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1 Lafayette Parish School System Curriculum Map Mathematics: Grade 5 Unit 4: Properties in Geometry (LCC Unit 5) Time frame: 16 Instructional Days Assess2know Testing Date: March 23, 2012 Refer to Blackboard for Activities and/or Resources This unit focuses on geometric concepts involving plane figures, and includes the concepts of transformations, rotational symmetry, angle measurement, and coordinate graphing. Guiding Questions 1. Can students use mathematical terms to classify and describe the properties of 1- and 2-dimensional shapes? (GLE 24) 2. Can students describe the properties of a circle and identify its parts? (GLE 24) 3. Can students classify angles? (GLE 15, 21) 4. Can students identify and use a protractor as a tool to measure angles? (GLE 20) 5. Can students recognize motions in a plane (reflections, rotations, translations) and use the appropriate terminology to describe the motion(s)? (GLE 25) 6. Can students identify the degree of rotation? ( = 90⁰; = 180⁰; = 270⁰) (GLE 25) 7. Can students identify figures that have line and rotational symmetry? (GLE 26) 8. Can students identify and plot points on a coordinate grid using appropriate terminology (x, y axis) in the first quadrant? (GLE 27) Vocabulary List The set of words at the end of each unit are for vocabulary development throughout the year, not for isolated memorization or testing. ONE-DIMENSIONAL point, line, ray, line segment, plane, angle, vertex, parallel lines, intersecting lines, perpendicular lines, degrees, protractor, acute angle, obtuse angle, right angle, straight angle TWO-DIMENSIONAL polygon, regular polygon, quadrilateral, parallelogram, square, rectangle, rhombus, trapezoid, triangle, isosceles triangle, scalene triangle, equilateral triangle, acute triangle, obtuse triangle, right triangle, pentagon, hexagon, octagon, circle, radius, diameter, chord, circumference, congruent, similar, line symmetry, rotational symmetry TRANSFORMATIONS translation, reflection, rotation COORDINATE GRID origin, ordered pair, axis Critical Skill Builders: Continue using the Review Sheets to revisit the GLEs associated with fractions and decimals. During Unit 4 it is strongly recommended that one day a week you present data that requires students to review the meaning of mode, range, and median. LPCC Comprehensive Curriculum

2 Lafayette Parish School System Curriculum Map Mathematics: Grade 5 Unit 4: Properties in Geometry (LCC Unit 5) Time frame: 16 Instructional Days assess2know Testing Date: March 23, 2012 Grade Level Expectations TLW be able to: Instructional Notes/Strategies Resources Focus 4-1: One- and Two-Dimensional Geometry (9 instructional days suggested) 15. Model, measure, and use the One-Dimensional (E) names of all common units in the US and metric systems (M-1) 20. Identify appropriate tools and (I) units with which to measure time, mass, weight, temperature, and length (M-3) 21. Measure angles to the nearest (I) degree (M-3) 24. Use mathematical terms to (E) classify and describe the properties of 2-dimensional shapes, including circles, triangles, and polygons (G-2) 26. Identify shapes that have (I) rotational symmetry (G-3) Identify one-dimensional figures (point, line, line segment, and ray) in pictures and real-world objects. Draw and label one-dimensional figures. Compare and contrast parallel and perpendicular lines. Identify, draw, and classify angles as acute, obtuse, right, and straight. Measure angles to the nearest degree. Identify the protractor as the tool used to measure angles. Two-Dimensional Describe the properties of a triangle, quadrilateral, pentagon, hexagon, octagon, decagon (number of sides, number of angles) Classify a quadrilateral as a parallelogram, rectangle, rhombus, square, and/or trapezoid. The students should be using the protractor that will be used for ileap testing. **Prior to measuring the angle, the students should classify the angle as acute or obtuse. This will determine the reasonableness of their measure. Students can be 2 degrees off from the actual measure. als-interactive.html Parallelogram a four-sided figure with two pairs of parallel sides. Rectangle a four-sided figure with 4 right angles. Students want to describe a rectangle as having two long sides and two short sides. Emphasize with the students that any foursided figure with 4 right angles is a rectangle; it has nothing to do with the length of the sides. Rhombus a four-sided figure with 4 equal sides Refer to Blackboard for additional Activities and/or Resources Harcourt GLEs 15, 20, pp (angles & polygons) 20.2 pp (measure and draw angles) GLE pp (lines/angles) 20.4 pp (circles) 20.5 pp (congruent & similar) p. 436 (#18 - #21) p. 458 (322 - #25) 21.1 pp (triangles) 21.2 pp (quadrilaterals) GLE pp (symmetry) Constructed Response H34 PA55 (Task A-p.516) PA64 (Task B-p.608) Picture inaccurate Project Lift #17, #23, and #33 Linking Math GLE 21: A34 GLE 24: A35 Triangles missing angle measure 38

