Focus on 2014 Content: Math Mastery - GED Testing Service

<strong>Focus</strong> on 2014 Content: Math Mastery 

Bonnie Goonen & Susan Pittman-Shetler – July 17 & 18, 2013

Session Objectives 

• Identify content of the Mathematics module of 

the 2014 GED ® test 

• Explore essential mathematical practices and 

behaviors 

• Discuss beginning strategies for the classroom 

• Identify resources that support the transition to 

the next generation assessment 

© Copyright 2013 GED Testing Service LLC. All rights reserved. 

2

The Magic of Algebra 

• Think of a number and write it down. 

• Double the number. 

• Add 10. 

• Divide by 2. 

• Subtract your original number from this new number. 

• The final number is 5. 


3

MATHEMATICAL REASONING 

NEW REALITIES 


4

Check Your Skills 


5

What we know . . . 

• People have a “lovehate” 

relationship with 

mathematics 

– Twice as many 

people hated it as 

any other school 

subject 

– It was also voted the 

most popular subject 

Associated Press Poll 


6

2002 Series GED ® test 

2014 GED ® test 

• One test with two parts, one of 

which allowed use of calculator 

• Content 

– 25-30% Number Operations, 

Number Sense 

– 25-30% Measurement and 

Geometry 

– 25-30% Data, Statistics, and 

Probability 

– 25-30% Algebra, Functions 

and Patterns 

• Casio fx260-Solar 

• One test with calculator 

allowed on most items 

• Content 

– 45% - Quantitative Problem 

Solving 

• Number operations 

• Geometric thinking 

– 55% - Algebraic Problem 

Solving 

• Texas Instruments - TI 30XS 

• Integration of mathematical 

practices 


7

Mathematical Reasoning 

• Some items require 

– procedural skill 

– fluency 

– problem solving 

• Presented in academic 

and workforce contexts 

• Statistics and data 

interpretation standards 

are also included in 

other tests 


8

What’s new in the Mathematical 

Reasoning domain 

• Identify absolute value of a rational number 

• Determine when a numerical expression 

is undefined 

• Factor polynomial expressions 

• Solve linear inequalities 


9

What’s new in the Mathematical 

Reasoning domain 

• Identify or graph the solution to a one variable 

linear inequality 

• Solve real-world problems involving 

inequalities 

• Write linear inequalities to 

represent context 

• Represent or identify a 

function in a table or graph 


10

What’s not directly assessed on the 2014 

GED ® Mathematical Reasoning Test 

• Select the appropriate operations to solve problems 

• Relate basic arithmetic operations to one another 

• Use estimation to solve problems and assess the 

reasonableness of an answer 

• Identify and select appropriate units of metric and 

customary measures 

• Read and interpret scales, meters, and gauges 

• Compare and contrast different sets of data on the 

basis of measures of central tendency 

• Recognize and use direct and indirect variation 

07/2013 

11

Then - 2002 GED ® test 

Ms. Nguyen is a real estate agent. One of her clients is considering 

buying a house in the Silver Lakes area, where 6 houses have 

recently sold for the following amounts: $160,000; $150,000; 

$185,000; $180,000; $145,000; $190,000. What should Ms. Nguyen 

report as the Median price of these houses 

1) $160,000 

2) $170,000 

3) $180,000 

4) $190,000 

5) Not enough information is given. 

Note: Method for 

determining median was 

provided in the test 

booklet. 


12

Now – 2014 GED ® test 


13

New Mathematical Tools 


14

TI-30XS MultiView Calculator 


15

It’s Your Turn! 

"Calculators can only 

calculate - they 

cannot do 

mathematics." 

-- John A. Van de Walle 

http://education.ti.com/en/us/products/calc 

ulators/scientific-calculators/ti-30xsmultiview/classroom-activities/activitiesexchange 


16

MATHEMATICAL PRACTICES 


17

Mathematical Practices 

• Practices 

– Mathematical fluency 

– Abstracting problems 

– Building solution pathways and lines of reasoning 

– Furthering lines of reasoning 

– Evaluating reasoning and solution pathways 

• Most practices are not specific to any one 

particular area of mathematics content 


18

Problem Solving In Your Classroom 

What opportunities 

do your students 

currently have to 

grapple with nonroutine 

complex 

tasks and to… 

…. reflect on their 

thinking and 

consolidate new 

mathematical ideas 

and problem solving 

solutions 


19

Solution Pathways = Problem Solving 

Polya’s Four Steps to Problem Solving 

Understand 

the problem 

Look back 

(reflect) 

Devise a 

plan 

Carry out 

the plan 

Polya, George. How To Solve It, 2nd ed. (1957). Princeton 

University Press. 


