Using Systems of Equations to Solve Word Problems

We read through five of the six word problems and discussed how to set them up using two different variables, as we agreed that setting up the equations is more difficult than actually solving the problems. Students were asked to complete the six word problems for Monday.

Students also took a 2 problem quiz over solving systems of equations.

Tonight's Homework: Complete both pink worksheets.

Systems Practice

Today, students practiced using each of the three methods for solving systems of equations (graphing, substitution and linear combinations) to prove that all three methods result in the same solution.

Tonight's Homework: Lesson 7.3 ( 27, 31, and 33). You need to solve each problem three different ways (using graphing, linear combinations and substitution).

Using Linear Combinations to Solve Systems of Equations

The third method of solving systems of equations is called linear combinations. Students received a handout that described the steps for what to do when using this method to determine the intersection of two lines. Lesson 7.3 also has a great explanation for what to do, should you want to read it.

Tonight's Homework: Complete the three examples on the handout, as well as Lesson 7.3 ( 18 - 24, even). Once again, be sure to show all steps, including the check step, for each problem.

Using Substitution to Solve Linear Systems of Equations

Today, we solved the same problems we graphed on Friday using a different method. We substituted one part of one equation in for a variable in the second equation, and then used our algebra skills to determine the value of the remaining variable. Many students liked this method of solving the problem better, although it did, in some cases, require a few more steps.

Tonight's Homework: Complete the three problems on the Guided Practice for Using Substitution worksheet, and include check steps. Also, do Lesson 7.2 (18 - 22 even).

Two More Concept Tests Are Done!

Students took the tests over Concepts 8 and 9 today in class. Most finished the tests with about 10 minutes to spare.

Tonight's Homework: Read pages 777 and 778. Then do the odd problems on page 778. Enjoy the weekend.

Graphing Two Lines on the Same Coordinate Plane

When you graph two lines on the coordinate plane, sometimes they will intersect. When they do, how can you determine the exact coordinates of the point of intersection? If you find the proper point, and then substitute the x and y values back into each of the original equations, you should end up with true statements, like 5 = 5.

This idea is explained well in your text book. See Lesson 7.1.

Tonight's Homework: Lesson 7.1 ( 17 - 19, 20 - 28 even ). Also, be sure to come to class prepared to take the tests over Concepts 8 and 9.

Reviewing Perpendicular and Parallel Lines

Students reviewed how to find the equation of a line given the slope and a point. This is a necessary skill to master before taking the test over Concept 8. We reviewed the answers to the practice questions for Concept 8 and 9.

Tonight's Homework: Page ( 1 - 12, 19, and 20 - 25 ). Try to get a parent to sign your weekly grade slip and return it to class on Wednesday.

Note: I will not be available for help during resource on Wednesday, January 20th. The test over concepts 8 and 9 has been moved to Friday, January 22nd.

Creating Equations for Lines Parallel or Perpendicular to a Given Line

Students were shown how to determine the equation of a line parallel to a given line when given a point. This same general idea can be applied to determining the equation of a line perpendicular to a given line. Students had time in class to complete a series of 6 question allowing them to practice these skills.

Tonight's Homework: Complete the Practice Tests for Concepts 8 and 9. Most of all, enjoy the long weekend!

Graphing Inequalities and Writing Inequalities from Graphs

Today, we used the palms to correct some of our homework. Students realized that the palm is limited to using only the function form of an equation or inequality. To check equations and inequalities written in standard form, they must be converted to function form first.

Students completed a review sheet on graphing inequalities. This review sheet will be a great resource for students as they prepare for next week's test.

Tonight's Homework: Lesson 6.5 ( 49 - 59, odd) and page 366 ( 13 - 22 )

Multiplying Inequalities by a Negative = Arg!!

Students were reminded of the rules related to working with inequalities. When you multiply or divide these types of problems by a negative number, the inequality sign must be switched.

Tonight's Homework: Page 802 ( 27 - 35 )

Graphing Inequalities on the Coordinate Plane

Today we looked at inequalities and how they are displayed on the coordinate plane. We first looked at inequalities written in standard form. After converting these equations, we determined the x and y intercepts of the line. We plotted the points and then determined whether the line should be dotted ( < or > ) or solid ( ≤ or ≥ ). Once the line is on the graph, we used a test point (I suggested using the origin whenever possible) to see which side of the line should be shaded.

Students completed 4 sample problems in class.

Tonight's Homework: Lesson 6.5 ( 24 - 60, even ). Feel free to put two problems on each grid, but be sure to use two different colors.

Discrete and Continuous Data in the Real World

Students spent most of the class period working on a series of two worksheets relating what we've been studying to real-life situations. The worksheets (Nickels and Dimes and Linear Functions for Word Problems) serve as review sheets, pulling together many of the topics we've been studying in December and January.

Tonight's Homework: Complete both sides of the two worksheets you received in class today (Nickels and Dimes and Linear Functions for Word Problems). Be sure to show work!

Reviewing Linear Function Vocabulary

Today we reviewed vocabulary related to linear functions. Terms like y-intercept, slope, x-intercept, standard form of an equation, function form of an equation, and slope intercept form were all revisited. We also discussed real-life examples of functions can explain things, like salary over time, number of hats on heads as the temperature changes, cell phone and taxi cab charges, and power bills.

Tonight's Homework: Finish both sides of the worksheet you started in class.

Stacking Cups Analysis and Let's Party!

We used the Stacking Cups data to help look at our cups in a different way. We saw the cups as made of two parts: the "lip" and the remainder of the cup. Using this breakdown, we could see that the height of the stack of cups was a function of the number of cups in the stack multiplied by the "lip" distance, and added to the distance of the remainder of one cup.

After this, we looked at another set of discrete data--eating licorice, one bite at a time. Students measured the length of a piece of licorice, and then recorded the length of the rope after each successive bite.

Tonight's Homework: Complete the "Let's Party" worksheet.

Welcome Back!

Happy New Year! Students received weekly grade slips today. All missing work should be taken care of as soon as possible.

Today, we stacked different types of cups to discover relationships between the height of the stack and the number of cups in the stack. We talked about this being an example of discrete data, rather than continuous data. We will finish our conversation about the data collected tomorrow.

Tonight's Homework: Get your grade slip signed. Complete the Stacking Cups worksheet (both sides).