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Title: Teaching fractions and ratios for understanding : essential content knowledge and instructional strategies for teachers
Author(s): Susan J Lamon
Publisher: Routledge
Year: 2012
ISBN: 9780415886123,0415886120,9780203803165,0203803167

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Title: Teaching fractions and ratios for understanding : essential content knowledge and instructional strategies for teachers Author(s): Susan J Lamon Publisher: Routledge Year: 2012 ISBN: 9780415886123,0415886120,9780203803165,0203803167

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Read chapter 9 (Fractions as Operators).

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You should work on all of the problems at the end of chapter 9 beginning on page 203.

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An effective abstract is your first opportunity to hone your message.

An abstract is a succinct description of your work. It should ...

Explain why your work is important - set the context and pre-empt the question "So what?"

Describe the objective(s) of your work. What areyou adding to current knowledge?

Briefly explain the methods. Unless the research is about methods, this should not be a major focus of your abstract (or your poster).

Succinctly state results, conclusions, and recommendations. This is what most people want to know. Do not say "We present the results of our study and recommendations for action" - tell them what you found and recommend!
We do not recommend including an abstract on your poster. It is redundant, because a poster is already a succinct description of your work. Writing a good abstract, however, is an important part of having your work accepted for presentation at a conference. An abstract can also serve as an outline for your poster, which can be thought of as an illustrated abstract.

Here are some resources from the American Society of Agronomy ( with permission) to help you write more effective abstracts (and papers, in fact).

Checklist and Sample Abstract: a one-pager that focuses on the qualities of a good abstract. You might have to adapt this to your field, but the overall philosophy holds regardless of field.

Be a Better Author: a 2-page piece that deals with abstracts and writing in general. (From the Jan/Feb 2002 issue ofAgronomy Journal.)

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An Effective Abstract | Creating Effective Poster Presentations

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An effective abstract is your first opportunity to hone your message. An abstract is a succinct description of your work. It should ... Explain why your work is important - set the context and pre-empt the question "So what?" Describe the objective(s) of your work. What areyou adding to current knowledge?

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Slides 3 & 4 Help

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Organizers of nursing conferences depend on nurses who have created new programs or are doing research to submit their work for presentation at conferences. Through these presentations, nursing knowledge is disseminated.

If you belong to a professional organization, you've probably received at least one call for abstracts. Arriving well in advance of the conference date, this is an invitation to submit an abstract for presentation at the conference. You may have the choice of submitting an abstract for either an oral (podium) presentation or a poster presentation. Poster presentations can be a good way to get started presenting your work-and they're a great opportunity to get feedback and suggestions from colleagues.

Congrats! Now get started.

It's exciting to get a letter or e-mail telling you that your poster proposal has been accepted for a conference. But don't waste timing resting on your laurels. When asked what they've learned about doing posters, many experienced presenters say they wish they'd begun their poster design earlier because the process took much longer than they anticipated. So to avoid a time crunch, start designing your poster shortly after your abstract is accepted.

Unlike an oral presentation, the poster itself should do most of the talking about your project. Good design matters. It allows you to tell the "story" of your work more effectively.

Begin by carefully reviewing the poster guidelines for the conference. These guidelines specify what size the poster should be and how it will be displayed-tabletop, corkboard, or easel. Poster size affects how much information you can put on the poster. Allowable poster sizes for conferences vary widely.

Poster content should closely follow the format of the abstract you submitted. But keep in mind that a poster is not an abstract. With a poster, your goal is to tell a clear, simple story of your work. If your poster topic is a project or an organizational innovation, see Sample conference poster for ideas on what content to put where by clicking on the PDF icon above.

In contrast, a poster that presents research findings should include:

background and significance of the study

aims of the study

methods

results

discussion and implications.

Many healthcare organizations and universities have graphic design resources available to assist with poster design. Some organizations even ask presenters to use a specific template. Today many posters are designed with Microsoft PowerPoint templates, but you can also lay out the sections of your poster on a large piece of poster board (available at art supply or office supply stores) before finalizing it. Or you might consider using an Internet vendor (such as www.makesigns.com). Many vendors not only guide you through poster design but also can print and ship your poster.

