sect. 1 chapter 2
TRANSCRIPT
UntitledA conditional is a statement in two parts, a hypothesis and a
conclusion. When the conditional is written in the "ifthen" form, the
"if" is the hypothesis, and the "then" is the conclusion.
If today is Monday, then tomorrow is Tuesday. hypothesis conclusion
Conditional statements are either True or False. If a Counterexample can be given for a statement, then it is considered to be False.
If x is an integer, then x >0.
Is this true or false? Can you find a counterexample?
Rewrite each statement into "ifthen" form.
Two lines intersect in exactly one point.
Points on the same line are collinear.
a.
b.
If John lives in Florida, then he lives in Miami.
a.
b.
The converse of a conditional statement is formed by flipping the hypothesis and conclusion.
If today is Monday, then tomorrow is Tuesday. hypothesis conclusion
Conditional:
Converse: If tomorrow is Tuesday, then today is Monday. hypothesisconclusion
Hypothesis: The animal is a fish.
Conclusion:
Conditional:
Conditional: If your Principal is Ms. Bright, then you must attend Eastbay Middle School.
Statement: A fish has gills.
Truth Value: True or False
Statement: Animals who live in water are fish. Hypothesis:
Conclusion: Conditional:
Hypothesis:
Conclusion:
If the animal is a fish, then it has gills.
Converse: Truth Value: True or False
Converse: Truth Value: True or False
Converse: Truth Value: True or False
Sect. 1 Chapter 2
A biconditional statement is when you join two true statements, the
conditional and converse, using the phrase "if and only if." If today is Monday, then tomorrow is Tuesday.
Today is Monday, if and only if tomorrow is Tuesday.
Conditional:
Biconditional:
Try these: Conditional:
Truth Value: True or False Converse: Truth Value: True or False
If we are celebrating Breast Cancer Awareness month, then we are in the month of October.
Conditional:
Truth Value: True or False Converse: Truth Value: True or False
If angle A is obtuse, then m A = 100
We can write great Biconditional statements by using the dictionary as a resources. See the definition below for an equilateral triangle, as stated in your glossary.
equilateral triangle- a triangle whose sides are all congruent (pg 752)
Conditional:
Converse: Truth Value: True or False
If a triangle has sides that are all congruent, then the triangle is an equilateral triangle.
Definition:
Conditional:
Converse:
Definition: pentagon:
Sometimes definitions are written poorly, and do not serve as good definitions. Determine whether these definitions are written accurately. If not, name a counterexample!
Conditional:
Converse:
Definition: Butterfly - an insect with wings.
Counterexample:
Conditional:
Converse:
Definition:
Counterexample:
Counterexample:
acute angle: angle smaller than 90
Below are several figures that are categorized into Whatnots and Not Whatnots. Try to find the characteristics that separate each group, and then determine which figures are whatnots in the last section.
Biconditional:
Biconditional:
Biconditional:
Biconditional:
Sect. 2 Chapter 2
We've talked about inductive reasoning as a reasoning based on observation to predict what would happen next (ex. patterns).
If it's cloudy it's going to rain.
Deductive reasoning is based more on actual facts and statements.
If the clouds are heavy with water, then it's going to rain.
There are two laws we can use with deductive reasoning:
Law of Detachment: if p q is true, and p is true, then q has to be true.
Law of Syllogism: if p q, and q r, are true, then p r has to be true.
If a quadrilateral is a square, then it contains four right angles.
Truth value: True or False
p-
q-
p q: If a quadrilateral is a square, then it contains four right angles.
Truth value: True or False
q r: If a quadrilateral contains four right angles, then it's a rectangle.
Truth value: True or False
p r:
Determine if you can use any of the above laws to arrive to a conclusion for the following:
1. Given: If the electric power is cut, then the refrigerator does not work.
The electric power is cut.
Conclusion:
Law of:
2. Given: If an angle is obtuse, then it cannot be acute.
The angle is not acute.
