Modeling Prompt

Although this prompt primarily uses math learned in prior grades, the modeling demands are representative of work appropriate in high school.

You may want to limit the complexity by suggesting that the wall will be built by stacking the blocks on the ground, without footing, mortar, or rebar.

A more extended version of the activity might explore a more involved way to build the wall than in the sample response. A landscape contractor would probably pour a concrete footing, have concrete joints between the blocks, and fill the interior of the blocks with concrete. This involves making assumptions about the size of the footing (12 inches wide by 8 inches deep would be appropriate), and estimating the volume of concrete needed to fill the footer, the blocks, and the joints between the blocks. Concrete blocks are actually \(\frac{3}{8}\) inch shorter than the nominal dimensions given in each direction to allow for a \(\frac{3}{8}\) inch thick joint between them. Also, it is common to reinforce such a wall with rebar (steel rods that reinforce concrete in construction). Instructions on how to set the rebar are available on the web. This level of complexity would involve thinking about the geometry of the blocks and how they are stacked in an alternating pattern.

A homeowner is going to build the raised bed garden enclosed by a low concrete block wall shown in the plan, up against an existing garden wall and fill the space with soil to grow plants. The homeowner will do all the work and will buy the materials. How much will it cost to make the garden?

See teacher instructions for version 1.

A homeowner is going to build the raised bed garden shown in the plan, against an existing garden wall. The homeowner will build the new wall by stacking concrete blocks without mortar, and then fill in the walled space with garden soil. The concrete blocks have dimensions 8 inches x 8 inches x 16 inches. The wall will be capped by capstones that have dimensions 8 inches x 2 inches x 16 inches. The homeowner will do all the work and will buy materials. How much will they cost?

See teacher instructions for version 1.

A homeowner is going to build the raised bed garden shown in the plan, against an existing garden wall. The homeowner will build the new wall by stacking concrete blocks without mortar, and then fill in the walled space with garden soil. The concrete blocks have dimensions 8 inches x 8 inches x 16 inches. The wall will be capped by capstones that have dimensions 8 inches x 2 inches x 16 inches. Concrete blocks cost $1.50 each, capstones cost $1.00 each, and garden soil costs $36 per cubic yard. The homeowner will do all the work and will buy materials. How much will they cost?