20

Value of Teaching with Problems 

• Places students’ attention on 

mathematical ideas 

• Develops “mathematical power” 

• Develops students’ beliefs that they 

are capable of doing mathematics and 

that it makes sense 

• Provides ongoing assessment data 

that can be used to make instructional 

decisions 

• Allows an entry point for a wide range 

of students 


21

A Few Problem-Solving Strategies 

• Look for patterns 

• Consider all possibilities 

• Make an organized list 

• Draw a picture 

• Guess and check 

• Write an equation 

• Construct a table or graph 

• Act it out 

• Use objects 

• Work backward 

• Solve a simpler (or similar) problem 


22

Let’s SOLVE a Math Problem 

Even Albert Einstein said: 

“Do not worry about your difficulties in 

Mathematics. I can assure you mine 

are still greater.” 


23

SOLVE a Problem 

S tudy the problem (What am I trying to find) 

O rganize the facts (What do I know) 

L ine up a plan (What steps will I take) 

V erify your plan with action (How will I carry out 

my plan) 

E xamine the results (Does my answer make 

sense If not, rework.) 

Always double check! 


24

S = Study the problem 

What is the problem 

asking me to do 

Find the question. 

We are going to practice 

SOLVE with this one! 

A painter rented a 

wallpaper steamer at 9 

a.m. and returned it at 4 

p.m. The painter found 

rental costs as high as 

$15.00 per hour. He paid 

a total of $28.84. What 

was the rental cost per 

hour 


25

O = Organize the Facts 

What facts are provided in order 

for you to solve the problem 

• Identify each fact. 

• Eliminate 

unnecessary facts. 

• List all necessary 

facts. 

A painter rented a wallpaper 

steamer at 9 a.m. and 

returned it at 4 p.m. The 

painter found rental costs as 

high as $15.00 per hour. He 

paid a total of $28.84. What 

was the rental cost per hour 


26

L = Line Up a Plan 

• Select the operations to use. 

• State the plan/strategy that you will use in words. 

I will use a multi-step approach. First, I will calculate 

the elapsed time that I had the steamer in number of 

hours. Next, I will divide the total rental amount by 

the number of hours I rented the steamer. This will 

provide me with the hourly rate. 


27

V = Verify Your Plan 

9 – 10 = 1 hr. 

10 – 11 = 1 hr. 

11 – 12 = 1 hr. 

12 – 1 = 1 hr. 

1 – 2 = 1 hr. 

2 – 3 = 1 hr. 

3 – 4 = 1 hr. 

Total 7 hrs. 

$28.84 / 7 = $4.12 


28

E = Examine the Results 

(Is it reasonable Does it make sense 

Is it accurate) 

$4.12 IS reasonable because it is 

substantially less than the total rental 

amount. Also, the answer is a decimal 

number because the total rental amount 

is a decimal number. If one estimates - 

$28.84 is close to 28 and 7 goes into 28 

four times. Therefore, the painter paid 

$4.12 per hour for the machine. 


29

Let’s SOLVE 

S 

O 

L 

V 

E 


30


31

07/2013 


32

What are the big ideas that I want 

students to remember . . . 

40 days 

(the test) 

40 months 

(college) 

40 years 

(life) 


33

Some Big Ideas in Quantitative 

Reasoning 

• Number sense concepts (rational numbers, absolute 

value, multiples, factors, exponents) 

• Spatial visualization 

• Dimensions, perimeter, circumference, and area of 

two-dimensional figures 

• Dimensions, surface area, and volume of threedimensional 

figures 

• Interpret and create data displays 

• Probability, ratio, percents, scale factors 

• Graphic literacy 


34

Some Big Ideas in Algebra 

• Variable 

• Symbolic Notation 

• Equality 

• Ratio and Proportion 

• Pattern Generalization 

• Equations and Inequalities 

• Multiple Representations of Functions 


35

Mathematics is like a video game; 

If you just sit and watch, 

You’re wasting your time. 


