ALGEBRA I – JOURNALING
QUESTION:
What is your favorite thing about math? What is your least favorite thing about math? Be honest and explain.
ALGEBRA I – JOURNALING
QUESTION:
Give examples of where you might find/use math in every day life in the verbal, numerical, graphical, and symbolic forms.
ALGEBRA I – JOURNALING
QUESTION (Section 1-1):
What does it mean to “simplify” and expression?
ALGEBRA I – JOURNALING
QUESTION (Section 1-2):
Explain the purpose of using the order of operations in math.
ALGEBRA I – JOURNALING
QUESTION (Section 1-3):
What are the Three Golden Rules for Solving Equations?
ALGEBRA I – JOURNALING
QUESTION (Sections 1-4 and 1-5):
Explain why it is okay to switch the order when you add or multiply numbers but why it is not okay to switch the order when you subtract or divide numbers.
ALGEBRA I – JOURNALING
QUESTION (Sections 1-4 and 1-5):
Match each sentence on the left with the correct expression on the right. Explain why you matched them up the way that you did; and explain the difference between the expressions.
Five times the sum of a5N + 3
number and three.
Three more than five5(N + 3)
times a number.
ALGEBRA I – JOURNALING
QUESTION (Sections 1-6 and 1-7):
Many do not like to do word problems. Do you like to do word problems? Yes or no. If you answered yes, explain what you like about them. If you answered no, explain why you do not like them.
ALGEBRA I – JOURNALING
QUESTION (Sections 1-6 and 1-7):
There are five main steps in the problem solving process:
1)Organize
2)Variable
3)Equation
4)Solve
5)Check
Explain what you would do for each step when solving a word problem. Explain what you think the importance is of each step.
ALGEBRA I – JOURNALING
QUESTION (Section 1-8):
Describe the basic characteristics of each of the following number families:
Counting (Natural) Numbers:
Whole Numbers:
Integers
Rational Numbers
Irrational Numbers
Real Numbers
ALGEBRA I – JOURNALING
QUESTION (Section 1-9):
Define and explain each of the following terms:
Opposite
Absolute Value
ALGEBRA I – JOURNALING
QUESTION:
After going through one chapter in the book, we have developed a pretty regular classroom routine. What things do you like about the routine? What things do you NOT like about the routine? Do you have any ideas for ways to improve the things we do in class? Explain.
Your comments can help me make the class more enjoyable for you!!!!!
ALGEBRA I – JOURNALING
QUESTION (Section 2-1):
Write an example that illustrates each of the following properties:
a) Reflexive –
b) Symmetric –
c) Transitive –
d) Closure –
e) Commutative –
f) Associative –
g) Substitution –
ALGEBRA I – JOURNALING
QUESTION (Section 2-1):
What is the difference between a term and a factor?
ALGEBRA I – JOURNALING
QUESTION (Sections 2-2, 2-3, and 2-4):
In your own words, explain the rules for adding positive and negative numbers. Use example problems if it helps you.
In your own words, explain the rules for subtracting positive and negative numbers. Use examples problems if it helps you.
ALGEBRA I – JOURNALING
QUESTION (Section 2-5):
What is the definition of the distributive property?
Explain why the distributive property does not violate the rules for order of operations. In other words, why is it okay to multiply before you simplify the parentheses.
What is purpose of the distributive property? Give an example of a situation where it is useful.
ALGEBRA I – JOURNALING
QUESTION (Section 2-6):
Explain in your own words what multiplication is. Then, come up with examples of different ways that multiplication is symbolized in Algebra.
ALGEBRA I – JOURNALING
QUESTION (Section 2-6):
Briefly explain the rules for multiplying positive and negative numbers.
ALGEBRA I – JOURNALING
QUESTION (Section 2-7):
What is an integer?
What does the word consecutive mean?
Give an example of 3 consecutive integers. Give an example of 3 consecutive even integers. Give an example of 3 consecutive odd integers.
ALGEBRA I – JOURNALING
QUESTION (Section 2-8):
Explain in your own words what division is. Then, come up with examples of different ways that division is symbolized in Algebra.
ALGEBRA I – JOURNALING
QUESTION (Section 2-8):
Explain what the following phrase means: “the reciprocal of a product of two non-zero numbers equals the product of their reciprocals.”
ALGEBRA I – JOURNALING
QUESTION (Section 2-9):
One of the cardinal rules in Algebra is that you can never divide a number by zero. Explain why you cannot divide by zero.
ALGEBRA I – JOURNALING
QUESTION (Sections 3-1 and 3-2):
What are the “Three Golden Rules” for solving equations? Explain what each step means in your own words.
ALGEBRA I – JOURNALING
QUESTION (Sections 3-1 and 3-2):
What are the steps in the order of operations? Why is the order of operation important to solving equations?
