BY MICHAEL YEE, CLASS OF 2015 Calculate that! Tips and Tricks on How to Get the Most Out of the TI-83/84 Calculator for High School Math and Science

Your Calculator is Powerful! Most students in Penncrest’s more advanced math classes know how to do arithmetic, graph functions, edit lists, do regression models, and do statistical tests on their TI-84’s. But your calculator is more powerful than you think! In this PowerPoint, I’ll: Teach you about the three main data types in the calculator. Show you how to store numeric values to variables, and what applications this skill has in math and science class.

All TI-83/84 calculators have this special button. It allows you to store values to variables by using this syntax: Value  Variable (The arrow is made with the store key.) Variables  Alphabetic variables – green ALPHA key, then any key (e.g. ALPHA, 9 gives you Q)  Lists – blue 2 nd key, then numbers 1-6 (e.g. 2 nd, 1 gives you List 1, or L 1 for short)  Strings/Equations – VARS menu The Store Button

All TI-83/84 calculators have this special button. It allows you to store values to variables by using this syntax: Value  Variable (The arrow is made with the store key.) Variables  Alphabetic variables – green ALPHA key, then any key (e.g. ALPHA, 9 gives you Q)  Lists – blue 2 nd key, then numbers 1-6 (e.g. 2 nd, 1 gives you List 1, or L 1 for short)  Strings/Equations – VARS menu

The Store Button All TI-83/84 calculators have this special button. It allows you to store values to variables by using this syntax: Value  Variable (The arrow is made with the store key.) Variables  Alphabetic variables – green ALPHA key, then any key (e.g. ALPHA, 9 gives you Q)  Lists – blue 2 nd key, then numbers 1-6 (e.g. 2 nd, 1 gives you List 1, or L 1 for short)  Strings/Equations – VARS menu Cool Transition As you will see, there are many applications of the calculator’s store function in math and science class. But first, let’s learn about the three data types the calculator uses. As you will see, there are many applications of the calculator’s store function in math and science class. But first, let’s learn about the three data types the calculator uses. Next 

Three Main Data Types You can put three different types of data into the calculator’s home screen: (Numerical Values) {Lists} “Strings” Each of these data types has a different syntax and usage. Once you know about all of them, you’ll be a calculator wizard!

Numerical Values The most basic type of value Most arithmetic calculations return a numeric value. No syntactical markings required when typing (can use parentheses according to PEMDAS). Aligned to the right when it’s an output.

Numerical Values The most basic type of value Most arithmetic calculations return a numeric value. No syntactical markings required when typing (can use parentheses according to PEMDAS). Aligned to the right when it’s an output.

Numerical Values The most basic type of value Most arithmetic calculations return a numeric value. No syntactical markings required when typing (can use parentheses according to PEMDAS). Aligned to the right when it’s an output. Both letters (variables) and numbers are numeric values. The default value for any alphabetic variable is zero.

Lists Numbers arranged and cataloged in a sequence. Useful for statistical information, data collection during labs Marked by curly brackets { } when typing in home screen. Lists when displayed as an output retain the brackets and are aligned to the right.  You can also use the List Editor (STAT, EDIT…)

Lists Numbers arranged and cataloged in a sequence. Useful for statistical information, data collection during labs Marked by curly brackets { } when typing in home screen. Lists when displayed as an output retain the brackets and are aligned to the right.  You can also edit lists by using the List Editor (STAT, EDIT…)

Lists Numbers arranged and cataloged in a sequence. Useful for statistical information, data collection during labs Marked by curly brackets { } when typing in home screen. Lists when displayed as an output retain the brackets and are aligned to the right.  You can also edit lists by going to STAT, EDIT… Home Screen vs. List Editor – Comparison Home Screen List Editor Click XX

Strings Literal sequences of text not meant to work with mathematical operations Mostly used for programming – allows a program to display text on the home or graph screen

Strings Literal sequences of text not meant to work with mathematical operations Mostly used for programming – allows a program to display text on the home or graph screen

Strings Literal sequences of text not meant to work with mathematical operations Marked by quotation marks. When displayed as an output, the string loses the quotation marks and is (uniquely) aligned to the left You can convert strings to equations to be graphed!

Strings Literal sequences of text not meant to work with mathematical operations Marked by quotation marks. When displayed as an output, the string loses the quotation marks and is (uniquely) aligned to the left You can convert strings to equations to be graphed!