Conclusion:
Conclusion:
Sect. 3 Chapter 2
When we reason in Algebra, we try to provide a logical explanation for, or justify, each step we do to solve a problem.
In addition to the postulate, theorems, and properties we've discussed so far, here are a few others we need to recall from our past.
2+4= 2+4, 6=6 24= 24, 2=2 2(4)=2(4), 8=8 2/4=2/4, 0.5=0.5
a=2, b=3, c=4 2(3+4)= 2(3)+2(4)
2(7)= 6+8 14=14
a=2, b=2, c=4
Justify each step for solving the problems below.
1. BC = 3x + 2 and CD = 5x - 10. Solve for x.
a. Given: BC= CD. (its shown the picture)
b.3x + 2=5x - 10 Substitution property ( you substituted the lengths of the segments with their names)
c. 3x +2+10= 5x Addition Property of Equality (you are combining like terms)
d. 2+10= 5x-3x Subtraction Property of Equality (you are combining like terms)
e. 12= 2x Simplify
f. x= 6 Division Property of Equality ( divided by 2)
a
d. 90 + 6x = 180
2. ABC= Q therefore Q = ABC
Sect. 4 Chapter 2
2 3 4
Angles 1 and 2 are vertical angles, which means they are congruent.
Angles 3 and 4 are vertical angles, which means they are congruent.
Angles 1 and 3 are supplementary, because together they form a line, which is 180. So are Angles 1 and 4, and 4 and 2. To be supplementary, angles do not have to be adjacent, or beside each other.
1 2
Here, angles 1 and 2 are adjacent, and they are also complementary, because they form 90 together.
Using the diagram, find the following:
1. A pair of complementary angles.
2. A pair of supplementary angles.
3. A pair of vertical angles.
4. What can you conclude about the diagram above?
Find the missing variables for the diagrams below.
1. 2.
In the previous lesson, we learned how to justify our answers when solving problems. When you write your justifications using sentences to create a paragraph, you are creating a paragraph proof.
a.
b.
c.
d.
a.
b.
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images/clipboard(10).png
annotationmetadata/metadata(9).xml
annotationmetadata/metadata(7).xml
settings.xml
imsmanifest.xml
ADL SCORM CAM 1.3 metadata.xml What's New in SMART Notebook 10.8
metadata.xml
preview.png
assessment.xml
metadata.rdf
metadata.db
page6.svg
Education Standards and Cognitive Levels What’s new in SMART Response 2012 Education Standards and Cognitive Levels When creating questions, tag them with: · Education standards from your local state/province · Cognitive levels from several popular cognitive level scales · Custom tags that you create Tags in your tag library can now be easily re-used!
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What's New What’s new in SMART Response 2012 Robust Teacher Tools reporting · Tag questions with education standards in your region · Tag questions with cognitive levels · Create reports by education standards or cognitive levels · Easily generate reports by student or class · Compare performance across students or classes Future-proof your investment · Send assessments to any web-enabled mobile device · Include image-based questions in web assessments · Use remotes mixed with mobile devices Other new features and enhancements · Deliver assessments one question at a time in whole class mode · Include Text questions when using mixed PE and XE remotes · Use multiple Response receivers for classes over 100 students · Response VE is localized in 18 languages · Response 2012 Mac is localized in 9 languages
page1.svg
New Reports What’s new in SMART Response 2012 New Teacher Tools Reports See at a glance how students and classes are doing. Sixteen new reports are now available in Teacher Tools!!