3 Lafayette Parish School System Curriculum Map Mathematics: Grade 5 Unit 4: Properties in Geometry (LCC Unit 5) Time frame: 16 Instructional Days assess2know Testing Date: March 23, 2012 Grade Level Expectations TLW be able to: Instructional Notes/Strategies Resources Explain why a square is a rectangle but a rectangle is not necessarily a square and why a square is a rhombus and a parallelogram. Identify and classify triangles by the length of the sides and the measure of the angles. Draw, identify, and measure the parts of a circle. (radius, diameter, chord) Explain why a circle is not a polygon. Associate perimeter with the distance around a polygon and circumference with the distance around a circle. Apply the concept of congruence, similarity, and symmetry. Identify line and rotational symmetry. Trapezoid a four-sided figure with only one pair of parallel sides. Square a four-sided figure with 4 right angles (rectangle), four congruent sides (rhombus), and two pairs of parallel sides (parallelogram). A square should be taught as a special rectangle and a special rhombus. Just like a pet is both a dog and a mammal, a shape can be both a square and a rectangle. One is specific and one is general. Literature Connection: The Greedy Triangle by Marilyn Burns Shapes by Henry Pluckrose Grandfather Tang s Story by Ann Tompert A Cloak for the Dreamer by Aileen Friedman Sam Johnson and the Blue Ribbon Quilt by Lisa Campbell Ernest Sir Cumference and The First Round Table by Cindy Neuschwander Some students may have difficulty recognizing rotational symmetry. Have them trace a figure onto tracing paper. Then have them place the traced figure on top of the original and rotate it to match the original. It must match before returning to its starting point to have rotational symmetry. Students have to visualize that the figure is rotated around a center point. LCC Activities See the Activity Alignment Document for ideas 1 Technology Connection /maths/shape_space/angles/play.shtml es/flash.php?&file=angle g_shapes.html Game.html 1 These activities are listed for your consideration. All activities, chosen from the LCC or elsewhere, must be chosen to achieve the GLEs embedded in each unit. 39

4 Lafayette Parish School System Curriculum Map Mathematics: Grade 5 Unit 4: Properties in Geometry (LCC Unit 5) Time frame: 16 Instructional Days assess2know Testing Date: March 23, 2012 Grade Level Expectations TLW be able to: Instructional Notes/Strategies Resources Focus 4-2: Transformation (5 instructional days suggested) 25. Identify and use appropriate (I) terminology for transformations (e.g., translation as slide, reflection as flip, and rotation as turn) (G-3) Transformations Transform a figure or identify type of transformation. Distinguish between a clockwise and counter-clockwise turn. Identify rotations as a quarter (¼) or 90º turn, a ⅓ or 120º turn, a half (½) or 180º turn, a ¾ or 270º turn or a complete or 360º turn. Relate the degree of turn to the correspondent fraction. Transform a figure in the first quadrant of a coordinate plane. Predict the results of a transformation. Students can associate the sl in translation with a slide and the fl in reflection with a flip. Given a paper circle, the students will fold the circle in half vertically and then horizontally. When students open the folded circle, they should recognize four equal parts. Each part is a right angle. Knowing the measure of a right angle is 90, students will be able to conclude that a complete turn around the center of the circle is 360. Students can then conclude that a half-turn or two right angles is 180. Then 1/4 of a turn or a quarter turn is 90, therefore, ¾ of a turn is 270. Refer to Blackboard for additional Activities and/or Resources Harcourt 21.3 pp (transformations) p. 512 (tessellations puzzle) Project Lift #31 Linking Math B14 LCC Activities See the Activity Alignment Document for ideas 1 Technology Connection ur/gamesroom/transform/golftrans.html 1 These activities are listed for your consideration. All activities, chosen from the LCC or elsewhere, must be chosen to achieve the GLEs embedded in each unit. 40

