Question

unit 2: expressions and equations
lesson #3: swbat substitute a number for a variable in an expression to simplify an expression after substituting.
warm - up:

1. five less than four times a number

a) 5x - 4
b) 4n - 5
c) 4 - 5n
d) 5 - 4n

1. which verbal expression does not represent 9 - x?

a) x less than nine
b) x decreased by nine
c) subtract x from nine
d) the difference of nine and x

1. fact: an algebraic expression is composed of various parts.

• a number that multiplies to the variable
• a letter that can stand for a number of a quantity with specific units
• a number that stands alone

1. order of operations review:

p
e
md
as

1. if you see a number written as 4(7), what is happening?

if you see 9y, what is happening?
what is the coefficient and variable in - 10b?

• is a coefficient
• is a variable

Explanation:

1. Question 1: "Five less than four times a number"

• Explanation:
• Let the number be \(n\). Four times the number is \(4n\). Five less than \(4n\) means we subtract 5 from \(4n\), which gives the expression \(4n - 5\).
• Answer: B. \(4n - 5\)

1. Question 2: "Which verbal - expression does not represent \(9 - x\)?"

• Explanation:
• Option A: "x less than nine" can be written as \(9 - x\).
• Option B: "x decreased by nine" should be written as \(x - 9\), not \(9 - x\).
• Option C: "subtract x from nine" is \(9 - x\).
• Option D: "the difference of nine and x" is \(9 - x\).
• Answer: B. x decreased by nine

1. Question 3: In the expression \(2n+5\)

• Explanation:
• The number that multiplies the variable \(n\) is 2, so 2 is the coefficient.
• \(n\) is a letter that can stand for a number of a quantity with specific units.
• 5 is a number that stands alone, which is the constant.
• Answer:
• - a number that multiplies to the variable: 2
• - a letter that can stand for a number of a quantity with specific units: \(n\)
• - a number that stands alone: 5

1. Question 4: Order of operations review

• Explanation:
• The order of operations is Parentheses (P), Exponents (E), Multiplication and Division (MD - from left to right), and Addition and Subtraction (AS - from left to right).
• Answer:
• P: Parentheses
• E: Exponents
• MD: Multiplication / Division (from left to right)
• AS: Addition / Subtraction (from left to right)

1. Question 5:

• Explanation:
• When you see \(4(7)\), it means 4 times 7, or multiplication.
• When you see \(9y\), it means 9 times \(y\), or 9 is the coefficient of \(y\) and there is a multiplication operation.
• In \(- 10b\), - 10 is the coefficient and \(b\) is the variable.
• Answer:
• If you see a number written as \(4(7)\), what is happening? Multiplication.
• If you see \(9y\), what is happening? Multiplication (9 is the coefficient of \(y\)).
• What is the coefficient and variable in \(-10b\)? - 10 is a coefficient, \(b\) is a variable.

Answer:

1. Question 1: "Five less than four times a number"

• Explanation:
• Let the number be \(n\). Four times the number is \(4n\). Five less than \(4n\) means we subtract 5 from \(4n\), which gives the expression \(4n - 5\).
• Answer: B. \(4n - 5\)

1. Question 2: "Which verbal - expression does not represent \(9 - x\)?"

• Explanation:
• Option A: "x less than nine" can be written as \(9 - x\).
• Option B: "x decreased by nine" should be written as \(x - 9\), not \(9 - x\).
• Option C: "subtract x from nine" is \(9 - x\).
• Option D: "the difference of nine and x" is \(9 - x\).
• Answer: B. x decreased by nine

1. Question 3: In the expression \(2n+5\)

• Explanation:
• The number that multiplies the variable \(n\) is 2, so 2 is the coefficient.
• \(n\) is a letter that can stand for a number of a quantity with specific units.
• 5 is a number that stands alone, which is the constant.
• Answer:
• - a number that multiplies to the variable: 2
• - a letter that can stand for a number of a quantity with specific units: \(n\)
• - a number that stands alone: 5

1. Question 4: Order of operations review

• Explanation:
• The order of operations is Parentheses (P), Exponents (E), Multiplication and Division (MD - from left to right), and Addition and Subtraction (AS - from left to right).
• Answer:
• P: Parentheses
• E: Exponents
• MD: Multiplication / Division (from left to right)
• AS: Addition / Subtraction (from left to right)

1. Question 5:

• Explanation:
• When you see \(4(7)\), it means 4 times 7, or multiplication.
• When you see \(9y\), it means 9 times \(y\), or 9 is the coefficient of \(y\) and there is a multiplication operation.
• In \(- 10b\), - 10 is the coefficient and \(b\) is the variable.
• Answer:
• If you see a number written as \(4(7)\), what is happening? Multiplication.
• If you see \(9y\), what is happening? Multiplication (9 is the coefficient of \(y\)).
• What is the coefficient and variable in \(-10b\)? - 10 is a coefficient, \(b\) is a variable.