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Eureka Module 3:
Expressions
Resource Packet
Goals:
Use the Order of Operations to rewrite numeric and algebraic expressions.
Write an algebraic expression to represent the relationship between any term
in the sequence and its position in the sequence.
Understand the five key properties of numbers: associative properties,
commutative properties, identity properties, distributive property, and the
multiplicative property of zero.
Rewrite and simplify expressions using the different properties of numbers
by recognizing the relationships of terms, coefficients, variables and
constants.
Add and subtract linear expressions.
Improve your ability to break down word problems and write them using
algebraic expressions.
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Number Property Matching Practice
(use page 368 as a resource if needed)
Matchingletter Number Property Definition
1. Identity property of
multiplication A. Numbers can be multiplied in any order, and the sum will be the same.
2. commutative property
of addition B. A factor can be distributed through multiplication to two or more addends.
3. inverse property of
multiplication C. Any number multiplied by 0 produces a product of 0. 4. identity property of
addition D. Any number can be multiplied by 1 without changing its value.
5. associative property
of addition E. In a multiplication expression, grouping symbols, such as parentheses, can be moved without changing the product.
6. distributive property
of multiplication F. Any number multiplied by its reciprocal equals 1.
7. Multiplicative Property
of Zero G. Any number added to its inverse equals 0. 8. associative property
of multiplication
H. Numbers can be added in any order, and the sum will be the same.
9. commutative property
of multiplication I. In an addition expression, grouping symbols, such as parentheses, can be moved without changing the sum.
10.inverse property of
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Warm Up:
Use the Distributive Property to find the area of the figure below in at least two different ways.(Hint: use only one “=” sign per solution.)
First Possible Answer: _________________________________________________ Second Possible Answer: _________________________________________________
Warm Up:
Use the Distributive Property to find the area of the figure below in at least two different ways. (Hint: use only one “=” sign per solution.)Total Area: _________________________________________________________ First Possible Answer: _________________________________________________ Second Possible Answer: _________________________________________________
8 12 2 5
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7 11 3 5
6 Exercise 1:
Exercise 2:
7 Exercise 4:
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Translating Word Problems into Algebraic Expressions:
You subscribe to m magazines. Your friend subscribes to 2 fewer magazines than you. Write an expression to represent how many magazines you both subscribe to?
(Build on the problem) Using the problem above, write an expression to represent what is the total cost of the magazines if each your magazines cost $3.75 and your friend’s magazines cost $2.50.
Carl bought 6 cans of tennis balls which cost d dollars per can and two new rackets at r dollars each. He also paid his monthly tennis club membership fee of $15. Write an expression in simplest form that represents the total amount that Carl spent.
The walking trail at the park is a loop that covers a distance of m miles. Melissa walked 3 loops each on Monday and Wednesday and 4 loops on Friday. On Sunday, Melissa walked 8 miles. Write an expression in simplest form that represents the total distance that Melissa walked this week.
9 Write an expression in simplest form for the perimeter of the triangle below.
2x - 3
4x + 8
10 Problem #1:
Tonya charges $3.50 per hour to baby-sit. The sequence $3.50, $7.00, $10.50, $14.00, … represents how much she charges for each subsequent hour. For example, $10.50 is the third term that represents how much she charges for 3 hours. Use x to represent the number of hours Tonya babysits. Use the table to predict the next terms in the sequence? Write an expression using the variable “x’ and use it to predict the amount of money Tonya will earn for 19 hours.
Make a Table:
(x) Rule = (y)
Make an expression: ___________________________________________
11 Problem #2:
Luther starts jogging 8 minutes on the first day and then increases his time by 4 minutes each day. Use x to represent the number of days Luther has been running. Use the table to predict the next terms in the sequence? Write an expression using the variable “x’ and use it to predict the amount of time Luther will jog on the 19th day.
Make a Table:
(x) Rule = (y)
Make an expression: ___________________________________________ Make a Graph:
12 Problem #3:
The enrollment at Grove Middle School is expected to increase by 40 students each year for the next 5 years. If their current enrollment is 600 students, find their enrollment after each of the next 5 years.
Make a Table:
(x) Rule = (y)
Make an expression: ___________________________________________ Make a Graph:
13 Subtracting Linear Expressions – Use Additive Inverse to rewrite expressions as addition
Additive inverses have a sum of zero. Multiplicative inverses have a product of 1. Fill in the
center column of the table with the opposite of the given number or expression, then show the proof that they are opposites. The first row is completed for you.
Expression Opposite? Proof of Opposites
1 −1 1 + (−1) = 0
3
−7
−1
2 𝑥
3𝑥
𝑥 + 3
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NAME ____________________________________________ DATE ____________________________ PERIOD _____________
Vocabulary Review
SCORE____________
Additive Identity Property algebra algebraic expression arithmetic sequence Associative Property coefficient Commutative Property constant counterexample
define a variable Distributive Property equivalent expressions factor factored form geometric sequence like terms monomial
Multiplicative Identity Property
Multiplicative Property of Zero property sequence simplest form simplify term variable
Choose from the terms above to complete each sentence.
1. The numbers 2, 5, 8, 11, … are an example of a(n) ___________ .
2. The numerical factor of a multiplication expression that contains a variable is called a (n) ___________.
3. Each number in a sequence is called a(n) ___________.
4. A (n) ___________ contains variables, numbers, and at least one operation.
5. Expressions that have the same value are called ___________.
6. A (n) ___________ is a term without a variable.
7. An algebraic expression is in ___________ if it has no like terms and no parentheses.
8. ___________ contain the same variables to the same powers.
1. ___________________ 2. ___________________ 3. ___________________ 4. ___________________ 5. ___________________ 6. ___________________ 7. ___________________ 8. ___________________
