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?