7th Grade Math Unit 1
Algebraic Reasoning
Name: ___________________________ Period: _______
Common Core State Standards CC.7.NS.1 - Apply and extend previous understandings of addition and subtraction
to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
CC.7.EE.1 - Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients.
CC.7.EE.2 - Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
Scope and Sequence Day 1 Lesson 1-1 Day 5 Lesson 1-4
Day 2 Lesson 1-2 Day 6 Lesson 1-5
Day 3 Quiz Day 7 Review
Day 4 Lesson 1-3 Day 8 Test
IXL Modules
SMART Score of 80 is required Due the day of the exam
Lesson 1 4.G.4 Simplify expressions using order of operations and parentheses
Lesson 2 7.S.1 Properties of addition and multiplication
Lesson 3 6.X.3 Evaluate variable expressions with whole numbers
6.X.4 Evaluate multi-variable expressions
6.X.5 Evaluate variable expressions with decimals, fractions and
mixed numbers
Lesson 4 6.X.1 Write variable expressions
6.X.2 Write variable expressions: word problems
Lesson 5 6.X.12 Add and subtract like terms
Lesson 1-1
Order of Operations
Warm-Up
Vocabulary
A numerical expression is made up of ____________ and ____________. When simplifying a
numerical expression, ____________ must be followed so that everyone gets the
____________ answer. That is why mathematicians have agreed upon the order of operations.
Order of Operations
(Use the acronym PEMDAS or “Please Excuse My Dear Aunt Sally)
P Parenthesis Perform operations within grouping symbols
E Exponents Evaluate Powers
M Multiply & Divide Do this IN ORDER from left to right D (even if division comes first)
A Add & Subtract Do this IN ORDER from left to right. S (even if subtraction comes first)
Examples: Using the Order of Operations
Simplify the following expressions. Use order of operations to justify your answer:
3 + 15 ÷ 5
44 – 14 ÷ 2 · 4 + 6
3 + 23 · 5
2 + 24 ÷ 6
28 – 21 ÷ 3 · 4 + 5
2 + 32 · 4
Examples: Using the Order of Operations with Grouping Symbols
Simplify the following expressions. Use order of operations to justify your answer: Helpful Hint: When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set.
42 – (3 · 4) ÷ 6
[(26 – 4 · 5) + 6]2
24 – (4 · 5) ÷ 4
[(32 – 4 · 4) + 2]2
Examples: Application
Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression (5 + 3 · 3) · 4 to find how many miles she ran last month.
Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate the expression 3 · 4 · 7 + 30 to find out how many words will she know at the end of seven weeks.
Lesson 1-2
Properties of Numbers
Warm-Up
Vocabulary
Commutative Property You can ____________ numbers in any order and
____________ numbers in any order. Associative Property When you add or multiply, you can ____________
the numbers together in any ____________.
Identity Property The ____________ of 0 and any number is the
number. The ____________ of 1 and any number is the
number.
Distributive Property A property in which ____________ is applied to
addition or subtraction of two or more numbers in which each
term inside a set of parentheses can be multiplied by a
____________ outside the parentheses.
Examples: Identify Properties of Addition and Multiplication
Tell which property is represented.
(2 6) 1 = 2 (6 1)• • • •
3 + 0 = 3
7 + 9 = 9 + 7
7 1 = 7•
3 + 4 = 4 + 3
(5 1) 2 = 5 (1 2)• • • •
Examples: Using Properties to Simplify Expressions
Simplify each expression. Justify each step.
21 + 16 + 9
20 9 5• •
17 + 14 + 3
12 3 5• •
Examples: Using the Distributive Property to Multiply Mentally
Use the distributive property to solve the following:
6(54)
4(27)
8(19)
9(14)
Lesson 1-3
Variables and Algebraic Expressions
Warm-Up
Vocabulary
Variable A letter that represents a number that can
____________.
Constant A value that ____________ change. Algebraic Expression An expression that consists of one or more variables. It
will also often contain constants and ____________.
Evaluate ____________ a number for the variable in an algebraic
expression.
Examples: Evaluating Algebraic Expressions
Evaluate k + 9 for each value of k.
k = 5
k = 2
Evaluate a + 6 for each value of a.
a = 3
a = 5
Multiplication and division of variables can be written in several ways…
Examples: Evaluating Algebraic Expressions Involving Order of Operations
Evaluate each expression for the given value of the variable (do not forget to use the order of operations).
4x - 3, for x = 2
s 3 + s, for s = 15÷
5x2 + 3x, for x = 2
3x - 2, for x = 3
r 3 + r, for r = 12÷
4y2 + 2y, for y = 3
Examples: Evaluating Algebraic Expressions with Two Variables
Evaluate + 4b, for a = 3 and b = 2.a6
Evaluate + 2x, for w = 4 and x = 2.8w
Lesson 1-4
Translate Words into Math
Warm-Up
Examples: Evaluating Algebraic Expressions with Two Variables Write each phrase as an algebraic expression.
the quotient of a number and 4
w increased by 5
the difference of 3 times a number and 7
the quotient of 4 and a number, increased by 10
a number decreased by 10
r plus 20
the product of a number and 5
4 times the difference of y and 8
When solving real-world problems, you may need to determine the ____________to know
which operation to use.
Examples: Translating Real-World Problems into Algebraic Expressions
Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how are he can drive in h hours.
On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly.
Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours.
At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour.
Lesson 1-5
Simplifying Algebraic Equations
Warm-Up
Vocabulary
Term A number, a variable, or a product of ____________ and
____________ separated by + and -.
Coefficient A number that is ____________ by a variable in an
algebraic expression. A variable by itself has a coefficient of 1.
Like Terms Terms with the same variables raised to the
same
____________. The coefficients ______ ______
have to be the same.
Examples: Identifying Like Terms
Identify like terms in the list.
3t 5w2 7t 9v 4w2 8v
2x 4y3 8x 5z 5y3 8z
Combining Like Terms Combining like terms is like ____________ similar objects.
4x + 5x = 9x To combine like terms that have variables, ____________ or ____________ the coefficients.
Examples: Simplifying Algebraic Expressions
Simplify
6t - 4t
45x - 37y + 87
3a2 + 5b + 11b2 - 4b + 2a2 - 6
5y + 3y
2(x2 - 13x) + 6
4x2 + 4y + 3x2 - 4y + 2x2 + 5
Examples: Geometry Application Write an expression for the perimeter of the triangles. Then simplify the expression.