Algebra I/II 2017-18
Dear Parents
Welcome to the 2017-2018 School Year
Our class goal this year is no different than it has been in the past. That is to prepare ourselves in such a way as to have the option in high school to reach the highest levels of math offered. In the last several years, we at SASEAS have had great success in placing our 8th graders in Geometry, Advanced Algebra I, or Algebra II. Last year for the first time the State of Ohio offered 8th graders the opportunity to take an “End of Course” test for Algebra I by which they were able to test out of and gain high school credit for Algebra I. Our students did exceptionally well with nearly 93% of them placing in the two highest assessment categories out of five categories. Please see the separate document showing a student score sheet with the SASEAS School average just 4 points shy of the Advanced range. There is no reason why our current 8th graders cannot do as well.
Chapter 1 and 2 in your student’s Algebra Text is a compilation of prior year knowledge, and as such we will be reviewing and assessing student understanding of previously covered concepts so as to determine the trajectory of our course. We will be covering this review material in an expeditious fashion.
My intention is to take these students through a complete course in Algebra I by the end of January AND inject into the course a substantial amount of preparation for high school Algebra II or even more advanced course work. We will make every effort to differentiate not so much the instruction as the assessment of student learning so as to account for the various levels of student math aptitude.
In chapter 1, your child will write and evaluate algebraic expressions, operate with positive and negative numbers, simplify expressions, and graph points in the coordinate plane.
Students will translate words into algebraic expressions.
Verbal Expression / Algebraic ExpressionSam is 2 years younger than Sue, who is y years old. Write an algebraic expression for Sam’s age. / y - 2
“younger” means “less than”
They will evaluate algebraic expressions by substituting values for the variables.
Evaluate y - 2 for y - 18.
y - 2 = 18 - 2 Substitute 18 for y.
= 16 Subtract.
These rules summarize how to operate with signed numbers.
Adding with the Same Sign Add the absolute values of the numbers and use the same sign as the numbers. / -4 + (-12) = -16Think: 4 + 12 = 16 and the result is negative because both numbers are negative.
Adding with Different Signs Find the difference of the numbers’ absolute values and use the sign of the number with the greater absolute value. / 3 + (-8) = -5
Think: 8 - 3 = 5 and the result is negative because -8 has the greater absolute value.
Subtracting
Add the opposite of the second number. / 5 - (-4) = 5 + 4 = 9
Think: To subtract -4, add -4.
Multiplying or Dividing with the Same Sign
The result is positive. / -4 · (-5) = -20
Think: Same signs make positive.
Multiplying or Dividing with Different Signs
The result is negative. / 42 ÷ (-7) = -6
Think: Different signs make negative.
The expression 63 is called a power. 63 = 6 · 6 · 6 = 216. Students will study both positive and negative square roots.
= 5 because 52 = 25.
- 49 = -7 because ( -7)2 = 49.
Some square roots are equal to decimals that never end and never repeat. These numbers are irrational and belong to one of the classifications of the real numbers.
Real NumbersNatural Numbers / Counting numbers: 1, 2, 3, …
Whole Numbers / Natural numbers and zero: 0, 1, 2, 3, …
Integers / Whole numbers and their opposites: …, -3, -2, -1, 0, 1, 2, 3, …
Rational Numbers / Numbers that can be expressed as a ratio (fraction) of two integers. Includes all numbers whose decimal forms are either terminating decimals (4, 2.5) or repeating decimals (0.33…).
Irrational Numbers / Numbers that cannot be expressed as a ratio of two integers. Includes numbers whose decimal forms never terminate and never repeat, such as p and 2 .
If an expression contains more than one operation, the order of operations dictates which operation to do first. Students can remember the order by Please Excuse My Dear Aunt Sally.
Evaluate 42 · 6 - (2 + 3).
42 · 6 - (2 + 3) = 42 · 6 - (5) Parentheses and all grouping symbols
= 16 · 6 - (5) Exponents
= 96 - 5 Multiplication and Division (left to right)
= 91 Addition and Subtraction (left to right)
The Commutative, Associative, and Distributive Properties are valid for all real numbers and will help students simplify expressions.
Commutative Property (ordering) / a + b = b + a / ab = baAssociative Property (grouping) / (a + b) + c = a + (b + c) / (ab)c = a(bc)
Distributive Property
(multiplying across addition) / a(b + c) = ab + ac
10x2 and -8x2 are terms—the parts of an expression that are separated by + or - signs.
Like terms can be combined: 10x2 - 8x2 = 2x2.
The coordinate plane is defined by two perpendicular axes intersecting at the origin. An ordered pair (x, y) can be graphed by moving left or right from the origin according to the x-coordinate, and then up or down according to the y-coordinate.
Students will graph functions such as y = x2 - 5 by generating ordered pairs. Ordered pairs are generated by picking a value for x (input), substituting it into the function, and then finding the value of y (output).
In Chapter 2, your child will solve a variety of equations in one variable,
including equations that result from proportion and percent problems.
An equation is a mathematical statement showing two expressions are
equal. A solution to an equation is a value of the variable that makes the
equation true.
Equations are solved by isolating the variable using inverse operations.
You must perform the same inverse operations on both sides of the
equation.
Many equations require multiple steps to isolate the variable. The variable
might appear several times, or on both sides of the equation.
A formula is an equation that states a relationship between several
quantities. Solving a formula for a given variable is similar to solving a
multi-step equation.
For example, d = rt can be written as by dividing both sides by t.
A ratio is a comparison of two quantities. A ratio such as 2 boys to 5 girls
can be written as 2:5 or . A proportion is an equation that relates two
equivalent ratios. For example, is a proportion.
When part of a proportion is unknown, you can use a variable for the
unknown quantity and solve by using cross products.
Ratios and proportions have many useful applications, including rates,
scale drawings, similarity, and indirect measurement.
A percent is a ratio that compares a number to 100. You can solve many
percent problems with the proportion .
Percents can be used to calculate commissions, interest, tips, markups,
and discounts.