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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 ( )
Exponents 43
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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