Simplify Fractions Accurately Every Time!

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#Mathematics

In my experiences teaching math to 4th, 5th, and 6th graders, few things in their math education pose greater stress or a lower level of self-confidence than simplifying fractions. Students tend to fall into one of three categories with this particular skill: 1) they have no idea what to do; 2) they can sometimes get lowest terms but it is stressful and their error rate is high; or 3) they can usually simplify a fraction accurately but they do not have a process that they feel confident works every time.

I had the great privilege of teaching every level of math learner imaginable; from those who speak very little English, to those who come to me fearing and hating math, to those who were born with mathematical gifts–and every type of learner in between.

4th, 5th and 6th grade are really “fraction-heavy” grade levels for math students. This is when they’re learning or perfecting all the prerequisite skills for fraction operations, learning to perform fraction operations, and learning how to convert between fractions, decimals, and percentages. Fractions, fractions, fractions!  Even the math teacher gets a bit burned out on the amount of time we have to spend on fractions. And don’t even get me started on standardized testing in which students must show mastery of fraction operations during these years. Is it any wonder all but the most gifted tend to strongly dislike their math education? They fear it. Math feels unnecessarily difficult and complicated to them. The first thing I taught kids when they got to my math classroom is “everyone can be successful in math”, because everyone truly can… I’m living proof.

I try to let easy things be easy and to think up ways to un-complicate things that look and feel complicated to kids (and to adults!). A frustrated child, a fearful child, an angry or crying child…is not a learning child. They need confidence so they can avoid these feelings and experiences. When we know we have a process for doing something that looks hard, and this process works every time, we have an easier time believing in ourselves. When we believe in ourselves we are not frustrated, not fearful, not angry, not crying. If I taught math to children but didn’t read their faces and body language and use what I saw to guide my instruction, I would be doing them a huge disservice. How they feel about it DOES matter. I’ve seen how students feel about fractions…

So I created a document that lays out the process I teach my 5th and 6th graders. I make them take the notes and use the process before I share it in Google Classroom, because writing it and being forced to refer back to it during practice is part of the process of truly knowing it. Eventually math notebooks are lost or trashed, and students move on to higher grade levels, so I do eventually give them access to this document. After a few summer breaks and some years go by, they can refresh their recollection and reaffirm their confidence in their ability to get lowest terms accurately and quickly with confidence that they got the right answer. Because they NEED confidence.

It is important to know that the more they use these steps carefully and in order, the less they’ll need to use them or to have a document for reference. Their mastery of these skills will deepen with practice and expand their understanding of the mathematical concepts. The behaviors will become automatic, and the memorized process will almost certainly deepen into conceptual mastery they can build upon as they grow in their math education. I posted it in Google Classroom for fifth and sixth grade math students. I wanted to put it out here for parents and for anyone else who needs it.

How to Get Lowest Terms Accurately and Quickly, or Prove You Already Have It

Know your prime numbers! Here is a link to chart that shows which numbers are prime. https://www.helpingwithmath.com/printables/tables_charts/4oa4-prime-numbers01.htm

Forgot how to factor? Watch this video: https://www.youtube.com/watch?v\

  1. Is the denominator prime? If yes, you have lowest terms. You cannot simplify this fraction any further. If no, go on to number 2.
  2. Is the numerator 1? If yes, you have lowest terms. If no, go on to number three.
  3. Is the numerator a factor of the denominator? If yes (meaning numerator divides evenly into denominator), divide denominator by numerator. Example: the fraction 5/25. The numerator is 5 which is a factor of the denominator. Divide both the numerator and the denominator by 5 and you have lowest terms (⅕) as proven by numbers 1 and 2 above. In this case the numerator is a prime number. This works even if the numerator is not prime. Take the example of the fraction 4/16. Four is not prime, but it is a factor of 16. Divide the numerator and the denominator by 4 and you get 1/4. You can prove this is lowest terms by refering to the rule in number two above; the numerator is now 1 so you have lowest terms-guaranteed.

If you’ve tried everything in 1 thru 3 above and don’t have lowest terms, start factoring. You will have to do this if the numerator is not Prime and you don’t know if it is a factor of the denominator.

Find the Greatest Common Factor (GCF) of both numerator and denominator. Divide numerator and denominator by that factor and you will have lowest terms. Use your rules of divisibility to speed up the process.

Keep in mind that knowing and using prime factorization makes finding lowest terms so much easier. Here is a great video on how to find all the prime factors of any number. https://www.youtube.com/watch?v=XGbOiYhHY2c&t=211s

Here are the rules of divisibility. Knowing these will help you a great deal throughout your entire math education.  

Use your tools! Be an efficient math student!

