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Chapter 5
Expressions
(part 3)
Day…..1. Translating Written Expression
s
2. Writing Numerical Expressions
3. Writing Algebraic Expressions
4. Unit Summary
5. End of Unit Assessment
Day 1
Bell WorkDirections: Simplify the following expressions. Show all of your work!
1. 5x(3y – 2w) - 18xy + 9w - 11xw + 7w
2. 12( 13 – 8) + - 87
3. 19a – 12c + - 32a + 19c
4. 8e – 7 + e - 4f + 37f + 23
5. 6m – 12p + 4p + 9m when: m = 7 and p = 6
6. 11k + + 7k – 4j when: k = 3 and j = 8
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation.
Expressions that have the same value.
Numerical Expression -
Algebraic Expressions -
Translate -
Equivalent Expressions-
Evaluate-
Equation -
To find the value of an algebraic expression by replacing variables with a given quantity.
A combination of numbers and operations.
Mathematical statement indicating quantities are not equivalent
To change from one form or language to another.
Inequality -
A mathematical statement indicating quantities are equivalent
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Identify key terms for addition, subtraction,
multiplication, and division.
Key Terms for Addition• Increased +• Added +• Combine +• Plus + • And + • Climbed +• Rose +• Together +• Sum ( + )• Average ( + ) then ÷
Key Terms for Subtraction
• Subtracted -• Decreased –• Reduced -• Minus -• Less - • Lower - • Dropped -• Difference ( - )
Key Terms for Multiplication
• Times x• Each x• Of x• Multiply x• Half x½ • Double x2• Twice x2• Triple x3• Product ( x )
Key Terms for Division• Divided ÷• Shared ÷• Cut ÷• Split ÷• Ratio of ÷• Quotient ( ÷ )
*****Remember division is written in fraction form in algebra*****
Example: 18 ÷ 3 will be written as
Key Terms for Exponents
• Squared • Cubed • To the fourth power • To the fifth power • Etc.….
Key Terms for Order• Than switch• Sum ( + )• Difference ( - )• Product ( x )• Quotient ( ÷ )• First • Then• Next• Last
Key Terms for Equations
• Is =• Equals =• Equivalent =
Key Terms for Inequalities
• Greater than ≥• Less than ≤• Is not equal to ≠
I Can….
Translate written expressions to numerical
form.
Verbal ExpressionsEssential Understanding:
• Algebraic word problems are just expressions written in word form. They are used to
describe real life situations and to solve real life problems.
Example:
• The key to successfully solving an algebraic word problem is to translate the expression
from word form to numerical form. To do this, we follow a few very simple steps.
Step 1: Know your vocabulary.
Step 2: Read the problem CAREFULLY.
Step 3: Code the problem.
Step 4: Determine what is know (what numbers are given)
Step 5: Determine what is unknown (what variables are given)
Step 6: Determine what operation(s) to used based on what the question is asking/telling.
Step 7: Translate expression/equation
Step 8: Solve if necessary
Examples:
Partner PracticeClear your desk of everything except for your white board, a marker, an eraser,
and the provided page.
Quickly and Quietly
Expression Show DownInstructions:• Players sit back to back.• Each player uses his/her white board to translate the 1st expression on
the provided game page.• Once both players have finished, the youngest player yells “Draw” (In an
INSIDE voice)• Both players quickly turn and compare answers.• If both players have the same answer, the oldest player records the
answer on their answer sheet.• If players do not have the same answer, they must discuss the expression
and reach the same conclusion before recording the answer.• Play continues unit all expressions have been translated and recorded or
time runs out.• The first 3 teams to correctly translate all 15 expressions will receive a
prize.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Bell WorkDirections: Translate the following expressions to numerical form.
1. Four more that the difference of six and two.
2. Fifteen less than the product of nine and a number.
3. Eleven added to the quotient of thirty six and six.
4. A number reduced by seven.
5. The product of nine and number divided by two less than the
product ten and number.
Homework Check
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation.
Expressions that have the same value.
Numerical Expression -
Algebraic Expressions -
Translate -
Equivalent Expressions-
Evaluate-
Equation -
To find the value of an algebraic expression by replacing variables with a given quantity.
A combination of numbers and operations.
Mathematical statement indicating quantities are not equivalent
To change from one form or language to another.
Inequality -
A mathematical statement indicating quantities are equivalent
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Translate expressions from word to numerical
form.
Group WorkToday you will practice reading, writing, translating, and solving algebraic word
problems.
Clear your desk of everything except for a pencil and a blank sheet of paper.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell WorkDirections: Translate and solve the following algebraic expressions/equations.
1. Fifteen less than eight times ten is _____
2. The product of six and five divided by five times two is __________
3. One hundred fifty more than the difference of eleven times three
and thirty.
4. The sum of a number and seventeen is twenty.
5. The product of eight and a number is fifty six.
6. Eight times a number x plus three times a number y minus five
times a number y plus eleven times a number x.
Homework Check
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation.
Expressions that have the same value.
Numerical Expression -
Algebraic Expressions -
Translate -
Equivalent Expressions-
Evaluate-
Equation -
To find the value of an algebraic expression by replacing variables with a given quantity.
A combination of numbers and operations.
Mathematical statement indicating quantities are not equivalent
To change from one form or language to another.
Inequality -
A mathematical statement indicating quantities are equivalent
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Translate numerical expressions to word form.
Translating Expressions to Word Form
Essential Understanding:• Translating expressions from numerical to word form is
quite simple……..if you know your vocabulary. You simply write it like you see it. The tricky part is being creative.
Examples:1. 2 + 3 two plus three, three more than two, two increased by three, etc…
2. 14 - 73. 8x + 74. (5+7) – 95. 7x + 5y + 9y – 8x +11x
Your Turn….
Please clear your desk of everything except your white board and white
board supplies.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell WorkDirections: Translate the following expressions into word form.
1. 12 + 15 = 27
2. 8x + 4
3. + 3
4. (7 * 3) – 6x
5. 7x +3 = 45
Homework Check
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation.
Expressions that have the same value.
Numerical Expression -
Algebraic Expressions -
Translate -
Equivalent Expressions-
Evaluate-
Equation -
To find the value of an algebraic expression by replacing variables with a given quantity.
A combination of numbers and operations.
Mathematical statement indicating quantities are not equivalent
To change from one form or language to another.
Inequality -
A mathematical statement indicating quantities are equivalent
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Solve, evaluate, simplify, and translate expressions.
Chapter Summary
Please clear your desk of everything except for a pencil and the provided
cloze notes.
Write the Room
Please pack up everything except for a pencil, a calculator, and a blank piece of
paper.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
Directions: Silently study your notes and
vocabulary. Think of any questions you may have
before we begin the assessment.
Homework Check
Vocabulary•
•
•
•
•
•
•
A combination of variables, numbers, and at least one operation.
Expressions that have the same value.
Numerical Expression -
Algebraic Expressions -
Translate -
Equivalent Expressions-
Evaluate-
Equation -
To find the value of an algebraic expression by replacing variables with a given quantity.
A combination of numbers and operations.
Mathematical statement indicating quantities are not equivalent
To change from one form or language to another.
Inequality -
A mathematical statement indicating quantities are equivalent
Properties• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will
be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Simplify, solve, evaluate, and translate expressions
and equations.
End of Unit Assessment
Please clear your desk of everything except for a pencil
and a calculator.
Wrap it Up
• Review
• Questions
• Exit Tickets