2012-13 and 2013-2014 Transitional Comprehensive Curriculum

Grade 5 Mathematics

Unit 5: Properties in Geometry

Time Frame: Approximately four weeks

Unit Description

This unit focuses on geometric concepts involving plane figures, and includes the concepts of angle measurement and coordinate graphing.

Student Understandings

Students can analyze characteristics and properties of polygons and circles. They can use appropriate tools to measure angles and use spatial reasoning to solve problems.

Guiding Questions

1. Can students classify and describe the properties of circles and polygons?2. Can students measure and identify types of angles?3. Can students identify and plot points on a coordinate grid?

Unit 5 Grade Level Expectations (GLEs) and Common Core State Standards (CCSS)Grade-Level Expectations

GLE # GLE Text and BenchmarksMeasurement21. Measure angles to the nearest degree (M-3-M)Geometry24. Use mathematical terms to classify and describe the properties of 2-

dimensional shapes, including circles, triangles, and polygons (G-2-M)27. Identify and plot points on a coordinate grid in the first quadrant (G-6-

M)ELA CCSS

CCSS# CCSS TextWriting Standards W.5.2a Write informative/explanatory texts to examine a topic and convey ideas

and information clearly.a. Introduce a topic clearly, provide a general observation and

focus, and group-related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension.

Speaking and Listening StandardsSL.5.1c Engage effectively in a range of collaborative discussions (one-on-one,

in groups, and teacher-led) with diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly.

c. Pose and respond to specific questions by making comments that

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contribute to the discussion and elaborate on the remarks of others.

SL.5.4 Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace.

Language StandardsL.5.6 Acquire and use accurately grade-appropriate general academic and

domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships.

Sample Activities

Activity 1: Geometry Vocabulary (GLE: 24; CCSS: SL.5.1c, L.5.6)

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 professor-know-it-all (view literacy strategy descriptions). Tell students that one group will be called on randomly to come to the front of the class to be a team of “professors-know-it-alls.” Select one group to come up and place their index cards on the floor or tape them to the wall. The students in each 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 4th grade. Do not worry if the students do not think of all of the vocabulary words. This is just an introduction.

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Activity 2: More Geometry Vocabulary (GLE: 21, 24; CCSS: L.5.6)

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 35 or 57 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 the 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.

Review the terms point, line, line segment, ray, and plane that were taught in previous grades.

Activity 3: Arm Angles (GLE: 21; CCSS: SL.5.1c, W.5.2a)

Materials List: paper, pencils, students themselves, Measuring Angles BLM

Begin the activity by reviewing the terms, angle and vertex. Tell students that angles are measured in degrees. Display the Measuring Angles BLM. Allow the students to discuss the different types of angles on the page (acute, right, obtuse, and straight) using the Round Robin discussion (view literacy strategy descriptions) strategy. This strategy allows students to quickly share their ideas or solutions with a group of peers. Students are encouraged to write down their ideas and which are then shared with the teacher and class. Place students in groups of three to five to form a circle. Ask students to discuss the different types of angles on the Measuring Angles BLM. Have each student go

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Definition:A quadrilateral with only 1 set of parallel lines.

Characteristics:

4 sides, 1 set of parallel sides, can have right angles, can have symmetry

Illustration

Trapezoid

2012-13 and 2013-2014 Transitional Comprehensive Curriculum

around the circle and quickly share his/her ideas. Give the students some time to share and then ask them to write their ideas on a single piece of paper. Allow a spokesperson from each group to read their ideas to the class and have the class record those ideas in their math learning logs (view literacy strategy descriptions).

Ask students to estimate the measures of the acute and obtuse angles, but do not have them actually measure them in this activity. Ask students to model different types of angles (acute, obtuse, right, and straight) with their arms. After students have modeled these four types of angles, choose a degree measure between 0°and 180°, such as 45°. Have students model it and explain how they decided how wide to open their arms. They won’t be exact, but if there are large differences in the width of their spread arms, discussion should follow. Have them model measures such as 170°, 5°, 30°, and 92°. For each measure, ask students to name the type of angle.

Activity 4: Angle Measurement (GLE: 21)

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. Have students 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 30angle, ask students how they know that the angle measures 30 and not 150 . Since many protractors have a double scale, this will help the students avoid errors when using a protractor.

Activity 5: Circles (GLEs: 21, 24)

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 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

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toward the center. Each line should be labeled with multiples of 10, starting with 0 .

