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Math is all about problem solving. One of the best ways to help children learn math is to present them with a problem in which they have to devise their |
own strategies to find the solution(s). There is usually more than 1 way to solve math problems and children need the opportunity to discover shortcuts and their own algorithms to |
determine the appropriate solution, they should also justify their solution(s). The following math word problems are specific for children in the sixth grade and are divided into the main math |
cagegories: Number Concepts, Patterns and Algebra, Geometry and Measurement, Data Management and Probability. Children should be involved in problem solving activities every day. Problems for second grade students should be |
read to them. Students should also be able to describe why their solutions work or how they know it's the right solution. My favorite question to children is 'how do |
you know'. When they have to explain how they arrived at their answer, you immediately know the learning that has taken place. Patterns and Algebra Kelly's classroom organized an e-Pal |
club. 11 people joined the club. Each of of them sent an email to each of the members of the club. How many emails were actually sent? How do you |
know? Ticket sales for the bake sale were underway. Four people bought tickets on the first day of sales, twice as many people bought tickets on the second day and |
each day afterwards twice as many people bought tickets. How many tickets were sold after 16 days? Data Management and Probability Pet Parade: Mr. James has 14 cats, dogs and |
guinea pigs. What are all the combinations he could have? How many different types of pizza can you make with the following toppings: pepperoni, tomatoes, bacon, onions and green peppers? |
Show your answer. Sam bought 8 ball caps, one for each of her eight friends, for $8.95 each. The cashier charged her an additional $12.07 in sales tax. She left |
the store with a measely $6.28. How much money did Sam start with? Geometry and Measurement. Watch your favorite television show from beginning to end. Time each of the commercials |
and determine the percentage of commercial time for the entire show. Now determine the percentage of time the actual show is. What is the fraction of commercials? Two squares are |
Playing with Equations to Solve Problems Date: 09/16/2003 at 10:48:13 From: Mara Subject: To state the geometric property of an equation I need to give the geometric property common to all lines in the family x - ky = 1 I know that the answer is that all lines in this family have an x-intercept at x=1 but I am totally ... |
I was wondering if you knew how to go about solving this? Date: 09/16/2003 at 12:28:52 From: Doctor Peterson Subject: Re: To state the geometric property of an equation Hi, Mara. I don't think there is any method you can use to solve this sort of problem without a lot of thinking and testing. Let's see how I personally... |
as I can construct it, considering that I know the answer already!). Then I'll look at some alternative approaches you might take. We have x - ky = 1 and we want to know what property all these lines have in common. Probably, since this is an open-ended question and I don't expect it to be straightforward, I would star... |
the equation, getting a feel for how it works by trying a few special cases. I might take k = 0, 1, and -1 and graph those three lines, x = 1 x - y = 1 x + y = 1 I would find that they all intersect at (1,0), and my answer would be that all the lines seem to contain that |
point. (In a sense this is a more purely "geometric" property than the x-intercept, since it does not refer to the coordinates.) Then I would want to prove that this is true for ALL k, to make sure I hadn't fooled myself by choosing three cases that happened to intersect. Thinking of this as a point shared by all lines... |
would prove it by simply substituting x=1, y=0 in the general equation: x - ky = 1 1 - k*0 = 1 is true for all k so (1,0) is indeed on all the lines, not just the three I tried. Or, I might think of it as a common x-intercept, as you said; then I would do what you suggested and put the |
and then prove that conjecture. Now, is there any other way you might approach this? If you were really smart (and I might possibly have done this if I were faced with the equation afresh), you could just see that the equation looks like the two-intercept form, and gone directly to the proof. If you could do that, fine... |
such insight! You might instead just go through each form of the equation, starting probably with slope-intercept, and see whether any important feature (such as the slope or y-intercept) is constant. When that failed, it would be hard to move on to the point-slope or two-point form, because you would have to choose th... |
So you would probably next try the two- intercept form (which many studuents never see, so you're lucky). Your approach came close. When you solved for x, you just had to look and see that the x-intercept (the constant in that form) is always 1. But since that form, the slope-x-intercept form, is little-known, it's not... |
Problem: An oil drilling rig located 14 miles off of a straight coastline is to be connected by a pipeline to a renery 10 miles down the coast from the point directly opposite the drilling rig. Laying pipe under water |
