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Lesson plan Grade 7 Math

Sediment Limits at Silverthorn Creek: A Grade 7 Percent Lesson

A 50-minute lesson in which students chain two percent reductions on a construction site's sediment load, then write an inequality against a permit limit.

Objectives

  1. Students will apply two successive percent reductions to a single starting amount.
  2. Students will calculate the percent decrease between two stages of treatment.
  3. Students will write and interpret an inequality for a permitted daily limit.

Vocabulary

Key words: sediment, silt fence, percent decrease, permit

Teacher overview

Silverthorn Creek is fictional, and every load, percentage, and permit figure in this lesson was written for it. A road-widening project has stripped the soil beside the creek, and each storm washes sediment off the bare ground into the water, where it buries the gravel that fish need. The town requires two controls, a silt fence and a sediment basin, and the second one treats only what the first one misses. That sequence is where students most often go wrong. They add the two removal percentages, decide that a 65 percent fence plus a 40 percent basin removes 105 percent of the sediment, and conclude that nothing reaches the creek. The second percentage applies to the smaller amount that got past the first control, not to the original load.

Procedure

  1. Hook (5 min): Project a photograph or sketch of a bare construction slope beside a stream in the fictional town of Silverthorn. Ask students what happens to the loose soil in a heavy rain, and record the phrase "sediment washes into the creek" on the board. Tell students that the town's permit sets a daily limit and that today they will find out whether the site meets it.

  2. Model the sequence (10 min): Work one example on the board using numbers students will not see again on the handout. Suppose a different fictional site sends 900 pounds of sediment a day toward the creek. A silt fence catches 50 percent, which is 450 pounds, leaving 450 pounds moving past it. A basin then catches 20 percent of that 450 pounds, which is 90 pounds, leaving 360 pounds reaching the creek. Ask why the second step used 450 rather than 900, and write the answer on the board as a class sentence. Finish by asking what percent of the original 900 pounds still arrived, and show that 360 divided by 900 is 40 percent.

  3. Guided practice (12 min): In pairs, students redo the board example with the basin raised to 30 percent, then compare their result with the incorrect method of adding 50 and 30 to get 80 percent removal. Circulate and ask each pair to state, in one sentence, which number the second percentage is taken from. Bring the class back together and take two pairs' sentences.

  4. Independent work (15 min): Distribute the Student Handout. Students work items 1 through 10 on the fictional Silverthorn site, using calculators. Items 7 and 8 introduce the permit limit as an inequality, so pause the room at the ten-minute mark and read item 7 aloud, reminding students that a limit written as "no more than" becomes an at-most inequality.

  5. Formative check (5 min): Ask every student to hold up a card or write on a slip the answer to this question: after both controls, what percent of the original load reaches Silverthorn Creek? The target answer is 21 percent. If more than a quarter of the class writes 105 percent, 5 percent, or 40 percent, reteach step 2 with a bar model before moving on.

  6. Debrief (3 min): Ask two students to explain, using item 9, why a 15 percent cut gives the same result at the start or the end of the line. Close by naming the general rule that successive percent reductions multiply rather than add.

Sediment Limits at Silverthorn Creek: A Grade 7 Percent Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Silverthorn is a fictional town, and all of these numbers were written for this lesson. A construction site sits beside Silverthorn Creek. The site uses a silt fence first and a sediment basin second. Answer each item using the numbers it gives you.

  1. The site sends 1,600 pounds of sediment toward the creek each day. The silt fence catches 65 percent of it. How many pounds does the fence catch?
  2. Use item 1. How many of the 1,600 pounds get past the fence?
  3. The sediment basin catches 40 percent of the 560 pounds that get past the fence. How many pounds does the basin catch?
  4. Use items 2 and 3. How many pounds reach Silverthorn Creek each day after both controls?
  5. What percent of the original 1,600 pounds still reaches the creek? Round to the nearest whole percent.
  6. What is the percent decrease from the 560 pounds that got past the fence to the 336 pounds that reach the creek?
  7. Silverthorn's permit allows no more than 300 pounds of sediment per day. Let p stand for the pounds released each day. Write an inequality for what the permit allows.
  8. The site releases 336 pounds a day. By how many pounds does it exceed the 300-pound permit limit?
  9. The crew covers the bare soil, which cuts the 336 pounds by 15 percent. How many pounds would reach the creek then?
  10. Compare your answer to item 9 with the 300-pound permit limit. Explain whether the site now meets the permit, and whether a third control at the end that removed 15 percent would give a different result.

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: 1,040 pounds.
    Multiply the load by the removal rate: 1,600 x 0.65 = 1,040 pounds caught by the fence.
  2. Answer: 560 pounds.
    Subtract what the fence caught: 1,600 - 1,040 = 560 pounds moving past it.
  3. Answer: 224 pounds.
    Multiply the amount that got past the fence by the basin's rate: 560 x 0.40 = 224 pounds.
  4. Answer: 336 pounds.
    Subtract the basin's catch from what reached it: 560 - 224 = 336 pounds reaching the creek.
  5. Answer: 21 percent.
    Divide the amount reaching the creek by the original load: 336 / 1,600 = 0.21, which is 21 percent.
  6. Answer: 40 percent.
    The decrease is 560 - 336 = 224 pounds. Divide by the starting amount: 224 / 560 = 0.40, which is 40 percent. This matches the basin's stated removal rate, which is a useful check.
  7. Answer: p is at most 300 pounds per day.
    The phrase "no more than" means the released amount may equal 300 but may not go above it.
  8. Answer: 36 pounds.
    Subtract the limit from the release: 336 - 300 = 36 pounds over the permit.
  9. Answer: 285.6 pounds.
    A 15 percent cut leaves 85 percent: 336 x 0.85 = 285.6 pounds.
  10. Answer: Yes, 285.6 pounds is within the 300-pound limit, and a 15 percent control at the end would give the same result.
    The site now releases less than the permit allows, with about 14 pounds to spare. A 15 percent control at the end would also leave 336 x 0.85 = 285.6 pounds, because successive percent reductions multiply and their order does not change the product.

Differentiation

Support

Provide a bar model for the fictional Silverthorn load, drawn as a strip of 1,600 pounds with the fence's share shaded, so students can see that the basin acts only on the unshaded remainder. Students who stall on item 5 can be given the division setup 336 divided by 1,600 already written.

Extension

Ask students to find the smallest whole-number removal rate the fictional basin would need, with the fence unchanged at 65 percent, to bring the site under the 300-pound permit without covering the soil. Students should set up an inequality rather than testing values.

ELL supports

Preteach "sediment," "silt fence," and "permit" with a labeled cross-section of the site in the town of Silverthorn showing bare soil, the fence, the basin, and the creek in order. Provide the sentence frame for item 10: "The site meets the permit because ____, and a 15 percent cut at the end gives the same result because ____."

Extensions

Students can find their own state's construction stormwater permit online and compare its structure with the fictional Silverthorn limit, noting whether real permits set a pounds-per-day cap or a turbidity standard instead. A second follow-on has students design a three-control sequence for the same site and calculate the load reaching the creek, then explain why the order of the controls does not change the final amount.