Happy Halloween!

Students turned in their "What's in the Bank?" worksheets this afternoon, and then completed a problem solving activity in class.

Tonight's Homework: None, but do have a safe and happy Halloween!

Spreadsheets on the Handheld Computer

Students were introduced to using a spreadsheet this afternoon through the Palm handheld computer. We walked through some of the key features, and saw that if you enter a formula in a cell, along with a little data, the computer will actually give you the answer you're looking for.

Tonight's Homework: Complete the "What's in the Bank?" worksheets.

Combining Like Terms--A Conceptual Approach

Many students have demonstrated that they are having some difficulties understanding when and how to combine like terms in expressions and equations. To help make this less confusing, we talked about a banking situation, where loose change, stacks of money and drawers of money are all present. If each of these is represented by a variable, then it is easy to understand that you cannot combine drawers of money with loose change.

Tonight's Homework: Complete both sides of the two worksheets that were handed out in class today. These will be collected on Wednesday, October 31st.

Planting Bulbs and Pumpkin Quizzes

Students were given an opportunity to renew their pledges to live drug-free lives by planting a flower bulb in the algebra flower pot. Hopefully, these will bloom in the spring, and remind us of the pledges we've made.

After correcting homework, students took a pumpkin-shaped quiz over solving simple equations.

Tonight's Homework: Complete the purple worksheet.

Solving Equations With Variables on Both Sides of the Equal Sign

Today's lesson combines many of the topics we've worked on over the past two weeks and applies them to solving equations with the variable on both sides of the equal sign. Since our objective is to always isolate the variable, there will be paths to take to get to the solution. Students must guard against working too quickly, as this can lead to errors that will make the problems much harder than they really are. Examples of common errors include dropping negative signs, not distributing completely, or simple arithmetic errors.

Tonight's Homework: Lesson 3.4 ( 18 - 38, FCO ). Be sure to study for tomorrow's quiz!

Using Equations to Solve Word Problems

Taking word problems and translating them into mathematical symbols takes a little practice. Once this is done, solving the problem can take very little time. The key is to let the units (labels) of the numbers help you determine how to place the different components of the problem so you'll get an answer with the proper units.

Tonight's Homework: Lesson 3.3 ( 51 - 60 and 62 - 64 )

Solving Multi-Step Problems

We reviewed the table top problem and determined that we couldn't solve the problem without first converting the measurements to the same units.

Next, we reviewed how to solve equations that require more than one step. Key steps include combining like terms or multiplying by the reciprocal before getting too far into the solving. Be sure to look at example 5 in the book!

Tonight's Homework: Lesson 3.3 ( 10 - 41, FCO with check steps, 67 - 85 ). Wear red tomorrow!

One Step Equations Involving Multiplication or Division

We identified four properties of equality, including:
•Addition Property of Equality (if a = b, then a + c = b + c)
•Subtraction Property of Equality (if a = b, then a - c = b - c)
•Multiplication Property of Equality (if a = b, then ac = bc)
•Division Property of Equality (if a = b, then a/c = b/c but c ≠ 0)

Using these properties, we reviewed how to solve linear equations involving one step and multiplication or division. Sometimes it will be easier to multiply by the reciprocal than to divide by a fraction.

Because this is Red Ribbon Week, students received red wrist bands to signify their willingness to live drug free lives.


Tonight's Homework: Lesson 3.2 ( 14 - 45, FCO with check steps, 49 - 53 odd, and 62 - 64 )

Chapter 2 Test Results

Students received their chapter 2 tests today. Half of the class needs to really look over their problems, and determine what it is that is keeping them from being able to correctly complete the questions that were on the test. Retakes will begin next week, only after students have conferenced with me.

Because the class was shortened for a fundraising assembly, we did a geometry-based problem solving worksheet. Students are asked to solve the problem, communicate their reasoning, circle their answers to the problem, and then solve the problem a different way to verify that the answer is correct.

Tonight's Homework: Complete the brown problem-solving worksheet for Monday.