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 segment 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 segment 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 diameter?” (right) Draw another radius from the center 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 . The activity can also 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.

Activity 6: Common Shapes (GLE: 21, 24; CCSS: W.5.2a)

Materials List: Common Shapes BLM, paper, pencils, math learning logs

Give students a copy of the Common Shapes BLM. Have students trace or draw the shapes in their math learning logs (view literacy strategy descriptions). Have them write descriptions of each shape, using appropriate mathematical terms. Give attention to number of sides, relationships between sides (parallel, perpendicular, same length), number of angles, relationships between angles (angles all have the same measure, acute, right, obtuse), circumference, diameter, and radius. On the board or overhead, post some of the terms students are expected to include in the descriptions. Once completed, students can find partners to compare and clarify shapes and terms.

Activity 7: Polygons (GLE: 24; CCSS: SL.5.1c)

Materials List: Polygons Anticipation Guide, Common Shapes BLM, markers, The Internet (optional)

Begin the lesson by providing the students with the Polygons Anticipation Guide BLM. Use the anticipation guide (view literacy strategy descriptions) to appraise the students’ prior knowledge before the new concept is introduced and to evaluate knowledge gained through their exploration of the concept. This strategy is especially helpful to struggling and reluctant learners as it heightens motivation and helps students focus on important content. This guide will be completed individually and can be given in handout form,

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0 10 20 30

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written on the board, overhead or can be used with a document camera. Tell the students to respond to the statements and be prepared to explain their responses. Put students in pairs and have them compare and discuss their responses before beginning the “What’s My Shape?” activity. At this stage of the activity, emphasize that there are no “correct” answers and encourage students to discuss their responses. Use general discussion with the class to determine the accuracy of the statements. Tell the students they are about to participate in an activity to prove or disprove the answers generated on the anticipation guide.

Play the game “What’s My Shape?” Think of a shape on the Common Shapes BLM, but do not tell students the shape. Allow students to ask questions to determine the shape. Some types of questions allowed are the following: Does your shape have 4 sides? Does your shape have any sets of parallel lines? Does your shape have any right angles? Tell the students that as they answer, yes or no, to the questions, they should cover any shapes that could not be the shape. Those shapes are now eliminated. For the question, “Does your shape have 4 sides?” figures A, C, E, G, J, and L would all be covered because they

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do not have 4 sides. Periodically during the game, have students return to the anticipation guide and revise or reconfirm their initial responses. Engage students in a discussion about their responses to clarify any misconceptions.

The website www.nctm.org has a good lesson on what distinguishes a rectangle from a more general parallelogram. Once on the site, go to Lessons and Resources, Elementary, Illuminations, Lessons, and the Search tab. In the search box, type Geometry, Rectangles and Parallelograms. The lessons are in alphabetical order. This lesson can be accessed directly at http://illuminations.nctm.org/index_d.aspx?id=350.

Activity 8: Classes of Triangles (GLEs: 21, 24)

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. Have students 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 9: Geoboard Polygons (GLE: 21, 24, 27)

Materials List: Dot Paper Geoboards BLM, geoboards (optional), paper, pencils, The Internet (optional)

Place students into groups of four. Give students geoboards or use the Dot Paper Geoboards BLM. Have each student make or draw a quadrilateral. Students in each group should have different figures, either ones that are different sizes or different shapes. Have two students in each group discuss how their figures are alike and how they are different. Have students focus on parallel lines, types of angles, symmetry, etc. Have students make or draw other figures such as a shape with four sides and no right angles, a shape with three sides and one obtuse angle, or a shape with six sides. Do this activity one day with 3-sided shapes, the next with 4-sided, and then the third day focus on figures with more than four sides.

Consider introducing coordinate geometry by having students label each vertex of one of the figures drawn.

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Activity 10: Real-world Geometry (GLE: 24; CCSS: W.5.2a; SL.5.1c; SL.5.4)

Materials List: paper, pencils

Have students find examples of different plane figures in the classroom, at home, outside, or in a grocery store. Give the students a list of the figures that should be found. Some figures may be difficult to find. Students may find things such as polygons used as faces of traffic signs, or a rectangle as the face of a windowpane. Have students make sketches of the figures and note the location of each one. If a student says that a cereal box is a type of rectangle, stress that the faces of the box are rectangles, but the box itself is a rectangular prism.

