Transcript Chapter 5 Expressions (part 3)

Chapter 5
Expressions
(part 3)
Day…..
1. Translating Written Expressions
2. Writing Numerical Expressions
3. Writing Algebraic Expressions
4. Unit Summary
5. End of Unit Assessment
Day 1
Bell Work
Directions: Simplify the following expressions. Show all of your work!
1. 5x(3y – 2w) - 18xy + 9w - 11xw + 7w
2. 12( 13 – 8) + 45 - 87
3. 19a – 12c + 11𝑎2 - 32a + 19c
4. 8e – 7 +
72
e
9
- 4f + 37f + 23
5. 6m – 12p + 4p + 9m when: m = 7 and p = 6
6. 11k +
64
𝑗
+ 7k – 4j when: k = 3 and j = 8
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Equation - A mathematical statement indicating quantities are equivalent
• Evaluate-
To find the value of an algebraic expression by replacing variables
with a given quantity.
• Inequality - Mathematical statement indicating quantities are not equivalent
• Numerical Expression - A combination of numbers and operations.
• Translate -
To change from one form or language to another.
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
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•
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•
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•
•
•
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
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•
•
•
•
•
Divided ÷
Shared ÷
Cut ÷
Split ÷
Ratio of ÷
Quotient ( ÷ )
*****Remember division is written in fraction form in algebra*****
Example: 18 ÷ 3 will be written as
𝟏𝟖
𝟑
Key Terms for Exponents
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•
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•
•
Squared 𝑥 2
Cubed 𝒙𝟑
To the fourth power 𝒙𝟒
To the fifth power 𝒙𝟓
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 Expressions
Essential 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 Practice
Clear your desk of everything except for
your white board, a marker, an eraser,
and the provided page.
Quickly and Quietly
Expression Show Down
Instructions:
• 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 Work
Directions: 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
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Equation - A mathematical statement indicating quantities are equivalent
• Evaluate-
To find the value of an algebraic expression by replacing variables
with a given quantity.
• Inequality - Mathematical statement indicating quantities are not equivalent
• Numerical Expression - A combination of numbers and operations.
• Translate -
To change from one form or language to another.
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 Work
Today 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 Work
Directions: 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
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Equation - A mathematical statement indicating quantities are equivalent
• Evaluate-
To find the value of an algebraic expression by replacing variables
with a given quantity.
• Inequality - Mathematical statement indicating quantities are not equivalent
• Numerical Expression - A combination of numbers and operations.
• Translate -
To change from one form or language to another.
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 - 7
3. 8x + 7
4. (5+7) – 9
5. 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 Work
Directions: Translate the following expressions into word form.
1. 12 + 15 = 27
2. 8x + 4
3.
36
3
+3
4. (7 * 3) – 6x
5. 7x +3 = 45
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Equation - A mathematical statement indicating quantities are equivalent
• Evaluate-
To find the value of an algebraic expression by replacing variables
with a given quantity.
• Inequality - Mathematical statement indicating quantities are not equivalent
• Numerical Expression - A combination of numbers and operations.
• Translate -
To change from one form or language to another.
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
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Equation - A mathematical statement indicating quantities are equivalent
• Evaluate-
To find the value of an algebraic expression by replacing variables
with a given quantity.
• Inequality - Mathematical statement indicating quantities are not equivalent
• Numerical Expression - A combination of numbers and operations.
• Translate -
To change from one form or language to another.
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