When teaching rules of divisibility I find that many students struggle with the rule for 7.  I teach them to lean on their math facts (do their 7’s in their head). The rule for 7 is confusing to students who already struggle with math so I don’t teach it, but I give it to them in the handout and instruct them to use it if they’re comfortable with it.

Happy mathing!

LW

This is a post I wrote a long time ago to help my own students. I wanted to move it out of my old defunct classroom blog and keep it out here for students and parents who are struggling with this aspect of math.

Sharing from “Life Lessons”

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I did not write this! Full credit below.

This is such an important topic, and something I think absolutely everyone experiences but may not realize what’s being done.

Educate yourself on these tactics and make choices about if/how you respond. These are, perhaps, the single largest and most sinister tactics of media/social media in today’s world. The use of these tactics is changing our society in ways that are catastrophic to our societal structure. They are destroying the way we relate to each other as human beings. They are so sinister that we will have a world we can no longer recognize or fix before we ever know something terrible happened. This is being done to millions of people by a Constitutionally-protected free press and on every social media platform in existence.

Here is a link to the full post. It is worth the 5 minutes it might take you to read it. I hope you will. https://lifelessons.co/critical-thinking/kafkatrapping/

written by Michael Frank, a New Zealand blogger, and really intelligent writer.

7 linguistic tricks people use to deceive and manipulate you

Kafkatrap, kafkatrapping

In this article I’ll expose seven linguistic tricks people use to deceive you:

Let’s begin:

Kafka trap

The Kafka trap might also be called the SJW trap.

Author Eric Raymond coined the term Kafkatrapping in his 2010 article in which he presented a style of argument that is common today with SJW’s, but has it’s origins in The Trial a book written in 1915 by Franz Kafka.

In The Trial the protagonist is arrested and accused of serious crimes which are never specified. He receives no explanation or description of the charges, and his refusal to acknowledge that he must be guilty is what makes him guilty.  The only way to stop his abuse is to admit that he is guilty.

Keep reading here: https://lifelessons.co/critical-thinking/kafkatrapping/

Looking for a Top-Notch Employee? Hire a Teacher!

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The state of K12 education in the U.S. has teachers sprinting out of our classrooms and into the job market. Why should you hire us? What types of jobs would a good teacher be qualified to do?

The best of the best in every profession have benefited from the skills of good teachers. Many will tell you that they had at least one teacher who changed their life.  Why is that? And how does that make us valuable to companies in the private sector?

We challenge and inspire. We lead by example. We are champion multi-taskers. We maintain the calm amid storm after storm. We are reliable and hard-working by nature. We have a deep love of fostering success. This is what attracted us to the classroom in the first place.  We have much to offer in the private sector.

Imagine for a moment a school run by adults who don’t show up, or are constantly tardy. Close your eyes and picture the havoc that a group of unsupervised 10-year olds can wreak in a matter of seconds. If you need reliable, you need me. I show up and I bring my A-game every day. Other people’s lives and futures depend on my A-game.

You need a highly effective communicator? Hire a teacher. While being solely responsible for every aspect of those little people all day every day, I am accountable to parents from every walk of life. There are some who have a master’s degree or higher. Others never graduated from high school. Often, I spend more waking hours with their children than they do. They have legitimate expectations. I owe them an answer to every question they ask. On a moment’s notice I might need to join an administrative conference and analyze the latest round of testing data in great detail. The people in this room have PhD’s. They expect results delivered to them on pie charts and bar graphs with numbers that justify the funding that will keep our doors open. Via email, phone, video chat, or in person I communicate with the utmost respect for, and understanding of, my audience. I am a communication chameleon.

Does your bottom line rely on sales? Selling knowledge is not so different from selling a product or a service. A teacher knows that for a student to learn anything meaningful, they have to come in every day willing to buy what we’re selling. Teachers aren’t lecturers, we’re engagers. We are relationship builders. Does “pi times the radius squared” excite you? Probably not. Every day a teacher has 25 to 30 little customers in the room. At the middle and high school level, we might have 120 of those little customers come through our classrooms every single day. We have to be experts at selling knowledge. If not, they don’t succeed which means we don’t succeed. In direct sales and in sales support, teachers come loaded with strategies for reaching every audience. We have the finely tuned ability to quickly learn what will appeal to the audience sitting in front of us, and can deliver it with the skill of a Tony Award winner. It’s all done live. There are no second chances.

You need someone who is organized.  Your business is fast-paced and you need someone who can multi-task very effectively. Look no further. Teachers are detailed planners and expert managers. Part of a good teacher’s planning is always planning to be flexible and to address the diverse needs of a few dozen different people simultaneously. Good teachers think on our feet and we do it with grace and dignity. We can to put out a fire with one hand while bandaging a boo-boo with the other hand, and never lose control of the 80 or 90 other important tasks that must be carefully completed today. Need grace under fire and results? Hire a teacher.