The maxim "less is more" is good advice to follow for a poster. Although you may be tempted to include every detail of your project or research, you won't have enough space to do this. What's more, you shouldn't do this; it would make your poster too busy.
Here are some design tips to follow:

Leave adequate white space. Some empty space is critical to readability and legibility. Without it, the reader has no visual pauses.

Convey your message clearly. The poster should capture the attention of attendees and convey at least one significant idea they'll remember. Most people spend 3 to 5 minutes viewing a poster, so use plain, descriptive language that leaves no doubt what your poster is about. Generally, posters are read from left to right; organize the content with this in mind. When possible, lead the viewer through the logical flow using bold take-home points or arrows.

Use a visual image. People retain visual images longer than the written word, so aim for at least one visual image-a photograph, an illustration, a graph.

Make it readable. Design the poster so it can be read from a distance of 4′ to 6′. To accomplish this, lettering has to be at least 1″ high. The title should be readable from 15′ to 20′ away, with letters 2″ to 3″ high. Try to have high contrast between the background and text. Generally, a lighter background with darker text is easier to read.

Pick fonts carefully. Arial and Tahoma are examples of nonserif fonts that work well for poster titles. Serif fonts, such as Times New Roman and Courier, are easier to read at smaller sizes and work well for body text. Having too many font types on a poster can be distracting, so use at most two to three fonts, with bold or italics for emphasis only. Avoid all uppercase letters (capitals) in your poster, as this makes material harder to read.

Use color sparingly. Although most presenters want colorful posters, color must be incorporated carefully. Blue and green are popular because they're considered calming.

Ask colleagues for help. If this is your first time designing a poster, ask an experienced colleague for help. Before the poster is printed, have colleagues familiar with your subject area review it for clarity and possible errors. Proofread the poster carefully before you transport it to the conference.

Transporting and setting up your poster

Posters can be delivered to the conference site by overnight services, such as FedEx or UPS, but many presenters prefer to hand-carry them in poster canisters or portfolios. Normally, posters are set up just before the conference begins. You should receive advance guidelines from conference organizers telling you how to set up your poster. If the poster will be attached to corkboard, find out if you're expected to bring the required materials (usually pushpins or Velcro strips) to adhere it.

Most professional meeting agendas set aside specific times for poster presentations. Many organizations offer continuing education credit for poster session attendance. Be aware that if your poster is accepted at a conference, a presenter familiar with the project or research is expected to be available during poster sessions to answer questions.

A networking opportunity

Poster presentations are excellent opportunities not just to showcase your work but also to network with colleagues who have similar interests. Effective presenters introduce themselves to attendees and "walk" them through their poster, often adding information that they think will interest them. Some attendees may want to take the information back to their organizations, so consider having handouts available
to distribute at the conference. Also, bring your business cards or written contact information to give to participants.

From poster to article?

Interest in your poster by conference attendees may inspire you to take the next step-turning it into an article. Often, journal editors attend specialty conferences and visit poster exhibits. This can be a good opportunity to query them about their journals' potential interest in your topic.

Presenting a poster is a chance to learn from attendees about aspects of your work that particularly resonate with your audience. This can give you a better idea of how to present your work in a journal article to ensure it's informative and interesting and provides clear implications for the nursing profession.

Poster sessions have become an important part of most professional conferences and are an excellent way for presenters to share their work. Enjoy the experience of proudly standing next to your poster and discussing your work with interested colleagues.
Selected references</b.
Blakesley D, Brizee A. Designing research posters. Purdue University Writing Lab. 2008. http://owl.english.purdue.edu/media/pdf/20080626013023_727.pdf. Accessed July 20, 2010.

Briggs DJ. A practical guide to designing posters for presentation. Nurs Stand. 2009;23(34):35-39.

Halligan P. Poster presentations: valuing all forms of evidence. Nurse Educ Pract. 2008;8:41-45.

Keely BR. Planning and creating effective scientific posters. J Contin Educ Nurs. 2004;35(4):182-185.

Moore LW, Augspurger P, King MO, Proffitt C. Insights on the poster presentation and presentation process. Appl Nurs Res. 2001;14(2):100-104.