Chapter 2 Test Today

Students completed the test over chapter 2 in class today.

Tonight's Homework: Lesson 3.1 ( 22 - 44, even, 45 - 52, and 60 - 75 ).

Solving One Step Linear Equations

After reviewing what will be on tomorrow's chapter 2 test, we reviewed how to solve linear equations that involve one step and addition or subtraction. Some protocols for solving and checking these types of problems were shared with students.

Tonight's Homework: Lesson 3.1 ( 13 - 43, odd).

Reviewing Probability and Odds

The chapter 2 test will be given on Thursday, October 18th. Students are encouraged to begin preparing for this test now.

Tonight's Homework: The assignment is on three different pages:
•Page 120 ( 1 - 21, all )
•Page 124 ( 49 - 52 )
•Page 125 ( 40 - 41 )

In addition, students may earn extra credit for completing all problems on page 816 and turning them in on Wednesday.

Probability and Odds

The topic for today is yet again a review--over probability and odds. Probability will always be represented as a number from 0 to 1, but never over 1. Odds, on the other hand, could be represented as a fraction that is over 1. Probability is defined as the ratio of a specific event happening to the total number of possibilities available. Odds is defined as the ratio of the chances of something happening to the chances of that same thing NOT happening.

Tonight's Homework: Lesson 2.8 ( 1 - 31, odd )

Reviewing Chapter 2--Part 1

Since we are nearly done with chapter 2, I thought it would be wise to have students review some of the topics that have been covered in the chapter. In addition, we are practicing our fraction operations today.

Tonight's Homework: Page 125 ( 1 - 39, all) and Page 783 ( 17 - 65, odd).

Dividing Real Numbers

Students reviewed the rules for division. Vocabulary includes reciprocal and inverse. We also talked about how dividing by zero is not possible (undefined) and the factorial symbol (!), what it means and how it is used.

Tonight's Homework: Lesson 2.7 ( 19 - 57, last column only, and 75 - 100 )

The Distributive Property

The distributive property is, by far, one of the most important properties an algebra student will use throughout the year. This property, though fairly straightforward, can cause problems when negative signs are introduced. This, coupled with order of operation mistakes, can turn relatively simple problems into nightmarish ones in no time at all. I am hoping that students will really make an effort to master the distributive property, which will, in turn, make future lessons a little easier.

Tonight's Homework: 2.5 ( 19 - 67, FCO, and 91 )

Multiplying Real Numbers

As we continue our review of real number properties, we focused on the properties that govern multiplication. In particular, we revisited the associative, commutative, identity, and inverse properties of multiplication.

Tonight's Homework: Lesson 2.5 (16 - 48, FCO, and 59 - 67, odd). We will take a short quiz over lessons 2.1 - 2.4 on Monday.

Adding and Subtracting Matrices

To help students further review adding and subtracting integers, the notion of matrix operations was introduced. Matrices are simple organizational mechanisms that can be used when a large number of related data needs to be manipulated. Students should read Lesson 2.4 before attempting to complete tonight's homework.

Tonight's Homework: Lesson 2.4 ( 7 - 29, odd). Reminder: The last day to take the chapter 1 retest is Wednesday, October 10th.

Subtracting Real Numbers

Subtracting numbers is not governed by a lot of rules. The important thing to remember when subtracting is that you can complete the problem by adding the opposite.

Tonight's Homework: 2.1 ( 18 - 50, FCO, 83 - 85 ) and 2.3 ( 16 - 69, FCO, 73 - 75, 81a and b )

Addition Properties

There are four major properties that apply to the addition of real numbers: Commutative, Associative, Additive Identity, and Additive Inverse. We reviewed each of these today before starting on Lesson 2.2. Students were reminded that these properties will show up on future quizzes and tests.

Chapter 1 tests were returned to students today. Retakes will begin on Wednesday, October 3rd, and must be completed by Wednesday, October 10th.

Tonight's Homework: Lesson 2.2 ( 12 - 30, FCO, 33 - 37, 37 - 49 odd, 56 - 60 )