ALGEBRA I – JOURNALING
QUESTION (Section 3-3):
Below is an example of a simplifying problem and an example of an equation. Solve each problem and then answer the questions.
1)What similarities are there about how you solve the two problems?
2)What differences are there about how you solve the two problems?
SIMPLIFY: 4(5) + 2SOLVE: 4x + 2 = 22
ALGEBRA I – JOURNALING
QUESTION (Section 3-4):
Write an equation for the word problem below. Do NOT solve the equation. Instead, explain the parts of your equation and why you wrote the equation that you did.
Problem Bob has $50 in his savings account. He saves $25 each week. How many weeks will it take Bob to have $1000 in his savings account?
ALGEBRA I – JOURNALING
QUESTION (Section 3-5):
Solve the equation below. Show your work for all steps. Explain in words what you are doing for each step.
5(2x + 7) = 10x – 25 + 17x – 2x
ALGEBRA I – JOURNALING
QUESTION (Section 3-6):
What are the five steps in the problem-solving plan? How can a chart be used to help get you organized in a word problem?
ALGEBRA I – JOURNALING
QUESTION (Section 3-7):
Explain in words what the following formulas mean in practical situations:
Cost per item Number of items = Total cost
Hour wage Number of hours = Income
Number of coins Value of coins = Total value
ALGEBRA I – JOURNALING
QUESTION (Section 3-7):
In a problem involving money (coins), why is it important to make sure that you use either cents or dollars throughout the entire problem?
ALGEBRA I – JOURNALING
QUESTION (Section 3-7):
Explain what the following equations mean when used in the context of profit-loss type word problem:
Profit = Sold – Bought (where Sold > Bought)
Loss = Bought – Sold (where Bought > Sold)
ALGEBRA I – JOURNALING
QUESTION (Section 4-1):
Explain what the following statement means:
“Just like multiplying is a fast way to add the same number over and over, exponents are a fast way to multiply the same number over and over.”
ALGEBRA I – JOURNALING
QUESTION (Section 4-2):
What are the criteria that make terms in a polynomial like terms?
In the polynomial below, which terms are like terms? Explain why they are like.
5x3y + 8x2yx – 9yx3 + xxxy – 2yx2x
ALGEBRA I – JOURNALING
QUESTION (Section 4-3):
Use the following terms to answer the questions below:
5x3, 4x3, 3y, and 2y
1)ADD the four terms together.
2)MULTIPLY the four terms together.
Explain the differences in what you do to solve each problem.
ALGEBRA I – JOURNALING
QUESTION (Section 4-4):
The rule for simplifying “power of powers” is to take the coefficient to the power and multiply the exponents. Use the expression below to explain why these rule work.
ALGEBRA I – JOURNALING
QUESTION (Section 4-5):
Evaluate each of the following expressions.
a) 3x(5x + 4x2y – 7xy) if x = 2 and y = 3
b) 12x3y – 21yx2 + 15x2 if x = 2 and y = 3
Did you get the same answers? Is there are way to tell if you would get the same answers before you evaluate? Explain.
ALGEBRA I – JOURNALING
QUESTION (Section 4-6):
Explain what the acronym “FOIL” stands for. Show an example of how to use “FOIL-ing” to distribute.
ALGEBRA I – JOURNALING
QUESTION (Section 4-7):
Rearrange the following formulas for the given variable. Explain each of your steps:
1)
2)
ALGEBRA I – JOURNALING
QUESTION (Section 4-8):
Suppose that Bob and Sam are each driving their cars. Explain how the distances that Bob and Sam each travel will compare (i.e. more, less, equal, etc.) in each of the following situations:
1)Bob leaves the school at 3:30 and drives to Wal-Mart. Sam leaves the school and 3:40 and catches up with Bob in the Wal-Mart parking lot.
2)Bob drives from Frankville to Postville. Sam drives from Frankville Road turnoff to Postville.
3)Bob drives east for 1 hour at 60 MPH. Sam drives west for 1 hour at 55MPH.
ALGEBRA I – JOURNALING
QUESTION (Section 4-9):
What are the area formulas for the following shapes?
1)Rectangle
2)Square
3)Parallelogram
4)Triangle
5)Trapezoid
6)Circle
ALGEBRA I – JOURNALING
QUESTION (Section 4-9):
Explain how you would find the area of the shaded region in the figure below:
ALGEBRA I – JOURNALING
QUESTION (Section 5-1):
Explain what the Greatest Common Factor (GCF) is for a group of numbers.
ALGEBRA I – JOURNALING
QUESTION (Section 5-2):
Evaluate the following expression:
if x = 3 and y = 4 and z = 2
Simplify the following expression. Then evaluate it if x = 3, y = 4, and z = 2.
