chapter 1 foundations for algebra 1.5 adding and subtracting real numbers
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Chapter 1 Foundations for Algebra 1.5 Adding and Subtracting Real Numbers. Tuesday September 6, 2011 Today we will review and practice adding and subtracting integers and rational numbers. Section 1.5 Checkpoint 1 Using a Number Line to Add or Subtract. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Chapter 1 Foundations for Algebra 1.5 Adding and Subtracting Real Numbers](https://reader036.vdocuments.site/reader036/viewer/2022081504/56813866550346895da01613/html5/thumbnails/1.jpg)
Chapter 1Foundations for Algebra
1.5 Adding and Subtracting Real Numbers
Tuesday September 6, 2011
Today we will review and practice adding and subtracting integers and rational
numbers.
![Page 2: Chapter 1 Foundations for Algebra 1.5 Adding and Subtracting Real Numbers](https://reader036.vdocuments.site/reader036/viewer/2022081504/56813866550346895da01613/html5/thumbnails/2.jpg)
Section 1.5 Checkpoint 1Using a Number Line to Add or Subtract
34
Use a number line to add or subtract real numbers:
7
)3(4 1
)3(4 7
)3(4 1
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
-6 -5 -4 -3 -2 -1 0 1 2 3
Move ______ to add , ____ to subtract. right left
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Section 1.5 Checkpoint 2Adding Integers and Rational Numbers
)8(16
Add and find the sum using these rules:
24 911 2
)3.11(2.9 1.2
4
1
3
2
12
11
When the signs are __________ , ____ and keep the sign.
When the signs are ________ , ________ and keep sign of the ______ number.
the same add
different subtractlarger
need common denominator
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Section 1.5 Checkpoint 3Subtracting Integers and Rational Numbers
)7(12
Subtract and find the difference using these rules:
5
28 10
)8.5(6.4 4.10
2
1
8
3
8
7
Subtraction is __________ of the __________.addition opposite
712
)2(8
8.56.4
2
1
8
3
need common denominator
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Assignment SheetTuesday 9/6
Algebra 1-Mr. GualandriRm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
1 9/6 TB p. 40 #17-39 all – In class
2 9/6 TB p. 43 #69-76 all – Homework
![Page 6: Chapter 1 Foundations for Algebra 1.5 Adding and Subtracting Real Numbers](https://reader036.vdocuments.site/reader036/viewer/2022081504/56813866550346895da01613/html5/thumbnails/6.jpg)
1 9/6 TB p. 40 #17-39 all – In class
![Page 7: Chapter 1 Foundations for Algebra 1.5 Adding and Subtracting Real Numbers](https://reader036.vdocuments.site/reader036/viewer/2022081504/56813866550346895da01613/html5/thumbnails/7.jpg)
1 9/6 TB p. 40 #17-39 all – In class
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Chapter 1Foundations for Algebra
1.6 Multiplying and Dividing Real Numbers
Wednesday Sept 7, 2011
Today we will review and practice multiplying and dividing integers and
rational numbers.
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Assignment Sheet
Algebra 1-Mr. Gualandri Rm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
1 9/6 TB p. 40 #17-39 all – In class
2 9/6 TB p. 43 #69-76 all – Homework
![Page 10: Chapter 1 Foundations for Algebra 1.5 Adding and Subtracting Real Numbers](https://reader036.vdocuments.site/reader036/viewer/2022081504/56813866550346895da01613/html5/thumbnails/10.jpg)
2 9/6 TB p. 43 #69-76 all – Homework
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Section 1.6 Checkpoint 4Multiplying Real Numbers
)15(6
Multiply and find the product using these rules:
90
3
112 4
5
3
10
7
50
21 24 16
When the signs are _________ the product is _______. the same positive
When the signs are _________ the product is ________. different negative
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Section 1.6 Checkpoint 5Simplifying Square Roots
81
Write the simplified form of the ___________ expressions:
9 16 4
121
49
11
7
36
1
6
1
square root
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Section 1.6 Checkpoint 6Dividing Real Numbers
)6(120
Divide and find the quotient using same rules as multiply:
20 )8.0(4.6 8
45
2
10
1
12
14412
When the signs are _________ the product is _______.
