Writing Linear Equations Cards Set #1

  1. Cards are color coordinated so that each color is a complete set.
  2. Within each set, every card is numbered in the lower right-hand corner.
  3. A number line from about -10 to 20 is needed – preferably a number line on the floor that students can walk on. Knotted ropes (a knot every foot) make a great number line.
  4. Do at least one example as a whole group: If I start on 1 and take steps of size 2, where will I land on my first step? my second step? etc. Discussion needs to take place to define “steps of size 2” – does it mean 2 small steps of 1 or a larger step that “skips” numbers on the number line – the later definition is easier for students to keep track of.
  5. Suggestion #1:

a. Cards 1 - 6

·  Put the students into groups of 4.

·  Give each group card #1.

·  Each group determines how to walk this off on the number line, then walks it off and records the landings on the card with dry erase markers.

·  One student from each group brings you back the card so you can discuss the results and ask questions to probe their understanding.

(How did you get these landings? Do you see a pattern? How do you know that you are right? etc.) to probe their understanding.

·  Send card #2 back with that student with the directions that a different student must bring back the solution.

·  Cards 1-6 are all similar: they give the start value and the step size; the students are asked to determine the landings. You may skip some of these cards with some of the groups; also, there are blank cards at the end of the deck so you can add additional problems if needed.

b. Cards 7 - 12

·  Cards 7-12 are all similar: Each card has the table filled out giving the step number and the landing. The students must determine the “start value” and the “step size”. This is harder for the students so you may not want to skip any of these cards with some of the groups. There are blank cards at the end of the deck so you can add additional problems if needed.

·  Stop after card 12 and have a class discussion.

·  Use the data from one of the cards and a graphing calculator.

·  Enter the step number in List1 and the landing in List2. (see pages 3-4 for calculator directions)

·  Display the graph. (Scatter plot with L1 on the x-axis and L2 on the y-axis)

·  Have the students enter an equation into the y= menu as a guess and then graph it to check to find the equation that “best fits” the data. Revise guesses as needed. The data is linear so they should be able to find the equation. Let them “legally cheat” by sharing their equation after they have found the correct one.

c.  Cards 13 – 21

·  Give each group card 13 (with the directions) and card 14.

·  Ask them to determine the equation by creating a scatter plot on the calculator and using

·  Continue the process of sending a different student for each card to report/discuss findings with you and to get the next card. It usually takes about 3-4 cards before some students notice the relationship between the “start value”, the “step size” and the equation. Cards 14-19 are similar.

·  Card 20 asks students to verbalize the relationship between the “start value”, the “step size” and the equation.

·  Card 21 has students test this relationship by predicting the equation. This is a good time to show them the table function on the calculator to test their prediction – after they type in their equation, they can look at the table and see if it matches the table on the card.

  1. Suggestion #2:

·  Put the students into groups of 4.

·  Give each group cards 1 - 4. They can work on them as a group with each student taking a different card and filling out the table.

·  After a set time, ask all the students that have card 1 (also card 2, 3, and 4) meet in a certain area. They are to discuss their answers and reach a consensus for their answers. Circulate to each group and ask questions (How did you get these landings? Do you see a pattern? How do you know that you are right? etc.)

·  Ask them to come back to their group and discuss their cards. Give each group cards 5 and 6 if you think they are needed.

·  Discuss their findings as a whole class.

·  Give each group cards 7- 10 and repeat the steps above with those cards. Cards 11 and 12 are also the same type of patterns.

·  Stop after card 12 and see directions above (part c).

Scatter Plots on the TI- Graphing Calculators

To create a scatter plot on the calculator, three things should take place before you press the GRAPH key:

1.  The x-coordinates and y-coordinates must be entered into lists.

2.  The window values must be defined.

3.  The stat plots options must be defined.

To enter the x-coordinates into L1

1.  Press LIST (TI-73) or 2nd STAT (TI-83/84)

2.  If necessary, use the left arrow key to scroll until L1 is in your screen.

3.  If L1 contains data, you can clear the list by using the up-arrow until the list name (L1 in this case) is highlighted; press CLEAR; press ENTER or the down-arrow ().

4.  To enter a number, type in the number and then press ENTER or the down-arrow ().

5.  Remember that you can edit the list using INS, DEL, or CLEAR.

6.  When you finish with your list, you can return to the Home screen by pressing QUIT (2nd MODE).

Use the same steps to enter the y-coordinates into L2.

Defining window values

Press WINDOW (located in the graph row.) Window values put specific boundaries on the display.

Xmin The minimum value on the X-axis. It must be less than Xmax. If you want to see the Y-axis, you must choose negative 1 or below.

Xmax The maximum value on the X-axis. I usually choose a number slightly higher than my largest X-value.

Dx When using the TRACE function, this determines the increments between X-values. The calculator automatically sets this value!

Xscl The distance between tick marks on the X-axis. To turn off the tick marks, set Xscl = 0

Ymin The minimum value on the Y-axis. It must be less than Ymax. If you want to see the X-axis, you must choose negative 1 or below.

Ymax The maximum value on the Y-axis. I usually choose a number slightly higher than my largest Y-value.

Yscl The distance between tick marks on the Y-axis. To turn off the tick marks, set Yscl = 0

Defining Stat Plot Options

1.  Press PLOT (2nd Y=) (TI-73) or STAT PLOT (TI-83/84)

2.  Make sure all plots are turned off except for Plot1 (You can turn them all off at one time by selecting 4:PLOTSOFF and pressing ENTER and ENTER again when PLOTSOFF is showing on the HOME screen.). Press PLOT or STAT PLOT to get back to that menu if you had to turn off the plots.

3.  Choose Plot1 by pressing ENTER

4.  Select On by pressing ENTER

5.  Scroll down with the arrow key and select  (the first option) on TYPE (this is a scatter plot)

6.  Scroll down with the arrow key and make sure L1 is showing for the Xlist (if L1 is not showing for your Xlist, press STAT (2nd LIST) and choose L1) (TI-73) or 2nd 1 (TI-83/84)

7.  Scroll down with the arrow key and make sure L2 is showing for the Ylist (if L2 is not showing for your Xlist, press STAT and choose L2) (TI-73) or 2nd 2 (TI-83/84)

8.  Scroll down with the arrow key and select the type of mark you prefer by pressing ENTER.

Make sure all equations in Y= are cleared or turned off. Press GRAPH and you should see your scatterplot.

Guessing the Line of Best Fit

1.  Press Y=

2.  Type in the equation that you think “best fits” the scatterplot.

3.  Press GRAPH

4.  Experiment until you find the equation that “best fits” your scatterplot by repeating steps 1-3. Make sure to clear your old equation.

Directions for Writing Linear Equations Cards Set #1 page 3 of 4