Solving Quadratics by Square Rooting

We went over homework and answered any questions from the assignment that were asked. If students are still struggling with simplifying square roots, they should make time to see a teacher outside of class for extra help. Our lesson today was on solving quadratic equations by using square roots to cancel the squared variable.

Homework: page 121 #2 - 26 even (not #20) and page 122 #1 - 6

Reminder: The quiz will be Friday. There is a review session available Friday before school in room 4303.

---

Reviewing square roots

The students needed some more practice working with simplifying square roots, so we took today to answer questions, do a practice worksheet, and not move forward with a new concept. This will push our quiz off to FRIDAY. This will also push our morning review session off to FRIDAY. It will still be in room 4303 at 7:45am.

Homework: Finish worksheet "Lesson 3.4 Practice" and Unit 2 Vocabulary

---

Dividing with square roots

We spent time today going over the assignment from the weekend. After that, our lesson covered how to work with division of square roots.

1. Simplify any radicals with perfect squares
2. Reduce the fraction, if possible ... check again for perfect squares
3. Rationalize the Denominator - this is a process of eliminating square roots from the denominator of a fraction. This can take two forms. One form has us multiply the top & bottom of the fraction by a radical that will make the denominator into a perfect square. The other form has us multiply the top & bottom of the fraction by the conjugate of the denominator. Conjugates are specially made to eliminate square roots when they are multipied together. Conjugates have the same numbers & radicals, but they have opposite signs in the middle.

Examples of conjugates: (4 + √3) and (4 - √3); also (6 - √10) and (6 + √10)

For more help rationalizing denominators, try http://www.purplemath.com/modules/radicals5.htm

In fact, all of the lessons at Purple Math are well written with several examples.

There will be a quiz on Wednesday. We will hold a review session Wednesday morning at 7;45 in room 4303 for that quiz.

Homework: page 144 #10 - 18 & page 145 #8 - 15

---

Square Roots

We reviewed simplifying square roots. We built on their previous knowledge of square roots by showing how to add, subtract, and multiply with radicals. It is important to remember that we must have like terms to add or subtract radicals (exact same square root). When multiplying radicals, we multiply their coefficients (the numbers on the outside) and we multiply the radicands (the numbers on the inside) separately.

Homework:
Due next Thursday - Unit 2 vocabulary definitions
Due Monday - Page 144: #1 - 9, #19 - 24 and page 145: #1 - 7, #16 - 20

There is a quiz scheduled for next Wednesday that will assess the students' understanding of simplifying square roots and using square roots to solve quadratic equations (lessons from today through Tuesday).

---

TEST

Yep, today is the test. Before the test, students had to total their earned points from the 9 assignments that we had for this half of Unit 1. Once those points were totaled, the pink homework stamp sheets were turned in to me. They will get a new homework stamp sheet tomorrow for the new assignments for the first half of Unit 2.

A few students needed the full classtime to complete the test. But, most students finished with enough time left in the period to start their homework assignment.

Homework: "Why Did Krok ..." worksheet with problems on simplifying square roots. These problems are review problems. Students must show work for each problem to get full credit tomorrow. Just a reminder: break up the number under the square root sign to find factors that are perfect squares so that they can be square rooted.

Example: √75 = √25 * √3 = 5 √3

---

Review

Class began today with a notebook quiz. The students had to have completed notes and assignments from the last 3 weeks to be able to answer the questions asked. After that was finished, we went over the review sheet and answered questions to prepare for tomorrow's test.

Homework: STUDY!!!

---

No school!

I hope every one is making the most of their day off from school.

The review session that was originally planned for today will now happen tomorrow morning, 7:45 am, in room 4303. We will push the test off to Thursday.

---

Rainy Monday Review

We began class by going over the homework from the weekend. Then we reviewed the differences in recursive and explicit forms of the sequence formulas. We identified formulas as one or the other form, and we found the first 5 terms of the sequence. We also built both of the forms of the sequence formulas for a couple given sequences. Finally, we started on a review worksheet for this week's test. This needs to be finished for homework.