When the signs are _________ the product is ________.
the same positive
different negative
When dividing fractions, it is helpful to use the fact that division is _____________ of the __________.reciprocalmultiplication
4
1
5
2 12144
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Section 1.6 Checkpoint 7Dividing Rational Numbers (Fractions)
2
5
4
3
Divide and simplify the quotient using the reciprocal rule:
10
3
8
9
y
x
4
3Evaluate and simplify when x = and y = :
3
2
To divide fractions, ________ by the __________.reciprocalmultiply
5
2
4
3
20
6
3243
3
2
4
3
2
3
4
3
8
9
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Assignment SheetWednesday 9/7
Algebra 1-Mr. Gualandri Rm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
1 9/6 TB p. 40 #17-39 all – In class
2 9/6 TB p. 43 #69-76 all – Homework
3 9/ 7 TB p. 49 #8-38 all – In class
4 9/7 TB p. 50 #41-47 all – Homework (use checkpoint #7)
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3 9/7 TB p. 49 #8-38 all – In class
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3 9/7 TB p. 49 #8-38 all – In class
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Chapter 1Foundations for Algebra
1.7 The Distributive Property
Thursday Sept 8, 2011
Today we will learn how to simplify expressions using the distributive property.
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Assignment Sheet
Algebra 1-Mr. Whitney Rm. 14-228 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
1 9/6 TB p. 40 #17-39 all – In class
2 9/6 TB p. 43 #69-76 all – Homework
3 9/7 TB p. 49 #8-38 all – In class
4 9/7 TB p. 50 #41-47 all – Homework (use checkpoint #7)
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5 9/8 TB p. 51 #69-74 all – In class
For #72-74, properties are listed on TB pages 26 and 27.
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4 9/7 TB p. 50 #41-47 all – Homework (use checkpoint #7)
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5 9/8 TB p. 51 #69-74 all – In class
For #72-74, properties are listed on TB pages 26 and 27.
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Section 1.7 Checkpoint 8Using the Distributive Property to
Simplify Expressions
)53(4 a
Use the distributive property to simplify each expression:
2012 a
6)15( x
)72(2 m
)13( y
630 x
414 m
13 y )1510( x 1510 x
8124
1y 23 y
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Section 1.7 Checkpoint 9Rewriting Fraction Expressions
4
13 x
Rewrite the expression as two fractions:
4
1
4
3 x
2
127 n
9
15a
62
7 n
3
5
9
1 a
4
1
4
3x
2
12
2
7n
9
15
9a
split fraction simplify
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Assignment SheetFriday 9/9
Algebra 1-Mr. Gualandri Rm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
1 9/6 TB p. 40 #17-39 all – In class
2 9/6 TB p. 43 #69-76 all – Homework
3 9/7 TB p. 49 #8-38 all – In class
4 9/7 TB p. 50 #41-47 all – Homework (use checkpoint #7)
5 9/8 TB p. 51 #69-74 all – In class
6 9/8 WB p. 27 Practice 1-7 #1-22 – In Class/finish HW
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Complete Practice Worksheet 1-7 from WB p. 27
Write answers on worksheet/workbook page.
Worksheet due Tuesday at beginning of class.
Worksheet will be graded as a Quiz.
Unit 2 Test and Portfolio due Friday Sept. 16th.
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Chapter 1Foundations for Algebra
1.8 An Introduction to Equations
Friday Sept 9, 2011
Today we will learn how determine if a number is a solution to a given equation.
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Section 1.8 Checkpoint 10Using Mental Math to find Solutions
128 x
Use mental math to find the solution to each equation:
4x
84
a
312 y
32a
56
n
9y
30n
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Section 1.8 Checkpoint 11Identifying the Solution to an Equation
6;32122 x
Is the given number a solution to the equation?
2
1;586 m
5;4416 n
55
1616
No
Yes
Yes
3224 3212)6(2
582
16
4)5(416
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Section 1.9 Checkpoint 12Identifying Ordered Pair Solutions
)10,3(;4xy
Is the given ordered pair (x,y) a solution to the equation?
