Riverside USD Scope and Sequence: 2.G.1 [2.6] Oklahoma Academic Standards Mathematics: 2.GM.1.1, 2.GM.1.4,

Transcription

1 1 U n t er r ich t splan Id entifying and Forg Polygons Altersgruppe: 2nd Grade Texas - TEKS: G2.8.GM.C, G3.6.GM.B Riverside USD Scope and Sequence: 2.G.1 [2.6] Oklahoma Academic Standards Mathematics: 2.GM.1.1, 2.GM.1.4, 2.N.2.6 Virginia - Mathematics Standards of Learning (2009): 1.12, 1.13, 2.16 Common Core: 2.G.A.1 Mathematics Florida Standards (MAFS): 2.G.1.1 Alaska: 2.G.1 Minnesota: , , Fairfax County Public Schools Program of Studies: 1.12.a.2, 1.12.a.3, 1.12.a.6, 1.13.a.1, 1.13.a.4, 2.16.a.5, 2.16.a.6 Nebraska Mathematics Standards: M A a, M A d South Carolina: 2.G.1, 3.G.1, 4.G.2 Indiana: 3.G.2, 4.G.5, 5.G.2 Georgia Standards of Excellence: M GSE 2.G.1 Virginia - Mathematics Standards of Learning (2016): 1.11.a Online-Ressourcen: Cut, P ast e and F i gure Opening Teacher present s Students pract ice Class discussion M at h Obj ect ives

2 2 P rac t i c e identifying a shape based on its attributes Learn to create a shape based on its attributes or its name De vel o p more comfort with identifying and composing shapes Ope ni ng 10 Prepare several cut-outs of differing sizes, colors, and styles for each of the following shapes: triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons. Examples of shapes of different styles for quadrilaterals are squares and rectangles. Additionally, you may wish to create some convex polygons and some concave polygons. You may decide not to call out the shapes as being convex or concave, but it is important not to limit the possibilities to only convex shapes. Essentially, the focus should be on attributes (the number of sides, angles, or vertices) that describe all shapes in a given category. Hold up each shape, one at a time, and ask the class: Does anyone know what kind of shape this is? As this may be the first time some of your students are classifying pentagons, hexagons, or octagons, be sure to follow each correct answer with a follow-up question. e.g., How do we know that this is a triangle? Try to coax responses that include some mention of traits, such as the number of edges. Be sure to note that color, size, and style have no bearing on

3 3 the deteration of the type of shape. Depending on the shape you show, you may get some more specific responses than intended at this moment. For example, if you show a rectangle, the general classification of quadrilateral is sufficient. If your students identify the shape as a rectangle, support this claim, then ask what kind of shape a rectangle is. You may wish to use a phrase such as family of shapes. e.g., a rectangle is in the quadrilateral family. Although counting the number of sides for each shape may be an easy process for your students to lean on, include some mention of vertices and angles (internal). For example, if your class correctly identifies a hexagon and gives the reason that it has 6 sides, continue by asking how many vertices that same shape has. Try to develop a connection between the number of vertices and the number of sides for polygons, so that your students expand their options for identifying shapes. Do the same with the number of angles. Now when your class identifies a shape and gives a reason, you can ask: How else could we know that this is a? Ideally, your class will start to use each attribute roughly equally. Once you feel your class can identify each type of shape based on its attributes, in general terms, move on to the episode for this lesson. T e ac he r prese nt s M at h game : Cut, P ast e and F i gure - P o l ygo ns f ro m T ri angl e s 8 Present Matific s episode Cut, P ast e and F i gure - P o l ygo ns f ro m T ri angl e s to the class, using the projector. The goal of this

4 4 episode is to compose triangles in order to form polygons with specified attributes. Each screen starts with only two items: triangles and glue. The triangles can be moved and rotated. When edges are aligned, the triangles can be glued together by dragging the glue to the shared edge. In the example above, the specified attribute for the final polygon is that it has 8 vertices. Ask your class to identify what type of shape will have 8 vertices. The edges of the triangles must be congruent in order to glue them together. Note that some edges will seem close, but the composite figure must be created from the given triangles and have smooth edges.

5 5 Above, the functionality for rotating is shown. Clicking on a shape will bring up the arrows, and subsequently dragging will rotate the shape about its center. If a shape is rotated near another shape, the shapes may be automatically aligned, provided the sides are very close to matching up. Continue to translate and rotate the triangles (and subsequent composite shapes), then glue the sides together. Gluing as you go may lose sight of the fact that all of the composite shapes originated from triangles; however, it does give you the chance to call out the different types of shapes (triangle, quadrilateral, pentagon, etc.). Below, the figure has been formed and glued as desired, yielding a polygon with 8 vertices. Note that this is a concave polygon, which is why having shapes of various styles was a key element of the opening. In the example below, 3 triangles were given. Composing 2 of those can form a quadrilateral (as desired), but the goal is to use all of the available triangles. Thus, this configuration is not sufficient. The third triangle must be included in the final composite shape. Again, be careful to orient this triangle correctly, as it is possible to simply form a larger triangle here.

6 6 Along the way, continue calling out shapes by their names. Also inquire about the attributes of the intermediate composite shapes you are forg. Even though a question may focus on vertices, include some mention of edges and angles. St ude nt s prac t i c e M at h game : Cut, P ast e and F i gure - P o l ygo ns f ro m T ri angl e s 10 Have the students play Cut, P ast e and F i gure - P o l ygo ns f ro m T ri angl e s their personal devices. Circulate, answering questions. Continue to encourage the unique strategies your students attempt to use, such as seeing if the largest simple shape will fit in the composite shape, then moving on to the next largest simple shape, and so on. Encourage the use of rotations. Your students may rule out a simple shape simply because it does not have the correct configuration at first.

7 7 Cl ass di sc ussi o n 12 Check in with your class to make sure they are confident in identifying polygons based on attributes. Have your class work in groups of 2 or 3. Your students will be drawing shapes based on either the name or a given attribute. Have one student draw at a time. The other student(s) should be checking the final shape and discussing whether the shape satisfies the given condition. Do a quick walk-around to check that the small groups are working together to decide if each shape is correct or if it needs revisions. Examples of the conditions for the shape that you can give to your students are: A pentagon A polygon with 6 edges A polygon with 4 angles Continue until each student has had a chance to draw a couple of times, and the class seems to have a firm grasp of drawing shapes based on the attribute or name given.