costs 500,000 dollars per mile. Laying pipe on land costs 300,000 dollars per mile. What combination of underwater and land-based pipe will minimize the total cost of the pipeline? For now I'd just like help drawing the picture because in |
The Physics Help Forum not working today, at least not from my ISP, so this goes here. It's basically a math deal anyway: The formula to calculate the force of a point of mass, let's call them planets, that results |
from its being gravitationally attracted by another point of mass is Newton's: Where is the force of the planet that results from the gravitational attraction exerted upon it by the other planet, is Newton's gravity constant, and are the respecive |
masses of the planets, and d is the distance between them. For simplicity's sake let's say all the planets considered are of the same mass, so we can write instead of . Now, if I'm not mistaken, the formula for |
calculating the force of a planet resulting from the gravitational attraction of more than two planets is: Where is the force on the jth planet resulting from the gravitational attraction of the other planets, and is the distance between the |
jth planet and the kth planet. My question is "where is the vector addition?" That is, when considering the force on one planet that results from the gravitational attraction of many other planets, we have to take into account not |
only the distance of the other planets from planet j but also their position with respect to it (right?). Take for example the simple case of three planets in the same plane. Planet j is at the origin. Planet k |
is one unit to the right of j on the x axis, while planet l is one unit up the y axis. If the masses all equal 1, then, by the formula above, the force on planet j would be: |
But is a function of both the distance and the position, right? So we must consider not only the Gravitational Forces individually exerted upon j by k and l, but also the angle at which these forces are exerted. That |
is, we must add the vectors. To add vectors you just plug in the x value and y value sums of the added vectors into pythagoras' formula. The force on planet j should therefore be: (Where is the angle subtended |
by a line drawn from planet j to planet x. I.e. and ) So, what am I missing here? I am fully aware that I, and not Newton, am missing something here. Someone please help point this out for me. |
The doping-drug Epo has an impact in the brain Sportsmen and women dope with the blood hormone Epo to enhance their performance. Researchers from the University of Zurich now discovered by animal testing that Epo has a performance-enhancing effect in the brain shortly after injection and not only after days |
by improving oxygen transport in blood. As Epo also increases motivation, it could be useful in treating depression. The well-known blood hormone Epo is not only used for medicinal purposes; some athletes misuse it for doping. It boosts the number of red blood cells, thereby increasing the transport of oxygen |
to the muscles. This leads to improvements in performance, which can especially give endurance athletes such as cyclists or marathon runners the edge. Epo has immediate impact on exercise performance In a recently published study, Max Gassmann, a veterinary physiologist from the University of Zurich, proved that Epo al... |
increases motivation in the brain as soon as it has been injected, without the number of red blood cells increasing. Gassmann's team tested exercise performance of differently treated mice, studying genetically modified mice that produce human Epo solely in the brain and mice that the researchers had injected with Epo |
and the hormone reached the brain thus by blood. Both mouse groups exhibited an increased performance on the treadmill compared to the untreated control animals. "We assume that Epo in the brain triggers a motivation boost to increase physical performance," explains Professor Gassmann. He and his team are now testing |
the performance-enhancing effect of Epo on volunteers. Epo probably has an impact on people's moods, too. It might thus be used in patients who suffer from depression. The latest experiments conducted by a German-Danish research group reveal that Epo can also alleviate the condition of patients suffering from schizophr... |
improving their mental performance. Provided by University of Zurich - Biker's warning! Erythropoietin hits blood vessels to raise blood pressure in the brain Dec 10, 2011 | not rated yet | 0 - A new way to boost red blood cell numbers Jan 10, 2008 | not rated yet | |
2013 | 4.8 / 5 (10) | 14 Pressure-volume curve: Elastic Recoil Pressure don't make sense May 18, 2013 From pressure-volume curve of the lung and chest wall (attached photo), I don't understand why would the elastic recoil pressure of the lung is... If you became brain-dead, would you want |
them to pull the plug? May 17, 2013 I'd want the rest of me to stay alive. Sure it's a lousy way to live but it beats being all-the-way dead. Maybe if I make it 20 years they'll... MRI bill question May 15, 2013 Dear PFers, The hospital gave us |
a $12k bill for one MRI (head with contrast). The people I talked to at the hospital tell me that they do not... Ratio of Hydrogen of Oxygen in Dessicated Animal Protein May 13, 2013 As an experiment, for the past few months I've been consuming at least one portion |