Reminder: tomorrow morning, review session, at 7:45 am, in room 4303

---

Sequence formulas

Today, we discussed how to define formulas (or rules) for sequences. This can be done with a recursive formula that defines each new term in the sequence by how to make it from the previous term. For example, the recursive formula for 5, 8, 11, 14, ... is:

• a₁ = 5 ← This is the starting or first term
• a_n = a_n-1 + 3 ← This is the what the sequence does, it adds 3 to the previous term.

This can also be done with an explicit formula which defines each new term in the sequence based on its position. For example, the explicit formula for 5, 8, 11, 14, ... is:

• First, we recognize that there is a rate of change of 3 for the terms in the sequence. This becomes the slope for the formula. We will start with a_n = 3n
• But, when we substitute n = 1 to find the first term, 3 * 1 = 3. This is 2 units short of the first term. We will add 2 to our formula to bring the output values up to the sequence terms.
• a_n = 3n + 2

Homework: Complete the handout with Sequences: Part 5 and Sequences Homework on the front and back. We will spend Monday reviewing all of the sequences concepts. We have a test scheduled for Wednesday. There will be a review session in the morning, Tuesday the 22nd, at 7:45 in room 4303.

Have a great weekend!

---

Sequences, day 1

We started learning about sequences today. We identified patterns in sequences of numbers. We also discussed how the term is each number, shape, or item in the pattern, and the index is the placement of the term in the sequence (1st, 2nd, 3rd, etc...).

Homework is ...
page 185: #1 - 3
page 187: #2 - 18 even
page 188: #2 - 16 even

We will have a test on Wednesday, September 23rd covering Transformations, Rates of Change, and Sequences. There will be a review session on Tuesday, September 22nd at 7:45 in room 4303. We will also review in class

---

Recovery information

All quizzes and tests have now been returned to the students for them to keep. They already learned of their grades for these tasks when they saw the grade handouts on Monday. However, we discussed the process for RECOVERY today. Recovery is only available for failing test grades. To be eligible, students must complete 90% of the homework assignments from the material on that test. I do not limit the number of times a student may use the recovery process. However, they are limited to only earning up to a 70% from recovery.

For the test on Unit 1 Part 1, the students must have earned 35 out of 39 points on the assingments. To do recovery on this test, they need to schedule time with me either before or after school to rework the problems that they missed. Recovery must be done by next Wednesday, September 23rd.

Recovery is not available for quizzes. However, there will be other opportunities later in the semester to improve quiz grades.

There is no homework for math today!

---

More Average Rates of Change

Today we continued working with average rates of change. However, the numbers were presented this time in function notation format rather than word problem. This lesson also appears in the textbook on pages 180 and 181, in lesson 3.12.

Homework is in the textbook. Page 183: #1 - 7. Page 184: #1 - 6

Remember, tomorrow is an Early Release Day. Tests and Quizzes will be returned along with going over the homework.

---

"Walking, Falling ..."

Today, I passed out grade sheets. These grade sheets should be shown to your parents, signed, and returned for a stamp. All entered grades for our class can be seen, including the most recent test and quiz. Those graded tasks will be returned on Wednesday. I am just waiting for everyone to have taken them.

We went over "Walking ..." from last Wednesday. This handout introduced the concepts of rate of change and average rate of change. We investigated how Dwain's speed remained constant at 4 feet per second, while Bryan's speed changed each of the first 5 seconds. However, they both ended their race in a tie.

We ended class by starting "... Falling ..." Remember, although there is a constant change to the speed of the falling ball, it is still a changing speed. It has a constant increase or acceleration of 9.4 (this is the acceleration due to gravity on Earth). The formula to calculate the average rate of change is:

change in distance

------------------------

change in time

Homework: Finish "... Falling ..."

---

Quiz Day!!!

Today, we had a quiz on Parent Functions and Function Transformations. We have been working with these concepts since Tuesday last week.

Remember to bring "Walking ... Part 1" to class with you on Monday. You were assigned to finish the handout on Wednesday. We will go over that and continue discussing Rates of Change next week.

Have a great weekend!

---