<p>This lesson introduces students to geometric shapes and their attributes. At the end of this lesson, students will:<br>- identify and classify triangles, quadrilaterals, and their special cases.<br>- discuss the similarities and differences between shapes (such as rhombuses and rectangles), including three-dimensional shapes.</p>

<p>- What properties of shapes help to distinguish what the shape is called?<br>- How can we classify shapes into groups with similar properties?<br>&nbsp;</p>

<p>- <strong>Line:</strong> A straight path extending in both directions with no endpoints.<br>- <strong>Line Segment:</strong> A part of a line with two endpoints.<br>- <strong>Parallel Lines:</strong> Lines that never intersect and are always the same distance apart.<br>- <strong>Plane:</strong> A flat surface that extends infinitely in all directions.<br>- <strong>Ray:</strong> A straight path extending in one direction from a given point.<br>- <strong>Intersecting Lines:</strong> Two lines that share one or more points in common.<br>- <strong>Angle:</strong> Two rays that start from the same common point.<br>- <strong>Point of Intersection:</strong> The point where two lines meet.<br>- <strong>Perpendicular Line:</strong> A line that intersects another line at a right angle.<br>- <strong>Acute Angle:</strong> An angle that is smaller in measure than 90 degrees, but is greater than 0 degrees.<br>- <strong>Obtuse Angle:</strong> An angle that is greater in measure than 90 degrees, but smaller in measure than 180 degrees.<br>- <strong>Straight Angle:</strong> An angle that measures 180 degrees.<br>- <strong>Vertex:</strong> The common point shared by the two rays that make up an angle.<br>- <strong>Collinear:</strong> Three points are said to be collinear if all three of the points lie on the same line.<br>- <strong>Coplanar:</strong> Objects that lie in the same plane.<br>- <strong>Right Angle:</strong> An angle that measures 90 degrees.<br>- <strong>Prism:</strong> A three-dimensional solid that has two congruent and parallel faces that are polygons.<br>- <strong>Rectangular Prism:</strong> A solid figure in which all six faces are rectangles.<br>- <strong>Pyramid:</strong> A solid figure with a polygon base and triangular sides that meet at a single point.<br>- <strong>Parallelogram:</strong> A quadrilateral whose opposite sides are parallel and congruent.<br>- <strong>Rhombus:</strong> A parallelogram with four equal sides.</p>

<p>- copies of laminated 8"x10" shape sheets (M-G-1-2_Shape Sheets)<br>- tag board cut into strips<br>- tape<br>- copies of Quadrilateral Set (M-G-1-2_Quadrilateral Set)<br>- copies of Sample Decision Flowchart (M-G-1-2_Sample Decision Flowchart)&nbsp;<br>- Blank sheets of paper (as many sheets as you have students)</p>

<p>- Evaluating student responses during the "Family Feud"-style game will be subjective, but it is important to consider whether students are reasoning their answers prior to replying to the question.<br>- Asking students to illustrate and justify each option in their flowchart will help with the assessment of their work.<br>&nbsp;</p>

<p>Active Engagement, Modeling, and Explicit Instruction<br>W: In this lesson, students will study and review basic two- and three-dimensional shapes, including their properties, representation, and identification. Students will discover how different types of quadrilaterals relate to one another and how shapes mix to produce new shapes.<br>H: The Shape Sheets in the Resources folder provide visual representations to help students understand and remember each shape's concept and qualities. Furthermore, stressing language with students strengthens their ability to create their own representations and assess representations from various sources.<br>E: A pair practice using crossing and parallel lines on paper increases student awareness of broader geometric structures. More broadly, it enables students to compare comparable forms at smaller and bigger scales, such as shapes on a computer screen against similar shapes on a photograph or drawing. The pair activity that follows reinforces this visual exercise by incorporating the logical structure of classification.<br>R: The lesson's Sample Decision Flowchart emphasizes the importance of decision-branching for accurate identification and naming. As students discover the unique properties of each polygon, they must assign it to the right decision branch.<br>E: To identify quadrilaterals, utilize the Sample Decision Flowchart, which considers both the individual properties of each object and the general characteristics of quadrilaterals. It may be especially useful to locate one or more quadrilaterals that are not rectangles, parallelograms, or trapezoids.<br>T: When employing quadrilaterals in activities and assignments, refer to the decision flowchart to select the appropriate kind. The graphic decision flowchart, paired with the written questions, gives multiple entrance points into the topic for different types of learners. Students who participate physically in the "Family Feud"-style game in Activity 2 are more likely to recall the experience and pay attention to the characteristics of the various forms.<br>O: This lesson was created to provide students with a thorough understanding of the differences between different types of quadrilaterals, as well as the characteristics of other basic two-dimensional and three-dimensional shapes. Students are given the opportunity to learn in three different ways: kinesthetic, auditory, and visual.<br>&nbsp;</p>

