## Section 1 (Apex Pg 1 – 20)

**Objectives**

- Translate everyday language into mathematical sentences.
- Convert mathematical sentences into variables and expressions.
- Interpret the different parts of mathematical sentences.

**Key Words**

- Variable – an unknown or changeable quantity
- Constant – a value in a formula that does not change (unlike a variable).

- Expression – a combination of numbers, variables, and operations that does not contain an equals sign or inequality sign. An expression that includes variables is often called an algebraic expression.
- Coefficient – a number that multiplies a variable.
- Term – part of algebraic expressions. Terms are separated by + or – signs. A term may include a number, a variable, or both. The variable may have an exponent.
- Operator – a symbol that represents a mathematical process, such as addition, subtraction, multiplication, or division.
- Substitution – the process of replacing a variable with a number or expression.
- Variable Expression – a math expression that contains one or more variables. An expression that does not contain any variables is called a numerical expression.

**Notes**

- Examples of Variable Phrases & Letters
- Half the height of the building: 1/2 * h
- The number of buildings: b
- The length of the rope: l
- The number of ropes: r
- Half the speed of the car: 1/2 * s
- The number of cars: c
- The number of different colors on the page: c
- The number of pages: p

- Writing Variables Mathematically
- Change the variable (word) to a letter
- Decide which math word should be used (see chart below)

- Sum: Add
- ex. The sum of 35 and the number of carrots: 35 + c
- ex. The sum of cups of coffee and 18 donuts: c + 18

- Difference: Subtract
- ex. The difference of $25 and the price of a movie ticket: 25 – m
- ex. The difference of pizza slices and the 3 you ate: p – 3

- Product: Multiply
- Write products of variables with numbers, then letters: ex. 3x, 45t, 500m, etc.
- ex. The product of 50 and the number of employees: 50e
- ex. The product of 40 and distance to the finish line: 40d

- Write products of variables with numbers, then letters: ex. 3x, 45t, 500m, etc.
- Quotient: Divide
- ex. The quotient of $30 and your siblings: 30 / s
- ex. The quotient of chocolate left and the 4 people who ate it: c / 4

**Math Code Words**

Addition

- sum
- plus
- add / added to
- in all
- are
- altogether / together
- total / in total of
- increased by
- spend / spent
- combined
- joined
- both
- and (between 2 #s)
- more / more than
- how many

Subtraction

- minus
- different / difference
- decreased by
- are not
- left / left over
- less / less than
- from
- fewer
- remain
- subtract
- off
- “er”words
- spent
- how many more
- how many did not have
- how much more
- take away … from
- taller / shorter

Multiplication

- times
- by / multiplied by
- double / triple
- twice
- product / product of
- of / multiple of
- each (before the question)
- every (before the question)
- apiece (before the question)
- per (before the question)

Division

- divide
- quotient
- separate
- equal / equally
- divvy up / cut up
- dish out
- half / third (and other fractions)
- parts
- share
- split
- each (in the question)
- every (in the question)
- apiece (in the question)
- per (in the question)

**Examples of Mathematical Phrases**

- z increased by 8: z + 8
- 5 less than y: y – 5
- The number of plates on the table minus the 4 saved for dessert: p – 4

**Simplify the Numerical Parts of Phrases**

- Add the constants together
- Rewrite the phrase mathematically

- ex. k + 31 – 11 – 5: add 31 – 11 – 5 following integer rules.
- 31 – 11 = 20.
- 20 – 5 = 15.
- So, k + 15 is the answer.

- ex. j + 16 – 48 + 4: combine 16 and -48 following integer rules.
- 16 – 48 = -32.
- -32 + 4 = -28.
- So, j – 28 is the answer.

- ex. k – 24 / 4: start with 24 / 4.
- 24 / 4 = 6.
- So, k – 6 is the answer.

- ex. 7 * 5 * n: multiply 7 * 5 first.
- 7 * 5 = 35.
- So, 35n (remember that you remove the times sign when you are writing the product of a number and a variable).

## Section 2 (Apex Pg 21 – 28)

**Objectives**

- Express answers to problems as solution sets.
- Construct a step-by-step strategy for problem solving by asking yourself questions.

**Key Terms**

- Equation – a mathematical statement that says two expressions are equal.
- Inequality – a mathematical sentence that has two or more expressions separated by inequality signs (<, >, ≤, ≥, or ≠).
- Mathematical Sentence – comparisons of two mathematical expressions. The sentence is called an equation if the two expressions are equal.

**Mathematical Sentences MUST have equality or inequality symbols**

- ex. The number of apples in the box plus 5 more adds up to 16 apples: m + 5 = 16
- ex. The original price of a computer was reduced by $250. The new discounted price is $1499: p – 250 = 1499
- ex. A high school had 140 students at the start of the year, but then some students left the school. After that, the school had 126 students: 140 – s = 126
- ex. Pedro charged $933 to his credit card. Even after the cost of his next purchase, he was still under his credit limit of $1500: 933 + c < 1500
- ex. Diana has 235 pokemon cards. If Becca were to double the number of pokemon cards that she has, she would still have fewer than Diana has: 2b < 235
- ex. Ms. Haze’s algebra class has too many students in it. If the class were split exactly in half to form 2 new classes, each class would have no more than 17 students in it: s ÷ 2 ≤ 17
- ex. Cathy checks the temperature at 10:00 p.m. She notices if the temperature falls by 5 more degrees, it will break the record-low temperature for that date, which is 46 degrees: t – 5 < 46