![Page 1: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/1.jpg)
Chapter 1
Expressions and Patterns
LSowatsky 1
![Page 2: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/2.jpg)
1.1A Powers and Exponents
I can use powers and exponents.
LSowatsky 2
![Page 3: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/3.jpg)
Vocabulary: Factor – two or more numbers multiplied together to
form product
LSowatsky 3
![Page 4: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/4.jpg)
Example: Write each power as a product of the same factor.a) 84
b) 45
LSowatsky 4
![Page 5: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/5.jpg)
Evaluate – find the value of
Example: Write powers in standard form (without exponents) by evaluating the expression.
a) 63
b) 34
LSowatsky 5
![Page 6: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/6.jpg)
Write numbers in exponential form:
Write in exponential form.
LSowatsky 6
9 9 9 9 9 9 9
![Page 7: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/7.jpg)
Homework:
p.27 #11 – 32, 34
LSowatsky 7
![Page 8: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/8.jpg)
1.1B Numerical Expressions
I can evaluate expressions using the order of operations
LSowatsky 8
![Page 9: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/9.jpg)
Vocabulary:
Numerical expression – an expression with all numbers and operations; use order of operations to evaluate
LSowatsky 9
![Page 10: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/10.jpg)
Order of Operations:The order we perform mathematical operations so everyone gets the same value.
![Page 11: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/11.jpg)
Please Excuse My Dear
Aunt Sally
This will
help to you
to remember
the order of
operations.
![Page 12: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/12.jpg)
Add +
Subtract -
Multiply x
Divide
Please Excuse My Dear Aunt Sally
P
E
M
D
A
S
Parentheses ( )
Exponents 43
![Page 13: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/13.jpg)
Examples:
a) 14 + 3(7 – 2)
b)
LSowatsky 13
212 3 2
c) 24 2 5 3
![Page 14: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/14.jpg)
LSowatsky 14
![Page 15: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/15.jpg)
Homework:
p.31 #10 – 27, 30 - 34
LSowatsky 15
![Page 16: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/16.jpg)
1.1C Algebraic Expressions
I can evaluate simple algebraic expressions.
LSowatsky 167.EE.4
![Page 17: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/17.jpg)
Vocabulary:Variable – symbol that represent an unknown quantity
LSowatsky 17
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
![Page 18: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/18.jpg)
Example: Evaluate
1) t – 4 if t = 6
2) 5x + 3y if x = 7 and y = 9
3) 5 + a2 if a = 5
LSowatsky 18
![Page 19: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/19.jpg)
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.
LSowatsky 19
1st: define a variable!
![Page 20: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/20.jpg)
Homework:
p.36 #9 - 27
LSowatsky 20
![Page 21: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/21.jpg)
1.1D Properties
I can us commutative, associative, identity and distributive properties to solve problems.
LSowatsky 21
7.NS.1d, 7.EE.1, 7.EE.2
![Page 22: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/22.jpg)
Vocabulary:
Equivalent expressions – expressions that have the same value
* Properties have equivalent expressions
LSowatsky 22
Statements that are true for all numbers
![Page 23: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/23.jpg)
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)
LSowatsky 23
![Page 24: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/24.jpg)
Use the distributive property to rewrite each expression. Then evaluate it.1) 8(5 + 7)
2) 6(7) + 6(2)
LSowatsky 24
![Page 25: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/25.jpg)
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.
![Page 26: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/26.jpg)
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.
![Page 27: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/27.jpg)
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
![Page 28: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/28.jpg)
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
![Page 29: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/29.jpg)
Example: Find mentally. Justify each step.
LSowatsky 29
5 13 20
![Page 30: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/30.jpg)
Homework:
p.40 #9 – 35 odd, 38
LSowatsky 30
![Page 31: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/31.jpg)
1.2B Sequences
I can describe the relationships and extend terms in arithmetic sequences.
LSowatsky 317.EE.4
![Page 32: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/32.jpg)
Vocabulary:
Sequence –
Term –
Arithmetic sequence -
LSowatsky 32
![Page 33: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/33.jpg)
Example: Describe the relationship between the terms in the arithmetic sequence 7, 11, 15, 19, ….
LSowatsky 33
![Page 34: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/34.jpg)
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.
LSowatsky 34
![Page 35: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/35.jpg)
Homework:
p.47 #6 - 25
LSowatsky 35
![Page 36: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/36.jpg)
1.3B Squares and Square Roots
I can find squares of number and square roots of perfect squares.
LSowatsky 36
![Page 37: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/37.jpg)
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.
![Page 38: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/38.jpg)
Square Numbers
![Page 39: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/39.jpg)
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
![Page 40: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/40.jpg)
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
![Page 41: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/41.jpg)
Square Root
A number which, when multiplied by itself, results in another number.
Ex: 5 is the square root of 25.
5 = 25
![Page 42: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/42.jpg)
LSowatsky 42
Index number
Radical
Radicand
![Page 43: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/43.jpg)
LSowatsky 43
![Page 44: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/44.jpg)
Homework:
p.55 #10 - 28
LSowatsky 44
![Page 45: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/45.jpg)
1.3C Estimate Square Roots
I can estimate square roots.
LSowatsky 45
![Page 46: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/46.jpg)
Estimating Square Roots
27 = ?
Since 27 is not a perfect square, we
have to use another method to
calculate it’s square root.
![Page 47: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/47.jpg)
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.
![Page 48: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/48.jpg)
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.
![Page 49: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/49.jpg)
Estimating Square Roots
Example: 27
25 3530
What are the perfect squares on each side of 27?
36
![Page 50: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/50.jpg)
Example: estimate to the nearest whole number
LSowatsky 50
89
![Page 51: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/51.jpg)
Example: Estimate to the nearest whole number.
LSowatsky 51
116
![Page 52: Chapter 1mrssowatskysmath.weebly.com/uploads/1/3/3/0/... · Estimating Square Roots To calculate the square root of a non-perfect square: Place the values of the adjacent perfect](https://reader036.vdocuments.net/reader036/viewer/2022081615/5fd6282805c8f361036924df/html5/thumbnails/52.jpg)
Homework:
p.59 #7 – 17, 19 - 22
LSowatsky 52