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Shape Mix Up! In this lesson, students explore classifying quadrilaterals into different categories. They also plot the shapes on x and y coordinate grids. NC Mathematics Standard(s):GeometryPrior knowledge (4th grade): NC.4.G.1 - Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. NC.4.G.2 - Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines.NC.4.G.3 - Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry.NC.5.G.3 - Classify quadrilaterals into categories based on their properties.Explain that attributes belonging to a category of quadrilaterals also belong to all sub-categories of that category.Classify quadrilaterals in a hierarchy based on properties. Additional/Supporting Standards:NC.5.G.1 - Graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems.Standards for Mathematical Practice:Math Practice 6: Attend to precisionStudents label the axis of the line graph correctly. Students carefully create the polygons on the grid paper. Students will identify the coordinates for the vertices of each shape. Math Practice 7: Look for and make use of StructureStudents will correctly sort the polygons by their attributes. The students will then use the grid paper to represent the different polygons and identify the coordinates for the shape. Student Outcomes: I can classify quadrilaterals into categories based on their properties.I can graph points in the first quadrant of a coordinate plane, and identify and interpret the x and y coordinates to solve problems. Math Language:What words or phrases do I expect students to talk about during this lesson? Polygon, quadrilateral, square, parallelogram, trapezoid, polygon, rhombus/rhombi, rectangle, triangle, pentagon, hexagon, cube, half/quarter circle, circle, coordinate system, coordinate plane, first quadrant, points, lines, axis/axes, x-axis, y-axis, horizontal, vertical, intersection of lines, origin, ordered pairs, coordinates, x-coordinate, y-coordinateMaterials: For each team of 2:Activity sheets for each lessonGraph paperShape cut outs ( Note the shape set mentioned in this lesson has triangles. Students will recognize that triangles are not quadrilaterals and therefore they are not parallelograms. Feel free to use another set of shapes if you wish.)Advance Preparation: Provide images of shapes for each pair of students Provide graph paper for use of graphing polygonsLaunch:Introduction of Activity/Activate Prior knowledge of Shapes - 10 minutes Prior knowledge (4th grade): NC.4.G.1 - Draw and identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. NC.4.G.2 - Classify quadrilaterals and triangles based on angle measure, side lengths, and the presence or absence of parallel or perpendicular lines.NC.4.G.3 - Recognize symmetry in a two-dimensional figure, and identify and draw lines of symmetry.Say: In previous grades, you have been able to classify shapes based on angle measure, side lengths, and the presence of parallel or perpendicular lines. Let’s review some shape attributes that we learned from last year. Create a Venn diagram or other chart to show what the students remember. Ex. Venn Diagram below from 4th grade unpacking.(Consider including images of shapes from previous year, as well as parallel and perpendicular lines.) Say: Today we are going to further explore the attributes (properties) of shapes. I want you to focus on different groups of shapes and why some shapes may fit into more than one category.Explore:Activity 1: Sorting Shapes by Attributes- 20-30 minutesIntroduce the Task Say: Today we are going to work in partners and sort polygons based on their attributes. While sorting your polygons be sure to discuss with your partner the attributes you are sorting by and the reasoning behind your choices. (Make sure that your students know what vertices are before starting this explore activity.)Distribute the Activity Sheets for Activity 1 and Blackline Masters. Say: Once you and your partner have finished, switch seats with another group and check their shape sorts.Questions for Teacher to Pose while walking around during partner work: What attributes help you identify a quadrilateral? (A polygon with 4 sides.)What types of quadrilaterals are parallelograms? How do you know? (Parallelograms are polygons with two pairs of parallel sides. The opposite or facing sides are of equal length and opposite angles are of equal measure. )What types of quadrilaterals have 4 right angles? ( Squares and rectangles)Can a square be a rectangle? Can a rectangle be a square? (All rectangles are not squares. A rectangle is a quadrilateral with four right angles; it is equiangular. A square is a rectangle, which has four equal sides; a square is both equiangular and equilateral.)Is a trapezoid a quadrilateral? Is it a parallelogram? Why or why not? ( A trapezoid has four sides, so it is a quadrilateral, but only one set of parallel sides so it is not a parallelogram.)What do you notice about these two shapes? How are they similar? How are they different? Solutions may vary depending on the shapes chosen by each set of partners. Teacher Support:Properties of QuadrilateralsIrregular PolygonsDiscussion Questions: (Wrap up)What are some challenges you faced during this task? Identifying shapes with double parallel lines, right angles, and deciding if some shapes could be in more than one category. What were some similarities and differences between the shapes in this activity?Shapes have parallel lines and perpendicular lines.Is there a specific shape that you struggled with placing in the correct category? Why do you think you struggled with it? A square can be classified as a rectangle, but not all rectangles are squares.Note the hierarchy for classifying quadrilaterals from the NCDPI Unpacking DocumentActivity 2: Creating Coordinate Grids of Polygons- 30 minutes Say: (Bring the class back together) Now that you have sorted the polygons by their attributes, you will work with your partner and use graph paper to plot your shapes and identify coordinates for vertices of each shape. Say: You will create a graph with an (x,y) axis on the graph paper provided. You will choose which 3 different shapes, and then create all 3 shapes on the sheet of graph paper. After you have them placed where you want, you will record the coordinates of the vertices of each shape. (Depending on students’ familiarity with using coordinate grids, you may wish to create the grid together or provide a grid. Say: After you have plotted the shapes and identified the coordinates for each, you will give the coordinates of the different shapes to another set of partners. The new partner group will plot the coordinates you have given them on a different (x,y) axis sheet. Once they have plotted all points, they will connect the coordinates in the order they were plotted and identify the names of the different shapes. Discussion Questions: (Wrap up)What attributes did you have to consider as you drew each shape? Were there some shapes that were more challenging to create on the grid? Why might that be? Once the shapes were drawn using the given coordinates, were you able to correctly identify the shapes? What did you notice about the coordinates of the different shapes? Were the attributes of the different shapes useful in helping you identify the names of the shapes? Evaluation of Student UnderstandingInformal Evaluation: Use questions such as the ones suggested in the Explore portion to informally evaluate student understanding of the hierarchy of shapes.Meeting the Needs of the Range of LearnersIntervention: In Activity Two there are two graphs provided in the Activity Sheets to offer to students for differentiated instruction. Extensions: During Activity 2, some students can attempt to actually draw the shapes instead of using the shape cut outs. Possible Misconceptions/Suggestions:Possible MisconceptionsSuggestions1. Students label the line graph incorrectly (the x-axis and y-axis).2. It doesn’t matter which coordinate comes first.3. A rhombus is a square.4. A parallelogram is a rectangle.5. A rectangle is a square.1. Provide a graph with the (x,y) axis labeled. 2. Showing examples of other grids and coordinates. Give an example (x,y).3. This is sometimes true. It is true when a rhombus has 4 right angles. It is not true when a rhombus does not have any right angles.4. This is sometimes true. It is true when the parallelogram has 4 right angles. It is not true when a parallelogram has no right angles.5. A square can be classified as a rectangle, but not all rectangles are squares. Activity Sheet Activity #1: Sort HeadingsParallelogramsSquareTrapezoidRhombusNot ParallelogramsQuadrilateralsRectanglePolygons Activity #1: Resources ContinuedThis link will allow you to download the Blackline Masters You will need: Assorted Shapes #45, #46Activity #2: Graph Paper ................
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