Sherman RO. Writing abstracts for podium and poster presentations. In: Saver C. ed. Anatomy of Writing for Publication for Nurses. Indianapolis, IN: Sigma Theta Tau International; 2011.

University of Buffalo Libraries. Poster presentations: designing effective posters. http://library.buffalo.edu/asl/guides/bio/posters.html. Accessed July 20, 2010.

Rose O. Sherman is director of the Nursing Leadership Institute and associate professor of nursing at the Christine E. Lynn College of Nursing at Florida Atlantic University in Boca Raton. She can be reached at rsherman@fau.edu.

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How to create an effective poster presentation - American Nurse

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Organizers of nursing conferences depend on nurses who have created new programs or are doing research to submit their work for presentation at conferences. Through these presentations, nursing knowledge is disseminated. If you belong to a professional organization, you've probably received at least one call for abstracts.

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Dive deeper into key topics through detailed, easy to follow guides and solution sets. Take your understanding to the next level with easy to understand books by James Tanton.

Build Your Skills

Explore mathematics with our comprehensive courses. Lesson content that reveals new approaches to learning will help you understand rather than just memorize solutions.

Explore Courses

Believing that mathematics really is accessible to all, James Tanton is committed to sharing the delight and the beauty of the subject. Learn more about the instructor at G'Day Math!

About G'Day Math!

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Dive deeper into key topics through detailed, easy to follow guides and solution sets. Take your understanding to the next level with easy to understand books by James Tanton. Build Your Skills Explore mathematics with our comprehensive courses. Lesson content that reveals new approaches to learning will help you understand rather than just memorize solutions.

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Have you ever seen an abacus? It just a set of rods with beads on it. On a basic abacus each rod has ten beads which you slide to the top. But the idea is that when you do slide all ten beads to the top, you push them back down again and slide just one bead up on the next rod over. People have been using abaci for millennia for counting and doing arithmetic.

But the amazing thing is, if you take this familiar idea and tweak it just a little, a whole new universe of amazing mathematics opens up to you. Instead of using beads and rods, draw dots and boxes. Instead of sliding beads, make them explode. Now you have ... you got it ... Exploding Dots!

Primary School: See the arithmetic algorithms as a beautiful story and see the role they play in advanced high-school mathematics.

High School: Start at the beginning and within 20-30 minutes you'll be doing polynomial algebra and infinite sums with astounding clarity. You will see the WHOLE story of arithmetic and algebra united.

Very early grades: Our partner company Matific is offering a suite of pre-Exploding Dots activities for young students still learning about numbers and place value and beginning arithmetic.

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Have you ever seen an abacus? It just a set of rods with beads on it. On a basic abacus each rod has ten beads which you slide to the top. But the idea is that when you do slide all ten beads to the top, you push them back down again and slide just one bead up on the next rod over.

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Khan Academy and the Effectiveness of Science Videos

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Read chapter 9 (Fractions as Operators).

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You should work on all of the problems at the end of chapter 9 beginning on page 203.

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Read chapter 1 (Proportional Reasoning: An Overview)

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You should work on all of the problems at the end of chapter 1 beginning on page 14.

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Read chapter 5 (Proportional Reasoning)

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You should work on problems 24 - 38 beginning on page 128.

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Read chapter 1 (Proportional Reasoning: An Overview)

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You should work on all of the problems at the end of chapter 1 beginning on page 14.

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Read chapter 5 (Proportional Reasoning)

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You should work on problems 24 - 38 beginning on page 128.

