3 Dot Md Dot 6 More Ideas From Vdw

Ideas Inspired by Teaching Student-Centered Mathematics

Rectangle Compare - Square Units (K-3, p.237): Students are given a pair of rectangles that are either the same or very close in area. They are also given a model or drawing of a single square unit and an appropriate ruler. (The units can be either centimeters or inches, and the ruler should clearly measure the appropriate unit. Students must be familiar with rulers.) The students are not permitted to cut out the rectangles or even draw on them. The task is to use their rulers to determine, in any way that they can, which rectangle is larger or whether they are the same. They should use words, drawings, and numbers to explain their conclusions. Some suggested pairs are as follows:

4 x 10, 5 x 8, 5 x 10, 7 x 7, 4 x 6, 5 x 5

Students need experiences counting the inside squares of figures. (Note: They do not need to know the formula for area – this will not help them understand the meaning of area.) Give students index cards or color tiles and ask them to find the area of objects in the classroom. They should cover the objects and count the number of cards or tiles.

Using twelve color tiles, how many different rectangles can you make? This helps children see that different figures can have the same area.
Ask the students to make figures on a geoboard or grid paper for a given area. Talk about how different figures can have the same area.
Find some things or objects in the classroom that have a greater area than your desk. Explain how you know.
Find some things or objects in the classroom that have a smaller area than your desk. Explain your thinking

Problem Solving
Give students color tiles and ask them to find the area of objects in the classroom, such as a book. They should estimate how many tiles are needed to cover the object and then cover the object and count the number of tiles used.

To help children see that different figures can have the same area, ask them to use twelve color tiles to see how many different rectangles they can make.

Ask students to draw a shape on their 2 cm grid paper that has an area of 18. Have students compare their figure with another figure and describe how the figures are different. Repeat this process with a different area such as 24 or 36.

Match My Area
Assign students into pairs.Distribute centimeter grid paper to each student. One student outlines or shades in a simple shape (without showing the partner) and tells the other student the area of that shape. The other student then creates a figure with the same area. The students then show each other their shapes to check that the areas match. A bonus point may be given if the students have matching figures in addition to matching areas.

Growing Area
Select a number of color tiles to give each student. Ask students to create a design with the smallest area. Ask students to create a design with the largest area. Another variation would be to give the students a specific area to create.