# Go to Grade 5 Everyday Mathematics Sample Lesson

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1 McGraw-Hill makes no representations or warranties as to the accuracy of any information contained in this McGraw-Hill Material, including any warranties of merchantability or fitness for a particular purpose. In no event shall McGraw-Hill have any liability to any party for special, incidental, tort, or consequential damages arising out of or in connection with the McGraw-Hill Material, even if McGraw-Hill has been advised of the possibility of such damages. Go to Grade 5 Everyday Mathematics Sample Lesson

2 Objective To explore the geometric properties of polygons. 1 Teaching the Lesson materials Key Activities Students sort geometric shapes into sets according to various rules. They identify geometric properties of polygons by playing Polygon Capture. Key Concepts and Skills Identify the types of angles formed by polygons. [Geometry Goal 1] Compare and classify polygons. [Geometry Goal 2] Use relationships and properties to sort polygons. [Geometry Goal 2] Math Journal 1, p. 80 Math Journals 1, Activity Sheets 3 and 4 Student Reference Book, pp. 142 and 328 Study Link 3 6 Game Masters (Math Masters, pp ) See Advance Preparation 2 Ongoing Assessment: Recognizing Student Achievement Use journal page 80. [Geometry Goal 2] Ongoing Assessment: Informing Instruction See page 191. Ongoing Learning & Practice materials Students practice and maintain skills through Math Boxes and Study Link activities. 3 Differentiation Options Math Journal 1, p. 81 Study Link Master (Math Masters, p. 87) materials READINESS Students sort attribute blocks by two properties at a time. ENRICHMENT Students describe the polygons that are formed when diagonals are drawn in polygonal regions. ELL SUPPORT Students sort shapes according to their attributes by playing What s My Attribute Rule? Game Masters (Math Masters, pp. 508 and 509) Teaching Master (Math Masters, p. 88) attribute blocks 1 six-sided die Additional Information Advance Preparation For Part 1, have students cut out the polygons and Property Cards from Activity Sheets 3 and 4 in the journal. Copy and cut apart the shapes on a transparency of Math Masters, page 494. These are the same shapes that are on Activity Sheet 3. Technology Assessment Management System Journal page 80 See the itlg. Grade 5 Everyday Mathematics Teacher's Lesson Guide 2007 Wright Group/McGraw-Hill Lesson

7 Date Time back to lesson LESSON 3 7 Completing Partial Drawings of Polygons Gina drew four shapes: equilateral triangle, square, rhombus, and hexagon. She covered up most of each figure, as shown below. Can you tell which figure is which? Write the name below each figure. Then try to draw the rest of the figure. Explain how you solved this problem. 80 Grade 5 Everyday Mathematics Student Math Journal 2007 Wright Group/McGraw-Hill

8 Date Time back to lesson LESSON 3 7 Math Boxes 1. Measure angle B to the nearest degree. 2. Key: 2 home runs Player Home runs Joe Yoshi B Gregg Maria The measure of angle B is about. a. Who had the most home runs? b. Who had four home runs? c. How many home runs did Maria have? d. Did any player have fewer than three home runs? Round to the nearest... tenth. whole number. hundredth. 4. Complete each pattern. 17,,, 62,, 92 39,,,, 75, 84 57,,, 33,, 17 15,,, 33,, List all the factors for Write the prime factorization for Grade 5 Everyday Mathematics Student Math Journal 2007 Wright Group/McGraw-Hill 81

9 Date Time back to SRB Polygon Capture Pieces H JO C B M N A I D K G L P F E Grade 5 Everyday Mathematics Student Math Journal 2007 Wright Group/McGraw-Hill Activity Sheet 3

10 Date Time back to SRB Polygon Capture Property Cards (Front) NOTE: The backs of the first two rows of cards are labeled "Angles." There is only one right angle. one or more right All angles are right no right There is at least one acute angle. At least one angle is more than 90. All angles are right no right sides are Only one pair of sides is no parallel sides. All sides are the same sides are Some sides have the same sides have the same Wild Card: Pick your own side property. NOTE: The backs of the las two rows of cards are labeled "Sides." Grade 5 Everyday Mathematics Student Math Journal 2007 Wright Group/McGraw-Hill Activity Sheet 4

11 Name Date Time back to lesson STUDY LINK 3 7 Odd Shape Out In each set of shapes, there is one shape that doesn t belong. Cross out that shape and tell why it doesn t belong. (There may be more than one possible reason. What s important is having a good reason for crossing out a shape.) Reason: 2. Reason: 3. Reason: 4. Copyright Wright Group/McGraw-Hill Reason: 5. Make up your own Odd Shape Out problem on the back of this page. Practice 6. 1,042 2,834 4, ,062 3, , Grade 5 Everyday Mathematics Math Masters 2007 Wright Group/McGraw-Hill 87