)4,15(;15
1yx
)6,4(;63 xy
44
66
No
Yes
No
1210 )3(4)10(
)4(1)15(5
1
6)4(3)6(
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Assignment SheetFriday 9/9
Algebra 1-Mr. Gualandri Rm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
3 9/7 TB p. 49 #8-38 all – In class
4 9/7 TB p. 50 #41-47 all – Homework (use checkpoint #7)
5 9/8 TB p. 51 #69-74 all – In class
6 9/8 WB p. 27 Practice 1-7 #1-22 – In Class/finish HW
7 9/9 WS p31 Extra Practice 1-8 #1-25 – In Class/finish HW
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Complete Extra Practice Worksheet 1-8
Write answers on worksheet.
Worksheet due Tomorrow at beginning of class.
Unit 2 Test and Portfolio due Friday Sept. 16th.
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7 9/9 WS Extra Practice 1-8 #1-25 – In Class/finish HW
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Chapter 1Foundations for Algebra
1.9 Patterns, Equations, and Graphs
Monday Sept 12, 2011
Today we will learn how to create a graph and use an ordered pair to
predict an outcome.
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Section 1.9 Checkpoint 13Using a Table to Make an Equation
Complete the table and use x and y to make an equation.
Age in yearsx
Height of Tree inches
y
3 78
5 130
182
8 208
10 260
axy
3)(78 axy 26
26a
A type of Florida palm tree grows 26 inches per year.
7
Use the pattern in the table to make an equation that models the relationship
5)(130 a7)(182 a8)(208 a10)(260 a
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Section 1.9 Checkpoint 14Using a Table to Make Graph
Use the table of values for x and y to make a graph.
Number of weeks,
x
Weight of pig in kg,
y
0 32
1 38
2 44
3 50
4 56 x
y
0 1 2 3 4 5
60
50
40
30
20
10
Weeks
Wei
ght
in k
ilogr
ams
The weight of a domestic pig is recorded over four weeks.
Use the data in the table to model and complete the graph.
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Section 1.9 Checkpoint 15Using a Graph to Make a Prediction
Use the graph to answer the questions below.
x
y
1 2 3 4 5 6 7 8
30
25
20
15
10
5
People
Tic
ket
Cos
t ($
)
The graph shows the ticket cost for people attending a football game.
Write the ordered pair (x, y) that represents the ticket cost for 5 people to attend the game. How much will 5 tickets cost?
Draw a line through the points and use it to predict the ticket cost for 8 people.
)20,5( $20
About $32
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Assignment SheetTuesday 9/13
Algebra 1-Mr. Gualandri Rm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
3 9/8 TB p. 49 #8-38 all – In class
4 9/8 TB p. 50 #41-47 all – Homework (use checkpoint #7)
5 9/9 TB p. 51 #69-74 all – In class
6 9/9 WB p. 27 Practice 1-7 #1-22 – In Class/finish HW
7 9/12 WS p. 31 Extra Practice 1-8 #1-25 – In Class/finish HW
8 9/14 WS p.35 Extra Practice 1-9 #1-20 – In Class/finish HW
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Chapter 1Foundations for Algebra
1-5 through 1-9
Thursday Sept 15, 2011
Today we will review sections 1-5 through 1-9 and prepare for the Unit 2
test and portfolio check.
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Assignment SheetWednesday 9/14
Algebra 1-Mr. GualandriRm. 14-139 Name ______________________ Unit 2 Foundations for Algebra Portfolio Assignment List
3 9/7 TB p. 49 #8-38 all – In class
4 9/7 TB p. 50 #41-47 all – Homework (use checkpoint #7)
5 9/8 TB p. 51 #69-74 all – In class
6 9/8 WB p. ?? Practice 1-7 #1-22 – In Class/finish HW
7 9/9 WS Extra Practice 1-8 #1-? – In Class/finish HW
8 9/14 WS p.35 Extra Practice 1-9 #1-20 – In Class/finish HW
9 9/15 Test Review TB p. 79 #1-19 all
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9 9/15 Test Review TB p. 79 #1-19 all
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9 9/15 Test Review TB p. 79 #1-19 all
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9 9/8 Test Review TB p. 79 #1-19 all
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9 9/15 Test Review TB p. 79 #1-19 all
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Chapter 1Foundations for Algebra
1-5 through 1-9
Friday Sept 16, 2011
Today we will take the Unit 1 test and turn in portfolios for a grade.
