1. Using Geoboards

2. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). This entire cluster asks students to understand that certain attributes define what a shape is called (number of sides, number of angles, etc.) and other attributes do not (color, size, orientation). Using geometric attributes, the student identifies and describes squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres. Throughout the year, Kindergarten students move from informal language to describe what shapes look like (e.g., “That looks like an ice cream cone!”) to more formal mathematical language (e.g., “That is a triangle. All of its sides are the same length”).

3.  Create a rectangle. If I turn my geoboard, will my rectangle look like your rectangle?  Create a square. If I turn my geoboard, will my square look like your square?  Create a triangle. If I turn my geoboard, will my triangle look like your triangle? K.G.2 Correctly name shapes regardless of their orientations or overall size. K.G.3 Identify shapes as two dimensional (lying in a plane, “flat”) or three dimensional (“solid”).

4.  Draw a triangle, square, and a rectangle.  Now, look at your partner’s 3 flat shapes.  What do you notice? What looks the same? What looks different? K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).

5. Reason with shapes and their attributes. Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: attribute, feature angle, side, triangle, quadrilateral, square, rectangle, trapezoid, pentagon, hexagon, cube, face, edge, vertex, surface, figure, shape, closed, open, partition, equal size, equal shares, half, halves, thirds, half of, a third of, whole, two halves, three thirds, four fourths, partition, rows, columns.

6. Common Core StandardUnpacking 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Second Grade students identify (recognize and name) shapes and draw shapes based on a given set of attributes. These include triangles, quadrilaterals (squares, rectangles, and trapezoids), pentagons, hexagons and cubes. Example: Teacher: Draw a closed shape that has five sides. What is the name of the shape? Student: I drew a shape with 5 sides. It is called a pentagon. Example: Teacher: I have 3 sides and 3 angles. What am I? Student: A triangle. See, 3 sides, 3 angles.

7. Common Core StandardUnpacking 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. 2 nd grade students partition circles and rectangles into 2, 3 or 4 equal shares (regions). Students should be given ample experiences to explore this concept with paper strips and pictorial representations. Students should also work with the vocabulary terms halves, thirds, half of, third of, and fourth (or quarter) of. While students are working on this standard, teachers should help them to make the connection that a “whole” is composed of two halves, three thirds, or four fourths. This standard also addresses the idea that equal shares of identical wholes may not have the same shape. Example: Teacher: Partition each rectangle into fourths a different way. Student A: I partitioned this rectangle 3 different ways. I folded or cut the paper to make sure that all of the parts were the same size.

8.  Teacher: In your 3 pictures, how do you know that each part is a fourth?  Student: There are four equal parts. Therefore, each part is one-fourth of the whole piece of paper.  NOTE: It is important for students to understand that fractional parts may not be symmetrical. The only criteria for equivalent fractions is that the area is equal, as illustrated in the first example above.

9.  Example: How many different ways can you partition this 4 by 4 geoboard into fourths?

10.  Student A: I partitioned the geoboard into four equal sized squares.  Teacher: How do you know that each section is a fourth?  Student A: Because there are four equal sized squares. That means that each piece is a fourth of the whole geoboard.  Student B: I partitioned the geoboard in half down the middle. The section on the left I divided into two equal sized squares. The other section I partitioned into two equal sized triangles.  Teacher: How do you know that each section is a fourth?  Student B: Each section is a half of a half, which is the same as a fourth.

11. Common Core StandardUnpacking 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. In second grade, students identify and draw triangles, quadrilaterals, pentagons, and hexagons. Third graders build on this experience and further investigate quadrilaterals (technology may be used during this exploration). Students recognize shapes that are and are not quadrilaterals by examining the properties of the geometric figures. They conceptualize that a quadrilateral must be a closed figure with four straight sides and begin to notice characteristics of the angles and the relationship between opposite sides. Students should be encouraged to provide details and use proper vocabulary when describing the properties of quadrilaterals. They sort geometric figures and identify squares, rectangles, and rhombuses as quadrilaterals.

12. Parallelograms include: squares, rectangles, rhombi, or other shapes that have two pairs of parallel sides. Also, the broad category quadrilaterals include all types of parallelograms, trapezoids and other four-sided figures. Example: Draw a picture of a quadrilateral. Draw a picture of a rhombus. How are they alike? How are they different? Is a quadrilateral a rhombus? Is a rhombus a quadrilateral? Justify your thinking. A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are beside each other.