Benchmark Numbers: Everyone Can ‘DO’ Fractions, Decimals and Percents!

How do your students generally feel about fractions? decimals? percentages? Do they moan and groan and say “I hate these” or “I can’t DO… (fractions, decimals, percents)”

How about yourself? How much do you enjoy computations and problem solving involving fractions, decimals and percentages?

A common challenge for many of our learners is their ability to work with a particular set of number concepts: fractions, decimals, and percents. Our learners have often developed ‘mental blocks’ to these mathematical concepts and even develop anxiety upon hearing the terms. Yet anyone entering an adult education classroom has already had years of experience in solving problems and mental math involving fractions, decimals, and percentages. Honest!

Think back over the past 24 hours. How often did you use fractions? Think about a percentage? Interact with a decimal?(other than as part of instruction)

Ok now, how often did you use or encounter the concept of  ½? 10%? .25? How about quarters, dimes or dollars?

Clearly, adults encounter and use these types of benchmark numbers every day in various facets of their lives – in their work, with their families, and out in the community. See if these examples sound familiar:

• “Split that with your sister – each of you can have HALF.”
• “I want to see a 100% team effort!”
• “Thank you for shopping with us, you saved $3.75.”

Helping students to realize that they ALREADY SUCCESSSFULLY USE  fractions , decimals and  percentages is one way to combat anxiety and “I can’t” attitudes. Another recommendation is to incorporate activities using these friendly ‘fractional numbers’ into instruction with ALL learners – even those still learning their basic math facts.¹ Note that these recommendations are not limited to adult education – the Common Core State Standards for Mathematics call for fractional concepts to be explicitly taught at the 3^rd grade level, and introduced less directly even earlier (via telling time, comparing measurements, dividing shapes into parts, etc.). These standards also state: 

“Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.”  (CCSS-M Introduction)

Thus of course, as always, it is important to keep it REAL. Instruction should be based in everyday contexts that are meaningful to your specific group of learners. Here are some example contextual activities from the EFF Preparing for Work Curriculum that address fractional concepts:   A Typical Day/Time on Task

It is also important to note that many adult learners working at more advanced levels of math instruction may have an incomplete understanding of fractional concepts. They may have memorized a process, or algorithm, but cannot easily or readily apply it to real-world situations, or easily convert from fractions to decimals to percentages. Again, some work with basic benchmarks can help – even those who think they ‘know’ fractions, etc..

 Could your students easily move from ‘80 out of 100’ to ‘80 percent’ to ‘8 tenths’?Do they seem to confuse fractions, decimals and percentages or give up when asked?

In Algebraic Thinking in Adult Education (2010), Lynda Ginsburg emphasizes the importance of making connections among multiple representations of the same information – symbols, tables, graphs, etc.²   This idea applies to number concepts for fractions, decimals and percents as well.  Learners need instruction and practice in understanding the equivalencies between fractions, decimals, and percentages to deepen their conceptual understanding of these numbers. Activities that mix together fractions, decimals and percentages, and/or ask students to move from one representation to its equivalent (10% to 1/10 to .1) are effective tools for both assessing and strengthening understanding. Comparing Numbers is one example of such an activity (also from the EFF Preparing for Work Curriculum).

Please share with us your tips and tricks for helping adult students to understand number concepts relating to ‘fractional parts’ (fractions, decimals or percentages).
OR
Try out one of the ideas in this post, and let us know how it worked for your learners (and you).  Below is one last resource to help get you started!

Using Benchmarks: Fractions, Decimals, and Percents – STUDENT BOOK – Lesson 5: One-tenth³ http://empower.terc.edu/pdf/Using_Benchmarks.pdf

We look forward to hearing from you and your class!

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To learn more about teaching Benchmarks in the EFF online mini-course,  How Close is Close Enough?: Improving Estimation Skills  or in the EFF Preparing for Work curriculum, contact us via eff@utk.edu.

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Post Contributor:
Duren Thompson, EFFTIPS Content and Technical Editor, Center for Literacy Studies

 References and Resources

¹ National Council of Teachers of Mathematics, Principles and Standards for School Mathematics,  (2000) Reston, VA.   Pages 33-35

² Lynda Ginsburg (2010); Algebraic Thinking in Adult Education  National Institute for Literacy, Washington, DC. http://lincs.ed.gov/publications/pdf/algebra_paper_2010V.pdf  (reference error corrected 7-27-12)

³ Using Benchmarks: Fractions, Decimals, and Percents Schmitt, Steinback, Donovan, Merson, & Kliman (2006) Key Curriculum Press, Emeryville, CA. http://empower.terc.edu/  (Part of the EMPower mathematics Curriculum developed at TERC)