Speed Math inequalities: http://education.jlab.org/sminequality/index.html Inequality Game: http://www.math-play.com/Inequality-Game.html
Refer to File Transfer for Scantron Score information
http://www.newton.dep.anl.gov/askasci/math99/math99228.htmX or the ‘unknown’ was originally referred to as ‘thing’ or ‘object’ of couple of derivatives of translation you end with a shortened version ‘x’. Also noted that the Greek word ‘xenos’ is the word for unknown or stranger also shortened to x.
Checkor X if you would like me to work through or skip the next three slides. You can use these slides as a starting point for your direct instruction and family support.
One variable (kind) = one dimension
Open or ClosedLeft or Right
Point out inequalities have more than one solution Call out open dot on graph
You can review this slide on your own time, however it explains the math behind ‘Flipping the Sign’
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Scantron Reflection On the whiteboard: share your thoughts about taking the Scantron Performance Series Math assessment
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Personal Needs Reflection Did you come to any conclusion about your own personal development needs in Mathematics? List your thoughts in the chat window.
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Scantron Data
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Math is a Journey
Build your Toolbox
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Connect what you like
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Connect what you know
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Embrace how you learn
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Practice
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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)
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Arrive on Time (leave early if you take the long way)
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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?)
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Building Your Toolbox
Your math toolbox includes the tools, resources, formulas, rules, strategies and tricks, you learn and collect, during your journey.
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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
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Getting Started Why X?
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Solving Equations – the same but different Which tool do you grab from your toolbox?
Do you guess and check?
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Do you use Transformations of Addition and Subtraction to isolate the fraction?
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Do you convert your fraction to a decimal?
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Do you use Transformations of Multiplication and Division to remove the fraction?
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Do you graph or use a table of values?
From this: To this:
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Solving Equations – Mel’s Route Steps:
Given
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Transformation by Multiplication
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Simplify
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Transformation by Subtraction
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Simplify
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Transformation by Multiplication
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Solution
Is the equation true when x = – 14?
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Solving Equations – Mel’s Route Graphed Only one solution satisfies this equation. Is the equation true when x = – 14?
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Solving Equations – Checking Mel’s Route Is the equation true when x = – 14? Steps:
Given
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Substitute (replace) x with – 14
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Divide with Product Rule
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Simplify with Product Rule
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Simplify by addition
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Solution
Is the equation true when x = –14? YES
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No Really! Inequalities - the same but different From this: What is the same? What is different? How will the solution change? What might trip us up? To this:
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Solving Inequalities – Mel’s Route Steps:
Given
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Transformation by Multiplication
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Simplify
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Transformation by Subtraction
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Simplify
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Transformation by Multiplication – flip the sign
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Solution
Is the inequality true when x < – 14?
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Solving Inequalities – Mel’s Route Graphed Is the inequality true when x < –14? Are their one, none or many solutions? Is –14 included in the solution?
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Solving Inequalities – Checking Mel’s Route We already know –14 is not included, so now choose an easy number left of –14 and substitute (replace) and solve. By selecting –20 and solving, we learn numbers left or smaller than –14 are true solutions of this inequality. Many solutions satisfy this inequality. Values less than but NOT including -14 are all solutions.
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Why Flip the Sign? 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: This shows when an inequality is multiplied by –1, the inequality is reversed. Therefore: is the same as:
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Breakout Rooms
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Now What’s Wrong? Look at the problems below. Indicate if the problem is algebraically correct, explain your answer. Look at the problems below. Select points on number line to check the solution and accuracy of the graph. Explain your findings.
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Inequalities – Your Route
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Let’s Play Solutions Why did the surfer dude cross the ocean?
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Teacher Toolbox
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
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Speed Math inequalities: http://education.jlab.org/sminequality/index.html