Have students, in a group of 4, select a plane geometric figure (other than a rectangle) of their choice. Ask them to demonstrate their understanding of the properties of their chosen figure by completing a RAFT writing (view literacy strategy descriptions) assignment. This form of writing gives students the freedom to project themselves into unique roles and to look at content from unique perspectives. From these roles and perspectives, RAFT writing can be used to describe a point of view, envision a potential job or assignment, or solve a problem. It is the kind of writing that when crafted appropriately, should be creative and informative.R – Role (role of the writer – salesperson)A – Audience (to whom the RAFT is being written – billboard sign makers)F – Form (the form the writing will take – a letter)T – Topic ( the subject of the focused writing – to get billboard sign makers to switch from the standard rectangular billboard sign to the shape chosen by the group. The groups should share their writing with the class. Students should listen for accuracy and logic in each RAFT.

Activity 11: Faces and Bases of 3-D Figures (GLE: 24; CCSS: L.5.6)

Materials List: solid figures, paper, pencils, math learning logs

Display solid figures such as cubes and other rectangular prisms, cylinders, cones, spheres, and different types of pyramids. Discuss the terms faces, bases, edges, and vertices. Have students choose two of the figures and in their math learning logs (view literacy strategy descriptions), write a paragraph about how the figures are alike and how they are different. Make sure that students include the types of plane figures that are parts of the 3-D figures. For example, a square pyramid is composed of a square base and 4 triangular faces. Have students share with the class their comments about the different figures.

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Activity 12: Properties of Geometric Figures (GLEs: 21, 24; CCSS: L.5.6)

Materials List: Properties of Geometric Figures BLM, pencils

This activity will help students summarize the important attributes of different types of geometric figures. Draw a word grid (view literacy strategy descriptions) like the one below. To take full advantage of word grids, they should be co-constructed with students, so as to maximize participation in the learning process. Provide students with a blank word grid, the Properties of Geometric Figures BLM. In the first column, have students list the types of geometric figures they have been studying. In the other column headings, have them think of properties of the geometric figure, such as these: has only 3 sides and must have 4 right angles. Students should write A for always, S for sometimes, and N for never. Once the word grid is complete, students should be given time to review the differences and similarities among geometric figures. They can quiz each other over the information in the grid in preparation for tests or other class activities.

Sample Word Grid

Properties

Figure has only 3 sides

has at least 1

right angle

all sides congruent

equilateraltriangle A N A

trapezoid N S Nsquare N A A

A = always S = sometimes N = never

Activity 13: Coordinate Grids (GLE: 27)

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 spaces 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.

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Activity 14: Plot That Figure! (GLEs: 24, 27)

Materials List: Plot that Figure BLM, pencils, The Internet (optional), rulers

Provide students with 2 copies of the Plot that Figure BLM. Call out the coordinates of vertices (using whole number coordinates) for various two-dimensional 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 that could be used:

Grid 1Point 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)Grid 2Point 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)Grid 3Point 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)Grid 4Point 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 2nd copy of the BLM, have students draw simple figures, name the figures, and state the coordinates of each vertex.

The website http://mathforum.org/cgraph has a good lesson called Chameleon Graphing. The lesson provides an introduction to graphing in a coordinate plane.

Sample Assessments

General Assessments

Portfolio assessments could include the following:o Anecdotal notes made during teacher observationo Any of the journal entries, or one of the explanations from the specific

activitieso Corrections to any of the missed items on the tests

On any teacher-made written tests, include at least one of the following:o One problem that requires the use of manipulatives or drawings, such as

this: Choose 3 types of triangles and use a ruler and protractor to accurately draw an example of each kind of triangle chosen.

o One problem that requires the student to explain his/her reasoning such as this: Can a triangle be both right and equilateral?

o One question involving real-life such as this: Describe places at home where a rectangle, a square, a circle, and a triangle could be found.

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Journal entries could include the following: o Explain how rectangles and trapezoids are alike and how they are

different.o Explain how to plot the point 2,4 on a coordinate grid.o Write an autobiography/self-description from a shape’s point of view.

Read the description to a partner and see if the partner can guess the shape.

Activity-Specific Assessments

Activity 4 : Provide students with protractors and the Angle Measures BLM. Have students measure the angles to the nearest degree and classify the angles.

Activity 6 : Provide students with the Which Shape Does not Belong? BLM. Have students decide which shape does not belong and explain why.

A. B. C. D.

Activ ity 7 : Draw a rectangle on the board. Have students use geometric terms to describe 3 properties of the figure and also write all of the names of the figure.

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