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New Reports What’s new in SMART Response 2012 New Teacher Tools Reports Have better access to student and class level performance data. Get reports on: · Performance against local education standards, cognitive levels, and custom tags · Individual students or classes · Comparisons between students or classes Create a report and: · Save it to Teacher Tools · Generate a PDF to print or share · Export the data to CSV format
page16.svg
Mac Localization What’s new in SMART Response 2012 Mac Localization SMART Response Mac is now localized in the following languages: · English · French · German · Spanish (European) · Spanish (International) · Danish · Italian · Dutch · Portugese (Brazil)
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Saving Reports in Teacher Tools What’s new in SMART Response 2012 Saving Reports in Teacher Tools Save reports to Teacher Tools so they're easily accessible from one place. Change the report's properties to update it!
page24.svg
Assessment Delivery Modes What’s new in SMART Response 2012 Assessment Delivery Modes Teachers can now choose to deliver their assessment in self-paced or whole class mode. In self-paced mode, students can answer all questions at their own pace (same as in Response 2011). In whole class mode, students can only answer the question currently displayed on the Notebook page.
page0.svg
VE Enhancements What’s new in SMART Response 2012 Response VE Enhancements Images for each question are now displayed on students' devices when using Response VE. Response VE is now also localized in 18 languages. Students can zoom in on the image if needed A thumbnail of the Notebook page appears as part of the question
page3.svg
Mixed Mode Enhancements What’s new in SMART Response 2012 Mixed Mode Enhancements Teachers now have greater flexibility when using Mixed Mode. Exclude remotes that you don't use to access more functionality. Unselect this option to use Text questions with PE and XE remotes in Mixed Mode!
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Multiple Receiver Support What’s new in SMART Response 2012 Multiple Receiver Support Use multiple Response receivers with the same teacher computer for larger classes or groups of students. Each receiver appears in Teacher Tools
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Welcome! Welcome to SMART Response 2012 interactive response software Review new features and get started quickly To access this guide later, go to: SMART Response Software What's New Guide Then click the "What's new in SMART Response" link on the last page.
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Reports Preview What’s new in SMART Response 2012 Reports Preview Preview reports before saving or printing them. Use the Next and Back buttons to quickly review each student's progress in the Preview window.
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Start exploring Now try it yourself! Start exploring and creating. For additional help, tutorials or information on training sessions, use the Help menu or go to . smarttech.com/training
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If today is Monday, then tomorrow is Tuesday. hypothesis conclusion
Conditional statements are either True or False. If a Counterexample can be given for a statement, then it is considered to be False.
If x is an integer, then x >0.
Is this true or false? Can you find a counterexample?
Rewrite each statement into "ifthen" form.
Two lines intersect in exactly one point.
Points on the same line are collinear.
a.
b.
If John lives in Florida, then he lives in Miami.
a.
b.
The converse of a conditional statement is formed by flipping the hypothesis and conclusion.
If today is Monday, then tomorrow is Tuesday. hypothesis conclusion
Conditional:
Converse: If tomorrow is Tuesday, then today is Monday. hypothesisconclusion
Hypothesis: The animal is a fish.
Conclusion:
Conditional:
Conditional: If your Principal is Ms. Bright, then you must attend Eastbay Middle School.
Statement: A fish has gills.
Truth Value: True or False
Statement: Animals who live in water are fish. Hypothesis:
Conclusion: Conditional:
Hypothesis:
Conclusion:
If the animal is a fish, then it has gills.
Converse: Truth Value: True or False
Converse: Truth Value: True or False
Converse: Truth Value: True or False
Sect. 1 Chapter 2
A biconditional statement is when you join two true statements, the
conditional and converse, using the phrase "if and only if." If today is Monday, then tomorrow is Tuesday.
Today is Monday, if and only if tomorrow is Tuesday.
Conditional:
Biconditional:
Try these: Conditional:
Truth Value: True or False Converse: Truth Value: True or False
If we are celebrating Breast Cancer Awareness month, then we are in the month of October.
Conditional:
Truth Value: True or False Converse: Truth Value: True or False
If angle A is obtuse, then m A = 100
We can write great Biconditional statements by using the dictionary as a resources. See the definition below for an equilateral triangle, as stated in your glossary.
equilateral triangle- a triangle whose sides are all congruent (pg 752)
Conditional:
Converse: Truth Value: True or False
If a triangle has sides that are all congruent, then the triangle is an equilateral triangle.