of Jell-O or unflavored Knox gelatin per day. I'm 64, in very... Alcohol and acetaminophen May 13, 2013 Edit: sorry for the typo in the title , can't edit I looked around on google quite a bit and it's very hard to find precise information on the... Marie Curie's leukemia |
May 13, 2013 Does anyone know what might be the cause of Marie Curie's cancer - More from Physics Forums - Medical Sciences More news stories A new report suggests that improved health care and significant reductions in drug costs might be attained by breaking up the age-old relationship between |
physicians and drug company representatives who promote the newest, ... Medications 17 hours ago | 5 / 5 (1) | 0 Federal health regulators say an experimental insomnia drug from Merck can help patients fall asleep, but it also carries worrisome side effects, including daytime drowsiness and suicidal thinking. Medicatio... |
19 hours ago | not rated yet | 0 (AP)—Former Navy Secretary Richard J. Danzig, who has served as a bio-warfare adviser to the president, the Pentagon, and the Department of Homeland Security, urged the government to stockpile an anti-anthrax drug while ... Medications May 20, 2013 | 5 / |
5 (1) | 0 Europe's medicines watchdog said Friday the benefits of acne drug Diane-35, also widely used as a contraceptive, outweigh the risk of developing blood clots in the veins—when correctly prescribed. Medications May 17, 2013 | not rated yet | 0 Singapore's Agency for Science, Technology and Research |
(A*STAR) and Switzerland's Cytos Biotechnology AG today announced that the first healthy volunteer has been dosed in a Phase 1 clinical trial with their ... Medications May 17, 2013 | 5 / 5 (1) | 1 Each day, an average of nine people are killed in the United States and |
more than 1,000 injured by drivers doing something other than driving. 7 minutes ago | not rated yet | 0 (Medical Xpress)—We spend about a third of our life asleep, but why we need to do so remains a mystery. In a recent publication, researchers at University of Surrey and |
University College London suggest a new hypothesis, ... 2 minutes ago | not rated yet | 0 Johns Hopkins researchers say they have discovered specific chemical alterations in two genes that, when present during pregnancy, reliably predict whether a woman will develop postpartum depression. 2 hours ago | not rated |
Huntington's disease (HD), predicting clinical decline in people carrying the HD gene more than 10 years before ... 29 minutes ago | not rated yet | 0 Children who have suffered maltreatment are 36% more likely to be obese in adulthood compared to non-maltreated children, according to a new study |
Cancer debate: Are tumors fueled by stem cells? How can a cancer come back after it's apparently been eradicated? Three new studies from American, Belgian, British and Dutch researchers are bolstering a long-debated idea: that tumors contain their own pool of stem cells that can multiply and keep fueling the cancer, se... |
kill those cells, apart from how they attack the rest of the tumor. Stem cells in healthy tissues are known for their ability to produce any kind of cell. The new research deals with a different kind, cancer stem cells. Some researchers, but not all, believe they lurk as a persisting feature in tumors. Over the past de... |
in tumors like breast and colon cancers. But this research has largely depended on transplanting human cancer cells into mice that don't have immune systems, an artificial environment that raises questions about the relevance of the results. Now, three studies reported online Wednesday in the journals Nature and Scienc... |
mice. That and other factors mean the new findings still won't convince everyone that cancer stem cells are key to finding more powerful treatments. But researcher Luis Parada, of the University of Texas Southwestern Medical Center in Dallas, believes his team is onto something. He says that for the type of brain tumor... |
applies to other cancers, he said, then even if chemotherapy drastically shrinks a tumor but doesn't affect its supply of cancer stem cells, "very little progress has actually been made." The three studies used labeling techniques to trace the ancestry of cells within mouse tumors. Collectively, they give "very strong ... |
molecular and cellular biology at Baylor College of Medicine in Houston. He did not participate in the work but supports the theory, which he said is widely accepted. Parada's team worked with mice genetically primed to develop a certain type of brain tumor. The scientists genetically labeled particular cells in the tu... |
patients. It kills growing tumor cells and temporarily stops the cancer's growth. After treatment, when the tumor started growing again in the mice, the researchers showed that the vast majority, if not all, of its new cells had descended from the labeled cells. Apparently these were the tumor's cancer stem cells, they... |
cells from mouse brain cancers to study them and perhaps get some leads for developing therapies to eradicate them. He also said that preliminary study of human brain tumors is producing results consistent with what his team found in the mice. Parada's study appears in Nature. In a second Nature report, British and Bel... |
