Geometry Manipulative Elementary Geometry Manipulative

Geometry Manipulative

Elementary Geometry Manipulative

Introducing complex math problems can be difficult to introduce to elementary students. Yet, there are many patterns within mathematics that, if explained properly, can be learned by young eager minds. Thus, it is with this in mind that this geometry lesson aims to teach angle relationships to fifth graders.

The math level being explored is that of the fifth grade. This is an old enough age to begin implementing algebraic and geometrical conceits within the curriculum. Within this grade level, there are three major standards presented by the National Council of Teachers of Mathematics (NCTM): multiplicative thinking, equivalence, and computational fluency, (National Council of Teachers of Mathematics 1989). Thus, it is a perfect age for the beginning basics of geometry. Understanding the formula for finding missing degrees of angles seems very simple but needs a clear and concise explanation. Therefore, within this lesson plan, the concept of angles, degrees, and the relationships between parallel lines and their corresponding angles will be introduced alongside the corresponding algebraic strategy for finding missing variables. In working with the unknown variable, x in most cases, students begin to understand equivalence by using x as a factor which completes a specific sequence. For example, it is clear within angles that if you know one degree within a split sector, you can find the other with the knowledge that the two equal 180 degrees. Thus, the known degree plus the unknown (x) will equal 180 degrees. This concept will satisfy the beginning workings of multiplicative thinking, equivalence, and computational fluency. In order for students to grasp this concept they will need to work with the provided handout and their pencils.

After practice with this hand out, students should be able to grasp the geometrical concepts of degree relationships and adjacent angles. This will not only introduce elementary students to geometry, but also begin the complicated thinking associated with algebraic concepts. Using the formula to plug in the known degrees and then find the x is the beginning of much more abstract algebraic thinking.

Handout

Circles rule our lives and have rules of their own! Each circle measures to 350 degrees, and with this knowledge we can begin to find unknown angles!

If a circle measures 360, that means that a half circle measures half -- 180 degrees. In a half circle, there are many different angle combinations. But, we know that they all equal out to 180 degrees.

Knowing this, we can find the great unknown!

Well, we know that the total of the two angles equals 180 degrees. Therefore, angle 1 = angle 2 = 180 degrees.

Let's just plug the numbers into the equation.

63 + x = 180.

The first step is to isolate the variable, in this case the x. We do this by getting rid of the 63 on the left side of the equal sign. How? Well 63 is a positive number, so the equation really reads