Definition:
Conditional:
Converse:
Definition: pentagon:
Sometimes definitions are written poorly, and do not serve as good definitions. Determine whether these definitions are written accurately. If not, name a counterexample!
Conditional:
Converse:
Definition: Butterfly - an insect with wings.
Counterexample:
Conditional:
Converse:
Definition:
Counterexample:
Counterexample:
acute angle: angle smaller than 90
Below are several figures that are categorized into Whatnots and Not Whatnots. Try to find the characteristics that separate each group, and then determine which figures are whatnots in the last section.
Biconditional:
Biconditional:
Biconditional:
Biconditional:
Sect. 2 Chapter 2
We've talked about inductive reasoning as a reasoning based on observation to predict what would happen next (ex. patterns).
If it's cloudy it's going to rain.
Deductive reasoning is based more on actual facts and statements.
If the clouds are heavy with water, then it's going to rain.
There are two laws we can use with deductive reasoning:
Law of Detachment: if p q is true, and p is true, then q has to be true.
Law of Syllogism: if p q, and q r, are true, then p r has to be true.
If a quadrilateral is a square, then it contains four right angles.
Truth value: True or False
p-
q-
p q: If a quadrilateral is a square, then it contains four right angles.
Truth value: True or False
q r: If a quadrilateral contains four right angles, then it's a rectangle.
Truth value: True or False
p r:
Determine if you can use any of the above laws to arrive to a conclusion for the following:
1. Given: If the electric power is cut, then the refrigerator does not work.
The electric power is cut.
Conclusion:
Law of:
2. Given: If an angle is obtuse, then it cannot be acute.
The angle is not acute.
Conclusion:
Conclusion:
Sect. 3 Chapter 2
When we reason in Algebra, we try to provide a logical explanation for, or justify, each step we do to solve a problem.
In addition to the postulate, theorems, and properties we've discussed so far, here are a few others we need to recall from our past.
2+4= 2+4, 6=6 24= 24, 2=2 2(4)=2(4), 8=8 2/4=2/4, 0.5=0.5
a=2, b=3, c=4 2(3+4)= 2(3)+2(4)
2(7)= 6+8 14=14
a=2, b=2, c=4
Justify each step for solving the problems below.
1. BC = 3x + 2 and CD = 5x - 10. Solve for x.
a. Given: BC= CD. (its shown the picture)
b.3x + 2=5x - 10 Substitution property ( you substituted the lengths of the segments with their names)
c. 3x +2+10= 5x Addition Property of Equality (you are combining like terms)
d. 2+10= 5x-3x Subtraction Property of Equality (you are combining like terms)
e. 12= 2x Simplify
f. x= 6 Division Property of Equality ( divided by 2)
a
d. 90 + 6x = 180
2. ABC= Q therefore Q = ABC
Sect. 4 Chapter 2
2 3 4
Angles 1 and 2 are vertical angles, which means they are congruent.
Angles 3 and 4 are vertical angles, which means they are congruent.
Angles 1 and 3 are supplementary, because together they form a line, which is 180. So are Angles 1 and 4, and 4 and 2. To be supplementary, angles do not have to be adjacent, or beside each other.
1 2
Here, angles 1 and 2 are adjacent, and they are also complementary, because they form 90 together.
Using the diagram, find the following:
1. A pair of complementary angles.
2. A pair of supplementary angles.
3. A pair of vertical angles.
4. What can you conclude about the diagram above?
Find the missing variables for the diagrams below.
1. 2.
