section we discuss basic geometric shapes and figures such as points, lines, line segments, planes, angles, triangles, and quadrilaterals. The three pillars
More informationActivities Grades K 2 THE FOURSQUARE QUILT. Put triangles together to make patterns.
Activities Grades K 2 www.exploratorium.edu/geometryplayground/activities THE FOURSQUARE QUILT Put triangles together to make patterns. [45 minutes] Materials: FourSquare Quilt Template (attached) Triangle
More informationDear Grade 4 Families,
Dear Grade 4 Families, During the next few weeks, our class will be exploring geometry. Through daily activities, we will explore the relationship between flat, twodimensional figures and solid, threedimensional
More informationMaking tessellations combines the creativity of an art project with the challenge of solving a puzzle.
Activities Grades 3 5 www.exploratorium.edu/geometryplayground/activities EXPLORING TESSELLATIONS Background: What is a tessellation? A tessellation is any pattern made of repeating shapes that covers
More informationTessellations. Practice 1 Identifying Tessellations. In each tessellation, color the repeated shape. Example
Name: Chapter Date: Practice 1 Identifying In each tessellation, color the repeated shape. Example 1. 2. 3. Lesson 14.1 Identifying 133 Is each pattern a tessellation of a single repeated shape? Write
More informationLesson Plans. Isaiah A.J. Walters Designer Educator
Lesson Plans Isaiah A.J. Walters Designer Educator Symmetry Activity Centre #1 Complete the Photograph Materials: Magazine Picture Glue Stick Pencils and Pencil Crayons Scissors Blank Paper Instructions:
More informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
More informationSession 5 Dissections and Proof
Key Terms for This Session Session 5 Dissections and Proof Previously Introduced midline parallelogram quadrilateral rectangle sideangleside (SAS) congruence square trapezoid vertex New in This Session
More informationTransformations Worksheet. How many units and in which direction were the xcoordinates of parallelogram ABCD moved? C. D.
Name: ate: 1. Parallelogram ABC was translated to parallelogram A B C. 2. A shape is shown below. Which shows this shape transformed by a flip? A. B. How many units and in which direction were the xcoordinates
More informationFractions In Action! Dawn Jesse
Fractions In Action! Dawn Jesse Fractions In Action Dawn Jesse Fractions In Action is an interactive activity that consists of direct instruction, cooperative learning and is inquire based. As the students
More informationWarning! Construction Zone: Building Solids from Nets
Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have
More informationMATHEMATICS Y6 Geometry 6750 Use coordinates and extend to 4 quadrants Equipment MathSphere www.mathsphere.co.uk
MATHEMATICS Y6 Geometry 675 Use coordinates and etend to quadrants Paper, pencil, ruler Equipment MathSphere 675 Use coordinates and etend to quadrants. Page Concepts Children should be familiar with
More informationCBA Fractions Student Sheet 1
Student Sheet 1 1. If 3 people share 12 cookies equally, how many cookies does each person get? 2. Four people want to share 5 cakes equally. Show how much each person gets. Student Sheet 2 1. The candy
More informationGeometry Enduring Understandings Students will understand 1. that all circles are similar.
High School  Circles Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps,
More informationGeometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
More informationMinnesota Academic Standards
A Correlation of to the Minnesota Academic Standards Grades K6 G/M204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley
More informationClassifying Lesson 1 Triangles
Classifying Lesson 1 acute angle congruent scalene Classifying VOCABULARY right angle isosceles Venn diagram obtuse angle equilateral You classify many things around you. For example, you might choose
More informationGAP CLOSING. 2D Measurement GAP CLOSING. Intermeditate / Senior Facilitator s Guide. 2D Measurement
GAP CLOSING 2D Measurement GAP CLOSING 2D Measurement Intermeditate / Senior Facilitator s Guide 2D Measurement Diagnostic...4 Administer the diagnostic...4 Using diagnostic results to personalize interventions...4
More informationISAT Mathematics Performance Definitions Grade 4
ISAT Mathematics Performance Definitions Grade 4 EXCEEDS STANDARDS Fourthgrade students whose measured performance exceeds standards are able to identify, read, write, represent, and model whole numbers
More informationFRACTIONS TANGRAMS WITH. Larry Ecklund
FRACTIONS WITH TANGRAMS Larry Ecklund Table Contents Getting Started 5 Tangram Pieces 9 Tangram Puzzles 10 Geometric Tangram Puzzles 17 Tangram Investigations 23 Parts One 29 More Investigations 37 Problem
More informationInvestigating Relationships of Area and Perimeter in Similar Polygons
Investigating Relationships of Area and Perimeter in Similar Polygons Lesson Summary: This lesson investigates the relationships between the area and perimeter of similar polygons using geometry software.
