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Lesson plan · Grade 11 · 45 minutes

Savings Plan

I can write a sequence explicitly and recursively, read a balance as a partial sum, and use the arithmetic and geometric series formulas.

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Standard
F-IF.A.3 CCSS-Math
A-SSE.B.4 CCSS-Math
Shape
Explore first
Grouping
Whole class for the hook, then pairs on devices.
You need
The tool on the projector and on student devices. Notebooks for the derivations.
Tool
curioclass.org/tools/savings-plan/
  1. Hook5 min
  2. Explore15 min
  3. Make sense10 min
  4. Apply10 min
  5. Exit check5 min

Before class

  • Open Race on Penny vs ten. Plan A puts in $10 every week; Plan B starts with one cent and doubles it every day.
  • Every deposit is rounded to the cent, so the ledger is exact. The shortcut can differ by a few cents for multiply plans.

Hook 5 min

  1. Read the two plans aloud. "A 30-day race. Who wins?" Take a vote before anyone touches anything.
  2. Most pick Plan A. "Let's find out, day by day."

Explore 15 min

  1. Walk the days on the projector: hover the chart, or Tab to it and use the arrow keys. A leads until day 11, when the penny passes it.
  2. Pairs open the Ledger and find the day 30 deposit by itself ($5,368,709.12). "How does that compare with everything Plan A puts in?"
  3. Pairs switch between What you have and What goes in. "Which one is the sequence and which is the series?"
  4. Pairs try Log scale and Who leads on two other races, and write each plan's rule both ways, explicit and recursive, checking against the card.

Make sense 10 min

  1. On the board, name the terms: a_n is one deposit, S_n is the balance after n deposits. "Point to each one on the chart."
  2. For Plan A, press Show the shortcut and step through it. "Why does every column add to the same thing?"
  3. For Plan B, step through the multiply shortcut. "Why does almost everything cancel?" Step 5 lands on the same $10,737,418.23 as the Ledger.
  4. Students copy both formulas, each with the race's numbers filled in.

Apply 10 min

  1. Pairs open Plan Desk and take the first two customers. Each has a goal, a deadline and a cap on any one deposit.
  2. Before pressing Run the plan, pairs check their plan with the right series formula on paper. One run per customer.
  3. Ask: "Ivy's goal is $2,000. How can you prove no plan works without trying them all?"

Exit check 5 min

On a card: "A plan starts at $3 and adds $2 each week. Write the rule both ways and find the balance after 10 weeks." Then: "A plan starts at $1 and triples each day. Write the sum for 8 days as a formula." Cards that use a_n where S_n belongs show who needs the chart again.

Support and stretch

  • Support: stay with add plans until the explicit and recursive rules are solid.
  • Support: keep the Ledger open next to the chart while pairs write rules.
  • Stretch: "The halving plan adds less and less forever. Why can it never pass $128?"
  • Stretch: finish the whole Plan Desk season and aim for a perfect $225.

Short on time

  • Penny vs ten race with the vote (8 min).
  • Show the shortcut for B as a class (7 min), then the exit card (5 min).

How each button works is in the teacher notes. From Curio Class, free under CC BY 4.0: change it, print it, share it.