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Video transcript

We're asked to identify the percent, amount, and base in this problem. And they ask us, 150 is 25% of what number? They don't ask us to solve it, but it's too tempting. So what I want to do is first answer this question that they're not even asking us to solve. But first, I want to answer this question. And then we can think about what the percent, the amount, and the base is, because those are just words. Those are just definitions. The important thing is to be able to solve a problem like this. So they're saying 150 is 25% of what number? Or another way to view this, 150 is 25% of some number. So let's let x, x is equal to the number that 150 is 25% of, right? That's what we need to figure out. 150 is 25% of what number? That number right here we're seeing is x. So that tells us that if we start with x, and if we were to take 25% of x, you could imagine, that's the same thing as multiplying it by 25%, which is the same thing as multiplying it, if you view it as a decimal, times 0.25 times x. These two statements are identical. So if you start with that number, you take 25% of it, or you multiply it by 0.25, that is going to be equal to 150. 150 is 25% of this number. And then you can solve for x. So let's just start with this one over here. Let me just write it separately, so you understand what I'm doing. 0.25 times some number is equal to 150. Now there's two ways we can do this. We can divide both sides of this equation by 0.25, or if you recognize that four quarters make a dollar, you could say, let's multiply both sides of this equation by 4. You could do either one. I'll do the first, because that's how we normally do algebra problems like this. So let's just multiply both by 0.25. That will just be an x. And then the right-hand side will be 150 divided by 0.25. And the reason why I wanted to is really it's just good practice dividing by a decimal. So let's do that. So we want to figure out what 150 divided by 0.25 is. And we've done this before. When you divide by a decimal, what you can do is you can make the number that you're dividing into the other number, you can turn this into a whole number by essentially shifting the decimal two to the right. But if you do that for the number in the denominator, you also have to do that to the numerator. So right now you can view this as 150.00. If you multiply 0.25 times 100, you're shifting the decimal two to the right. Then you'd also have to do that with 150, so then it becomes 15,000. Shift it two to the right. So our decimal place becomes like this. So 150 divided by 0.25 is the same thing as 15,000 divided by 25. And let's just work it out really fast. So 25 doesn't go into 1, doesn't go into 15, it goes into 150, what is that? Six times, right? If it goes into 100 four times, then it goes into 150 six times. 6 times 0.25 is-- or actually, this is now a 25. We've shifted the decimal. This decimal is sitting right over there. So 6 times 25 is 150. You subtract. You get no remainder. Bring down this 0 right here. 25 goes into 0 zero times. 0 times 25 is 0. Subtract. No remainder. Bring down this last 0. 25 goes into 0 zero times. 0 times 25 is 0. Subtract. No remainder. So 150 divided by 0.25 is equal to 600. And you might have been able to do that in your head, because when we were at this point in our equation, 0.25x is equal to 150, you could have just multiplied both sides of this equation times 4. 4 times 0.25 is the same thing as 4 times 1/4, which is a whole. And 4 times 150 is 600. So you would have gotten it either way. And this makes total sense. If 150 is 25% of some number, that means 150 should be 1/4 of that number. It should be a lot smaller than that number, and it is. 150 is 1/4 of 600. Now let's answer their actual question. Identify the percent. Well, that looks like 25%, that's the percent. The amount and the base in this problem. And based on how they're wording it, I assume amount means when you take the 25% of the base, so they're saying that the amount-- as my best sense of it-- is that the amount is equal to the percent times the base. Let me do the base in green. So the base is the number you're taking the percent of. The amount is the quantity that that percentage represents. So here we already saw the percent is 25%. That's the percent. The number that we're taking 25% of, or the base, is x. The value of it is 600. We figured it out. And the amount is 150. This right here is the amount. The amount is 150. 150 is 25% of the base, of 600. The important thing is how you solve this problem. The words themselves, you know, those are all really just definitions.

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Solving percent problems (video) | Khan Academy

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We're asked to identify the percent, amount, and base in this problem. And they ask us, 150 is 25% of what number? They don't ask us to solve it, but it's too tempting. So what I want to do is first answer this question that they're not even asking us to solve.

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A lot of percent problems turn out to be easy to solve when you give them a little thought. In many cases, just remember the connection between percents and fractions and you're halfway home:

Solve simple percent problems

Some percents are easy to figure. Here are a few.

