Madison Public Schools R.E.A.C.H/Gifted and Talented Unit Plan Title: Patterns and Symmetry in Geometric Shapes
Grade: 4
Content Area: STEM Objective: ​
As a means of enrichment, students will ● Build shapes, patterns, and tilings with the Zome System ● Analyze the properties of their shapes in terms of angles and parallel lines ● Analyze their shapes for the existence of reflectional, multiple reflectional and rotational symmetry Time Allotted:​
40 minute sessions once a week for 6 weeks; with the flexibility to extend to 8 weeks NAGC Standards: 1.7. Cognitive and Affective Growth. Students with gifts and talents recognize their preferred approaches to learning and expand their repertoire. 2.4. Learning Progress and Outcomes. Students with gifts and talents demonstrate advanced and complex learning as a result of using multiple, appropriate, and ongoing assessments. 3.4. Instructional Strategies. Students with gifts and talents become independent investigators. CCCS: CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.MATH.PRACTICE.MP4 Model with mathematics. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. CCSS.MATH.CONTENT.4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two‐dimensional figures. CCSS.MATH.CONTENT.4.G.A.2 Classify two‐dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. CCSS.MATH.CONTENT.4.G.A.3 Recognize a line of symmetry for a two‐dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line‐symmetric figures and draw lines of symmetry. Lessons Session 1: ​
Zometool Rules, basic vocabulary ● nomenclature: nodes, struts, ● if it works, it works perfectly ● don’t break it apart, take it apart ● do not crush models ● return parts to case precisely ● Dimensionality: face, edge, vertex, 0D, 1D, 2D, 3D, ie, point, line, polygon Session 2: ​
Angles: right, acute, obtuse ● What are the properties of these angles? How do we know? ● Which combination of struts and nodes create each of these angles? ● Why do you think that is? ● Build some polygons ‐ identify the angles in these shapes Session 3: ​
Lesson 3 Lines: Parallel, perpendicular, intersecting ● What are the properties of these types of lines? How do we know?
● Which combination of struts and nodes create each of these lines? ● Why do you think that is? ● Build some polygons ‐ identify the lines and angles in these shapes Session 4:​
Basic Shapes ● Build basic shapes: rectangles, triangles, pentagons, hexagons, octagons. ● What do you notice about their parts? How many nodes? How many struts? What shape is the hole facing up on the node? ● What struts do you need to build a right triangle? Why? ● Can you build a triangle using any combination of struts? why or why not? ● What patterns do you notice about these shapes and the Zomes needed to make them? Session 5:​
Reflection Symmetry, Multiple reflection symmetry, Rotational symmetry ● build the basic 2D Zome shapes: triangle, rectangle, pentagon, hexagon ● discuss the words symmetry and reflection ● identify lines of reflection symmetry for the shapes ● discuss rotational symmetry ● identify lines of rotational symmetry for the shapes by executing a ​
production ​
of the lines that make the sides of the shapes. Identify rotational symmetry in these new shapes Session 6:​
Plane patterns ● Discuss concepts: tessellation and tiling; discuss tilings of the ​
Alhambra​
, slideshow ​
here​
. ● discuss M C Escher; view slideshow ​
here ● Groups or individuals will build a “flat pattern” (all nodes touch the table), each formed from a tiling repetition of one of the basic shapes. ● Groups will examine each others’ tessellations for reflection Symmetry, multiple reflection symmetry, and rotational symmetry Resources/Helpful Links: ● Zome Materials: Zometool Kit Lesson Extensions/ Presentation Options: ● Extend tiling patterns; create more complex tilings ● investigate M C Escher, start ​
here​
, o ​
Escher, tilings and geometry,​
​
here​
.