Test day

Students are taking their test today on the quadratic concepts that we have been working with for the last 2 weeks.

This weekend is a math "holiday". Sunday's date is 3.14 which is also the common approximation used for pi. To celebrate this, students have been offered an extra credit opportunity to wear a shirt on Monday with some notes about pi on it. They received a handout with the information in class today.

Next week, we will start working with radicals (square roots) and rationals (fraction). Our next test is scheduled for April 1st.

---

Review

We started class by going over homework. Then, student receive their Unit 4 Part 2 tests. For the most part, these grades were an improvement over previous tests. Students also receive a grade printout showing their current grade (with this most recent test). The statistics projects are not graded yet so those scores do not appear on the handout. Students should get their parents to sign off on the grade sheet.

Students received a review packet in class today. It is due tomorrow for a homework check and then we will go over it to prepare everyone for Thursday's test.

---

Systems of Equations - NonLinear

We used the review of systems of linear equations on Friday to jump to systems of non-linear equations today. Our lesson has systems that are either 1 linear & 1 quadratic equation OR 2 quadratic equations.

Students should be able to find solutions on a graph. To do this, identify where the graphs meet. There could be no solutions (no intersection), 1 solution, 2 solutions, or infinitely many solutions (when the graphs overlap completely).

Students should also be able to find solutions by working with the equations. To do this follow these steps:

1. Confirm that both equations are solved for y. If not, get y by itself.

 

2. Substitute the first expression for y in the second equation. Solve for x. This can be done by either (1) setting the equation equal to 0, factoring, and solving for x from the factors; or (2), only when b = 0, set x² equal to the constant value and then square rooting both sides. Remember, when using method #2, the solution is the positive & negative of the value acquired through square-rooting.

 

3. Substitute the solved value(s) for x into either of the two equations and solve for y.

 

4. To check the solutions, substitute the ordered pairs into both equations to verify the values are correct.

Example:

Homework: Worksheet on Solving Systems of Non-Linear Equations.

There will be a TEST on Thursday covering all quadratic concepts from last week and this week. Students will receive a review worksheet tomorrow in class.

 

 

Systems of Equations - Linear

We discussed the online test that all students should have finished at least once by today. Students are encouraged to retest their *missed problems* to raise their score. I do not suggest that students completely retake a *new* test. They should build on the test that they already answered some of the problems correctly. I will record and only use the highest score that they achieve. At this time, I have not received a test score from every student. They have until midnight to complete a test and not receive a ZERO for this week's assignment.

Today's lesson is review of 8th grade concepts: solving systems of linear equations. Their handout has directions and examples for solving a system of linear equations with three different methods.

Solving a System by Graphing:

• Step 1: Graph each equation on the same coordinate plane.


• Step 2: Identify where the two graphs meet (if anywhere). The point where the graphs meet is a solution of the system. It is possible for the two lines to be parallel and never intersect. Parallel lines have no common points, so the system has no solution.


• Step 3: Check the solution by substituting the values of x and y into both equations. Verify that it solves both equations.


• Example:

Solving a System by Substituting:

• Step 1: Solve one of the equations for either of its variables.


• Step 2: Substitute the expression from step 1 into the other equation and solve for the other variable.


• Step 3: Substitute the solved value from step 2 into either of the original equations and solve for the remaining variable.


• Step 4: Check the solution by substituting the values of x and y into both equations. Verify that it solves both equations.


• Example:

Solving a System by Eliminating:

• Step 1: The goal is to make one of the variables have opposite values for its coefficients in the two equations (like -5x and +5x ... or +4y and -4y). If the equations do not already have this requirement, then select one of the variables to affect. Multiply everything in the equation to get the desired coefficient on the selected variable. You may need to multiply both equations by different values to meet this requirement.


• Step 2: Add the two equations together by collecting like terms. Some students remember this step from last year when they wanted to either get "0x" (zero-x, but called ox) or "+ 0y" (plus zero-y, but called toy). Solve for the remaining variable.


• Step 3: Substitute the solved value from step 2 into either of the original equations and solve for the remainging variable.


• Step 4: Check the solution by substituting the values for x and y into both equations. Verify that it solves both equations.
• Example: Note ... the step numbers in the example below are each one value higher than the way I numbered my steps above.
  
  
  

Homework: Worksheet on Systems of Linear Equations

---

Quadratics, Day 3

Our third lesson with quadratics is our final version of graphing quadratics. Today we discussed the vertex form of the quadratic function: y = a (x - h) ² + k. This form makes is the easiest for identifying the vertex of the parabola.

• The vertex is located at (h, k). Students need to remember that they switch the sign of what the "see" inside the parenthesis in the equation for h. The value of k is exactly what they "see" to the right of the parenthesis in the equation.
• Use a table to select values near the vertex. Substitute these values in for x and solve for y. Get at least 5 points on the graph.
• Plot these points and draw a U-shaped curve.

Homework: Worksheet on Graphing Quadratics in Vertex Form

Don't forget to do your vocabulary and your online EOCT practice test. Both are due tomorrow!!!

---

Delayed Start today

Due to the 2-hour delay today, Milton High School started with 3rd period classes. This means that I did not see my 1st period class.

My other IAA classes took a notebook quiz and a county wide Checkpoint Test. 1st period already took the notebook quiz last week. And, 1st period just will not take the checkpoint test due to our schedule. The Checkpoint Test is a diagnostic test to assess how much information from the entire year the IAA students know right now. The results of this test will NOT affect a student's grade in anyway. Its purpose is to show me what information I may need to reteach before our final exam.

Yesterday, students were given a handout explaining how to access a website (www.usatestprep.com) that has practice tests correlated to our final exam. They have a weekly assignment to take the "Large Test" for "Mathematics 1" each week by Friday.

There is no new homework today. If students did not finish yesterday's worksheet, then they have tonight to do it. Or, they can use tonight to take care of their weekly EOCT Practice Test assignment.

---

Quadratics - Intercept form

Students found out yesterday that graphing quadratics in standard form does not lend itself well for locating the x-intercepts. Sometimes the graph crosses between two "nice" integers. Sometimes the graph crosses the x-axis a significant distance away from the vertex and requires extra work to locate. So, today's lesson is about the intercept form which identifies the x-intercepts very easily.

Intercept form: y = a (x - p) (x - q)

• To find the x-intercepts in this form, set the factors equal to 0 and solve for x: (p, 0) and (q, 0).
• To find the vertex and the axis of symmetry in this form, remember that the graph is symmetrical, meaning that the AOS will have to be in the middle of the intercepts. To find this location, average p and q. This calculates the x-value of the vertex. Substitute this into the equation and solve for y.
• Pick another value for x near the vertex and find it corresponding y value. Plot all points and draw a smooth U-shaped curve.

Homework: Worksheet on Graphing Quadratics in Intercept Form

---