Finding 100% of a number: Remember that 100% means the whole thing, so 100% of any number is simply the number itself:

100% of 5 is 5

100% of 91 is 91

100% of 732 is 732

Finding 50% of a number: Remember that 50% means half, so to find 50% of a number, just divide it by 2:

50% of 20 is 10

50% of 88 is 44

Finding 25% of a number: Remember that 25% equals 1/4, so to find 25% of a number, divide it by 4:

25% of 40 is 10

25% of 88 is 22

Finding 20% of a number: Finding 20% of a number is handy if you like the service you've received in a restaurant, because a good tip is 20% of the check. Because 20% equals 1/5, you can find 20% of a number by dividing it by 5. But you can use an easier way:

To find 20% of a number, move the decimal point one place to the left and double the result:

20% of 80 = 8 2 = 16

20% of 300 = 30 2 = 60

20% of 41 = 4.1 2 = 8.2

Finding 10% of a number: Finding 10% of any number is the same as finding 1/10 of that number. To do this, just move the decimal point one place to the left:

10% of 30 is 3

10% of 41 is 4.1

10% of 7 is 0.7

Finding 200%, 300%, and so on of a number: Working with percents that are multiples of 100 is easy. Just drop the two 0s and multiply by the number that's left:

200% of 7 = 2 7 = 14

300% of 10 = 3 10 = 30

1,000% of 45 = 10 45 = 450

Make tough-looking percent problems easy

Here's a trick that makes certain tough-looking percent problems so easy that you can do them in your head. Simply move the percent sign from one number to the other and flip the order of the numbers.

Suppose someone wants you to figure out the following:

88% of 50

Finding 88% of anything isn't an activity that anybody looks forward to. But an easy way of solving the problem is to switch it around:

88% of 50 = 50% of 88

This move is perfectly valid, and it makes the problem a lot easier. As you learned above, 50% of 88 is simply half of 88:

88% of 50 = 50% of 88 = 44

As another example, suppose you want to find

7% of 200

Again, finding 7% is tricky, but finding 200% is simple, so switch the problem around:

7% of 200 = 200% of 7

Above, you learned that to find 200% of any number, you just multiply that number by 2:

7% of 200 = 200% of 7 = 2 7 = 14

Solve more-difficult percent problems

You can solve a lot of percent problems using the tricks shown above. But what about this problem?

35% of 80 = ?

Ouch - this time, the numbers you're working with aren't so friendly. When the numbers in a percent problem become a little more difficult, the tricks no longer work, so you want to know how to solve all percent problems.

Here's how to find any percent of any number:

1. Change the word of to a multiplication sign and the percent to a decimal.

Changing the word of to a multiplication sign is a simple example of turning words into numbers. This change turns something unfamiliar into a form that you know how to work with.

So, to find 35% of 80, you would rewrite it as:

35% of 80 = 0.35 80

2. Solve the problem using decimal multiplication.

Here's what the example looks like:

So 35% of 80 is 28.

As another example, suppose you want to find 12% of 31. Again, start by changing the percent to a decimal and the word of to a multiplication sign:

12% of 31 = 0.12 31

Now you can solve the problem with decimal multiplication:

So 12% of 31 is 3.72.

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A lot of percent problems turn out to be easy to solve when you give them a little thought. In many cases, just remember the connection between percents and fractions and you're halfway home: Solve simple percent problems Some percents are easy to figure. Here are a few.

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Interactivate: Simple Monty Hall

Simple Monty Hall: Choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Staying or switching between the two remaining doors.

On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Student development of numerical models and simulations integrated with core curriculum provides an opportunity to gain practical experience in computational science. Additionally, the National Computational Science Institute (NCSI) provides nation-wide workshops portraying resources and instructional ideas to middle school, high school, and undergraduate instructors for use in the classroom. Resources and materials offered to these instructors are available free of charge from Shodor's website and are largely developed by Shodor student interns. Shodor's academic program efficiently guides participants from excitement to experience to expertise through computational explorations, research opportunities, and service.

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Interactivate: Simple Monty Hall On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Student development of numerical models and simulations integrated with core curriculum provides an opportunity to gain practical experience in computational science.

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Read chapter 11 (Ratios and Rates)

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You should work on all the problems at the end of the chapter beginning on page 248.

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In preparation for the third assessment, please make sure you have read and understand the examples on pages 226 and 236

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Watch the Tutorial before next week.

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Colonist: Play Settlers of Catan Alternative - Free Online Game

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Online board game alternative to the popular game Settlers of Catan and PlayCatan. Colonist allows you to play now without the need to download or sign in.