5 Lafayette Parish School System Curriculum Map Mathematics: Grade 5 Unit 4: Properties in Geometry (LCC Unit 5) Time frame: 16 Instructional Days assess2know Testing Date: March 23, 2012 Grade Level Expectations TLW be able to: Instructional Notes/Strategies Resources Focus 4-3: Coordinate Grid (2 instructional days suggested) 27. Identify and plot points on a (I) coordinate grid in the first quadrant (G-6) Grid Identify the point of origin as (0, 0). Graph and label ordered pairs in the first quadrant. Name the ordered pair that is described. Relate the x/y axis to the ordered pair. Identify the ordered pair for points given. Emphasize with students that they start at the point of origin. The first number in the ordered pair tells them how many units to the right and then the second number refers to the number of units up. The students are only working with ordered pairs in the first quadrant. For example: Start at the origin. Move two units to the right and three units up. Name the ordered pair. Literature Connection: The Fly on the Ceiling by Dr. Julie Glass Harcourt 6.2 pp (graph ordered pairs) Constructed Response PA55 (Task B-p.516) Project Lift #18 Linking Math None LCC Activities See the Activity Alignment Document for ideas 1 Technology Connection mathfest/dinosaur.html 1 These activities are listed for your consideration. All activities, chosen from the LCC or elsewhere, must be chosen to achieve the GLEs embedded in each unit. 41

6 Refer to Blackboard for Additional Activities Activity 1: Geometry Vocabulary (GLE: 21, 24, 25) *From Unit 5 Materials List: index cards, pencils Have students work in groups to think of geometry vocabulary words. They should write each word in large print on an index card. Have each group write at least 20 words. The words could be ones such as square, pyramid, intersecting, symmetry, flip, angle, congruent. After writing their 20 words, have the groups sort them into categories that make sense to them. The categories could be ones such as types of lines, 2-dimensional shapes, or 4-sided shapes. To demonstrate that students have learned the content, use the professor-know-it-all (view literacy strategy descriptions) strategy. Tell students that one group will be called on randomly to come to the front of the class to be a team of professor-know-it-alls. Select one group to come up and place their index cards on the floor, or tape them to the wall. The team should be able to explain their categories and answer questions about their sorting choices. Other students should listen for accuracy and logic in the professors answers to their questions. After about 5 minutes or so, ask a new group to take its place in front of the class. The new group should add their words to these categories or make new categories. Sometimes a word will be placed into more than one category, such as radius could be placed with circles or with line segments. Discussion is critical in this activity. This is a way to informally see what the students know about geometry and provides a chance to review terms from 4 th grade. Do not worry if the students do not think of all of the vocabulary words. This is just an introduction. Activity 2: More Geometry Vocabulary (GLE: 21, 24, 25) *From Unit 5 Materials List: index cards, pencils To develop students knowledge of key vocabulary, have them create vocabulary cards (view literacy strategy descriptions) for terms related to geometry. Distribute 3 x 5 or 5 x 7 inch index cards to each student, and ask them to follow directions in creating the sample card. On the board, place a targeted word in the middle of the card, as in the example. Ask the students to provide a definition. It is best if a word can be defined in students own words. Write the definition in the appropriate space. Next, have students list the characteristics or a description and illustrate the term. Throughout the unit, as students come across key terms, have them create vocabulary cards for each term. Allow time for students to review their cards and quiz a partner on the terms to hold them accountable for accurate information on the cards. 42

7 You may want to review the terms point, line, line segment, ray, and plane from 4 th grade. Activity 4: Angle Measurement (GLE: 21) *From Unit 5 Materials List: Measuring Angles BLM, protractor, paper, pencils, index cards Provide pairs of students with a protractor and the Measuring Angles BLM. Demonstrate how to use a protractor to measure angles A C. Ask students to measure angles 1-6 with their protractors and record the angle measure to the nearest degree. It may help students to extend the rays to measure the angles. Have both students in each pair measure the angles. Make sure that their measurements are close. Consider accepting an error range of 2 degrees either way in the measurements. Students should classify each angle. Call out different angle measures in whole degrees. Using their protractors, have student pairs draw the appropriate angle on index cards and exchange with other student pairs who will verify the measurements of the drawings. On one of the angles, such as a 30 angle, ask students how they know that the angle measures 30 and not150. Since many protractors have a double scale, this will help the students avoid errors when using a protractor. 43

