Writing Inequalities to Describe Graphical Representations

Today, we switched things up and looked at pictures of systems of inequalities to see if we could write a series of statements that described the shaded region of the graph. The number of statements depends on the shape of the shaded region. A triangular shaded region will have 3 different inequalities to describe it, while a rectangular shaded region will have 4 inequalities that describe the region.

Tonight's Homework: Complete both sides of the blue worksheet on Linear Inequalities. Remember to graph the problems on the front side. In addition, complete the 3 problems on the Systems study guide sheet.

Note: The test over linear inequalities will be given in class on Friday, February 3rd. Start preparing for it now!

Looking at Systems of Inequalities

Today, we looked at how to graph a system of inequalities, and use the shaded portions to determine the solution to a multi-pronged problem.

Tonight's Homework: SOA ACE 5 (5-8, 13, 14) and Investigation 5.4 all problems

Relating Linear Inequalities to Real-Life Situations

Students used most of the period to work on problems related to real-life uses of inequalities. We talked about limiting car travel each month, limiting our carbon footprint by riding in more gas-efficient vehicles, and making candy combinations.

Tonight's Homework: There are three things for you to complete over the weekend:
•Green worksheet on graphing linear inequalities (both sides)
•Shapes of Algebra book, ACE 5 (1 - 4, 15)
•Finish the Candy Combinations worksheet (for Tuesday)

Buying Combinations of Munchies and Toasties

Relating algebra to real-life situations can sometimes be difficult for students to comprehend. Today, we began working on a problem that uses many of the algebra concepts and skills we've been learning about this year. Students were at first a bit confused by the problem, but after breaking it down into smaller parts, most saw the relevance in the questions being asked.

Tonight's Homework: Read Problems 5.1 and 5.2 in the Shapes of Algebra book. Create a data table and graph for the Candy Combination problem you received in class today. Be sure it reflects the limitations described in the problem.

More on Graphing Inequalities

Using the handheld computers, we graphed several types of inequalities. We noted that the handheld was able to show the differences between solid and dotted lines.

Tonight's Homework: Home Book page 7 ( 33 - 44 )

Another Test Bites the Dust!

Students took time in class to take the test over concept 8. Those who finished early were able to work on tonight's homework.

Tonight's Homework: Home Book 2: Read pages 3-5, and do problems 2-32, even.

Graphing Linear Inequalities: A Preview

Students graphed several inequalities. The rules for graphing them are similar to those used to graph equations, with one difference: The inequality sign requires attention to whether a dashed (dotted) or solid line is used, and the graph will need to be shaded either above or below the line

Tonight's Homework: Complete both sides of the worksheet on graphing inequalities. This will be due on Monday.

One More Time: Parallel and Perpendicular Lines

Performance on concept test 7 was either really good or rather poor. Students reflected on how they prepared for the test, and hopefully realized that not studying the material can influence the way they perform on the test. Students were reminded that the next test will be given on Friday, January 20th. It will cover linear equations: determining slope from two points, writing equations for parallel and perpendicular lines to a given line, and writing equations in standard form. We reviewed these processes again today.

Tonight's Homework: CME, page 371 (5 - 9). Although the directions state to write equations for parallel lines only, I would like you to do each problem twice--once following the book's directions, and a second time, finding the equation of the line perpendicular to that line going through the point listed.

Concept Test 7 is Now History!

We finally were able to take the test over concept 7 this morning.

Tonight's Homework: CME, page 338 (12 - 14)

MLK Assembly Shortens Class

We continued our work on writing equations for lines that are parallel or perpendicular to a given line.

Tonight's Homework: CME, page 338 (12 - 14) and be sure to study for the test over linear equations (concept 7). It will be given in class on Tuesday.

Rare Work Day!

Because 17 students missed class today because of the Shelly Moon assembly, we turned today into a work day for those who were present. Most students were able to get a good start on their homework.

Tonight's Homework: Pink Cookie Application worksheet and CME, pages 317 (7), 333 (7) and 342 (8). The test over concept 7 will now be given in class on Tuesday, Jan. 17th. Concept test 8 will be given later in the week.

Collinearity and Writing New Equations for Parallel or Perpendicular Lines

Students learned about collinearity today. Points that are collinear have the same slope. In addition, we learned how to find equations for lines that are parallel or perpendicular to a given line. The steps include:
•determine the slope of the new line (m or the negative reciprocal of m)
•write a new equation in slope-intercept form using the new slope
•use a point on the original line to replace the x and y values in the new equation so you can solve for b
•put the new b value in the new equation

Note: Because so many students will be missing class tomorrow (to present or listen to personal narratives), concept 7 test will now be given on Tuesday, January 17th (not tomorrow, as previously announced).

Tonight's Homework: CME, page 316 (1), 330 (1) and 341 (3)

More on Standard Form of an Equation

Writing the standard form of an equation allows you to easily determine the x and y intercepts of the equation. Simply substitute 0 in for x and solve the equation for y. This will give you the y-intercept. By substituting 0 in for y, you can find the x-intercept. Plotting these two points will allow you to draw the line that the equation describes. Using the picture, you can then determine the slope, if asked to do so.

Tonight's Homework: Complete both sides of the yellow Linear Equations worksheet.

Standard Form of a Linear Equation

After correcting homework, we took a look at a second way to write linear equations. Having the equations in slope-intercept form is extremely useful when trying to graph an equation. When asked to find the x and y intercepts of a given equation, this form is not as useful. Writing the equation in standard form is another way to express linear equations, and this would be extremely helpful for finding the intercepts. The standard form of an equation is Ax + By = C. In this equation, A, B and C need to be integers (not fractions) and A must be positive.

Tonight's Homework: Complete the blue worksheet on Standard Form of the equation.

Review over Linear Equations

Students took notes about what to expect on the upcoming concept tests over linear equations. It looks like we'll be taking the concept 7 test on January 12th, and the concept 8 test will be given on either January 17th or 18th.

Tonight's Homework: Complete the practice worksheet for the concept 7 test and the purple worksheet with graphs about lines.

Let's Party!

Yes, it's true, we had a party in math class today. Well, maybe not a true party, but students ate red vines and drank either lemonade or water in order to collect data that related to linear functions. After collecting the data, students graphed their information on a grid and tried to come up with an answer to the question: "How big is your bite/sip?" This proved a bit more difficult, since the data was not as predictable as it had been in previous activities. Nonetheless, students did a great job of figuring out the rates of change and the rules.

Tonight's Homework: Complete the Let's Party! and yellow analysis worksheets.

Welcome Back!

Welcome back! Here's hoping your break was a relaxing one, and that you didn't forget too much math over your time off.

We looked at the Zap It 2 worksheet to remember things like rate of change, y-intercept, and slope-intercept form of an equation. Students received their weekly grade slips, and were encouraged to complete any missing work listed on the slips.

Tonight's Homework: Get your grade slip signed (graded assignment this week). If there are missing assignments listed on your grade slip, be sure to get them done.