Reviewing for Concept 17 Test

Given that nearly half of the class is involved in track and that there's a track meet this afternoon at Sheldon, I chose to make today a work and review day. Students spent the majority of the period working on review sheets to help them prepare for the upcoming concept 17 test, which will be given in class on Tuesday, May 5th.

Tonight's Homework: Complete what you did not complete in class. There are four worksheets due tomorrow: White, green, light pink and bright pink. Be sure to do both sides of the paper!

Special Product Cases for Multiplying Polynomials

We continued to FOIL binomials while looking at special situations, hoping to discover a shortcut in the process. When squaring a particular binomial, you can use a shortcut several students suggested to save time. When multiplying the sum and difference of two terms, there is a different shortcut that you can use.

( a + b ) ( a - b ) = a^2 - b^2

( a + b ) ( a + b ) = a^2 + 2ab + b^2

( a - b ) ( a - b ) = a^2 - 2ab + b^2

We also started talking about the zero product rule, and how it relates to the quadratic equation and x-intercepts of parabolas.

Tonight's Homework: Lesson 10.3 ( 16 - 38, even, 44, 48, and 52 ).

Multiplying Polynomials

After reviewing the distributive property, students learned how to multiply polynomials. We began with multiplying a monomial by a binomial, then a trinomial and then a quadrinomial. The important thing to remember is to record all answers using standard form (decreasing degree of terms). Once students got the hang of doing this, we began multiplying binomials by binomials, and then trinomials. The FOIL method of multiplying was formally introduced.

Tonight's Homework: Lesson 10.2 ( 30 - 40 even, 52 - 60 even, but not 56 ).

Classifying Polynomials by Term and Degree

We learned how to classify polynomials by number of terms. Vocabulary includes monomial, binomial, trinomial and polynomial. We then learned how to classify polynomials by degree (0 to n, and by name, including constant, linear, quadratic, cubic, and quartic). Students were introduced to the standard form for writing polynomials (in order of degree).

Students received expanded grade slip information (handwritten slips attached to the printed grade. For one day only, students turning in late work will receive reduced credit, which will only help buoy up grades. This offer ends at 3:30 p.m. on Tuesday, April 28th.

Tonight's Homework: Lesson 10.1 ( 7 -12, 49 - 60, FCO ). Try a couple of problems using the vertical format and then a couple more using the horizontal format.

Sixteen Tests Are History!

Students took the sixteenth concept test today. Only three more to take for the year!!!!

Students turned in their notes from the projects, and also completed a critique.

Tonight's Homework: None. Remember, all retakes for previous concept tests must be taken (and passed) by May 7th. Failure to do so will result in an "incomplete" grade entered on your progress report on May 8th.

Preparing for Concept Test 16

Today, we worked through a variety of problems related to parabolas. Questions related to cheerleading, ski jumps, cliff jumping and lawn sprinklers were addressed. Some of the problems required use of the quadratic equation while others did not.

Students are urged to review their practice worksheet (purple) tonight as a way to prepare for tomorrow's concept test.

Tonight's Homework: Assorted story problems from sections 9.1, 9.3, 9.5 and 9.7.

Quadratic Applications in the Real World

We learned about the Falling Object Model, which can help you determine the location of an object when it is dropped from a given height. Objects fall towards the earth at a given rate, and the model can help you determine how long it will take an object to fall to the ground.

Another useful model that involves quadratics is the Falling Objects with Initial Force Model. Divers, gymnasts, and bullet motion all use this model to describe the path of motion.

These models will be used in tomorrow's homework.

Tonight's Homework: Complete the problems on the purple practice worksheets.

Negative b over 2a Determines Line of Symmetry . . .

and also the x value of the vertex of a parabola. Students finished presentations today, and then we related the assignment to a portion of the quadratic equation. Students saw how the negative b over 2a portion of the equation related to the line of symmetry. Once the line of symmetry is found, plugging the x value into the original equation will give you the y value of the vertex. Oh, how sweet is that?

Tonight's Homework: Lesson 9.3 ( 24 - 43, last column only, and 72 - 74 ). By the way, we will be taking the 16th concept test on Thursday.

Concept Test 15 Taken Today

Two more student presentations were made today, leaving about 3 for next week. After the presentations, students turned in homework and then took the concept 15 test. This included two parts: a post test to measure growth and the actual concept test.