In nearly every successful business today, technology skills are a must. Look no further than the teacher who is applying for your open position. I have expert Microsoft Office and Google Suite skills. Word processing skills are like food and water. Try writing a lesson plan or designing an assessment without them. Spreadsheets are how we track student data and measure progress. I can make charts, graphs, and pivot tables to analyze and track all kinds of data.

I am an expert researcher, writer, and editor. These are, perhaps, the most undervalued tools a teacher has in the arsenal. Textbooks are expensive. They are often outdated and schools lack funding. Even the newest textbooks are incomplete or fail to address a specific student need. A good teacher can quickly find, organize, and track information on any topic. Our ability to research, evaluate, consolidate, document, and present information as a series of logical arguments is unrivaled.

In your business you need a team player with a positive attitude. You need someone who is effective working independently. Look no further. Good teachers independently run our whole show every day. We set the tone in our classrooms. If we aren’t positive, nobody can be positive. Believing you can do it is 9/10 of being able to do it. A good teacher has a “bring it and I can do it” attitude. A good teacher is doing the job right without regard for who is watching.

We manage workflow. We are excellent staff developers. We are trained to create measurably productive work environments with whatever tools are available. We are thinkers. We are lifelong learners. We are cross-functional team players who manage multiple projects in a fast-paced environment every day. We thrive on it.

Please take a second look at that resume you received from a teacher. To interview that candidate is well worth an hour of your time.

LW

It’s Been A Very Long Time, So I’ll Start with Comfort Food

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I haven’t published anything in quite awhile. When you’re a teacher, you give up a great deal of personal freedom. People Google you, and if they don’t like what they find it can make an entire school year or even your entire employment experience unliveable.  Many of my teacher friends use only their first and middle names on their social media. But I digress…

I have been itching to find myself again and start writing without fear of retribution. That’s a pretty tall order in today’s world, so I’ll start with a great recipe.

The flavor of this shepherd’s pie is addictive. My husband typically has thirds and I finish the last of it for breakfast the next day.  This is a great dish if you need to prepare comfort food. You can add more veggies if you prefer. They are not needed for flavor, but more ingredients will make it go farther. Peas, green beans, and corn are some common add-ins. This recipe is completely gluten free, and nobody will ever know if you don’t tell them.  Enjoy!

Gluten Free Shepherds Pie Recipe

Ingredients
1 lb lean ground beef or lamb (I use 90% lean beef and love it. Lamb is the traditional Irish recipe. You could also do 1/2 lb of each)
1 tbsp oil or butter (use to sauté carrots, onion, and garlic)
2 to 3 large carrots , diced
1 medium onion , chopped
1 1/2 teaspoons minced garlic
2 tbsp tomato paste
1 tbsp Gluten Free Worcestershire sauce (most are GF; Aldi brand and L&P are safe options)
2 cups gluten free beef stock
4 medium potatoes , peeled and cut into large chunks (if you want to cut down the workload, use 1 large or 2 regular size packages of Idahoan instead. The Buttery Homestyle turned out great!!)
2 tbsp butter (not needed if you use the Idahoan potatoes)
2 tbsp GF flour (optional for thickening if needed)
1/2 cup shredded cheese (optional)
1 Tablespoon Marjoram
salt to taste (about 1/2 teaspoon)
pepper to taste (about 1/4 teaspoon
Instructions
Heat one tablespoon of oil or butter in a pan with the garlic, onion and carrots. Gently sauté for 3 – 4 minutes.
Add the lamb or beef and brown over a medium heat just until no longer pink, stirring frequently. Spoon off excess fat if necessary but be conservative; there is a lot of flavor in the pan liquid that you don’t want to drain away.
While the meat is browning with garlic, onion and carrot, boil the peeled potatoes in slightly salted water for 10-15 minutes until soft, but not soggy. Drain, then mash together with the remaining butter. You want to mashed potatoes to be thick.
Add the tomato paste and Worcestershire sauce to meat mixture and mix well. Add the beef stock, bring to a bubbly simmer, then cover pan and cook for about 20 minutes on low heat.
After about 20 minutes uncover the pan and continue to cook on low heat for about 15 to 20 more minutes.
Pre-heat the oven to 350F.

After reducing the cooking liquid, if you think it’s too runny you can add some GF flour to thicken.  I have made this recipe a number of times and have never added a thickener.  It has never been runny. The key is to cook the liquid down slowly over a very low heat. Add a few minutes to that process if needed.

Put the cooked meat mixture into an ovenproof dish. Cover with a thick layer of the mashed potatoes spread out with a fork or rubber spatula. During the last 5 minutes of bake time you can add shredded cheese on top if you like.