8 Activity 5: Circles (GLEs: 21, 24) *From Unit 5 Materials List: paper plates, protractors, pencils, colored pencils Have students discuss some of the properties of circles. Circles are round, have no straight sides, are not polygons, are the base of a cone or cylinder, and the distance around them is called the circumference. Give each student a paper plate and a protractor. These are special plates that have 36 crimps or fingers around them. They can be found at most grocery stores and the Styrofoam ones work better than the paper ones. The edges look similar to with crimps all around the plate. Students may have trouble finding the center, so consider labeling the center of each plate. The crimps have lines that extend toward the center. Each line should be labeled with multiples of 10, starting with When students have labeled the full plate, also label the crimp at 0 as360. Discuss the fact that a circle has 360 in it. Have students draw a line from one side of the plate, starting at 0, go through the origin, and continue to the other side of the plate. Ask where the line ends? (180 ) Talk about the terms diameter and radius. Draw a radius from the center to the 90 mark. Ask, What kind of angle is formed by the intersection of this radius and the drawn diagonal? (right) Draw another radius from 0 to 270. What kind of angle is formed by the intersection of this radius and the drawn diameter? (right) Introduce the term central angle. A central angle in a circle is any angle that has a vertex at the center of the circle. This activity can help students better understand turns or rotations of 90, 180, 270, and 360 and can be used to introduce circle graphs. Have the students use different colored markers to draw the different radii. Additionally, have students use their protractors to measure some of the different angles that they have drawn on the plates to reinforce using a protractor 44

9 Activity 8: Classes of Triangles (GLEs: 15, 21, 24) *From Unit 5 Materials List: What Kind of Triangle? BLM, paper, pencils, rulers, protractors Give each group of 4 students the What Kind of Triangle? BLM. Assign 2 students in each group triangles A, B, and C. Assign the other 2 students, triangles D, E, and F. Using rulers, have students measure the sides of the triangles to the nearest centimeter. Using protractors, ask students to measure the angles to the nearest degree. Students should label each triangle by the types of sides and by the types of angles. Consider allowing a 2 degree difference in the angle measures, but tell them that the measures of the 3 angles of a triangle must equal 180. The angles will be easier to measure if students extend the length of the sides. Have students then draw, using rulers and protractors, six different types of triangles. Ask questions such as these: Did anyone draw a right scalene triangle? Is it possible? If not, why not? Did anyone draw an equilateral obtuse triangle? Is it possible? If not, why not? Activity 12: Geometric Shapes: Transformations (GLE: 25) *From Unit 5 Materials List: Move the Figures BLM, pencils, paper, Internet access optional Provide each student with the Move the Figures BLM. Develop the definition of translation by having students trace Figure A, slide it to a new location, and then trace the figure again. Be sure to reinforce the use of correct terminology. Remind students that they may have referred to the movement in earlier grades by calling it a slide, but the correct mathematical term is translation. Repeat the activity with reflection and rotation. Introduce the term transformation indicating that translations, reflections, and rotations are different types of transformations. To reinforce the skill and the terminology, have students trace or draw Figure B on a sheet of paper. Give students a transformation to perform on this shape. Students should draw and label the transformation. Continue the process until students can perform the given transformation upon demand. NCTM, has a lesson on transformations. Once on the site, go to Lessons and Resources, Elementary, Illuminations, Lessons, Grades 3-5, Geometry, Paper Quilts. Or access the page directly at In this lesson, students investigate fractional parts of a whole and use transformational geometry to make 4-part quilt squares. 45

