Objective

The objective of this activity is introduce the NumWorks graphing calculator.

This year we will be using the NumWorks graphing calculator in our math class! This activity will help you get to know the calculator and some of the features we will be using in this class.

The keyboard

Before we get started, let's take a closer look at the keyboard. You'll see it is arranged into three different zones.

The NumWorks calculator

In the bottom section, you will find basic operations and the number pad. Notice that there is only one minus key. Here you will also find the Ans key which allows you to use the most recent result in your calculations. To compute a calculation, press the EXE key.

In the middle section, you will find some advanced functions and commonly used values. What keys do you recognize in this section?

In the top row of the Advanced Functions section, you will find the shift key which gives you access to the yellow option of each key. The alpha key can be used select the alpha characters on each key. The xnt key is a quick way to enter xx (or other variables as needed). The var key opens a menu of stored values. The Toolbox Toolbox provides additional functions organized in categories. Finally, the Backspace key works just like on your computer or phone to backspace.

The top section is the Navigation Zone where you have arrow keys to navigate the screen, the OK key to make selections and a Back key to take you back to a previous menu. The Home button will return you to the home screen and the Power button turns the calculator on and off.

Navigate around the home screen. How many applications are there?

The applications

The NumWorks calculator is app-based, just like a phone. That means you will open different applications based on the task you are completing. Let's dive into some of the apps to see what they do!

Calculation

The calculation application

The Calculation application is where you will do all of your... calculations!

Navigate to the Calculation application and open it by pressing OK.

  1. Let's add some fractions! By hand, add 16+12\frac{1}{6}+\frac{1}{2}.
  2. 16+12\frac{1}{6}+\frac{1}{2}

    =16+36=\frac{1}{6}+\frac{3}{6}

    =46=\frac{4}{6}

    =23=\frac{2}{3}

  3. Check your work by using the calculator. To input 16\frac{1}{6}, press the one key followed by the division key. Then press the six key. Use the right arrow key to get out of the denominator before adding the other fraction. What do you notice about your answer?
  4. Summing one sixth and one half

    The calculator provides both the simplified fraction and decimal approximation.

  5. Use your calculator to subtract 95410\frac{9}{5}-\frac{4}{10}.
  6. Subtracting four tenths from nine fifths

  7. How do the results of the last two calculations differ?
  8. For the first calculation, the decimal result was an approximation and the "approximately equal to" symbol was used. In the second calculation, the decimal result was exact and the "equal to" symbol was used.

  9. Use the up arrow key to navigate into your calculation history. Do you see the three dots on the right side of the screen? That means there are additional results for that calculation. Navigate over to the three dots and press OK. What additional results are provided for this calculation?
  10. The three dots in the calculation history

    Additional results for seven fifths

    The additional results for 75\frac{7}{5} include the mixed fraction and Euclidean division representations.

  11. Press the Back key until you return to the editing bar. Now, open the Toolbox by pressing the toolbox key. Navigate through the Toolbox and list any functions that you know.
  12. The toolbox menu

    Student responses will vary.

Grapher

The grapher application

Graphing functions is simple within the Grapher application.

To open the Grapher application, first press the home key to return to the home screen. Then navigate to the Grapher application and open it by pressing OK.

Our goal will be to graph the linear function y=3x+5y=3x+5, look at its features and view the table.

Notice that there are three tabs at the top of the screen: Expressions, Graph and Table.

The Expressions tab is where you will enter your function.

  1. Press OK to Add an element. There are some templates you can use when entering expressions. For this example, select the y=xy=x template.

    The templates of the grapher application

  2. To enter the function y=3x+5y=3x+5, first use the left key to move your cursor to the left of the xx and add the coefficent 33. Now use the right key and finish the expression. Once your function is completed, press OK or EXE.

    Adding an equation to the grapher

The Graph tab will plot the graphs of your functions and provide tools for exploring key characteristics.

  1. To view the graph, either navigate down to Plot graph or up and over to the Graph tab and press OK.

    The graph of y=3x+5

  2. The auto zoom generally provides a window that you will find useful. Press the plus and minus keys to zoom in and out. To return to the auto zoom, navigate up and select "Auto".
  3. Use the left and right keys to trace the line. Navigate to x=2x=-2. What is the value of yy?

    Viewing the graph when x = -2

    When x=2x=-2, y=1y=-1.

  4. Press the four key followed by OK as a shortcut to quickly navigate to x=4x=4. What is the value of yy?

    Viewing the graph when x = 4

    When x=4x=4, y=17y=17.

  5. Navigate up and over to the Calculate menu and open it by pressing OK. Then open the Find menu. This menu provides tools for finding key characteristics of our graph. Use the Inverse image option to determine the value of xx when y=10.y=10.

    The find menu

    Inputting y = 10

    Viewing the graph when y = 10

    When y=10y=10, x=1.667x=1.667.

The Table tab provides a table of points for your function.

