Print this Page

1.2 – Variables and Problem Solving

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
    1. Change the variable (word) to a letter
    2. 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
        • 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

  1. Add the constants together
  2. 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

 

Alg 1A 1.02 - Less Than Greater Than

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alg 1A 1.02 - Inequalities

Alg1A Equations Reverse Operations Alg1A Integer Rules Alg1A 1.01 math sentences 02

 

Permanent link to this article: http://newvillagegirlsacademy.org/math/?page_id=198