Blog Archives

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 3rd 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!


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


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)

Teaching Text Structure and Signal Words: A Key to Reading Informational Text with Understanding


How much ‘informational text’ do you read in a day? (as opposed to narrative/fiction reading)? Consider ALL the reading you do – including all the ‘incidental’ and ‘necessary’ reading (like billboards, headlines, package directions, blogs, e-mail at work, etc.)

How much ‘informational text’ do you think your students read? How much do they NEED to do in order to reach their learning and career goals?

Informational (or expository) text is the text we use to learn about something. For most of us, informational text forms the majority of the necessary reading and writing we do in a day.  As adults at home, at work, or in our communities, we are constantly faced with informational text that we need to read with understanding.

EFF LogoIn recognition of this, the EFF Performance Continuum and the Curriculum Framework for the Read With Understanding standard emphasizes the importance of students reading a wide variety of different kinds of materials for varying purposes, particularly in real-world contexts. This aligns with the Common Core State Standards Initiative’s College and Career Readiness Anchor Standards for Reading which states:  Reading is critical to building knowledge in history/social studies as well as in science and technical subjects. …Students must be able to read complex informational texts in these fields with independence and confidence because the vast majority of reading in college and workforce training programs will be sophisticated nonfiction.

Yet research shows that informational text presents greater burdens to reading comprehension over narrative text. This can present a problem since so much of what we need and want to read as adults is, in fact, expository in nature.

What strategies do YOU use to read informational text? To make it easier to analyze and comprehend?

At home, at work, or in our communities, adults are constantly faced with informational text that we need to read with understanding. We all use a variety of strategies when trying to comprehend text. One strategy that might be especially helpful to us, and a strategy that we can teach to adult learners, is recognizing text structure.

We all use a variety of strategies when trying to comprehend text. One strategy that might be especially helpful to us, and a strategy that we can teach to adult learners, is recognizing text structure.  Every informational text has a structure. Depending on what the writer of the text wants to accomplish with it – the writer’s purpose – the information in the text will be organized into one of several possible structures.

So for instance:

If writers want to focus on…  the text structure might be:
 Steps in a process or a logical chain of events …………………  Sequence
 Similarities or differences between two ideas ………………….  Comparison / Contrast
 The impact of an event or the reasons that something happened  Cause / Effect
 Details to elaborate on a topic …………………………………..  Description
 A way to resolve a situation, or a suggested course of action …  Problem solution

Skilled readers are able to identify the structure of the texts they are reading – even if they are not aware that they are doing it (since the more skilled a reader is, the more “automatic” this kind of behavior becomes). This ability helps to clue them in on the purpose of the text and to understand what they are reading more deeply. Teachers can explicitly teach students how to recognize and use text structure (as part of the process of reading that is described by the EFF standard Read with Understanding).

What approaches or strategies might you – as an adult reader –  use to recognize different informational text structures? What strategies do you teach your students to use?

An important strategy that writers employ to help readers understand their main points is the use of “Signal Words”. Signal words are the words in a text that suggest its structure.  Skilled readers use these signal words to identify and follow the text structure that the writer of the text intended. Let’s consider the most common kinds of text structure and some of the signal words used for each.  [Click on the image below to view the full-sized pdf document.]

But WAIT, here’s an important note to remember  (making things just a bit more complicated): While one particular text structure will probably predominate in any given text, other structures may also be present in that text. In other words, texts may include more than one text structure. You will need to assist students to determine the primary text structure for a document. If readers are aware of text structures, they can select strategies for reading comprehension that are likely to be effective.

Many readers need direct instruction to develop awareness of basic text structures. Teachers should provide explicit and systematic instruction in text structure, supported by scaffolding. Here are some practices that can be especially effective:

Suggestions for Teaching Text Structure via Scaffolded Instruction

Please share with us your thoughts on strategies for supporting adult learners in reading Informational Text – its importance both in and outside the classroom, how you address it, any ‘ah-has’ you’ve had, etc. Below are some questions to get you started:

  • What kinds of informational texts do you use in the classroom? How do you find and select informational texts to use with your adult learners?
  • What kinds of strategies do you teach your students to use when reading informational text with understanding? How do you teach these strategies (what examples or approaches do you use)?

We look forward to reading your thoughts and experiences.


Learn more about teaching Text Structure for Informational Text in the EFF online mini-course,
Using Text Structure and Graphic Organizers: Strategies to Enhance Reading Comprehension
or via other EFF professional development materials/services!


Post Contributors:
Peggy McGuire, EFF Trainer & Content Expert, Center for Literacy Studies
Duren Thompson, EFFTIPS Technical Editor, Center for Literacy Studies

Estimation – What Strategies Do You Teach? How?


Research indicates that the vast majority of all calculations performed by adults in everyday life involve mental math…and that estimates are sufficient for around 60% of all our daily calculations.2  Yet further research repeatedly reveals that a majority of both K-12 students and college-educated adults have difficulty using estimation.1

This leads us to several interesting questions:

1)      How do we use estimation and mental math each day?
Consider yesterday – when, how, and how often did you use estimation?

2)      How do we think the adults/older youth we teach use estimation each day?

3)      What are some solid strategies for strengthening our learners’ estimation skills?

Please share with us your thoughts on estimation – its importance both in and outside the classroom, how you address it, any ‘ah-has’ you’ve had, etc.  Below are some comments from our Math Content expert, Donna Curry, to get you started:  Are you familiar with the estimation strategies she mentions? Do you teach them to your learners? How?

“Many folks are not aware that there are different strategies for estimation depending on your purpose or the situation. These different strategies, as well as how/when to use them, should be explicitly addressed with our adult learners.

Rounding is one strategy commonly presented in textbooks, but you can also do front end estimating (just looking at the digits furthest to the left – such as looking at 23 + 45 + 31 and changing them to 20 + 40 + 30 for an estimate).  Or, you could clump numbers to get similar clumps (such as 1.24 + 2.38 + 4.70 + 8.64 and clump 1.24 & 4.70 together to make about 6 since .24  + .70 is about 1, and then clump 2.38 & 8.64 to make about 11 since .38 and .64 is about 1).  In fact, even with rounding there is no “law” that requires that you round up or down – for example, when shopping I always round up to make sure I have enough money. When estimating, you always need to decide what makes sense for the situation (or your purpose)!

We need to help our learners realize that an estimate is used to get a sense for the number. In this way estimation is key to number sense. (It is not simply another chapter in the book!)” – Donna Curry

We look forward to your thoughts on Estimation and Estimation Strategies!


Learn more about teaching estimation strategies in the EFF online mini-course, How Close is Close Enough?: Improving Estimation Skills, or via other EFF professional development materials/services!


 Research on the Use of Estimation:

1Adding It Up: Helping Children Learn Mathematics, (2001) Jeremy Kilpatrick, Jane Swafford, Bradford Findell, National Academy Press Washington, DC. http://books.nap.edu/openbook.php?record_id=9822&page=1

2 Northcote, M., & McIntosh, M. (1999) What mathematics do adults really do in everyday life? Australian Primary Mathematics Classroom, 4(1), (pp19-21)