Concept of a rectangular array
Figure 7: (3 ∙ 3) Rectangular Array
I will work with my students in understanding rectangles and how to decompose or sub-divide these rectangles into arrays of squares using columns and rows, (see figure 7). I will work with my students in understanding that a specific region has a two dimensional space inside it. After this idea is mastered, I will work with my students to arrange arrays into nets to build and fold into boxes. They will then study the volume of the boxes in terms of 3 dimensional arrays of unit cubes.
A rectangular prism solid (a box) is what we will be using to understand volume. We will be using a unit cube as a standard example of a unit of volume. I will work with my students in understanding that the space within this solid is called volume. We can determine volume by counting the rows and columns of cubes or cubic units required to fill the prism. There are three dimensions to account for here: they will make layers that are rectangular arrays of unit cubes, and stack several of these layers of cubes into the boxes. I will have students use standard units of measurement to strengthen skills such as comparing, putting into order, and how to measure area and volume.
Before launching the lessons, I will engage students in a discussion about real-world geometry with a classroom poster/anchor chart. I will show how geometric shapes can be found in everyday life. I will ask students where they have seen these shapes in their daily lives. I will write on the anchor chart basic shapes and solids for area and volume we will be using for this unit, (see figure 8).
Figure 8: Basic shapes and solids
When my students work with a rectangular prism, I will use the activity of covering the surface area of a series of boxes representing rectangular prisms. Students will use wrapping paper to cover all the sides of the box. The students will understand when wrapped that that each side of the box when added together constitutes the surface area of a box. I will show them examples of boxes, such as cereal boxes or packing boxes, so that they can see how, when the box is decomposed that the box was actually formed by taking a flat piece of cardboard (with a few extra flaps) and folding it up into a rectangular prism or box. The amount of wrapping required the cover the box will be the surface area.
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