  1. To view the table, navigate up and over to the Table tab and press OK.

    Viewing the table

  2. The table displays the xx and yy values for x=0x=0 through x=10x=10. Copy down the values of yy in the table below.
    x 0 1 2 3 4 5 6 7 8 9 10
    y
    x 0 1 2 3 4 5 6 7 8 9 10
    y 5 8 11 14 17 20 23 26 29 32 35
  3. Let's say we wanted to know the value of yy when x=100x=100. Highlight any of the current x-values and type 100100. Press EXE. You will now see the value of yy in the table. What is yy?

    Viewing the table when x=100

    When x=100x=100, y=305y=305.

Solver

The solver application

Now let's head to the Solver application to solve equations and systems of linear equations.

To open the Solver application, first press the home key to return to the home screen. Then navigate to the Solver application and open it by pressing OK.

We want to solve the equation: 43(x2)=27x4-3(x-2)=2-7x.

  1. First, solve this equation by hand.

    43(x2)=27x4-3(x-2)=2-7x

    43x+6=27x4-3x+6=2-7x

    103x=27x10-3x=2-7x

    8=4x8=-4x

    x=2x=-2

  2. Now check your work by using the calculator to solve. Enter the Equations section by pressing OK.

    Opening the solver application

  3. Similar to the Grapher application, when you press OK to Add equation, you can either use an "Empty" template or one of the premade templates. Use the empty template and enter the equation 43(x2)=27x4-3(x-2)=2-7x.

    Entering the equation 4-3(x-2)=2-7x

  4. Navigate down to Solve the equation and press OK. What is the value of x?

    Viewing the solution

    The solution is x=2x=-2.

Now, let's use our Equation solver to solve a system of linear equations.

  1. Press the Back key to return to the equation editor.
  2. Use the backspace key to delete the equation.
  3. Use and edit the x+y=0x+y=0 template to enter the equation 7x6y=4-7x-6y=4.
  4. Add another equation and use the empty template to enter the equation x=3y+8x=-3y+8.

    Entering a system of linear equations

  5. Navigate down to Solve the system and press OK. What is the solution to this system?

    Viewing the solution

    The solution is (4,4)\left(-4,4\right).

Regression

The regression application

The Regression application plots scatterplots and provides the line of best fit.

To open the Regression application, first press the home key to return to the home screen. Then navigate to the Regression application and open it by pressing OK.

Just like with the Statistics app, the Regression app also has three tabs at the top of the screen: Data, Graph and Stats.

The table below shows the relationship between quiz scores (out of 20) and study time (in hours) for a few students in a class.

Study time (hours) 1.5 3 2.25 1.75 0.5 3.25 1 0 2.75
Score (out of 20) 15 19 17 16 8 20 12 4 19
  1. On the Data tab, enter the values of "Study time" into the X1 column and the values of "Score" into the Y1 column.

    Entering the data into the data tab

  2. Navigate up and over to the Graph tab to view the scatterplot.

    Viewing the scatterplot

  3. Use the left and right keys to navigate through the data points. Notice that the values of xx and yy appear in the bottom banner.
  4. How would you describe the relationship between Study time and Score?

    There appears to be a positive, linear relationship. The more time a student studies, the higher their quiz score is.

Let's find the line of best fit.

  1. While viewing the scatterplot on the Graph tab, press OK to open the list of regression models.
  2. Press OK on Linear.

    Viewing the line of best fit

  3. Use the left and right keys to navigate through the data points. While on a data point, use the up or down keys to navigate onto the line of best fit. What is the regression equation (round to the nearest hundredth)?
  4. Viewing the equation of the line of best fit

    The equation of the line of best fit is y^=4.65x+6.18\hat{y}=4.65x+6.18

  5. You can also find the equation of the line of best fit in the Regression menu. Press the Toolbox key to open the Regression menu and find the equation of the line.

    Viewing the equation of the line of best fit in the regression menu

We can use the equation of the line to make predictions for scores based on other study times.

  1. While in the Regression menu, navigate down to Predict Y given X and press OK.

    Viewing the tool Predict Y given X

  2. Predict the quiz score for a student who studied for 2 hours by entering 22 for xx. What is the predicted score?

    Inputting x=2

    Viewing the regression line when x=2

    A student who studies for 2 hours is predicted to score a 15.48 on average.

  3. Use the back key to return the the Regression menu and navigate down to Find X given predicted Y.

    Viewing the tool Find X given predicted Y

  4. Determine how many hours of studying a student would need in order to earn a score of 18 on the quiz by entering 1818 for yy.

    Inputting y-hat=18

    Viewing the regression line when y-hat=18

    It is predicted that to earn an 18, a student must study for 2.54 hours, on average.

The Stats tab provides summary statistics for our dataset.

  1. Navigate to the Stats tab and find the row Mean xˉ\bar{x}. This reports the mean or average for X1 and Y1.

    Viewing the stats tab

  2. What is the average amount of time these students studied (round to the nearest hundredth)?

    Viewing the average of X1

    The average amount of time studied by these students is 1.78 hours.

  3. What is the average quiz score for these students (round to the nearest hundredth)?

    Viewing the average of Y1

    The average score made by these students is 14.44.

Keep exploring!

There's a lot more you can do on the NumWorks calculator! Keep exploring the applications and check out the short tutorials at num.works/tutorials.