12 Name Date Time back to lesson LESSON 3 7 Vertex Connection If you draw a line segment from one vertex of a polygon to any other vertex that does not share a common side, new shapes will be formed inside the polygon. Connect pairs of vertices in these polygons. Name the new shapes as they are formed. Write the name of each new polygon and as many true statements as you can about the polygons. Be sure to use what you know about the definitions of angles and lines. pentagon hexagon kite kite New Polygon Properties pentagon New Polygon Properties New Polygon hexagon Properties Copyright Wright Group/McGraw-Hill 88 Grade 5 Everyday Mathematics Math Masters 2007 Wright Group/McGraw-Hill

13 Name Date Time back to lesson Polygon Capture Pieces H JO C B M N A I D K L P F G E Copyright Wright Group/McGraw-Hill 494 Grade 5 Everyday Mathematics Math Masters 2007 Wright Group/McGraw-Hill

14 Name Date Time back to lesson Polygon Capture Property Cards NOTE: The backs of the first two rows of cards are labeled "Angles." There is only one right angle. one or more right All angles are right no right There is at least one acute angle. At least one angle is more than 90. All angles are right no right sides are Only one pair of sides is no parallel sides. All sides are the same Copyright Wright Group/McGraw-Hill sides are Some sides have the same sides have the same Wild Card: Pick your own side property. NOTE: The backs of the last two rows of cards are labeled "Sides." Grade 5 Everyday Mathematics Math Masters 2007 Wright Group/McGraw-Hill 495

15 Name Date Time back to lesson What s My Attribute Rule? Directions Label one sheet of paper These fit the rule. 2. Label another sheet of paper These do NOT fit the rule. 3. Take turns. Roll the six-sided die once. The player with the lowest number is the first Rule Maker. 7. The Rule Maker chooses 3 or 4 blocks that do NOT fit the rule. The Rule Maker puts them on the sheet labeled These do NOT fit the rule. These do NOT fit the rule. 4. The Rule Maker shuffles and places the Attribute Rule Cards facedown. 5. The Rule Maker turns over the top Attribute Rule Card, but does not show it to the other players or tell them what the rule is. For example: large shapes, but not tri These do NOT fit the rule. 6. The Rule Maker chooses 3 or 4 attribute blocks that fit the rule on the card. The Rule Maker puts them on the sheet labeled These fit the rule. These fit the rule. These fit the rule. 8. The other players take turns choosing a block that they think might fit the rule and placing it on that sheet. 9. If the Rule Maker says No, the player puts the block on the correct sheet. If Yes, the player gets to suggest what the rule might be. The Rule Maker then tells the player whether his or her rule is correct. 10. The round continues until someone figures out the rule. That person becomes the Rule Maker for the next round. Copyright Wright Group/McGraw-Hill 508 Grade 5 Everyday Mathematics Math Masters 2007 Wright Group/McGraw-Hill

16 Name Date Time back to lesson What s My Attribute Rule? Cards small blue shapes large red shapes large shapes, but not triangles circles, but not red blue and yellow shapes, but not circles red and yellow small shapes not triangles or squares large triangles, but not yellow Copyright Wright Group/McGraw-Hill large circles, but not red large circles or squares Grade 5 Everyday Mathematics Math Masters 2007 Wright Group/McGraw-Hill 509

17 Geometry and Constructions back to lesson Polygons A polygon is a flat, 2-dimensional figure made up of line segments called sides. A polygon can have any number of sides, as long as it has at least three. The interior (inside) of a polygon is not part of the polygon. The sides of a polygon are connected end to end and make one closed path. D A vertex interior C B side The sides of a polygon do not cross. Each endpoint where two sides meet is called a vertex. The plural of vertex is vertices. Figures That Are Polygons 4 sides, 4 vertices 3 sides, 3 vertices 7 sides, 7 vertices Figures That Are NOT Polygons All sides of a polygon must be line segments. Curved lines are not line segments. The sides of a polygon must form a closed path. Prefixes A polygon must have at least 3 sides. The sides of a polygon must not cross. Polygons are named after the number of their sides. The prefix in a polygon s name tells the number of sides it has. tri- 3 quad- 4 penta- 5 hexa- 6 hepta- 7 octa- 8 nona- 9 deca- 10 dodeca one hundred forty-two Grade 5 Everyday Mathematics Student Reference Book 2007 Wright Group/McGraw-Hill