Tonight's Homework: Do Quiz 1 on page 524. By the way, if you are reading this, you'll be glad to know that 26 of you passed today's concept test on the first try. Yeah!

Shortened Class = Lots of Presentations!

Today's class was shortened due to the Talent Show Teaser assembly, which took place earlier in the day. Students submitted homework, and then 5 groups presented their findings to our investigation about the effect of b on the parabolic placement on the coordinate grid.

Students are reminded that the Concept 15 test will be given in class on Friday.

Tonight's Homework: Study for the concept test. To help you do so, complete Quiz 2 on page 547 and Quiz 3 on page 560.

Let the Presentations Begin

We reviewed vocabulary terms including radicand and discriminant. We then started working with quadratic equations with the hope of writing them in standard form and starting to solve them. Remember, if the discriminant is positive, then the equation will have 2 solutions.

Presentations began today, with 4 boys being brave enough to share their findings. At least two more groups will present their findings on Wednesday.

Tonight's Homework: Complete the blue and orange worksheets.

Using the Quadratic Formula to Determine x-Intercepts of a Parabola

We reviewed what the standard form of a quadratic equation looks like. Remember, having a positive "a" term is desirable, and may be required by future math teachers.

Using the quadratic formula, we learned how to find the x-intercepts of certain parabolas. Remember, not all parabolas have x-intercepts. You can tell how many x-intercepts a parabola has by evaluating the discriminant.

Tonight's Homework: Lesson 9.5 ( 10 - 18, 23 - 28 odd, 53 - 55 ). Be sure to thank the Easter Bunny for all the kind things s/he does to make you happy, and get a signature from the Easter Bunny as proof that you have done this.

Have an "eggs"-cellent weekend!

Graphing Quadratic Inequalities

We applied rules to graph linear inequalities to our study of parabolas. The rules are very similar. You must determine whether to use a dotted or solid line, and then determine where the shading will go on the graph. To determine the nature of the line defining the parabolic shape, look at the inequality sign. If you see the "<" or ">" sign, the line should be dotted. If a "≤" or "≥" sign is present, then use a solid line to define the parabola. Whenever possible, use the origin, or (0,0), to test your graph for where the shading should go.

Students had about 25 minutes to work on their group projects today. Presentations begin on Tuesday, April 14th.

Tonight's Homework: Read Lesson 9.7, and then do 9.7 ( 7 - 22 all ).

Applications of the Discriminant

Today, we learned that the nature of the simplified discriminant tells you how many, if any, x intercepts the parabola will have. This can be useful when trying to determine where to place the parabola and when trying to find the line of symmetry and vertex of the parabola.

Students had about 34 minutes to work with their partner on the "b" effect on the parabola project. Presentations will include use of the palm with appropriate examples as well as a creative presentation piece. Students will be graded on accuracy of the math presented, speaking skills, and creativity.

Tonight's Homework: Read Lesson 9.6, and then do problems 9 - 20 in this section.

What's a Discriminant, and Why Are We Using This in Math?

Students were introduced to the quadratic formula, and told they would need to memorize it within the next week or so. To help students accomplish this task, we focused on the discriminant, and how to evaluate this by using the coefficients of the terms of a quadratic equation written in standard form.

Tonight's Homework: Read section 9.1, and then do problems 23 - 44 on page 507.

We reviewed vocabulary related to parabolas and quadratic equations. Terms included vertex, line of symmetry, coefficient, table of values, maximum and minimum. We learned that the line of symmetry passes through the vertex, meaning you know the x-value of the vertex if you know the equation of the line of symmetry.

Students chose partners and began working on an investigation that will help them discover how "b" impacts the parabolas position on the coordinate grid. Students will spend the bulk of class time next week working on this project and preparing a creative oral presentation to deliver to the class during the week of April 13th.

Tonight's Homework: Page 521 ( 21 - 35, FCO, and 38 is extra credit).

Quadratic Equations and Standard Form

Students learned what the standard and "graphable" forms of quadratic equations look like. We noted similarities and differences between different types of quadratic equations that were not recorded in standard form. Given a quadratic formula, students reviewed how to create a table of values (x-y chart) and graph the function on the coordinate plane.

Tonight's Homework: Complete both sides of the hand out. Be sure to include a table of values for each of the problems, and write conclusions (more than one statement) about the resulting graphs.