10 Activity 13: Rotations (GLE: 24, 25) *From Unit 5 Materials List: Geoboard Rotations BLM, geoboards, pencils, Internet access optional Give students a geoboard and the Geoboard Rotations BLM. Ask students to make a figure of their choice on a geoboard. This activity is better if the figures are not too complex, but make sure that the figures do not have symmetry. Have students draw their figure on paper geoboard 1 and label it as original. Ask students to visualize how the figure would look if it were rotated 90. Have them rotate the figure 90 clockwise and draw it on one of the three remaining paper geoboards, but do not label it. Ask students to place the geoboard back in the original position, then rotate it 180 and draw this figure in one of the two remaining paper geoboards. Have students put the figure back in its original position and then rotate it either 270 clockwise or 90 degrees counterclockwise. Ask them to draw that figure on the remaining paper geoboard, exchange papers, and determine which rotation is shown by each picture. The National Library of Virtual Manipulatives has geometry lessons using virtual tangram manipulatives. Go to this site at or directly access this site at Using tangrams is one way to help students with transformations. Students must rotate and reflect the pieces to make figures Activity 14: Rotational Symmetry (GLE: 26) *From Unit 5 Materials List: Rotational Symmetry BLM, paper, pencils Provide groups of students with 2 copies of the Rotational Symmetry BLM. They should cut out the figures on the second copy. Have students begin with the equilateral triangle. They should place the cut-out triangle on top of the other equilateral triangle. Ask them to tell how many times they could rotate the triangle and have it match itself, or fit back into the original triangle. Once the students understand that the triangle can be matched three different times, introduce the term rotational symmetry. If a shape, when rotated less than360, still looks the same, the shape has rotational symmetry. Have students continue with the rest of the figures. Figures A, C, E, F, H, and I have rotational symmetry. Extend the activity by having students determine the number of degrees for the rotational symmetries. For example, a square has rotational symmetry at 90, 180, 270, and

11 Activity 15: Symmetry: Line and Rotational (GLE: 26) *From Unit 5 Materials List: pattern blocks, paper, pencils Use the SQPL (view literacy strategy descriptions) strategy to challenge students to further explore the concept of symmetry. Put the following statement on the board for students. If a figure does not have line symmetry, it cannot have rotational symmetry. In groups of 4, have students brainstorm (view literacy strategy descriptions) different questions they might need to answer to determine whether this statement is true or false. Each group should present one question to the class. Give the class time to read each question. Have students discuss which questions would help to prove or disprove this statement. If a shape can be folded on a line so that the two halves match, it has line symmetry. Some shapes can be folded in more than one way, so they have more than one line of symmetry. Give each group of students a set of pattern blocks. Have them determine the number of lines of symmetry for each block. To help students understand rotational symmetry, have them take one of the pattern block shapes and trace around it to form an outline. As they rotate the shape from 0 to 360, if it can fit into the outline without being flipped over, it is said to have rotational symmetry. The order of symmetry is the number of times it will fit into the outline. This parallelogram ABCD has an order of two. Have students draw outlines for the pattern blocks to help them decide if the shape has rotational symmetry. Note: All of the pattern blocks have rotational symmetry except the trapezoid. At the conclusion of the lesson, draw students attention to their SQPL questions and allow them to reflect on which ones were answer 47

12 Activity 17: Coordinate Grids (GLE: 27) *From Unit 5 Materials List: masking tape, paper, pencils, The Fly on the Ceiling optional Using masking tape, make a coordinate grid on the floor or on the playground. Emphasize the first quadrant only. Introduce the terms x-axis and y-axis. Have one student walk four spaces to the right on the x-axis and three space up on the y-axis. Explain that the point where the student is standing can be labeled (4,3). When labeling a point, the x-coordinate should always be listed first. Have other students walk to other points and write the coordinates. Place an object on the grid and ask students to explain how they would walk to get to that point. The book, The Fly on the Ceiling, is a good way to introduce the purpose of the coordinate plane Activity 18: Plot That Figure! (GLEs: 24, 27) *From Unit 5 Materials List: Plot that Figure BLM, pencils, Internet access optional, rulers Provide students with sheets 2 copies of the Plot that Figure BLM. Call out the coordinates of vertices (using whole number coordinates) for various twodimensional shapes. The students should plot the points, label the points, and connect them in the order presented to create a geometric shape. Ask students to identify the shape they created. Here are some points you may want to use. Grid 1 Grid 2 Grid 3 Grid 4 Point A (1, 2); Point B (6, 2); Point C (5, 4); Point D (2, 4). Connect A to B, B to C, C to D, and D to A. (trapezoid) Point A (1, 5); Point B (4, 5); Point C (4, 1). Connect A to B, B to C, and C to A. (right scalene triangle) Point A (2, 5); Point B (4, 5); Point C (4, 1); Point D (2, 1). Connect A to B, B to C, C to D, and D to A. (rectangle) Point A (1, 2); Point B (4, 2); Point C (2, 4); Point D (2, 6); Point E (1, 6). Connect A to B, B to C, C to D, D to E, and E to A. (pentagon) On the 2 nd copy of the BLM, have students draw simple figures, name the figures, and state the coordinates of each vertex. The website has a good lesson called Chameleon Graphing. The lesson provides an introduction to graphing in a coordinate plane 48