18 back to Study Link Geometry and Constructions Convex Polygons A convex polygon is a polygon in which all the sides are pushed outward. The polygons below are all convex. triangle quadrangle (or quadrilateral) pentagon hexagon heptagon octagon nonagon decagon Nonconvex (Concave) Polygons A nonconvex, or concave, polygon is a polygon in which at least two sides are pushed in. The polygons at the right are all nonconvex. Regular Polygons A polygon is a regular polygon if (1) the sides all have the same length; and (2) the angles inside the figure are all the same size. A regular polygon is always convex. The polygons below are all regular. quadrangle (or quadrilateral) pentagon hexagon equilateral triangle square regular pentagon octagon regular hexagon regular octagon regular nonagon 1. What is the name of a polygon that has a. 6 sides? b. 4 sides? c. 8 sides? 2. a. Draw a convex heptagon. b. Draw a concave decagon. 3. Explain why the cover of your journal is not a regular polygon. Check your answers on page 438. Grade 5 Everyday Mathematics Student Reference Book 2007 Wright Group/McGraw-Hill one hundred forty-three 143

20 180 0 back to student page Measurement Measuring an Angle with a Full-Circle Protractor Think of the angle as a rotation of the minute hand of a clock. One side of the angle represents the minute hand at the beginning of a time interval. The other side of the angle represents the minute hand some time later Example To measure angle ABC with a full-circle protractor: Step 1: Place the center of the protractor over the vertex of the angle, point B. Step 2: Line up the 0 mark on the protractor with BA. Step 3: Read the degree measure where BC crosses the edge of the protractor B The measure of angle ABC A C Example To measure reflex angle EFG: Step 1: Place the center of the protractor over point F E Step 2: Line up the 0 mark on the protractor with FG. Step 3: Read the degree measure where FE crosses the edge of the protractor F G The measure of angle EFG 330. Measuring an Angle with a Half-Circle Protractor Example To measure angle PQR with a half-circle protractor: Step 1: Lay the baseline of the protractor on QR. Step 2: Slide the protractor so that the center of the baseline is over the vertex of the angle, point Q. Step 3: Read the degree measure where QP crosses the edge of the protractor. two scales on the protractor. Use the scale that makes sense for the size of the angle that you are measuring Q The measure of angle PQR P R Grade 5 Everyday Mathematics Student Reference Book 2007 Wright Group/McGraw-Hill two hundred five 205

21 180 0 Measurement back to student page Drawing an Angle with a Half-Circle Protractor Example Draw a 40 angle. Step 1: Draw a ray from point A. Step 2: Lay the baseline of the protractor on the ray. Step 3: Slide the protractor so that the center of the baseline is over point A. mark Step 4: Make a mark at 40 near the protractor. two scales on the protractor. Use the scale that makes sense for the size of the angle that you are drawing Step 5: Draw a ray from point A through the mark A To draw a reflex angle using the half-circle protractor, subtract the measure of the reflex angle from 360. Use this as the measure of the smaller angle. Example Draw a 240 angle. Step 1: Subtract: Step 2: Draw a 120 angle. The larger angle is the reflex angle. It measures Check Your Understanding Measure each angle to the nearest degree Draw each angle angle angle angle Check your answers on page two hundred six Grade 5 Everyday Mathematics Student Reference Book 2007 Wright Group/McGraw-Hill

22 Games Polygon Capture Polygon Capture Pieces back to lesson Materials 1 set of Polygon Capture Pieces (Math Journal 1, Activity Sheet 3) 1 set of Polygon Capture Property Cards (Math Journal 2, Activity Sheet 4) Players 2, or two teams of 2 Skill Properties of polygons Object of the game To collect more polygons. Directions 1. Spread the polygons out on the table. Shuffle the Property Cards and sort them writing-side down into ANGLE-card and SIDE-card piles. (The cards are labeled on the back.) 2. Players take turns. When it is your turn: Draw the top card from each pile of Property Cards. Take all of the polygons that have both of the properties shown on the Property Cards in your hand. If there are no polygons with both properties, draw one additional Property Card either an ANGLEor a SIDE-card. Look for polygons that have this new property and one of the properties already drawn. Take these polygons. At the end of a turn, if you have not captured a polygon that you could have taken, the other player may name and capture it. 3. When all the Property Cards in either pile have been drawn, shuffle all of the Property Cards. Sort them writing-side down into ANGLE-card and SIDE-card piles. Continue play. 4. The game ends when there are fewer than 3 polygons left. 5. The winner is the player who has captured more polygons. N A K H L There is only one right angle. There is at least one acute angle. sides are sides are P JO I Polygon Capture Property Cards (writing-side up) one or more right At least one angle is more than 90. Only one pair of sides is Some sides have the same F C All angles are right All angles are right no parallel sides. sides have the same B E M D G no right no right All sides are the same Wild Card: Pick your own side property. Liz has these Property Cards: All angles are right angles, and All sides are the same She can take all the squares (polygons A and H). Liz has captured these polygons. 328 three hundred twenty-eight Grade 5 Everyday Mathematics Student Reference Book 2007 Wright Group/McGraw-Hill

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