Predicting Pattern Blocks on and off the Computer

Article excerpt

If used properly, manipulatives can support the learning of mathematics and motivate students. The intelligent use of manipulatives takes advantage of their features, especially the extra features of computer manipulatives (Clements and McMillen 1996). The use of manipulatives must be integrated into a sound mathematical lesson. In this article, we present one example of an activity that capitalizes on the particular advantages of physical and computer pattern blocks.

Predict and Cover

Goals of Predict and Cover

The activity titled Predict and Cover challenges primary-grades students to predict how many smaller pattern blocks will be needed to cover a larger pattern block (Akers et al. 1997). In so doing, children engage in the mathematical tasks of--

* identifying and describing two-dimensional shapes, focusing on the top face of the physical pattern block;

* fitting shapes together to cover a region and putting parts together to form a whole; and

* using known relationships to make predictions.

Children not only learn about geometric shapes but acquire important foundations of area and part-part-whole relationships, fundamentals that are crucial for learning and understanding both whole-number and fraction concepts. The following sections describe the Predict and Cover activity. Throughout this activity, we refer to the pattern blocks by the shape of their top faces. The pattern blocks are three-dimensional pieces--prisms--but we will focus on the shape of their bases. Thus, we refer to the green block, for example, as a "green triangle."

Free exploration

If your students have not explored relationships among pattern blocks, encourage them to make some pattern-block shapes by putting other blocks together. For example, have them study the red trapezoid and make it using other blocks.

As students make some blocks out of others, observe their work. Do they try to find several ways to cover a pattern block? In a follow-up discussion, share and record all the ways that they found.

Introduce Predict and Cover

Challenge students to use the relationships that they have explored to predict how many blocks will be needed to cover specific shapes. For example, show them an outline and ask what pattern block they could use to fill it in (see fig. 1). Students may suggest using the blue rhombus. Ask them to predict how many rhombuses would be needed to cover the whole figure. Then ask them to cover the figure and check their prediction.

Next, ask how many green triangles would be needed to cover the same figure. Some students may need to visualize each triangle and then count them. Others may be able to use the relationships between rhombuses and triangles to figure out how many triangles cover the shape. These students can imagine two green triangles in each rhombus. Still other students may analyze the numerical relationships; if nine rhombuses are needed, then eighteen triangles will be required.

Ask students to complete an activity sheet with several outlines. Emphasize the importance of recording the predictions. For some children, these predictions might be exact calculations; for others, estimates. You should accept both versions. As students work, watch what blocks they use and in what order. After covering the figure with one block, do they use this information to predict the number for a different block?

To help those students having difficulty, suggest that they move their larger-block covering to the side as they try to cover the figure with a smaller block. When they have covered about half the figure with the smaller block, ask them to predict how many blocks will cover the entire shape. Some students may benefit from "drawing in" the shapes to see how many will fit. Again, ask the class to discuss what they saw and how they solved the predict-and-cover problems.

Predict and Cover on the computer

After these experiences, have students explore similar predict-and-cover problems on the computer. …