skin tumors in mice. And in the journal Science, a Dutch group found such evidence in mouse intestinal polyps, which are precursors to colon cancer. Scott Kern of the Sidney Kimmel Comprehensive Cancer Center at Johns Hopkins University in Baltimore is skeptical about whether tumors contain cancer stem cells. He said t... |
relevant they are to people. The two European studies focused largely on lesions that can lead to tumors, he said. And as for Parada's brain cancer study, he said he believed the results could be explained without relying on the cancer stem cell theory. Copyright 2012 The Associated Press. All rights reserved. This mat... |
2013 | 4.8 / 5 (10) | 14 Pressure-volume curve: Elastic Recoil Pressure don't make sense May 18, 2013 From pressure-volume curve of the lung and chest wall (attached photo), I don't understand why would the elastic recoil pressure of the lung is... If you became brain-dead, would you want them to pull the plug? May 17,... |
to stay alive. Sure it's a lousy way to live but it beats being all-the-way dead. Maybe if I make it 20 years they'll... MRI bill question May 15, 2013 Dear PFers, The hospital gave us a $12k bill for one MRI (head with contrast). The people I talked to at the hospital tell me that they do not... Ratio of Hydrogen of O... |
in Dessicated Animal Protein May 13, 2013 As an experiment, for the past few months I've been consuming at least one portion of Jell-O or unflavored Knox gelatin per day. I'm 64, in very... Alcohol and acetaminophen May 13, 2013 Edit: sorry for the typo in the title , can't edit I looked around on google quite a bit an... |
find precise information on the... Marie Curie's leukemia May 13, 2013 Does anyone know what might be the cause of Marie Curie's cancer - More from Physics Forums - Medical Sciences More news stories Older prostate cancer patients with other underlying health conditions should think twice before committing to surgery o... |
in the UCLA ... Cancer 11 hours ago | not rated yet | 0 | Intensity-modulated radiation therapy has become the most commonly used type of radiation in prostate cancer, but research from the University of North Carolina suggests that the therapy may not be more effective than older, ... Cancer 13 hours ago | not rated y... |
a compound abundant in the Mediterranean diet takes away cancer cells' "superpower" to escape death. By altering a very specific step in gene regulation, this compound essentially re-educates cancer ... Cancer 14 hours ago | 4.8 / 5 (12) | 2 | (HealthDay)—For young adults needing either a chest or abdominopelvic comput... |
than the long-term risk of radiation-induced ... Cancer 15 hours ago | not rated yet | 0 In a new study described in the journal Oncogene, researchers reveal how a key player in cell growth, immunity and the inflammatory response can be transformed into a primary contributor to tumor growth. Cancer 20 hours ago | not r... |
scientist Tuesday played down "shock-horror scenarios" that a new virus strain will emerge with the potential to kill millions of people. 42 minutes ago | 5 / 5 (1) | 0 No new human cases of the H7N9 virus have been recorded in China for a week, national health authorities said, for the first time since the outbreak be... |
pollution was significantly associated with higher hyperactivity scores at age 7, according to new research from the University of Cincinnati (UC) and Cincinnati Children's Hospital ... 5 hours ago | not rated yet | 0 | |
Research finds novel airborne germ-killing oral spray effective in fighting colds and flu University Hospitals Case Medical Center clinical researchers will present findings about a one-two punch to prevent colds and flu in San Francisco at the Interscience Conference on |
Antimicrobial Agents and Chemotherapy (ICAAC) on September 9, 2012. The research team is presenting data in two poster presentations that a new oral antiseptic spray is effective in killing 99.9 percent of infectious airborne germs. Findings from these two presentations |
led to the development of Halo Oral Antiseptic, a first-of-its kind germ-fighting spray which is currently on store shelves. "Respiratory tract disease is a major cause of morbidity and mortality throughout the world," says Frank Esper, MD, infectious disease expert |
at UH Rainbow Babies & Children's Hospital and lead author of one of the studies. "Yet there has been limited progress in the prevention of respiratory virus infections. Halo is unique in that it offers protection from airborne germs such |
as influenza and rhinovirus." Dr. Esper and a team of researchers used glycerine and xanthan gum as a microbial barrier combined with cetylpyridinium chloride (CPC) as a broad-spectrum anti-infective agent to fight respiratory illnesses. To test this, clinical strains of |
2009 pandemic H1N1 were used as a prototype virus to demonstrate Halo's anti-infective activity in cell culture assays. "The glycerine and xanthan gum prevent the germs from entering a person's system and the CPC kills the germs once they're trapped |
there," explains Dr. Esper, who is also Associate Professor at Case Western Reserve University School of Medicine. Dr. Esper will present his findings that Halo will have clear benefit to aid against infection and reduce disease from epidemic, sporadic or |
