Mathematics Success Level E

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1 T877 [OBJECTIVE] The student will classify two-dimensional figures based on properties. [PREREQUISITE SKILLS] Lesson 29, knowledge of basic geometry terminology including: parallel sides, congruent sides, triangle, pentagon, hexagon, octagon, quadrilaterals, acute angle, right angle, obtuse angle, acute triangle, obtuse triangle, right triangle, properties [MATERIALS] Student pages S292 S300 Transparencies T890, T892, T894, T896, T898, and T900 Copy Master T888 (1 per student pair) Scissors [ESSENTIAL QUESTIONS] 1. When comparing and classifying two-dimensional figures, what is the first characteristic to consider? 2. How can I classify and compare triangles? 3. How can I classify and compare quadrilaterals? [WORDS FOR WORD WALL] quadrilateral, rhombus, rectangle, square, trapezoid, parallelogram, triangle, congruent sides, properties, isosceles triangle, equilateral triangle, scalene triangle, parallel sides, polygon, congruent angles, pentagon, hexagon, octagon [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) *For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson. [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete Representation

2 T878 Mathematics Success Level E [WARM-UP] (5 minutes IP, WG, I) S292 (Answers are on T889.) Have students turn to S292 in their books to begin the Warm-Up. Students will identify polygons by matching the name to the pictorial representation of the figure. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Verbal Description, Pictorial Representation} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night. [LESSON] (60 minutes M, GP, IP, WG, CP) SOLVE Problem (3 minutes WG, GP) T890, S293 (Answers on T891.) Have students turn to S293 in their books, and place T890 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn how to classify two-dimensional figures based on properties. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer} Sorting Two-Dimensional Figures - Concrete (8 minutes CP, WG, M, GP) T888, T890, S293 (Answers on T891.) 8 minutes M, GP, CP, WG: Place T888 on the overhead. Distribute copies of the Copy Master on T888 and scissors to each student pair. Make sure partners know their designation as Partner A or Partner B. {Verbal Description, Concrete Representation, Pictorial Representation}

3 T879 MODELING Sorting Two-Dimensional Figures Concrete Step 1: Have students cut apart the polygons on the dotted lines. With your partner, sort the polygons into groups by the number of sides. Identify each polygon in the group by name. Compare the polygons in each group using their properties. (The triangle is identified by angle. There are 6 quadrilaterals that can be identified by number of parallel sides, congruent angles, or congruent sides.) Step 2: Sort the polygons into groups according to the number of parallel sides for each polygon. With your partner, identify the name of the polygons in each group. (0 sets of parallel sides: the triangle and one of the pentagons; 1 set of parallel sides: the trapezoids and one pentagon; 2 sets of parallel sides: the square, parallelogram, rhombus, rectangle; 3 sets of parallel sides: the hexagon; 4 sets of parallel sides: the octagon.) Step 3: Continue to have students sort the polygons and compare them using the number of angles until time is called. Identifying Polygons - Pictorial (14 minutes CP, WG, M, GP, IP) T892, S294 (Answers on T893.) 4 minutes M, WG, CP, GP: Have students turn to S294 in their books, and place T892 on the overhead. Use the polygons that students cut apart as reference. Make sure partners know their designation as Partner A or Partner B. {Verbal Description, Concrete Representation, Pictorial Representation, Graphic Organizer}

4 T880 Mathematics Success Level E MODELING Identifying Polygons - Pictorial Step 1: *Teacher Note: All the polygons on the graphic organizer were not used in the concrete activity, but students should know the angle classification of triangles. Look at the first row of the graphic organizer. What is it asking you to do? (Identify the number of sides and draw a picture of an acute triangle.) Partner A, identify the number of sides on an acute triangle. (3) Record. Partner B, by what properties is an acute triangle identified? What is the largest angle in an acute triangle? (acute angle) Draw a picture of an acute triangle. Step 2: Have students complete the graphic organizer for the obtuse and right triangles. *Teacher Note: Discuss with students that this particular right triangle has two congruent sides, but not all right triangles are isosceles. Step 3: Look at the cut-out of the rhombus. Partner A, identify the number of sides on a rhombus. (4) Record. With your partner, determine if the rhombus can be identified using parallel sides, right angles, or congruent sides. (Yes, the rhombus has two sets of parallel sides.) Are the sets of parallel sides opposite each other? (Yes.) Does the rhombus have right angles? (No.) Does the rhombus have congruent sides? (Yes.) Partner B, draw a picture of a rhombus on the graphic organizer, making sure both pair of opposite sides are parallel and the four sides are congruent.

