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TI-PoW: Sam and Teri's Bank Accounts - The Math Forum

TI-PoW: Sam and Teri's Bank Accounts - The Math Forum

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Welcome!<br />

<strong>The</strong> Problem<br />

St<strong>and</strong>ards<br />

<strong>The</strong> Strategy<br />

<strong>The</strong> <strong>TI</strong>-Nspire<br />

<strong>Math</strong> <strong>Forum</strong> Teacher Packet<br />

<strong>TI</strong>-<strong>PoW</strong>: <strong>Sam</strong> <strong>and</strong> Teri’s <strong>Bank</strong> <strong>Accounts</strong><br />

Focus Activity: Make a <strong>Math</strong>ematical Model<br />

http://mathforum.org/mathtools/tool/162415/<br />

This packet contains a copy of the original problem used to create the activity, rationale <strong>and</strong><br />

explanation behind the “Make a <strong>Math</strong>ematical Model” focal activity, <strong>and</strong> some thoughts on why this<br />

activity works well with <strong>TI</strong>-Nspire technology.<br />

All of the problems <strong>and</strong> activities are samples of the <strong>Math</strong> <strong>Forum</strong>’s Problems of the Week, paired with<br />

activities from the Problem Solving <strong>and</strong> Communication Activity Series. We are highlighting activities<br />

<strong>and</strong> problems that make good use of <strong>TI</strong>-Nspire h<strong>and</strong>helds <strong>and</strong> software.<br />

Teachers <strong>and</strong>/or students are able to electronically access this <strong>and</strong> similar problems after setting up a<br />

login (free) available from the <strong>Math</strong> <strong>Forum</strong> @ Drexel. Sign up using the link on the Technology<br />

Problems of the Week (t<strong>PoW</strong>) login page, or use your existing KenKen® or Problems of the Week<br />

login–see this page for details: http://mathforum.org/tpow/about.html<br />

<strong>TI</strong>-<strong>PoW</strong>: <strong>Sam</strong> <strong>and</strong> Teri’s <strong>Bank</strong> <strong>Accounts</strong><br />

Spendthrift <strong>Sam</strong> <strong>and</strong> Thrifty Teri each have bank accounts. Currently<br />

<strong>Sam</strong> has $500, while Teri has $200.<br />

Every Friday afternoon <strong>Sam</strong> withdraws $15; he wants to have some<br />

spending money when he goes out with his friends on Saturday evenings. At the same time Teri<br />

makes a deposit of $12; she is planning for a rainy day <strong>and</strong> wants to have a nice "nest egg"<br />

ready.<br />

Use your <strong>TI</strong>-Nspire to help you solve this task:<br />

Use equations to show when their balances will be equal or as close as they will get.<br />

This problem presents an opportunity for students to think about patterns, units of measurement <strong>and</strong><br />

also to work on expressing the pattern as a formula that will lead them to thinking algebraically.<br />

If your state has adopted the Common Core State St<strong>and</strong>ards, this alignment might be helpful:<br />

Grade 8: Expressions & Equations<br />

8.EE.8. Analyze <strong>and</strong> solve pairs of simultaneous linear equations.<br />

<strong>Math</strong>ematical Practices<br />

4. Model with mathematics.<br />

This activity focuses on the strategy: Make a <strong>Math</strong>ematical Model. <strong>The</strong> activity walks the students<br />

through the following basic steps to developing a mathematical model:<br />

Relate values in the problem to quantities among the noticings <strong>and</strong><br />

Organize quantities <strong>and</strong> look for relationships among them<br />

Use examples to test <strong>and</strong> develop a mathematical model<br />

Check the model using multiple representations<br />

You'll find even more activities like this one from the Problem Solving Activities link in the left menu<br />

bar.<br />

In this activity we take advantage of the <strong>TI</strong>- Nspire technology’s linked representations. Students use<br />

the dragging capabilities to literally organize quantities into mathematical relationships. <strong>The</strong>y then test<br />

<strong>and</strong> use those relationships in a table to generate unknown quantities.<br />

<strong>The</strong> values students create in the spreadsheet then appear on their graphs. Students can check their<br />

equations by whether they go through the points generated by their examples.<br />

One important concept of representations to bring up is discrete vs. continuous graphs. How are the<br />

scatterplots helpful representations? How are the functions helpful? How does each relate to finding<br />

the solution?<br />

© 2012 Drexel University http://mathforum.org/


Join Us!<br />

Do your students like to use their mathematical imaginations? Wonder about math all around them?<br />

Discover <strong>and</strong> invent new patterns? Here are some ways for them to share their ideas <strong>and</strong> learn about<br />

other students' <strong>and</strong> mathematicians' ideas!<br />

http://mathforum.org/explorers/<br />

© 2012 Drexel University 2


<strong>The</strong> Activity<br />

Selected Screen Shots<br />

<strong>The</strong> problem Matching quantities <strong>and</strong> values Connecting quantities <strong>and</strong> relationships<br />

Organizing quantities & generating values Testing a model Comparing two accounts<br />

Solving the Problem<br />

Quantities <strong>and</strong> values Possible relationships Generated values (<strong>Sam</strong>)<br />

More generated values (<strong>Sam</strong>) <strong>Sam</strong>’s model Finding when the balances are closest<br />

© 2012 Drexel University 3

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