Strings Literal sequences of text not meant to work with mathematical operations Marked by quotation marks. When displayed as an output, the string loses the quotation marks and is (uniquely) aligned to the left You can convert strings to equations to be graphed! Cool Transition Intrigued? Now that you have the basics down, let’s apply what we’ve learned to make schoolwork and homework easier! Next 

Checking Algebra with Alphabetic Variables Let’s start with a simple problem: Factor the expression 4x 3 – 2x 4x 3 – 2x 22xxx – 2x 2x(2x 2 – 1) How do we know if we’re right? 2x()

Checking Algebra with Alphabetic Variables We can set an arbitrary value to x (I recommend a non-integer number.), then see if the two expressions are equal. 4x 3 – 2x 2x(2x 2 – 1)

Checking Algebra with Alphabetic Variables We can set an arbitrary value to x (I recommend a non-integer number.), then see if the two expressions are equal. 4x 3 – 2x 2x(2x 2 – 1)

Checking Algebra with Alphabetic Variables We can set an arbitrary value to x (I recommend a non-integer number.), then see if the two expressions are equal. 4x 3 – 2x 2x(2x 2 – 1) Our math is right!

Checking Calculus with Alphabetic Variables Let’s try differentiating: f(x) = 1.7x 2 + 2x – 3 f(x) = 1.7x 2 + 2x – 3 f’(x) = 3.4x + 2 Let’s see if we’re right.

Checking Calculus with Alphabetic Variables f(x) = 1.7x 2 + 2x – 3 f’(x) = 3.4x + 2

Checking Calculus with Alphabetic Variables f(x) = 1.7x 2 + 2x – 3 f’(x) = 3.4x + 2

Checking Calculus with Alphabetic Variables f(x) = 1.7x 2 + 2x – 3 f’(x) = 3.4x + 2 Our math is right!

Checking Calculus with Alphabetic Variables Now, let’s try an integral: ∫(4x 2 – 2x + 7)dx ∫(9x 2 – 2x + 7)dx 3x 3 – x 2 + 7x + C Let’s check it.

Checking Calculus with Alphabetic Variables Checking an indefinite integral requires a slightly different technique because we have to work around the constant of integration, which can be any real number. ∫(9x 2 – 2x + 7)dx 3x 3 – x 2 + 7x + C

Checking Calculus with Alphabetic Variables Checking an indefinite integral requires a slightly different technique because we have to work around the constant of integration, which can be any real number. ∫(9x 2 – 2x + 7)dx 3x 3 – x 2 + 7x + C

Checking an indefinite integral requires a slightly different technique because we have to work around the constant of integration, which can be any real number. (When using the calculator’s definite differentiation and integration functions, note that it sometimes gives a close estimate rather than the exact answer. The two numbers should match up for several decimal places.) Checking an indefinite integral requires a slightly different technique because we have to work around the constant of integration, which can be any real number. ∫(9x 2 – 2x + 7)dx 3x 3 – x 2 + 7x + C Checking Calculus with Alphabetic Variables Cool Transition Checking your math with the calculator is quick and easy, and it can be especially helpful if the problem is long and complex (e.g. logarithmic differentiation). But that’s not all you can do. Let’s see another application! Checking your math with the calculator is quick and easy, and it can be especially helpful if the problem is long and complex (e.g. logarithmic differentiation). But that’s not all you can do. Let’s see another application! Next 

Doing Physics with Alphabetic Variables Let’s do a multi-step physics problem. A 2 kg. ball is dropped from rest at a height of 4 m.  When does the ball hit the ground?  What is the ball’s velocity when it hits the ground?  What is the ball’s kinetic energy at 0.5 s?

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  When does the ball hit the ground? x = x at 2 x – x 0 = 0.5at 2 2(-h) = -gt 2 t = √2h/g t = √2(4m)/9.8 m/s 2

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  When does the ball hit the ground? x = x at 2 x – x 0 = 0.5at 2 2(-h) = -gt 2 t = √2h/g t = √2(4m)/9.8 m/s 2

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  When does the ball hit the ground? x = x at 2 x – x 0 = 0.5at 2 2(-h) = -gt 2 t = √2h/g t = √2(4m)/9.8 m/s 2 t = s

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s velocity when it hits the ground? v = at = -gt v = -9.8 m/s 2 ( s)