5 T881 8 minutes IP, CP: Have students work with their partners to complete the graphic organizer on S294. Monitor closely to make sure students are using the appropriate vocabulary. It is also important that students talk about the properties of the polygons before they draw the pictures. {Verbal Description, Graphic Organizer, Pictorial Representation} 2 minutes WG: Have students come back together as a class and share their results. {Verbal Description, Graphic Organizer, Pictorial Representation} Classifying Triangles by Properties - Abstract (5 minutes CP, WG, M, GP) T894, S295 (Answers on T895.) 5 minutes M, GP, WG, CP: Have students turn to S295 in their books, and place T894 on the overhead. Make sure partners know their designation as Partner A or Partner B. {Verbal Description, Pictorial Representation} MODELING Classifying Triangles by Properties - Abstract Step 1: Have students look at Problem 1. What is it asking you to do? (classify by angles) Have students look at the first triangle. Partner A, what is the largest angle in this triangle acute, right, or obtuse? (right) Record. If the largest angle is a right angle, Partner B, identify the name of the triangle. (right triangle) Record. Step 2: Have students look at the second triangle for Problem 1. Partner B, what is the largest angle in this triangle acute, right, or obtuse? (acute) Record. If the largest angle is an acute angle, Partner A, identify the name of the triangle. (acute triangle) Record. Step 3: Have students identify the classification of the third triangle and record.

6 T882 Mathematics Success Level E Step 4: Direct students attention to Problem 2. Compare the triangles with the triangles labeled in Problem 1. (They are identical.) What is Problem 2 asking you to do? (classify by sides) With your partner, compare the sides of the first triangle. (It has two congruent sides.) *Teacher Note: Discuss the use of hash marks to show congruency. If a triangle has 2 congruent sides, it is called an isosceles triangle. Record and label the isosceles triangle. With your partner, what can you conclude about the classification of the first triangle? (It can be classified by angles and sides, so it is a right, isosceles triangle.) Step 5: Look at the second triangle. Compare the sides of the triangle. (It has 3 congruent sides.) If a triangle has 3 congruent sides, it is called an equilateral triangle. Record and label the equilateral triangle. With your partner what can you conclude about the classification of the second triangle? (It can be classified by angles and sides, so it is an acute, equilateral triangle.) Step 6: Look at the third triangle. Compare the sides of the triangle. (It has no congruent sides.) If a triangle has no congruent sides, it is called a scalene triangle. Record and label the scalene triangle. With your partner what can you conclude about the classification of the third triangle? (It can be classified by angles and sides, so it is an obtuse, scalene triangle.) Step 7: Have students answer the questions at the bottom of page S295.

7 T883 Classifying Triangles in a Hierarchy - Abstract (9 minutes CP, WG, M, GP, IP) T896, S296 (Answers on T897.) 4 minutes M, GP, WG, CP: Have students turn to S296 in their books, and place T896 on the overhead. Make sure partners know their designation as Partner A or Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer} MODELING Classifying Triangles in a Hierarchy - Abstract Step 1: Direct students attention to the graphic organizer on S296. Look at the graphic organizer. You will be organizing by angle and side classification. Partner A, what property is used to classify the top three triangles? (angles) Look at the acute triangle. Partner B, how do you determine the classification of this triangle based on angles? (Largest angle is acute.) Record. Step 2: Have students look at the arrow leading to the triangles for the acute triangle. Partner A, how many acute triangles are shown? (3) If you classify by the property of sides, Partner B, explain to Partner A how you know that the acute triangle can also be an equilateral triangle. (All sides are congruent.) Record. Partner A, explain to Partner B how you know that the acute triangle can also be an isosceles triangle. (2 congruent sides) Record. Partner B, explain to Partner A how you know that the acute triangle can also be a scalene triangle. (no congruent sides) Record. Step 3: With your partner, can you conclude that an acute triangle is always an equilateral triangle? (No.) Can you conclude that an acute triangle is always an isosceles triangle? (No.) Can you conclude that an acute triangle is always a scalene triangle? (No.) With your partner, determine what you can conclude about the acute triangle. (Depending on the way it is drawn, an acute triangle can be classified using the sides as equilateral, isosceles, or scalene.)

8 T884 Mathematics Success Level E 4 minutes IP, CP: Have students work with their partners to complete the graphic organizer and answer the questions at the bottom of the page based on the graphic organizer. Monitor closely to make sure students are using the appropriate vocabulary. {Verbal Description, Pictorial Representation, Graphic Organizer} 1 minute WG: Have students come back together as a class and share their results. {Verbal Description, Graphic Organizer, Pictorial Representation} Classifying Quadrilaterals by Properties - Abstract (14 minutes CP, WG, M, GP, IP) T898, S297 (Answers on T899.) 5 minutes M, GP, WG, CP: Have students turn to S297 in their books, and place T898 on the overhead. Make sure partners know their designation as Partner A or Partner B. {Verbal Description, Graphic Organizer, Pictorial Representation} MODELING Classifying Quadrilaterals by Properties - Abstract Step 1: Direct students attention to S297. Look at the graphic organizer. You will be organizing and classifying quadrilaterals by properties. What property do all quadrilaterals have in common? (4 sides) With your partner, discuss other properties that describe quadrilaterals. (parallel sides, angles, congruent sides, and congruent angles) Step 2: Have students look at the quadrilateral at the top of the graphic organizer. With your partner, determine the properties of this quadrilateral. (It has four sides, no parallel sides, no congruent sides, and no right angles.) Are all of the other polygons on the graphic organizer quadrilaterals? (Yes.)

