Geometry Curriculum Track

In the fifth grade lessons, students are introduced to the coordinate plane, learn how to graph points in the first quadrant, and identify the coordinates of graphed points. They solve both real-world and mathematical problems by graphing points and interpreting the coordinates of points in context. They further refine their understanding of the relationships among the shape categories encountered throughout the K – 4 geometry lessons and create a complex classification of two-dimensional shapes using Venn diagrams.

Students are introduced to the basic structure of the coordinate plane and how it can be used to describe the location of points. They apply their understanding by graphing points given their coordinates and by describing the coordinates of graphed points.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.A.1
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP6

MyStemKits 3D Kits Used

  • Graphing Kit (optional)

Students apply their understanding of graphing on the coordinate plane. They will practice graphing points given the coordinates and describe the polygons created by connecting the points.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.A.1
  • CCSS.MATH.CONTENT.5.G.B.3
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP6

MyStemKits 3D Kits Used

  • Basic Shapes: Polygons
  • Basic Shapes: Quadrilaterals
  • Basic Shapes: Triangles
  • Loaded Dice (optional)

Students are introduced to two-variable data that can be graphed in the first quadrant of the coordinate plane. They collect, graph, and interpret data in context.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.A.2
  • CCSS.MATH.CONTENT.5.OA.B.3
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP4

MyStemKits 3D Kits Used

  • Bowling (optional)
  • Loaded Dice (optional)

Students are introduced to Venn and Euler diagrams as a means of displaying the relationships among sets of objects. They both construct and interpret Venn diagrams to show the relationships among real-world sets, sets of numbers, and sets of shapes.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.B.3
  • CCSS.MATH.CONTENT.5.G.B.4
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP7

MyStemKits 3D Kits Used

  • Basic Shapes: Circles
  • Basic Shapes: Polygons
  • Basic Shapes: Quadrilaterals
  • Basic Shapes: Triangles
  • Basic Shapes: Right Solids

Students review the angle types and triangle classifications. Then they use Venn diagrams to show the relationships among the sets of scalene, isosceles, equilateral, acute, right, obtuse, and equiangular triangles.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.B.3
  • CCSS.MATH.CONTENT.5.G.B.4
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP6

MyStemKits 3D Kits Used

  • Angle Tester
  • Basic Shapes: Triangles
  • Composing Polygons (optional)
  • Geometry Sticks: Customary (optional)
  • Geometry Sticks: Metric (optional)

Students review the defining attributes of the special quadrilaterals (parallelograms, trapezoids, kites, rectangles, rhombuses, and squares). Then they use Venn diagrams to show the relationships among these sets.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.B.3
  • CCSS.MATH.CONTENT.5.G.B.4
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP6

MyStemKits 3D Kits Used

  • Basic Shapes: Quadrilaterals

Students use the coordinate plane and polygons to create designs to reinforce graphing on the coordinate plane.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.A.1
  • CCSS.MATH.CONTENT.5.G.B.3
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP6

MyStemKits 3D Kits Used

  • Basic Shapes: Polygons
  • Basic Shapes: Quadrilaterals
  • Basic Shapes: Triangles
  • Decomposing Shapes
  • Tangram

Students use the coordinate plane and their knowledge of polygon attributes to engineer a map of a city that adheres to certain criteria.

Standards Addressed

  • CCSS.MATH.CONTENT.5.G.A.1
  • CCSS.MATH.CONTENT.5.G.B.3
  • CCSS.MATH.PRACTICE.MP2
  • CCSS.MATH.PRACTICE.MP6

MyStemKits 3D Kits Used

  • City Engineering

References
Clements, D. H. and Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, New York: Routledge.
National Governors Association Center for Best Practices, Council of Chief State School Officers Title: Common Core State Standards (Mathematics) Publisher: National Governors Association Center for Best Practices, Council of Chief State School Officers, Washington D.C. Copyright Date: 2010.

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