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s velocity when it hits the ground? v = at = -gt v = -9.8 m/s 2 ( s)

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s velocity when it hits the ground? v = at = -gt v = -9.8 m/s 2 ( s) v = m/s

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s kinetic energy at s? v = at = -gt v(0.123) = -9.8 m/s 2 (0.123 s)

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s kinetic energy at s? v = at = -gt v(0.123) = -9.8 m/s 2 (0.123 s)

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s kinetic energy at s? v = at = -gt v(0.123) = -9.8 m/s 2 (0.123 s) v(0.5) = m/s K = 0.5mv 2 K = 0.5(2 kg.)( m/s) 2

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s kinetic energy at s? v = at = -gt v(0.123) = -9.8 m/s 2 (0.123 s) v(0.5) = m/s K = 0.5mv 2 K = 0.5(2 kg.)( m/s) 2

Doing Physics with Alphabetic Variables A 2 kg. ball is dropped from rest at a height of 4 m.  What is the ball’s kinetic energy at s? v = at = -gt v(0.123) = -9.8 m/s 2 (0.123 s) v(0.5) = m/s K = 0.5mv 2 K = 0.5(2 kg.)( m/s) 2 K = 1.45 J Cool Transition Alphabetic variables are useful in physics because they allow you to retain numbers that you’ll need in later parts of the problem. It’s also faster and easier to type in a single variable than a number with nine decimal places. For our final example, let’s look at a sample lab. Alphabetic variables are useful in physics because they allow you to retain numbers that you’ll need in later parts of the problem. It’s also faster and easier to type in a single variable than a number with nine decimal places. For our final example, let’s look at a sample lab. Next 

Atwood Machine Lab Let’s suppose we’re doing a lab with an Atwood machine. Both m 1 and m 2 change by 100 grams for each trial. a t (the theoretical acceleration) of the system is modeled by: a H a m (the experimental acceleration) is modeled by:

m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) Atwood Machine Lab This is a data table on your lab sheet. You have to use your calculations and measurements to fill it out. First, let’s fill in the time column with data. You time how long it takes m 2 from a height of 3 m. Later, you’ll use the times for your a m calculation.

Atwood Machine Lab To fill out the rest of the table, we could use alphabetic variables, but we would have to store different mass and time values for every trial. Instead, let’s use the List Editor as a spreadsheet to make data entry more automatic. m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 )

Atwood Machine Lab To fill out the rest of the table, we could use alphabetic variables, but we would have to store different mass and time values for every trial. Instead, let’s use the List Editor as a spreadsheet to make data entry more automatic. m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 )

Atwood Machine Lab To fill out the rest of the table, we could use alphabetic variables, but we would have to store different mass and time values for every trial. Instead, let’s use the List Editor as a spreadsheet to make data entry more automatic. m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 )

Atwood Machine Lab You can edit L 5 and L 6 to be functions of the other lists as appropriate. Remember: m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 )

Atwood Machine Lab You can edit L 5 and L 6 to be functions of the other lists as appropriate. Remember: m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 )

Atwood Machine Lab m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) m 1 (kg)m 2 (kg)H (m)t (s)a t (m/s 2 )a m (m/s 2 ) You can edit L 5 and L 6 to be functions of the other lists as appropriate. Remember: Cool Transition This ends my lesson on the TI-83/84 family of calculators. I hope this self-guided PowerPoint helped you learn how better to use your calculator in school. It really helps you if you can use your technology to your advantage. But never forget that you’ll need to know how to do math by hand as well. This ends my lesson on the TI-83/84 family of calculators. I hope this self-guided PowerPoint helped you learn how better to use your calculator in school. It really helps you if you can use your technology to your advantage. But never forget that you’ll need to know how to do math by hand as well. Summary 

Summary Click on any of the links to revisit the lesson. Introduction  The store button The store button  Three types of data entry Three types of data entry  Numerical values Numerical values  Lists Lists  Strings Strings Applications  Checking the factoring of an algebraic expression Checking the factoring of an algebraic expression  Checking a Power Rule derivative Checking a Power Rule derivative  Checking a Power Rule integral (indefinite) Checking a Power Rule integral (indefinite)  Using alphabetic variables in a Newtonian dynamics problem Using alphabetic variables in a Newtonian dynamics problem  Using lists to simplify data collection from an Atwood Machine Using lists to simplify data collection from an Atwood Machine