Students will use quadrilateral Shape Makers in a Geometer's Sketchpad file in order to determine the different types of quadrilaterals they can make. They conclude by formulating the rules that each of the various Shape Makers follow. These activities help students refine their visual knowledge of various types of quadrilaterals, laying the foundation for their formulation of property-based knowledge of the shapes.
- Computers with Geometer's Sketchpad program
- Shape Makers Sketchpad file :
shapemakers.gsp (15.4 KB)
One computer classroom, classroom lab
Students can work individually or in groups of 2 or 3.
Standards / Connections:
- Correlation - EM 5.10
- NJ CCCS: Mathematics- 4.2A, 4.2E, 4.5A, and 4.5F
- NCTM Standard 12
Setting the Stage
- Begin by asking the students what the different types of quadrilaterals are.
If necessary, you may need to review types of quadrilaterals as
described in the Learn More
section of this activity.
- It could be helpful to have the quadrilateral flowchart drawn on the board, on the projector, TVator, or as a separate handout so the students can visually understand the relationships between the different types of quadrilaterals.
- Then, you should follow-up with the
following lead-in question:
- Can you determine which type of Shape Makers they are?
- Is there a strategy that works all the time?
Procedure (Doing the Activity)
- Print and distribute the Activity page.
- Open the
shapemaker.gsp Geometer's Sketchpad file on a projector or overhead and
draw their attention to the seven "squares" on the screen.
Remind them that they may "look" like squares but they are all different types of Shape Makers.
- For example, the parallelogram Shape Maker can take the shape of a square. This would be a good opportunity to ask the students if they can figure out why and check for their understanding of the over concepts of this unit.
- Bring the first Shape Maker, labelled A, to the white space and demonstrate how to click on and drag the four corners of the Shape Maker as indicated in the worksheet. End by guiding the students to the conclusion that the first Shape Maker is a Parallelogram Shape Maker.
- Scan around the room as the students enter their reasoning to the first Shape Maker into the table on their activity sheet.
- Identify any student who may not have understood the directions or didn't arrive at the conclusion with the rest of the class and take a couple of minutes to bring him/her up to speed.
- Ask the students either individually or in groups to complete
instructions and repeat the process to the rest of the Shape Makers and enter their findings onto the table.
- Once students have completed the
table they should respond to the question "What's the name of the Shape Makers? Why? "
individually and explain their answers. Time permitting, it is
recommended to have a class discussion about these questions after
students have been provided with sufficient time to complete their
This activity can be challenging for students who have never used the Geometer's Sketchpad program before and are not familiar with its tools and features. It is recommended that students receive instructions on using this program and become familiar with it prior to doing this activity.
After students have completed the shapemakers.gsp activity, ask
the students to print-out copies and hand in their sketches with the
shape makers correctly identified and expplained on their handout to serve as an assessment.
It is important for you to use, and encourage students to use, clear and precise language; otherwise, the resulting conceptual confusion will inhibit learning. In particular, it is especially important to use language that distinguishes between shapes and Shape Makers. For instance, one student who confused the Shape Makers with the shapes they make would say, "You can make rectangles into squares, but you can't make squares into rectangles." More accurately, this statement would be, "You can make the Rectangle Maker into a square, but you can't make the Square Maker into a rectangle." The term rectangle should be used to refer to a specific type of shape; the term Rectangle Maker should be used to refer to the dynamic computer object that can be used to make rectangular shapes on the screen. An analogy might be useful here. A piece of wire can be used to make various rectangular shapes. The Rectangle Maker, like the wire, is the thing used to make particular rectangles. The Rectangle Maker, like the wire, is not a rectangle; it can simply take on various rectangular shapes.
The precise language will help students eventually (after many explorations) develop clear distinctions between three related but distinct concepts. First, there are sets or classes of shapes - for example, the set of all rectangles. Second, there are Shape Makers for sets of shapes - for example, the Rectangle Maker. Third, there are examples of sets of shapes - for example, particular drawings of rectangles. These three concepts are related in important ways. Because the Rectangle Maker can make all examples of rectangles and can make only rectangles, a shape is a rectangle if and only if it can be made by the Rectangle Maker (within screen limitations). Students who distinguish between and properly relate examples, sets, and Shape Makers develop more powerful reasoning.
Thus, in addition to promoting clear communication, forcing students to distinguish between the terms they use for shapes and Shape Makers will regularly focus their attention on the conceptual differences between the two. Whether or not they completely understand this conceptual distinction at first, the regular attention to linguistic distinction will help students eventually come to a clear understanding fo these related concepts.
Extensions & Additional Activities