**Geometry Tools: Geoboards**

Instructions

Set expectations for students before handing out geo-boards. The rubber bands will only be used to create shapes on the geo-boards. Do not over stretch the rubber bands because they could snap and cause injury. Please wait for further directions on what we will be doing for the specific activity. You will use geoboards by extending rubber bands over pegs to create shapes. Hand geo-boards and rubber bands out to students.

Adaptations

Some students may have difficulty using his or her fine motor skills and this would make using the geoboards more complicated. We thought about providing those students with thin strips of paper in place of using rubber-bands to create shapes on geoboards. This will allow those students to still participate in the activity with the class.

Standards

Topic: Geometry

Grades: 2,3, & 6

Standards:

CCSS.Math.Content.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.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

CCSS.Math.Content.3.G.A.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

CCSS.Math.Content.6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Other Uses

Along with using geoboards in a whole-class setting, they can also be used during centers. In centers, students can complete a specific geoboard activity.

Geoboards can be used to help teach students about fractions, symmetry, and shape identification.

Second Grade

Standard:CCSS.Math.Content.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.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Objective: After students listen to the teacher’s instructions, students will be able to identify different shapes by their attributes.

Lesson Activity

Teacher will be at the front of the class describing shape attributes. Based on the descriptions given by their teacher, students will be able to make the shape on their geo-boards and be able to able to name the shape they have created. (e.g., this shape has 6 sides. Students should construct a hexagon. After the teacher will ask the students to raise their hand to identify the shape they created.)

Third Grade

Standard: CCSS.Math.Content.3.G.A.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Objective: Using the area of the geoboard, students will be able to partition the area into various fractions, showing understanding of splitting an area into equal parts (ex: half, fourths, sixths).

Lesson Activity

Teacher will begin by expressing her expectations to the students, describing how geoboards are to be used and the directions for the day’s activity. This will be a problem-based activity, requiring little step-by-step directions for students. Students will begin by finding a way to split the area of the geoboard into two equal parts. The teacher will ask students to hold up their geoboards, looking at the various ways students will have split his or her board into two equal parts (there will be three common answers). Students will continue to come up with various ways to split the area in half, documenting their findings on dot paper. Do we count the area by pegs in each area of by the number of squares (prompt students with this question)? As students continue to work, walk around assessing students. If students have grasped how to split the area into halves, see if they can move on and figure out how to split into thirds, fourths, etc. If students are struggling understanding the area is counted by the number of squares within each side, work with students individually, showing a figure where the number of pegs are equal on each side but have a different squares area. Share the students findings at the end of the lesson, showing different boards representing half, thirds, fourths, etc.

Sixth Grade

Standard: CCSS.Math.Content.6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Objective: After students listen to the teacher’s instructions, students will be able to find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles.

Lesson Activity

The teacher will be at the front of the classroom and will review with the students how to find the area of a triangle, parallelogram, and a rectangle. The teacher will explain that today they will be learning how to find the area of different polygons by composing them or decomposing them into triangles, rectangles, and parallelograms. Then the teacher will set expectations for what the students are supposed to do with their geo boards before passing them out. Following this the teacher will give students an example polygon on her geo board, and have the students make the same polygon on their own geo boards. The teacher makes sure that every student’s polygon is the same size as hers on their geo boards. After that the teacher will either tell the students to make the polygon into a rectangle or parallelogram using another rubber band. Or she will instruct them to break the polygon down into triangles using other rubber bands. (e.g., Students construct a trapezoid on their geo boards. Next the teacher will have students construct another trapezoid to make the polygon into a rectangle. Once students find the rectangle’s area make sure they divide the answer by two in order to get the original trapezoid’s area.)

Limitations for Geoboards

When finding area with a geoboard, you are unable to measure large amounts of area. The geoboard we are using only allows for small scaled shapes or arrangements. Also, rubber bands are physically unable to stretch beyond these smaller limits. As problems with area arise, another method could be using an electronic geoboard. This will prevent students from having to worry about rubber bands breaking. They will also be able to work with larger areas. An example of a website that has an electronic geoboard is: http://www.mathplayground.com/geoboard.html

Whole Class Limitations

Watching/observing everyone

Monitoring students

Keeping all students on task

Engagement Comparison

In Howard Gardner's Multiple Intelligences he discusses different ways students learn. One of the Multiple Intelligences is bodily kinesthetic; which is learning by participating in hands-on activities. Geoboards allows students to physically create shapes without using the traditional paper and pencil method. Using dot paper is a traditional way to teach students about area and shapes, but does not allow for physical manipulation. Geoboards creates a memorable geometric experience. As a group, we all remember using geoboards in elementary school and get excited when given the opportunity to use them.

**Authors:**

Mary Ann Ray

Catherine Ray

Dana Keister

Geoboard