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.