Ohio Resource Center
Lessons
How Do You Build Triangles?
Discipline
Mathematics
Kindergarten, 1, 2
Professional Commentary

In this lesson, students use pattern block cutouts to form triangles in a variety of ways. An applet, activity sheet, and possible solutions are included. This lesson is adapted from an article that appeared in the November 1993 issue of Arithmetic Teacher. (sw/jk)

Common Core State Standards for Mathematics
Kindergarten
Geometry
Analyze, compare, create, and compose shapes.
K.G.B.5
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).
K.G.B.6
Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”
Geometry
Reason with shapes and their attributes.
1.G.A.1
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
1.G.A.2
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Geometry
Reason with shapes and their attributes.
2.G.A.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.
Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (K–2)
A.
Describe and create plane figures: circle, rectangle, square, triangle, hexagon, trapezoid, parallelogram and rhombus, and identify them in the environment.
Benchmarks (3–4)
A.
Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects.
E.
Use attributes to describe, classify and sketch plane figures and build solid objects.
1.
Identify and sort two-dimensional shapes and three-dimensional objects. For example: a. Identify and describe two-dimensional figures and three-dimensional objects from the environment using the child's own vocabulary. b. Sort shapes and objects into groups based on student-defined categories. c. Select all shapes or objects of one type from a group. d. Build two-dimensional figures using paper shapes or tangrams; build simple three-dimensional objects using blocks.
1.
Identify, compare, and sort two-dimensional shapes; i.e., square, circle, ellipse, triangle, rectangle, rhombus, trapezoid, parallelogram, pentagon, and hexagon. For example: a. Recognize and identify triangles and rhombuses independent of position, shape or size; and b. Describe two-dimensional shapes using attributes such as number of sides and number of vertices (corners, or angles).
2.
Create new shapes by combining or cutting apart existing shapes.
2.
Predict what new shapes will be formed by combining or cutting apart existing shapes.
1.
Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face.
2.
Describe, classify, compare and model two- and three-dimensional objects using their attributes.
Principles and Standards for School Mathematics
Geometry Standard
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
Expectations (Pre-K–2)
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
Expectations (3–5)
identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;
classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;
investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
Use visualization, spatial reasoning, and geometric modeling to solve problems
Expectations (Pre-K–2)
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
Expectations (3–5)
identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;
classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids;
investigate, describe, and reason about the results of subdividing, combining, and transforming shapes;
build and draw geometric objects;