Explain why you got the answers that you did.
ALGEBRA I – JOURNALING
QUESTION (Section 5-3):
What does it mean to FACTOR something? Give several examples of different types of factoring.
ALGEBRA I – JOURNALING
QUESTION (Section 5-4):
Explain the relationship between FACTORING and FOILING (a.k.a. distributing).
ALGEBRA I – JOURNALING
QUESTION (Sections 5-7 and 5-8):
What are the steps that are followed to factor a quadratic polynomial?
ALGEBRA I – JOURNALING
QUESTION (Sections 5-7 and 5-8):
FACTOR the following quadratic polynomial. Explain, in words, each of the steps.
18 + x2 + 11x
ALGEBRA I – JOURNALING
QUESTION (Section 5-9):
What the similarities and differences between factoring an easy quadratic versus factoring a hard quadratic?
ALGEBRA I – JOURNALING
QUESTION (Section 5-5):
What are the three criteria that must be met in order for a polynomial to be a “difference of two squares”?
ALGEBRA I – JOURNALING
QUESTION (Section 5-6):
What are the four criteria that must be met in order for a polynomial to be a “squaring binomial”?
ALGEBRA I – JOURNALING
QUESTION (Sections 5-5 and 5-6):
Define square root. Explain how to find the square root of the following expressions:
a)121
b)16x2
c)144x2y6
d)(x + 2y)2
ALGEBRA I – JOURNALING
QUESTION (Section 5-10):
Explain what is meant by saying that: “factoring by grouping” has characteristics related to both GCF factoring and factoring quadratics.
ALGEBRA I – JOURNALING
QUESTION (Section 5-11):
Explain what the phrase “factor completely” means. How can you tell when a factor (a.k.a. a set of parentheses) is prime?
ALGEBRA I – JOURNALING
QUESTION (Section 5-12):
What is the rule of thumb that you can use to determine how many answers an equation will have?
How many answers will each of the following equations have?
a)x + 7 = 8
b)x4 – 7x3 + 4 = 7
c)x2 – 5x + 6 = 0
d)x3 – 7 = x
ALGEBRA I – JOURNALING
QUESTION (Section 5-13):
Suppose that you are solving a problem where you are asked to find the width of rectangle. As you solve the problem, you end up with two answers for the width: 8 and –10. How do you know which answer is correct? Explain.
ALGEBRA I – JOURNALING
QUESTION (Section 6-1):
Using the fractions below as an example, explain why you can cancel out the “x’s” in the fraction on the left, but why you cannot cancel out the “x’s” in the fraction on the right.
ALGEBRA I – JOURNALING
QUESTION (Sections 6-2 and 6-3):
What are the steps that you follow when multiplying fractions together?
What are the steps that you follow when dividing fractions?
ALGEBRA I – JOURNALING
QUESTION (Sections 6-2 and 6-3):
The following expressions are “opposites”:
2x – 1 and 1 – 2x
Explain why they are opposites. Explain how factoring out a –1 will switch the order of the terms.
ALGEBRA I – JOURNALING
QUESTION (Section 6-4):
Use the three-step method to find the LCD (Least Common Denominator) for the following fractions. Explain each step as you go.
28, 84, and 120
ALGEBRA I – JOURNALING
QUESTION (Section 6-5):
Explain the steps in the following addition problem. Show your work as you explain each step.
Explain the steps in the following addition problem. Show your work as you explain each step.
ALGEBRA I – JOURNALING
QUESTION (Sections 6-5 and 6-6):
What are the 5 steps that you follow in order to properly add and/or subtract fractions.
ALGEBRA I – JOURNALING
QUESTION (Sections 6-5 and 6-6):
Make a list of the similarities and differences between the following fractions:
a) b)
ALGEBRA I – JOURNALING
QUESTION (Section 6-7):
What are the steps that you follow when using long division to factor polynomials?
ALGEBRA I – JOURNALING
QUESTION (Sections 7-1 and 7-2):
What is the definition of a ratio? What is the definition of a proportion? Give an example of each.
ALGEBRA I – JOURNALING
QUESTION (Sections 7-1 and 7-2):
Explain the process for solving a proportion.
ALGEBRA I – JOURNALING
QUESTION (Sections 7-3 and 7-4):
What are the “Three Golden Rules” for solving equations? What the steps in the order or operations that are used for solving equations? Where does the new step (i.e. multiplying by the LCD) fit into these steps?
ALGEBRA I – JOURNALING
QUESTION (Sections 7-3 and 7-4):
Explain why you have to multiply every term in the equation by the same number (i.e. the LCD) in order to eliminate the fractions in the equation.