pandemic respiratory viral infections, particularly helping people at risk for severe respiratory illness including immune-compromised individuals with chronic lung disease, and military personnel. Another study on Halo will be presented by Mahmoud Ghannoum, PhD, of UH Case Medical Center, showing |
Halo's effectiveness against disease-causing pathogenic germs. The presentation asserts that respiratory and/or systemic infections through airborne and manually transmitted pathogenic microbes often enter the system through the mouth, making Halo, an oral spray that targets these pathogens, an effective way |
to prevent infections. Additionally, preliminary data from the researchers found that Halo completely kills all 11 clinical strains of whooping cough (Bordetella pertussis) against which the spray was tested. The results showed that when a person used three sprays of |
Halo, it destroyed airborne germs breathed in for up to six hours, even when people were eating and drinking. The concept of coating the back of the oral cavity to prevent germs from entering and then providing sustained antiseptic action |
to kill airborne germs was developed by a Cleveland company, Oasis Consumer Healthcare. "Exposure to airborne germs is inevitable – especially in crowded environments and when traveling," said Dr. Ghannoum, who is also the Director of the Center for Medical |
Mycology at Case Western Reserve University School of Medicine. "Unlike other products that support the immune system or protect from germs on surfaces or hands, Halo is the first and only product of its kind to offer protection from airborne |
germs." Provided by University Hospitals Case Medical Center - New study finds resistant organisms at core of soft contact lens corneal infections Jan 28, 2008 | not rated yet | 0 - Give dirty mouths a brush Apr 13, 2010 |
Bus, tram passengers warned to keep germs to themselves Jan 18, 2011 | not rated yet | 0 - Motion perception revisited: High Phi effect challenges established motion perception assumptions Apr 23, 2013 | 3 / 5 (2) | 2 |
- Anything you can do I can do better: Neuromolecular foundations of the superiority illusion (Update) Apr 02, 2013 | 4.5 / 5 (11) | 5 - The visual system as economist: Neural resource allocation in visual adaptation Mar 30, |
4.8 / 5 (10) | 14 Classical and Quantum Mechanics via Lie algebras Apr 15, 2011 I'd like to open a discussion thread for version 2 of the draft of my book ''Classical and Quantum Mechanics via Lie algebras'', available |
first time since the outbreak began in March. Diseases, Conditions, Syndromes 33 minutes ago | not rated yet | 0 A Nobel prize-winning scientist Tuesday played down "shock-horror scenarios" that a new virus strain will emerge with the potential to |
kill millions of people. Diseases, Conditions, Syndromes 51 minutes ago | 5 / 5 (1) | 0 Bacteria resistant to the antibiotic colistin are also commonly resistant to antimicrobial substances made by the human body, according to a study in |
mBio, the online open-access journal of the American Society for Microb ... Diseases, Conditions, Syndromes 5 hours ago | 5 / 5 (1) | 0 (AP)—Federal investigators probing the hantavirus outbreak blamed for three deaths at Yosemite National Park recommend |
that design changes to tent cabins and other lodging run by private concessionaires first be reviewed ... Diseases, Conditions, Syndromes 11 hours ago | not rated yet | 0 A new diagnostic test for a worm infection that can lead |
to severe enlargement and deformities of the legs and genitals is far more sensitive than the currently used test, according to results of a field ... Diseases, Conditions, Syndromes 12 hours ago | not rated yet | 0 | (Medical |
Xpress)—A three-year multinational study has tracked and detailed the progression of Huntington's disease (HD), predicting clinical decline in people carrying the HD gene more than 10 years before ... 44 seconds ago | not rated yet | 0 1 hour |
| 5 | New research suggests that a compound abundant in the Mediterranean diet takes away cancer cells' "superpower" to escape death. By altering a very specific step in gene regulation, this compound essentially re-educates cancer ... 14 hours ago |
| 4.8 / 5 (12) | 2 | Children who have suffered maltreatment are 36% more likely to be obese in adulthood compared to non-maltreated children, according to a new study by King's College London. The authors estimate that the |
prevention or effective ... 1 hour ago | not rated yet | 0 Salamanders' immune systems are key to their remarkable ability to regrow limbs, and could also underpin their ability to regenerate spinal cords, brain tissue and even parts |
News tagged with renewable energy Related topics: energy , wind turbines , electricity , solar panels , fossil fuels Renewable energy is energy generated from natural resources—such as sunlight, wind, rain, tides, and geothermal heat—which are renewable (naturally replenished). In 2006, about 18% of global final energy... |
renewables, with 13% coming from traditional biomass, such as wood-burning. Hydroelectricity was the next largest renewable source, providing 3% of global energy consumption and 15% of global electricity generation. Wind power is growing at the rate of 30 percent annually, with a worldwide installed capacity of 121,000... |
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