The Cyberchase kids are trying to buy the Encryptor chip at an auction that lasts 11 days. Each time there's a new bid, they must figure out how to earn enough money to top the existing bid. To do this, they use simple proportional reasoning to make a chart of their daily savings transactions and their total savings accumulation (balances). Students are asked to create data tables and to plot and analyze graphs of transactions and accumulations.
Part I: Learning Activity
1. Have the students work in pairs for this activity.
2. Read the following to the students:
"The Cyberchase kids are trying to buy the Encryptor chip at an auction. After a period of 11 days, the highest bidder gets the chip. The currency used is called a "snelfu." First, they must predict how many snelfus they need to earn in order to win the Encryptor chip. To understand the video segment, you need to understand two important concepts in banking and savings accounts. The first is the concept of a transaction, which is how much you deposit (put in) or withdraw (take out) each day. The second is the concept of the balance (or accumulation), which is how much is in the account each day after the transactions are totaled."
3. Distribute Handout 1: A Savings Plan .
4. Ask the students to complete Handout 1.
5. Tell the students that they will watch a video segment that shows how the Cyberchase kids planned and began earning the first snelfus for the auction.
6. Play the Earning 100 Snelfus QuickTime Video .
7. Discuss the CyberSquad's plan, and compare it with the different methods suggested by the students. (Make sure the students understand that in the instructions they were notrequired to deposit the same amount each day, even though the CyberSquad did it that way.) Ask the students to describe how their plans were similar to and different from the way the CyberSquad set up their earnings plan.
8. Read the following statement to the students:
"In the next video segment, Hacker and Wicked, the witch, make two new higher bids, forcing the CyberSquad to change their own predictions. Each time the CyberSquad change their prediction to be higher, they must figure out again how much they must earn per day in order to meet their bid. The CyberSquad ends up bidding 500 snelfus for the Encryptor chip. You will be asked to fill in a table showing how much the CyberSquad earned on each of the 11 days, recording the actual amounts they earned and saved.
9. Distribute Handout 2: Earning and Saving Snelfus . Review the meaning of the numbers and columns in the table.
10. Remind the students that they will watch a video segment and record the CyberSquad's actual transactions and balances on the table on Handout 2. Ask the students to pay careful attention to the video, because the Cyberchase kids' predictions change. Replay the segment if necessary, as students may not have recorded all the data during the first viewing.
11. Play the More Bidding Challenges QuickTime Video .
12. Once the students have completed their tables on Handout 2, ask them to complete the graphs and answer questions 1 and 2 on the handout. Remind them that they must complete the graphs using the data from the data table.
13. Discuss their graphs and their answers to questions 1 and 2. Ask the students to describe the patterns on the graphs and relate them to the patterns of numbers on the table.
14. Distribute Handout 3: Steady Snelfus .
15. Tell the students that Handout 3 requires them to use only constant transactions (transactions that are the same every day).
16. Ask students to complete Handout 3.
17. Discuss their answers to the questions on Handout 3, especially in relation to the questions on Handout 2. By the end of the discussion, they should understand that line graphs representing transactions and accumulations (balance) are different. They should understand and be able to predict that constant transactions result in a horizontal line on the transaction graph and a straight slanted line on an accumulation graph. These patterns on the two different graphs always correspond to each other.
Part II: Assessment
Assessment: Level A (proficiency): Ask students to figure out how long they will need to work to earn two related amounts, and have them graph two sets of constant transactions to compare the effects of these two different transaction patterns on the accumulation graphs.
Assessment: Level B (above proficiency): Introduce students to deposits and withdrawals as transactions. Ask them to complete an accumulation graph based on a set of deposits and withdrawals. They will then invent a series of deposits and withdrawals and a set of constant deposits and steady withdrawals, leading to the same final balance. Students will also compare the transaction and accumulation patterns in the two series of transactions.