ALGEBRA I – JOURNALING
QUESTION (Sections 7-5 and 7-6):
Describe the relationship between FRACTIONS, DECIMALS, and PERCENTS. Give some examples to illustrate your answer.
ALGEBRA I – JOURNALING
QUESTION (Sections 7-5 and 7-6):
Explain the process for converting from:
1)a fraction to a decimal.
2)a FRACTION to a PERCENT.
3)a DECIMAL to a FRACTION.
4)a DECIMAL to a PERCENT.
5)a PERCENT to a DECIMAL.
6)a PERCENT to a FRACTION.
ALGEBRA I – JOURNALING
QUESTION (Section 7-7):
A mixture problem uses a chart that generally looks like this:
AMOUNT / RATE or % / TOTALIngredient #1
Ingredient #2
TOTAL MIXTURE
In order to get the total column, you need to multiply the first two columns together. What do the numbers (or expressions) in the last column represent in terms of the total mixture?
ALGEBRA I – JOURNALING
QUESTION (Section 7-8):
The formula that relates speed, time, and distance is:
Rate (speed) Time = Distance
The formula for work is:
Work rate Time = Work Done
What are the similarities and differences between the two equations above? Can you come up with a generic equation that allows you to solve any problem that involves rates and/or ratios?
ALGEBRA I – JOURNALING
QUESTION (Section 7-9):
What does a negative exponent mean? Explain how you simplify a problem or expression that has negative exponents.
ALGEBRA I – JOURNALING
QUESTION (Section 7-9):
Complete the following chart:
Problem / Answer / Problem / Answer / Problem / Answer24 / 34 / 44
23 / 33 / 43
22 / 32 / 42
21 / 31 / 41
20 / 30 / 40
2–1 / 3–1 / 4–1
2–2 / 3–2 / 4–2
2–3 / 3–3 / 4–3
2–4 / 3–4 / 4–4
Describe the pattern that you see in your answers?
Do the rules for negative exponents make sense in terms of the pattern? Does the rule for taking something to the “zero” power make sense? Explain.
ALGEBRA I – JOURNALING
QUESTION (Section 7-10):
Write the following number in scientific notation:
56,700,000,000,000,000,000
Why do you use “ 10” in the expression? What does the exponent represent?
ALGEBRA I – JOURNALING
QUESTION (Sections 8-1):
a) How many solutions does the following equation have? Why does it have that many?
3x + 4 = 16
b) How many solutions does the following equation have? Why does it have that many?
y = 3x + 4
ALGEBRA I – JOURNALING
QUESTION (Section 8-2):
Sketch a picture of a coordinate plane. Label the key parts of the coordinate plane.
ALGEBRA I – JOURNALING
QUESTION (Section 8-3):
What does the slope of a line tell you about the graph of that line?
ALGEBRA I – JOURNALING
QUESTION (Section 8-4):
a) What does the graph of an equation represent?
b) Explain in words how the slope and y-intercept of a line are related to the equation and graph of that line.
c) Explain how to the use the slope and y-intercept as a shortcut for graphing a line.
ALGEBRA I – JOURNALING
QUESTION (Section 8-5):
Briefly explain (in words) the steps you need to follow to write the equation of a line for each of the following situations:
a)The graph of the line
b)The slope and a point
c)Two points
d)The x- and y- intercepts
e)A line that is perpendicular and a point
ALGEBRA I – JOURNALING
QUESTION (Section 8-6):
Briefly explain why the advantages and disadvantages to using a bar graph or line graph to illustrate a function.
ALGEBRA I – JOURNALING
QUESTION (Section 8-7):
Briefly define each of the following terms:
a)Function –
b)Domain –
c)Range –
Write an example of a function written in the following forms:
a)Function notation –
b)Arrow notation –
ALGEBRA I – JOURNALING
QUESTION (Section 8-8):
Below is a sketch of a PARABOLA. In your own words, describe the characteristics of the parabola with as much detail as possible.
ALGEBRA I – JOURNALING
QUESTION (Section 8-8):
Briefly define each of the following terms in your own words:
a)Parabola –
b)Vertex –
c)Axis of Symmetry –
d)Y-intercept
e)X-intercept
f)Open up/down –
ALGEBRA I – JOURNALING
QUESTION (Sections 8-9 and 8-10):
What does it mean for two quantities (or variables) to be directly proportional?
What does it mean for two quantities (or variables) to be inversely proportional?
ALGEBRA I – JOURNALING
QUESTION (Sections 8-9 and 8-10):
What is a constant of variation? Why do you have to have it when setting up a problem dealing with direct and inverse relationships?
ALGEBRA I – JOURNALING
QUESTION:
a)What were your favorite things about this class?
b)What were your least favorite things about this class?
c)What changes would you make for next year?
d)What suggestions would you give to someone taking this class next year?