8.3: Testing for Truth
This activity is intended to supplement Algebra I, Chapter 7, Lesson 6.
ID: 12175
Time required: 20 minutes
Activity Overview
In this activity, students will identify whether points lie within a shaded region that is bounded by linear inequalities. The focus is on testing the points for truth in the inequality. Students will use a graph to verify their answers.
Topic: Inequalities
- Students will visually determine the location of a point with regard to shading or the line itself. (Above, below, or on the line itself)
- Students will answer True or False as to whether a point satisfies multiple conditions established by linear inequalities.
Teacher Preparation and Notes
- Students will utilize a random number generator to create unique scenarios and answer questions about the points plotted as a result.
- Students will organize their thinking by using a table structure on the worksheet to answer True or False as to whether a point lies within a shaded region.
- Students will use the : menu to evaluate inequalities as true or false.
Associated Materials
- Student Worksheet: Testing for Truth, http://www.ck12.org/flexr/chapter/9617, scroll down to the third activity.
Problem 1 - Is a Point a Solution?
Students begin this activity by setting the random seed, so that students will not get the same sets of points throughout the activity. Instructions are given to use the last \begin{align*}4\end{align*} digits of their phone numbers, but other numbers could be used, such as house or apartment number or birthday (in the form MMDD). Enter 1 2 3 4 STO \begin{align*}\rightarrow\end{align*} MATH \begin{align*}\leftarrow\end{align*} ENTER ENTER to save the random seed.
Students will then generate random numbers in \begin{align*}L_1\end{align*} and \begin{align*}L_2\end{align*} as \begin{align*}x-\end{align*} and \begin{align*}y-\end{align*}coordinates. Press MATH \begin{align*}\leftarrow 5 (-) 10, 10, 3\end{align*}) STO \begin{align*}\rightarrow 2^{nd}\ [L1]\end{align*} ENTER. Repeat replacing \begin{align*}L_1\end{align*} with \begin{align*}L_2\end{align*} to generate the \begin{align*}y-\end{align*}coordinates.
The table on the student worksheet will make it easier for students to organize their thinking and to show their work.
What will students write if the point lands on the line itself? On the line is not included in the shaded region for this example, since the inequality is \begin{align*}y > -x - 2\end{align*}.
Students can also test the inequalities on the home screen to see if they are true or false. To test the given example, press \begin{align*}2^{nd}\ [L1]\ 2^{nd}\end{align*} [TEST] \begin{align*}3\ (-)\ 2^{nd}\ [L1] - 2\end{align*} The calculator will return either \begin{align*}1\end{align*} for True or for False. In this case, the first two coordinates do not satisfy the inequality but the third coordinate does.
Problem 2 - Generating Solutions
Have students use the table to record their answers on the student handout.
The emphasis here can be on dotted and solid lines, and \begin{align*}<, \le, >, \ge\end{align*} symbols.
Again, have students generate random numbers and store to \begin{align*}L_1\end{align*} and \begin{align*}L_2\end{align*}. Students can use the home screen to test but they can also graph the inequalities and determine if a point is a solution graphically.
The equations should look like the screen at the right. To change the “style” of the graph, move the cursor to the left of \begin{align*}Y=\end{align*} and press ENTER until you see either or , accordingly.
Problem 3 - Overlapping Region
The students must regenerate points until at least one lies within the triangle.
The students should use the table to record their answers on the student handout.
Encourage the students to continue generating ordered pairs if they can not easily see the grid in order to record the correct numbers. If the students can’t clearly determine whether the point lands on a line, or within or outside of the shaded region, don’t use that point for simplicity of discussion.
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