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END OF LESSON
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Section 1.5 Checkpoint 1Using a Number Line to Add or Subtract
34
Use a number line to add or subtract real numbers:
)3(4
)3(4
)3(4
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
-6 -5 -4 -3 -2 -1 0 1 2 3
Move ______ to add , ____ to subtract.
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Section 1.5 Checkpoint 2Adding Integers and Rational Numbers
)8(16
Add and find the sum using these rules:
911
)3.11(2.9
4
1
3
2
When the signs are __________ , ____ and keep the sign.
When the signs are ________ , ________ and keep sign of the ______ number.
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Section 1.5 Checkpoint 3Subtracting Integers and Rational Numbers
)7(12
Subtract and find the difference using these rules:
28
)8.5(6.4
2
1
8
3
Subtraction is __________ of the __________.
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Section 1.6 Checkpoint 4Multiplying Real Numbers
)15(6
Multiply and find the product using these rules:
3
112
5
3
10
7 24
When the signs are _________ the product is _______.
When the signs are _________ the product is ________.
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Section 1.6 Checkpoint 5Simplifying Square Roots
81
Write the simplified form of the ___________ expressions:
9 16 4
121
49
11
7
36
1
6
1
square root
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Section 1.6 Checkpoint 6Dividing Real Numbers
)6(120
Divide and find the quotient using same rules as multiply:
)8.0(4.6
45
2
12
144
When the signs are _________ the product is _______.
When the signs are _________ the product is ________.
When dividing fractions, it is helpful to use the fact that division is _____________ of the __________.
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Section 1.6 Checkpoint 7Dividing Rational Numbers (Fractions)
2
5
4
3
Divide and simplify the quotient using the reciprocal rule:
y
x
4
3Evaluate and simplify when x = and y = :
3
2
To divide fractions, ________ by the __________.
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Section 1.7 Checkpoint 8Using the Distributive Property to
Simplify Expressions
)53(4 a
Use the distributive property to simplify each expression:
6)15( x
)72(2 m
)13( y )1510( x
8124
1y
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Section 1.7 Checkpoint 9Rewriting Fraction Expressions
4
13 x
Rewrite the expression as two fractions:
2
127 n
9
15a
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Section 1.8 Checkpoint 10Using Mental Math to find Solutions
128 x
Use mental math to find the solution to each equation:
84
a
312 y
56
n
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Section 1.8 Checkpoint 11Identifying the Solution to an Equation
6;32122 x
Is the given number a solution to the equation?
2
1;586 m
5;4416 n
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Section 1.9 Checkpoint 12Identifying Ordered Pair Solutions
)10,3(;4xy
Is the given ordered pair (x,y) a solution to the equation?
)4,15(;15
1yx
)6,4(;63 xy
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Section 1.9 Checkpoint 13Using a Table to Make an Equation
Complete the table and use x and y to make an equation.
Age in yearsx
Height of Tree inches
y
3
5
182
8
10
A type of Florida palm tree grows 26 inches per year.
Use the pattern in the table to make an equation that models the relationship
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Section 1.9 Checkpoint 14Using a Table to Make Graph
Use the table of values for x and y to make a graph.
Number of weeks,
x
Weight of pig in kg,
y
0
1
2
3
4 x
y
0 1 2 3 4 5
60
50
40
30
20
10
Weeks
Wei
ght
in k
ilogr
ams
The weight of a domestic pig is recorded over four weeks.
Use the data in the table to model and complete the graph.
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Section 1.9 Checkpoint 15Using a Graph to Make a Prediction
Use the graph to answer the questions below.
x
y
1 2 3 4 5 6 7 8
30
25
20
15
10
5
People
Tic
ket
Cos
t ($
)
The graph shows the ticket cost for people attending a football game.
Write the ordered pair (x, y) that represents the ticket cost for 5 people to attend the game. How much will 5 tickets cost?
Draw a line through the points and use it to predict the ticket cost for 8 people.