Guide for the TI-83/84 Family of Calculators

This guide gives suggestions for selected activities of the Year 1 unit Patterns. The notes that you download contain specific calculator instructions that you might copy for your students.

Students will come in with a wide range of knowledge about graphing calculators and other technologies. The goal is for technology to become a tool that helps students ask and explore interesting questions. Students will have an opportunity to learn new things about graphing calculators during the open-ended Calculator Exploration. Until then, keep calculators available and let students discover and teach each other.

For one activity, this guide provides support for required calculator use in the text. For other activities these notes contain ideas about how to use calculators for enrichment or extension of the activities or hints and suggestions for pitfalls to avoid.

POW 1: The Broken Eggs: In their work on the first POW, students may wish to use their calculators to list possibilities for the number of eggs. For example, when they consider the statement “She knows that when she put the eggs in groups of three, there was one egg left over”, students might generate the sequence of numbers that match this statement on their calculators: 4, 7, 10, 13, and so on. In calculations that involve performing the same operation (in this case, adding 3) over and over again, the calculator provides a shortcut. This shortcut is described in the Patterns Notes in the section “Using the Previous Answer.”

Calculator Exploration: In this activity, students explore the capabilities of their graphing calculator without structured directions. Teachers have found that relatively unstructured exploration can help build students’ confidence about using technology. Students realize that they can figure out a great deal without asking for directions or help. For this reason, use the notes “TI Calculator Basics” conservatively with students. You might review the material to remind you of the things you will eventually want to bring out in discussions if they are not mentioned by students.

1-2-3-4 Puzzle: Students who use their calculators for this activity will want to find the square root command and the factorial command. They should also know that the calculator exclusively uses parentheses as grouping symbols. (That is, brackets and braces are reserved for other contexts.)

Uncertain Answers: The TI calculator follows the order-of-operations rules. Nevertheless, encourage students to use parentheses in long calculations. Parentheses make calculations easier to follow both on and off the screen.

Extended Bagels: In this activity, students use algebraic expressions to describe the relationship between two columns of a table. You can use algebraic expressions to generate tables like these on the TI calculator. You probably don’t want students to work with these tables on a calculator until they are more comfortable with the ideas of tables and algebraic expressions. The instructions in the section “Using Lists to Build a Spreadsheet” describe how to create the table of values containing Marcella’s bagel count.

Two calculator features create tables: TABLE and LIST. For instructions on using the TABLE feature, see “Graphing Basics”in The Overland Trail Notes. You will notice that the LIST features allow the calculator to function like a simple spreadsheet.

Do It the Chefs’ Way: Students frequently confuse the negative key with the subtraction key. The negative key, which is located beside the decimal key and has a negative in parentheses, changes the sign of the calculation that follows it. The subtraction key, which is located above the addition key, subtracts the next term from the previous term. You cannot begin a calculation with the subtraction key. Use the negative key to represent negative numbers. On the screen, a negative is shorter and raised when compared to subtraction.

Add It Up: It is possible to use the LIST feature of a TI calculator to build a sequence. It is also possible to sum this sequence. The steps to do this are fairly complicated, and the notation is different from the traditional sigma (Σ) notation, so avoid showing students the calculator procedure right away. However, if your students become comfortable with the activity and you have some extra time, they will probably enjoy seeing how quickly the calculator can sum complicated sequences.

Programming Borders: The note “Programming Your Calculator for Borders” is designed to assist with this activity. It does not address the general concept of a program, so you will still want to discuss that with the class. Instead, it focuses on the mechanics of creating and entering a simple program on a TI calculator.

The Patterns Notes contain a simple program BORDER, or BORDER1. Here are two modifications: BORDER2 includes some display. BORDER3 is a version that behaves the way the supplemental activity in the textbook implies; it is advanced and requires some commands not mentioned in the notes.

PROGRAM:BORDER

:Input S

:4S–4→K

:Disp K

PROGRAM:BORDER2

:Disp “SIDE LENGTH?”

:Input S

:4S–4→K

:Disp “TILES:”,K

PROGRAM:BORDER3

:ClrHome

:Disp “HOW WIDE IS THE”

:Disp “GARDEN?”

:Input W

:Disp “HOW LONG IS THE”

:Disp “GARDEN?”

:Input L

:Disp “HOW WIDE IS THE”

:Disp “BORDER?”

:Input B

:2*B*(W–2B)+2*B*(L–2B)+4*B*B→T

:(W–2B)*(L–2B)→S

:3*T+0.20*S→C

:ClrHome

:Disp “YOU WILL NEED”

:Output(2,1,T)

:Output(2,6,”TILES AND”)

:Output(3,1,”WILL HAVE TO”)

:Output(4,1,”COVER”)

:Output(4,7,S)

:Output(5,1,”SQUARE FEET WITH”)

:Output(6,1,”TOPSOIL.”)

:Output(7,1,”THIS WILL COST”)

:Fix 2

:Output(8,1,C)

:Float

:Output(8,9,”DOLLARS.”)