<p>Divide the students into three groups. Each group will be given four Shape Sheets (M-G-1-2_Shape Sheets). In each group, ask students to identify three features of each shape and write them on the shape. Then, ask students to cover each attribute by taping a piece of tag board over the attribute.</p><p>Example properties for each shape:</p><p>Right Triangle: Right angle, three sides, triangle, and three angles</p><p>Isosceles Triangle: Two congruent sides, two congruent angles, three sides and three angles.</p><p>Equilateral Triangle: All three sides are the same length, three sides and all angles have the same measurement.</p><p>Rhombus (nonsquare): Four sides, equal sides, opposite sides parallel, opposite angles congruent.</p><p>Parallelogram: Four sides, opposite sides parallel, opposite angles congruent; opposite sides congruent.</p><p>Trapezoid: Four sides, two opposing sides parallel, quadrilateral.</p><p>Rectangle: Four sides, opposite sides parallel, opposite sides congruent, congruent angles, right angles, parallelogram, and quadrilateral.</p><p>Square: Four sides, congruent sides, congruent angles, right angles, parallel sides, rectangle, parallelogram, quadrilateral, rhombus</p><p>Cone: Round base, 3-D, comes to a point, only one vertex</p><p>Cylinder: Two round bases, side is a "rolled-up" rectangle, 3-D</p><p>Rectangular Prism: Cube, box, six sides, opposite faces congruent, 3-D</p><p>Pyramid: 3-D, polygon base, triangular sides, four or more faces.</p><p><strong>Family Feud Activity</strong></p><p>Several students are probably familiar with this game. Two teams play against one another in turn. Depending on how many groups the class size can support, each team has three or four players.</p><p>Print the three properties of each form on the board in front of the classroom. Tape a sheet of paper over each individual attribute. Make sure that the paper covering each attribute can be readily removed without revealing the other attributes.</p><p>After each group has completed their attribute lists, the Shape Sheets (M-G-1-2_Shape Sheets) will be utilized to play a game similar to Family Feud. The rules are the following: The first group chose one of their shapes. The remaining two groups each send a representative to the central table. One student in the first group says, "Name an attribute of this shape," while another holds up a photograph of the shape. The group member who "rings in" first (you can have students ring a bell, raise their hand, speak their name, etc.) has the opportunity to provide a single attribute of the shape.</p><p>If the student correctly names one of the shape's covered attributes, the tag board covering that characteristic is removed, and the student's team is given the option to name the remaining two. The team receives one point for each correctly named attribute. If the team makes an inaccurate guess (either a attribute not applicable to the shape or one not stated), the other team has the opportunity to estimate the remaining attributes, gaining one point for each one correctly guessed. Once all three qualities have been discovered, the procedure is repeated, this time with a Shape Sheet (M-G-1-2_Shape Sheets) from the second group, as well as the first and third groups estimating the attributes. Repeat until all 12 Shape Sheets have been used. The team that scores the most points wins (prizes are optional).</p><p>Divide the students into pairs and give them each a blank sheet of paper. Explain to them that the sides of the paper form lines, but they are special types of lines. Ask the class the following:</p><p><strong>"Does the top and bottom of the paper intersect?"</strong> (<i>no</i>)</p><p><strong>"We have a particular name for lines that never intersect. Does anybody know what that name is?"</strong> (<i>parallel</i>)</p><p><strong>"Parallel lines are those that never meet, even if they might be drawn on indefinitely. Parallel lines are marked with the symbol | |: &nbsp;Look around the classroom; there are several parallel lines. Can you tell me what they are?"</strong> (<i>Give students time to look about and respond; answers will differ based on the objects in the room</i>.)</p><p><strong>"Look at the paper again. Take a look at the left and top sides of the paper. As you can see, these line segments meet in a unique way. Can somebody tell me what is unique about this intersection?"