More information11.3 Curves, Polygons and Symmetry
11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon
More informationPerformance Assessment Task Which Shape? Grade 3. Common Core State Standards Math  Content Standards
Performance Assessment Task Which Shape? Grade 3 This task challenges a student to use knowledge of geometrical attributes (such as angle size, number of angles, number of sides, and parallel sides) to
More informationGeometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
More informationBasic Understandings
Activity: TEKS: Exploring Transformations Basic understandings. (5) Tools for geometric thinking. Techniques for working with spatial figures and their properties are essential to understanding underlying
More informationProblem of the Month: William s Polygons
Problem of the Month: William s Polygons The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common
More information1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
NCTM STANDARD 1: Numbers and Operations Kindergarten Grade 2 1A: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Kindergarten Grade One Grade Two 1. Count
More informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
More informationSolving the Rubik's Revenge (4x4x4) Home PreSolution Stuff Step 1 Step 2 Step 3 Solution Moves Lists
Solving your Rubik's Revenge (4x4x4) 07/16/2007 12:59 AM Solving the Rubik's Revenge (4x4x4) Home PreSolution Stuff Step 1 Step 2 Step 3 Solution Moves Lists Turn this... Into THIS! To solve the Rubik's
More informationGeoGebra. 10 lessons. Gerrit Stols
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
More informationActivity Set 4. Trainer Guide
Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGrawHill Companies McGrawHill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES
More informationGeometry. Higher Mathematics Courses 69. Geometry
The fundamental purpose of the course is to formalize and extend students geometric experiences from the middle grades. This course includes standards from the conceptual categories of and Statistics and
More informationOneInch Graph Paper
OneInch Graph Paper Classroom Strategies Blackline Master II  1 49 HalfInch Graph Paper 50 Classroom Strategies Blackline Master II  2 TwoCentimeter Graph Paper Classroom Strategies Blackline Master
More informationPerformance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will
Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will discover and prove the relationship between the triangles
More informationGrade 4 Unit 3: Multiplication and Division; Number Sentences and Algebra
Grade 4 Unit 3: Multiplication and Division; Number Sentences and Algebra Activity Lesson 31 What s My Rule? page 159) Everyday Mathematics Goal for Mathematical Practice GMP 2.2 Explain the meanings
More informationWhat You ll Learn. Why It s Important
These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why
More informationGEOMETRY. Constructions OBJECTIVE #: G.CO.12
GEOMETRY Constructions OBJECTIVE #: G.CO.12 OBJECTIVE Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic
More informationSTRAND: Number and Operations Algebra Geometry Measurement Data Analysis and Probability STANDARD:
how August/September Demonstrate an understanding of the placevalue structure of the baseten number system by; (a) counting with understanding and recognizing how many in sets of objects up to 50, (b)
More informationLesson 1.1 Building Blocks of Geometry
Lesson 1.1 Building Blocks of Geometry For Exercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q 2. NQ. 3. nother name for NS is. 4. S is the of SQ. 5. is the midpoint of. 6. NS.
More informationStar and convex regular polyhedra by Origami.
Star and convex regular polyhedra by Origami. Build polyhedra by Origami.] Marcel Morales Alice Morales 2009 E D I T I O N M O R A L E S Polyhedron by Origami I) Table of convex regular Polyhedra... 4
More informationCommutative Property Grade One
Ohio Standards Connection Patterns, Functions and Algebra Benchmark E Solve open sentences and explain strategies. Indicator 4 Solve open sentences by representing an expression in more than one way using
More informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More informationAlgebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More informationNew York State Student Learning Objective: Regents Geometry
New York State Student Learning Objective: Regents Geometry All SLOs MUST include the following basic components: Population These are the students assigned to the course section(s) in this SLO all students
More information