Chapter 1

Expressions and Patterns

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1.1A Powers and Exponents

I can use powers and exponents.

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Vocabulary: Factor – two or more numbers multiplied together to

form product

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Example: Write each power as a product of the same factor.a) 84

b) 45

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Evaluate – find the value of

Example: Write powers in standard form (without exponents) by evaluating the expression.

a) 63

b) 34

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Write numbers in exponential form:

Write in exponential form.

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9 9 9 9 9 9 9

Homework:

p.27 #11 – 32, 34

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1.1B Numerical Expressions

I can evaluate expressions using the order of operations

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Vocabulary:

Numerical expression – an expression with all numbers and operations; use order of operations to evaluate

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Order of Operations:The order we perform mathematical operations so everyone gets the same value.

Please Excuse My Dear

Aunt Sally

This will

help to you

to remember

the order of

operations.

Add +

Subtract -

Multiply x

Divide

Please Excuse My Dear Aunt Sally

P

E

M

D

A

S

Parentheses ( )

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Examples:

a) 14 + 3(7 – 2)

b)

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212 3 2

c) 24 2 5 3

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Homework:

p.31 #10 – 27, 30 - 34

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1.1C Algebraic Expressions

I can evaluate simple algebraic expressions.

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Vocabulary:Variable – symbol that represent an unknown quantity

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Algebra – branch of mathematics that involves expressions with variables

Algebraic expression – expression that contains variables, numbers, and at least one operation

Coefficient – number that multiples the variable

Example: Evaluate

1) t – 4 if t = 6

2) 5x + 3y if x = 7 and y = 9

3) 5 + a2 if a = 5

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Define a variable – choose a variable to represent unknown quantityExample: Leah has read 20 pages of a book. She plans to read 5 pages each day from now on. Write anexpression that represents the total number of pagesshe will read.

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1st: define a variable!

Homework:

p.36 #9 - 27

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1.1D Properties

I can us commutative, associative, identity and distributive properties to solve problems.

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7.NS.1d, 7.EE.1, 7.EE.2

Vocabulary:

Equivalent expressions – expressions that have the same value

* Properties have equivalent expressions

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Statements that are true for all numbers

Distributive property:

Numbers:

3(4 + 6) = 3(4) + 3(6)

5(7) + 5(3) = 5(7 + 3)

Algebra:

a(b + c) = ab + ac

ab + ac = a(b + c)

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Use the distributive property to rewrite each expression. Then evaluate it.1) 8(5 + 7)

2) 6(7) + 6(2)

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Commutative Property

Commutative means that the orderdoes not make any difference.

a + b = b + a a • b = b • a

Examples

4 + 5 = 5 + 4

2 • 3 = 3 • 2

The commutative property does not work for subtraction or division.

Associative PropertyAssociative means that the grouping

does not make any difference.(a + b) + c = a + (b + c) (ab) c = a (bc)

Examples

(1 + 2) + 3 = 1 + (2 + 3)

(2 • 3) • 4 = 2 • (3 • 4)

The associative property does not work for subtraction or division.

Name the property

1) 5a + (6 + 2a) = 5a + (2a + 6)

commutative (switching order)

2) 5a + (2a + 6) = (5a + 2a) + 6

associative (switching groups)

3) 2(3 + a) = 6 + 2a

distributive

Identity Properties

1) Additive Identity

What do you add to get the same?

a + 0 = a

2) Multiplicative Identity

What do you mult. to get the same?

a • 1 = a

Example: Find mentally. Justify each step.

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5 13 20

Homework:

p.40 #9 – 35 odd, 38

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1.2B Sequences

I can describe the relationships and extend terms in arithmetic sequences.

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Vocabulary:

Sequence –

Term –

Arithmetic sequence -

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Example: Describe the relationship between the terms in the arithmetic sequence 7, 11, 15, 19, ….

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Example: Describe the relationship between the terms in the arithmetic sequence 0.1, 0.5, 0.9, 1.3, … Then write the next three terms in the sequence.

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Homework:

p.47 #6 - 25

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1.3B Squares and Square Roots

I can find squares of number and square roots of perfect squares.

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Square Number Also called a “perfect square”

A number that is the square of a whole number

Can be represented by arranging objects in a square.

Square Numbers

Square Numbers One property of a perfect

square is that it can be represented by a square

array.

Each small square in the array shown has a side

length of 1cm.

The large square has a side length of 4 cm.

4cm

4cm 16 cm2

Square Numbers

The large square has an area of 4cm x 4cm = 16

cm2.

The number 4 is called the square root of 16.

We write: 4 = 16

4cm

4cm 16 cm2

Square Root

A number which, when multiplied by itself, results in another number.

Ex: 5 is the square root of 25.

5 = 25

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Index number

Radical

Radicand

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Homework:

p.55 #10 - 28

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1.3C Estimate Square Roots

I can estimate square roots.

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Estimating Square Roots

27 = ?

Since 27 is not a perfect square, we

have to use another method to

calculate it’s square root.

Estimating Square Roots

Not all numbers are perfect squares.

Not every number has an Integer for a square root.

We have to estimate square roots for numbers between perfect squares.

Estimating Square Roots

To calculate the square root of a non-perfect square:

❖ Place the values of the adjacent perfect squares on a number line.

❖ Interpolate between the points to estimate to the nearest tenth.

Estimating Square Roots

Example: 27

25 3530

What are the perfect squares on each side of 27?

36

Example: estimate to the nearest whole number

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89

Example: Estimate to the nearest whole number.

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116

Homework:

p.59 #7 – 17, 19 - 22

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