9 T885 *Teacher Note: As the students move down the graphic organizer and Steps 3 5 are completed, make sure they notice that each tier has the properties from the quadrilateral above it. They are building a hierarchy of properties. Step 3: Look at the two quadrilaterals in the second tier of the graphic organizer. What quadrilateral is on the right? (trapezoid) Partner A, identify the number of parallel sides of the trapezoid. (1 pair) Record. Partner B, does the parallelogram have parallel sides? (Yes, it has two pairs of parallel sides that are on opposite sides of the parallelogram.) Record the properties that are different from the previous tier. *Teacher Note: Remind student that the hash marks are used to show congruency. Step 4: Look at the two quadrilaterals in the third tier of the graphic organizer under the parallelogram. Partner A, do they both have two pairs of parallel sides that are opposite each other? (Yes.) Partner B, explain to Partner A how the rectangle differs from the rhombus. (The rectangle has four right angles, and the rhombus does not. The rhombus had four congruent sides, and the rectangle does not; it only has 2 pairs of congruent sides.) Record the properties that are different from the previous tier. Step 5: Look at the last quadrilateral in the fourth tier under the rectangle and the rhombus. Partner A, does the square have two pairs of parallel sides that are opposite each other? (Yes.) Partner B, does the square have four right angles? (Yes.) Partner A, does the square have four congruent sides? (Yes.) Record the properties for the square that are different from the previous tier.

10 T886 Mathematics Success Level E Step 6: Direct students attention to the completed graphic organizer on S297 and use the following instructions to complete this step. With your partner, discuss what you noticed about the different tiers of the organizer. (The graphic organizer started with just the 4-sided quadrilateral, and each tier added other quadrilaterals that had additional properties.) Partner A, explain to Partner B what the properties of the parallelogram are in order. (The parallelogram is a quadrilateral with both pairs of opposite sides parallel.) Partner B, explain to Partner A what the properties of the rhombus are in order. (The rhombus is a quadrilateral with both pairs of opposite sides parallel and four congruent sides.) Step 7: Have students continue to take turns providing properties of the other quadrilaterals, in order, using the graphic organizer. Step 8: Have students look at Question 1. Partner A, what is this question asking? (if all squares are rectangles) Look at the graphic organizer. Partner A, describe the properties of the rectangle. (It has both pairs of opposite sides parallel, and it has four right angles.) Partner B, does the square have both pairs of opposite sides parallel and four right angles? (Yes.) Can you conclude that a square is a rectangle? Why? (It has the properties of a rectangle.) Record. With your partner, determine what property the square has in addition to the parallel sides and right angles. (It has 4 congruent sides.) 7 minutes IP, CP: Have students work with their partners to answer Questions 2 5 on S297 using the graphic organizer. Monitor closely to make sure students are using the appropriate vocabulary. {Verbal Description, Graphic Organizer, Pictorial Representation} 2 minutes WG: Have students come back together as a class and share their results. {Verbal Description, Graphic Organizer, Pictorial Representation}

11 T887 SOLVE Problem (5 minutes GP, WG) T900, S298 (Answers on T901.) Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (Students will be working with classification and comparison of two-dimensional figures.) {SOLVE, Graphic Organizer, Verbal Description} If time permits (10 minutes IP, CP) S299 (Answers on T902.) Have students complete graphic organizer and questions on page S299. [CLOSURE] (2 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. When comparing and classifying two-dimensional figures, what is the first characteristic to consider? (the number of sides the figure has) How can I classify and compare triangles? (by the number of sides and the largest angle) How can I classify and compare quadrilaterals? (by the properties of parallel sides, angles, and congruency of sides) [HOMEWORK] Assign S300 for homework. (Answers on T903.) [QUIZ ANSWERS] T904 T905 The quiz can be used at anytime as extra homework or to assess how students progress on understanding how to classify two-dimensional figures in a hierarchy based on properties.

Skill. 69 Graph Ordered Pairs. (First Quadrant) Using Skill 69 COMMON ERRORS. 285 Holt Mathematics. OBJECTIVE Graph ordered pairs (first quadrant)

Skill. 69 Graph Ordered Pairs. (First Quadrant) Using Skill 69 COMMON ERRORS. 285 Holt Mathematics. OBJECTIVE Graph ordered pairs (first quadrant) Skill Graph Ordered Pairs (First Quadrant) Using Skill OBJECTIVE Graph ordered pairs (first quadrant) Minutes Direct students attention to the definition at the top of the page. Work through the example