Lesson Plan Week 2 Patterns and Blocks

Building Congruent Hexagons

NJCCS
4.2.4 A Geometric Properties Grade 4
3. Identify and describe relationships among two-dimensional shapes: congruence.

Entry Skills:
For successful adaptation of this lesson, students should be familiar with the properties of and be able to identify the following geometric shapes: triangle, rhombus, hexagon, parallelogram, square and trapezoid.

Strategies Utilized for Achieving Objectives
• Direct Instruction
• Modeling
• Guided Practice
• Independent Practice
• Cooperative Learning

Materials: paper, pen/pencil, pattern blocks comprised of the following geometric shapes (triangle, rhombus, hexagon, parallelogram, square and trapezoid)


Introduction:
Students will be provided a bag of pattern blocks. Each student will be instructed to pull out a red trapezoid and come up with any arrangement of shapes that can be placed on top of and match that of the red trapezoid. (Only 2 possibilities exist—three green triangles and a combination of 1 blue rhombus and 1 green triangle). The concept of congruency will be discussed and defined as constructions of figures that have the same size and shape.

Procedure:
Students will now be instructed to pair up with another student or work independently if they choose on the following activity. The teacher will instruct students to pull out a yellow hexagon from their bag of pattern blocks. Using the introductory example to illustrate how various combinations of shapes can be constructed to match an original shape, students will be asked to find how many combinations can be made to match that of a yellow hexagon. (No two combinations can be repeated even though through rotation, the combinations visually look like a different solution). Students will also be instructed to write down their figure combinations on paper for a later class discussion. Approximately 15 minutes will be allowed for this exercise as the teacher walks around the room monitoring each group or individual student.


Follow Up Discussion:
A group discussion will occur following the 15 minute exercise. Students will be asked to verbalize their solutions as well as how they came to these conclusions. Solutions will be written on the board as students verbalize these.

Assessment:
Assessment and understanding will be based on participation in the activity and class discussion. The class discussion will focus in part on the thought process utilized by the students in this exercise and how conclusions were reached.

Problem Solving Strategies:
Some common thought patterns include equivalency and substitution, where students will replace objects within their pattern solution with another (for example recognizing two triangles are the equivalent of one rhombus). Elimination will be another cognitive process and problem solving strategy of focus in this lesson, as students will learn through experimentation which shape(s) cannot be utilized to construct a congruent hexagon. Additionally, some students may use a chart/table to construct all the combinations already used to avoid duplication of patterns.

Future Implications:
This lesson can be used as a lead in for future lessons on fractions. For example, students can see both visually and in a tactile manner that six triangles make up one whole hexagon, illustrating recognition one piece represents 1/6 of another. Additionally, in comparing geometric pieces to each other, students can see how a triangle (1/6 of a hexagon) compares in size to a trapezoid (1/2 of a hexagon). Finally, students can see how various fractional pieces can be added to the equivalent of a whole number (three triangles at 1/6 each plus 1 trapezoid at 1/2 equals 1 whole number).