In the previous lesson, we learned how to justify our answers when solving problems. When you write your justifications using sentences to create a paragraph, you are creating a paragraph proof.
a.
b.
c.
d.
a.
b.
images/clipPNG.png
images/clipboard(10).png
annotationmetadata/metadata(9).xml
annotationmetadata/metadata(7).xml
settings.xml
imsmanifest.xml
ADL SCORM CAM 1.3 metadata.xml What's New in SMART Notebook 10.8
metadata.xml
preview.png
assessment.xml
metadata.rdf
metadata.db
page6.svg
Education Standards and Cognitive Levels What’s new in SMART Response 2012 Education Standards and Cognitive Levels When creating questions, tag them with: · Education standards from your local state/province · Cognitive levels from several popular cognitive level scales · Custom tags that you create Tags in your tag library can now be easily re-used!
page2.svg
What's New What’s new in SMART Response 2012 Robust Teacher Tools reporting · Tag questions with education standards in your region · Tag questions with cognitive levels · Create reports by education standards or cognitive levels · Easily generate reports by student or class · Compare performance across students or classes Future-proof your investment · Send assessments to any web-enabled mobile device · Include image-based questions in web assessments · Use remotes mixed with mobile devices Other new features and enhancements · Deliver assessments one question at a time in whole class mode · Include Text questions when using mixed PE and XE remotes · Use multiple Response receivers for classes over 100 students · Response VE is localized in 18 languages · Response 2012 Mac is localized in 9 languages
page1.svg
New Reports What’s new in SMART Response 2012 New Teacher Tools Reports See at a glance how students and classes are doing. Sixteen new reports are now available in Teacher Tools!!
page4.svg
New Reports What’s new in SMART Response 2012 New Teacher Tools Reports Have better access to student and class level performance data. Get reports on: · Performance against local education standards, cognitive levels, and custom tags · Individual students or classes · Comparisons between students or classes Create a report and: · Save it to Teacher Tools · Generate a PDF to print or share · Export the data to CSV format
page16.svg
Mac Localization What’s new in SMART Response 2012 Mac Localization SMART Response Mac is now localized in the following languages: · English · French · German · Spanish (European) · Spanish (International) · Danish · Italian · Dutch · Portugese (Brazil)
page23.svg
Saving Reports in Teacher Tools What’s new in SMART Response 2012 Saving Reports in Teacher Tools Save reports to Teacher Tools so they're easily accessible from one place. Change the report's properties to update it!
page24.svg
Assessment Delivery Modes What’s new in SMART Response 2012 Assessment Delivery Modes Teachers can now choose to deliver their assessment in self-paced or whole class mode. In self-paced mode, students can answer all questions at their own pace (same as in Response 2011). In whole class mode, students can only answer the question currently displayed on the Notebook page.
page0.svg
VE Enhancements What’s new in SMART Response 2012 Response VE Enhancements Images for each question are now displayed on students' devices when using Response VE. Response VE is now also localized in 18 languages. Students can zoom in on the image if needed A thumbnail of the Notebook page appears as part of the question
page3.svg
Mixed Mode Enhancements What’s new in SMART Response 2012 Mixed Mode Enhancements Teachers now have greater flexibility when using Mixed Mode. Exclude remotes that you don't use to access more functionality. Unselect this option to use Text questions with PE and XE remotes in Mixed Mode!
page25.svg
Multiple Receiver Support What’s new in SMART Response 2012 Multiple Receiver Support Use multiple Response receivers with the same teacher computer for larger classes or groups of students. Each receiver appears in Teacher Tools
page19.svg
Welcome! Welcome to SMART Response 2012 interactive response software Review new features and get started quickly To access this guide later, go to: SMART Response Software What's New Guide Then click the "What's new in SMART Response" link on the last page.
page21.svg
Reports Preview What’s new in SMART Response 2012 Reports Preview Preview reports before saving or printing them. Use the Next and Back buttons to quickly review each student's progress in the Preview window.
page34.svg
Start exploring Now try it yourself! Start exploring and creating. For additional help, tutorials or information on training sessions, use the Help menu or go to . smarttech.com/training
SMART Notebook