MS Math SummitDecember 2009
Math Challenge
Scantron ReflectionOn the whiteboard: share your thoughts about taking the Scantron Performance Series Math assessment
Personal Needs Reflection
Did you come to any conclusion about your own personal development needs in Mathematics?
List your thoughts in the chat window.
Scantron Data
Total # Registered 288
Total # of Tests Complete 170
Total # of Tests Incomplete 26
Total # of Tests Spoiled 1
Overall Score Range 2714 – 3700
Overall SIP 80
Numbers & Operations 92
Algebra 77
Geometry 80
Measurement 75
Data Analysis & Probability 83
Math is a Journey
• Build your Toolbox• Connect what you like• Connect what you know• Embrace how you learn• Practice• Share
Rules of the Road
• Stay on the Road (don’t create your own path or make up math as you go)
• Obey the Law (don’t break any math rules)
• Arrive on Time (leave early if you take the long way)
• Travel Comfortable(use the tools you’re comfortable and confident)
• Check Your Location(check your work – is your answer reasonable and accurate? Did you answer the question?)
Building Your Toolbox
• Your math toolbox includes the tools, resources, formulas, rules, strategies and tricks, you learn and collect, during your journey.
Formulas
Projects
Vocabulary
Puzzles
Stories
Patterns
Symbols
Letters
Graphs
Tables
Lesson Objective
Solve and Graph single variable equations and inequalities
Toolbox Vocabulary: Toolbox Rules:
Equation/Inequality Addition Property of Equality
Equivalent Equations Multiplication Property of Equality
Transformations Reciprocal
Simplify Product Rules
Replacement Set
Reverse or ‘flip’ inequality signs
Open Dot or Closed Dot
Getting Started
9 2
92 x 7 7or x
Why X ?
Solving Equations – the same but different
92
2 x
Which tool do you grab from your toolbox?
• Do you guess and check? • Do you use Transformations of Addition and Subtraction to isolate the fraction?
• Do you convert your fraction to a decimal?• Do you use Transformations of Multiplication and Division to remove the fraction?
• Do you graph or use a table of values?
92 xFrom this:
To this:
14
14
41844
184
x
x
x
x
Solving Equations – Mel’s Route
14 1 x
Steps:
• Given• Transformation by Multiplication• Simplify• Transformation by Subtraction• Simplify• Transformation by Multiplication• Solution
92
2 x
9
22 2x
Is the equation true when x = – 14?
14
14
41844
184
x
x
x
x
Solving Equations – Mel’s Route Graphed
14 1 x
92
2 x
9
22 2x
Is the equation true when x = – 14?
Only one solution satisfies this equation.
Solving Equations – Checking Mel’s Route
Steps:
• Given• Substitute (replace) x with – 14 • Divide with Product Rule• Simplify with Product Rule• Simplify by addition• Solution
99
972
972
92
)14(2
92
2
x
Is the equation true when x = – 14?
Is the equation true when x = –14? YES
No Really! Inequalities - the same but different
What is the same?
What is different?
How will the solution change?
What might trip us up?
92
2 x
92
2 x
From this:
To this:
14
14
41844
184
x
x
x
x
Solving Inequalities – Mel’s Route
14 1 x
Steps:
• Given• Transformation by Multiplication• Simplify• Transformation by Subtraction• Simplify• Transformation by Multiplication – flip the sign
• Solution
92
2 x
9
22 2x
Is the inequality true when x < – 14?
14
14
41844
184
x
x
x
x
Solving Inequalities – Mel’s Route Graphed
14 1 x
92
2 x
9
22 2x
Is the inequality true when x < –14? Are their one, none or many solutions? Is –14 included in the solution?
Solving Inequalities – Checking Mel’s Route
92
2 x
Many solutions satisfy this inequality. Values less than but NOT including -14 are all solutions.
We already know –14 is not included, so now choose an easy number left of –14 and substitute (replace) and solve.
922
9202
9202
92
202
14x
By selecting –20 and solving, we learn numbers left or smaller than –14 are true solutions of this inequality.
Why Flip the Sign?
92
2 x This example requires Transformation of Multiplication and
Division. When working with inequalities, and using this transformation we’re instructed to ‘Flip the Sign’. Here’s the math behind the request:
ba
ab
abaa
ba
bbba
ba
0
0
This shows when an inequality is multiplied by –1, the inequality is reversed.
ba Therefore:
is the same as:
ba
Breakout Rooms
Now What’s Wrong?
53
15
3
3
153
x
x
x
Look at the problems below. Indicate if the problem is algebraically correct, explain your answer.
3
4144
14
x
x
x
Look at the problems below. Select points on number line to check the solution and accuracy of the graph. Explain your findings.
153 x 14 x
Inequalities – Your Route
1123 x
423
2 x
Let’s Play
Why did the surfer dude cross the ocean?
Solutions
• OLS Curriculum: Pre-Algebra A
U2 L2: Writing Inequalities
U2 L3 & L4: Writing Inequalities Part 1 & 2
U2 L6 & L7: Solving Other Equalities and Inequalities• OLS Curriculum: Pre-Algebra B
U1 L4: Inequalities
U1 L9: Equalities & Inequalities for Word Sentences
U5 L8: Equivalent Inequalities
U5 L9 & L10: Solving Inequalities by Several Transformations Part 1 & 2
OLS Curriculum: Algebra I: Unit 14: Inequalities• Mathematics Structure and Methods Course 2 Chapter 5
Teacher Toolbox
• Why is a negative times a negative a positive? • Why x?
• Speed Math inequalities: http://education.jlab.org/sminequality/index.html • Inequality Game: http://www.math-play.com/Inequality-Game.html
Quiz and Session Survey
Session Survey:https://vovici.com/wsb.dll/s/1673g41cf5
Pick up File Transfer Documents
Scantron Survey:https://vovici.com/wsb.dll/s/1673g41b2b
Scantron Performance Series FAQ’s:http://docs.achievementseries.com/PSHelp/Performance_Series.htm
Quick Inequality Quiz:http://www.surveygizmo.com/s/214728/inequalities-1-12-03-2009
Any Questions?
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