</strong> (<i>The sides connect at right angles</i>.)</p><p><strong>“The two sides meet at a straight angle. We have a term for lines that meet at right angles. Does anybody know what that name is?”</strong> (<i>perpendicular</i>)</p><p><strong>"Perpendicular lines are those that meet at right angles and are represented by the symbol ⊥. Take a look around the room and tell me about the perpendicular lines you see."</strong> (<i>Answers may change depending on what is in the room; guide students as necessary.</i>)</p><p>Give each group the same sheet of paper as the first, and instruct the students on the following activity: <strong>"Compare it to their first. Note that the tops of each sheet of paper are the same length. The bottoms are also the same length. Furthermore, the lengths of the right and left sides are all the same. The side measurements and angle measurements for these two pieces of paper are exactly the same. We have a name for shapes where the corresponding side and angle measurements are all the same. Does anybody know what that name is?"</strong> (<i>congruent</i>)</p><p><strong>"Congruent shapes are those in which all of the matching sides have the same length and angles. Congruent things are represented by the symbol:</strong></p><p>Divide the students into pairs and give each pair a list of quadrilateral. (M-G-1-2_Quadrilateral Set). <strong>"I've given each pair a list of different quadrilaterals. What you are going to do is arrange the shapes from the list in order from general to most specific. Consider this activity in terms of vehicles. The category of vehicle is general; it is anything you can drive or ride. In the same way, all of the shapes on the list are quadrilaterals; this is a general category. To be more specific within the category of vehicle, we may list a type of vehicle, such as a car. To be more specific, we may mention a car brand, such as Honda, and then a model, such as the Accord. Do you see how we moved from a general category of vehicle to a specific model of car? All vehicles are not cars, and all cars are not Honda Accords, but all cars are vehicles…as are trucks and buses and motorcycles; in the same way, all quadrilaterals are polygons, and all rectangles are quadrilaterals, but not all quadrilaterals are rectangles.”</strong></p><p>After students have listed the quadrilaterals in order of general to most specific, have each pair create a list of yes/no questions identifying the similarities and differences between the shapes next to each other on the list. For example, while comparing a parallelogram and a rectangle, students may ask, "Do rectangles have two sets of parallel lines?"</p><p>These questions should then be utilized to create a decision flowchart depicting the differences, similarities, and hierarchy of the various quadrilaterals. A partial sample decision flowchart is given for your reference (M-G-1-2_Sample Decision Flowchart). Discuss how students grouped their shape names. Although there is some space for variance in the order, require students to come at an agreed-upon order. Then, beginning at the top of the decision flowchart, have a few groups present their questions, and the whole class choose the best wording for each question. The end result is a decision flowchart for quadrilaterals that may be displayed in class.</p><p>Have students individually identify an object in the classroom that is a quadrilateral. Then have them utilize the decision flowchart created by the class to decide what form of quadrilateral it is. Have them answer each question on the decision flowchart to establish the type of quadrilateral; students should note the questions and answers, as well as explanations of their answers when appropriate (e.g., "The blackboard is/is not a square because it lacks four congruent sides. Or the window or wall is a square since all four sides are congruent.").</p><p><strong>Extension:</strong></p><p>Suggest several different and more complex shapes, both two and three dimensions and ask students to identify some of their attributes.<br>Two-dimensional examples:</p><p>regular pentagon [five congruent sides, five congruent angles, five congruent diagonals]</p><p>Nonregular hexagon [six sides, six angles, eight diagonals]</p><p>Three-dimensional example:</p><p>triangular prism [five faces, six vertices, and two parallel faces]</p>