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Lesson plan Grade 7 Math

Quarrymere's Treatment Wetland Plan: A Grade 7 Scale Lesson

A 55-minute grade 7 math lesson where students read actual lengths and areas from a fictional village's wetland site plan, then redraw one cell at a new scale.

Objectives

  1. Students will compute actual lengths from a scale drawing of a treatment wetland.
  2. Students will compute actual areas from scaled lengths rather than from scaled areas.
  3. Students will reproduce a rectangle from the plan at a second, smaller scale.

Vocabulary

Effluent
Effluent is the cleaned water that leaves a treatment plant at the end of the process. It is tested carefully before being released to a river, lake, or the ocean.

Also: scale, scale drawing, constructed wetland, treatment cell, area

Teacher overview

A constructed treatment wetland is a shallow, planted basin that a small community builds to polish the water leaving its wastewater plant before that water returns to a stream. The fictional village of Quarrymere has two such cells, and its engineers drew the site plan at a scale of 1 centimeter to 8 meters. Students read lengths off that plan, convert them to real distances, compute the real area of each cell, and then redraw one cell at a scale of 1 centimeter to 20 meters. The misconception to plan for is that area scales the same way length does: a student who multiplies the plan area of 33.25 square centimeters by 8 reports 266 square meters, when the correct figure is 2,128 square meters, because each of the two dimensions is multiplied by 8.

Procedure

Hook (5 min): Show students a floor plan of the classroom drawn at any convenient scale and ask how the drawing tells them the real length of the room. Establish that a scale is a rate connecting drawing units to real units, then introduce the fictional village of Quarrymere and its wetland plan.

Direct instruction (12 min): Write the scale 1 centimeter to 8 meters on the board. Model a rectangle that is not on the handout: a settling pond drawn 5 centimeters by 2 centimeters. Show that the real length is 5 times 8, or 40 meters, and the real width is 2 times 8, or 16 meters, so the real area is 40 times 16, or 640 square meters. Then show the trap: the drawing area is 10 square centimeters, and multiplying 10 by 8 gives 80, which is not the answer. Say plainly that both dimensions grow by the scale factor, so the area grows by 8 times 8.

Guided practice (12 min): Distribute the handout. Complete items 1 through 3 together for Cell 1, writing each multiplication on the board. Have pairs compare their work on item 4 before continuing.

Independent practice (18 min): Students complete items 5 through 10 on their own. Remind them that items 7 and 8 move to a new scale of 1 centimeter to 20 meters, so the real measurements stay the same while the drawing shrinks. Circulate and check that students divide by 20 rather than multiply.

Closure and exit ticket (8 min): Ask two students to explain in their own words why the plan area and the real area do not share the same scale factor. Then collect an exit ticket: "On the same plan at 1 centimeter to 8 meters, a rectangular sludge drying bed measures 3 centimeters by 2 centimeters. What is its real area in square meters?" If more than a quarter of the class reports 48 square meters, reteach the two-dimension idea before the next class.

Quarrymere's Treatment Wetland Plan: A Grade 7 Scale Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

The fictional village of Quarrymere built a two-cell treatment wetland. Its site plan is drawn at a scale of 1 centimeter to 8 meters. On the plan, Cell 1 is a rectangle 9.5 centimeters long and 3.5 centimeters wide. Cell 2 is a rectangle 6 centimeters long and 3.5 centimeters wide. The inlet channel is a straight line 4.25 centimeters long.

  1. What is the actual length of Cell 1, in meters?
  2. What is the actual width of Cell 1, in meters?
  3. What is the actual area of Cell 1, in square meters?
  4. What is the actual area of Cell 2, in square meters?
  5. What is the actual length of the inlet channel, in meters?
  6. What is the combined actual area of Cell 1 and Cell 2, in square meters?
  7. Quarrymere wants a second plan at a scale of 1 centimeter to 20 meters. How long would Cell 1's long side be on that new plan, in centimeters?
  8. How long would Cell 1's short side be on the new plan, in centimeters?
  9. What is the area of Cell 1 on the new plan, in square centimeters?
  10. How many times larger is Cell 1's area on the original plan than on the new plan?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 76 meters.
    The scale is 1 centimeter to 8 meters, so 9.5 times 8 equals 76 meters.
  2. Answer: 28 meters.
    Using the same scale, 3.5 times 8 equals 28 meters.
  3. Answer: 2,128 square meters.
    Multiply the two actual lengths: 76 times 28 equals 2,128 square meters. The plan area of 33.25 square centimeters is not multiplied by 8.
  4. Answer: 1,344 square meters.
    Cell 2 is 6 times 8, or 48 meters, by 3.5 times 8, or 28 meters. Then 48 times 28 equals 1,344 square meters.
  5. Answer: 34 meters.
    The channel is 4.25 centimeters on the plan, and 4.25 times 8 equals 34 meters.
  6. Answer: 3,472 square meters.
    Add the two cell areas: 2,128 plus 1,344 equals 3,472 square meters.
  7. Answer: 3.8 centimeters.
    The actual length is 76 meters, and at 1 centimeter to 20 meters the drawing length is 76 divided by 20, which equals 3.8 centimeters.
  8. Answer: 1.4 centimeters.
    The actual width is 28 meters, and 28 divided by 20 equals 1.4 centimeters.
  9. Answer: 5.32 square centimeters.
    On the new plan Cell 1 measures 3.8 by 1.4 centimeters, and 3.8 times 1.4 equals 5.32 square centimeters.
  10. Answer: 6.25 times.
    On the original plan Cell 1 covers 9.5 times 3.5, or 33.25 square centimeters. Then 33.25 divided by 5.32 equals 6.25. This is also 20 divided by 8, squared.

Exit ticket answer: 384 square meters. The bed is 3 times 8, or 24 meters, by 2 times 8, or 16 meters, and 24 times 16 equals 384.

Differentiation

Support

Give these students a worked card for the settling pond from the direct instruction, with the four steps labeled drawing length, real length, drawing width, real width, and real area. Let them complete items 1 through 6 only, and allow a calculator throughout.

Extension

Ask these students to find what the scale would have to be for Cell 1 to fit on a page with a usable width of 4 centimeters, then to state that scale in the form 1 centimeter to a whole number of meters and justify the choice.

ELL supports

Pre-teach "scale," "cell," "plan," and "actual" with a two-column card showing a small rectangle labeled in centimeters beside a large rectangle labeled in meters. Provide the frame "___ centimeters on the plan means ___ meters in real life" for items 1, 2, and 5.