36

Time Out for a Video Break! 


37

Research-Based Teaching Strategies 

• Effective questioning 

• Teacher responses 

• Use of manipulatives 

• Conceptually-based 

teaching 


38

Teaching Beyond the Facts 

“Trying to teach in the 21 st century 

without conceptual schema for 

knowledge is like trying to build a 

house without a blueprint.” 

H. Lynn Erickson 

Concept-Based Curriculum and Instruction 


39

Conceptual Teaching 

What is conceptual teaching 

• Using schema to organize new knowledge 

• Developing units around concepts 

• Providing schema based on students’ prior knowledge 

• Teaching knowledge/skill/concept in context 

What it’s not! 

• Worksheets 

• Drill 

• Memorization of discrete facts 


40

Best Practices Review 

Instructional 

Element 

Curriculum 

Design 

Professional 

Development 

for Teachers 

Recommended Practices 

• Ensure mathematics curriculum is based on challenging content 

• Ensure curriculum is standards based 

• Clearly identify skills, concepts and knowledge to be mastered 

• Ensure that the mathematics curriculum is vertically and horizontally articulated 

• Provide professional development which focuses on: 

o Knowing/understandi ng standards 

o Using standards as a basis for instructional planning 

o Teaching using best practices 

o Multiple approaches to assessment 

• Develop/provide instructional support materials such as curriculum maps and pacing guides 

and provide math coaches 

Technology • Provide professional development on the use of instructional technology tools 

• Provide student access to a variety of technology tools 

• Integrate the use of technology across all mathematics curricula and courses 

Manipulatives • Use manipulatives to develop understanding of mathematical concepts 

• Use manipulatives to demonstrate word problems 

• Ensure use of manipulatives is aligned with underlying math concepts 

Instructional 

Strategies 

• <strong>Focus</strong> lessons on specific 

• concept/skills that are standards based 

• Differentiate instruction through flexible grouping, individualizing lessons, compacting, using 

tiered assignments, and varying question levels 

• Ensure that instructional activities are learner-centered and emphasize inquiry/problem-solvi ng 

• Use experience and prior knowledge as a basis for building new knowledge 

• Use cooperative learning strategies and make real life connections 

• Use scaffolding to make connections to concepts, procedures and understanding 

• Ask probing questions which require students to justify their responses 

• Emphasize the development of basic computational skills 

Assessment • Ensure assessment strategies are aligned with standards/concepts being taught 

• Evaluate both student progress/performance and teacher effectiveness 

• Utilize student self-monitoring techniques 

• Provide guided practice with feedback 

• Conduct error analyses of student work 

• Utilize both traditional and alternative assessment strategies 

• Ensure the inclusion of diagnostic, formative and summative strategies 

• Increase use of open-ended assessment techniques 

• Curriculum Design 

• Professional 

Development 

• Technology 

• Manipulatives 

• Instructional 

Strategies 

• Assessment 


41

A Few Strategies to Get Started 

• Model, explain, and guide 

• Move towards self-regulation 

• Provide opportunities for algebraic 

thinking 

• Keep it real 

• Teach often to the whole class, in 

small groups, and with individuals 

• Set high expectations 


42

“High achievement always 

occurs in the framework of 

high expectation.” 

Charles F. Kettering (1876-1958) 


43

QUESTIONS, INSIGHTS, SUGGESTIONS 


44

Note: This presentation may be used and reproduced 

in its entirety for educational purposes in preparation 

for the 2014 GED ® test by including the following 

attribution text: 

Copyright © 2013 GED Testing Service LLC. All rights reserved. Used by 

permission. 

GED ® and GED Testing Service ® are registered trademarks of the 

American Council on Education (ACE). They may not be used or 

reproduced without the express written permission of ACE or GED Testing 

Service. The GED ® and GED Testing Service ® brands are administered by 

GED Testing Service LLC under license from the American Council on 

Education. 


45

Martin Kehe 

VP of Products, GED Testing Service 

Martin.kehe@gedtestingervice.com 

Bonnie Goonen 

Trainer/Consultant 

bv73008@aol.com 

Susan Pittman-Shetler 

Trainer/Consultant 

skptvs@aol.com 


46

Focus on 2014 Content: Math Mastery - GED Testing Service

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