Place dish on a baking sheet and bake for 20-25 mins until the gravy is starting to bubble out around the edges. Remove from oven and let stand for about 10 minutes before serving.

Eat well on your journey
LW

Teaching Grown-ups

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Homophones on the road

Homophones on the road

We’ve been out of school on fall break for two weeks.  This is a souvenir I received from someone really special.  This is one of those priceless little gifts that probably nobody else will really understand.  It’s from a husband and wife who come and mentor my little reading rock stars.  Not only do they mentor six of my little people every single week, but they fill-in on short notice when mentors are absent.  They do a lot of really nice things for me.  They are so precious and wonderful.

I often take a little time to give refresher info to the mentors so that they will understand what they’re doing with the kids they mentor each day.  Recently we’ve been working on multiple meaning words and homophones and so I’ve been giving the adults a refresher course on what, exactly, a homophone is.  That’s not common knowledge that we carry through life and use in daily conversation.  Even the most intelligent people forget some things.

So Sandi and David were driving through North Carolina over fall break when they passed this church.  They stopped and went back to take a picture of the homophone on the side of the road so they could show me that they’ve learned what I’m teaching!  It’s hanging on my bulletin board.

These are the kind of gifts that stick with me because they remind me that what I do matters and people care.  Probably silly to everyone else…priceless to me.

LW

Do you have an hour a week to help a second or third grade student become a better reader?  Click here to find out more about how to become a HOSTS mentor. http://www.wayne.k12.in.us/hosts/

Creating Healthy Eating Habits In Kids

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Advice for parents (particularly parents of young children): Don’t force your kids to eat food they don’t want, or make them feel obligated to clean the plate you, or someone else, loaded for them.  Yes, I’m dead serious.

Think outside the box. Have rules about trying a bite–just one bite. Fight that fight. Do it by always having something visible they know they like. Use it as incentive to get them to try one bite of whatever you’re eating or want them to eat.  Be satisfied with one bite, and have them try the same food two or three times in a year.  Be willing to accept that they won’t like certain things.  If they actually gag, move on.  Don’t offer that again. Offer healthier choices whenever possible, but let them have a say in what they eat, and let them stop eating when they’re full (no desert until at least an hour after dinner–no exceptions.)  If you don’t make it a power struggle, it won’t be a power struggle.  Say “would you like chicken or pasta?”  instead of “do you want chicken?”  Don’t ask “yes/no” questions when one of those choices isn’t acceptable to you.  This way you maintain the structure you want them to have while still letting them feel empowered.  

Our generation is walking proof that “you’ll eat what I cooked whether you want it or not, and you won’t leave the table until your plate is clean” teaches poor eating habits.  It creates adults with serious weight management issues who eat when we’re not really hungry and die of heart disease way too young.

We sit down to a family meal most every night, but we don’t necessarily all eat the same thing. Really, this is less of a big deal than you might think. My kids are now 14 and almost 12. This is how I’ve fed them their whole lives. It isn’t always simple, but I’m observing something really important. They eat only when they feel hungry, and they stop eating when they feel full. They know exactly how much food will satisfy them most of the time, so there is rarely much waste. They don’t eat out of boredom or for comfort. Food is nothing more or less than sustenance to them. They will even stop eating a treat and save it for later once they feel satisfied.

It is actually much easier to throw together an extra something I know my child will want to eat, than to fight with him and dole out consequences for not eating something he really didn’t want.  I’ve got bigger fish to fry–pun intended.  I also don’t care for the subconscious message we send when we say they have to take whatever is offered to them even if they don’t want it–think cigarettes, booze, drugs, and sexual advances.  Kids need to feel empowered to say no when it is appropriate (or imperative!) that they do so.  It’s not a concept, it’s a practice. They learn what they live.  Like everything else, it starts at home–good or bad. 

There is no perfect diet. There is only best case scenario.  The meat and poultry in this country are loaded with hormones and antibiotics. The fruit and veggies are loaded with pesticide and wax.  Most of the fish is farm raised and loaded with artificial color and preservatives.  Everything is loaded with sugar, salt, oil, and flour. Truly healthy food costs a fortune and is nearly impossible to find for the vast majority.  The best we can do for our kids is end the romance with food.  If we teach them discipline and reward them with choice, we create adults with tools for living right in multiple aspects of their lives.

LW

Does Summer Fun Equal Learning Loss?

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The short answer is YES!  With nothing resembling education, they lose the momentum they gained week over week all through the school year.  But, we don’t have to rain on their parade in order to maintain their academic success.

Like every parent out there, I want my kids to have a really fun summer.  Like every parent out there, I want my kids to get a great education.  NWEA testing at my son’s school a few years ago showed that students gained 1.7 years of educational growth during the school year, and lost 1 year over summer break!  As someone who works with students in remedial reading, I can tell you that my typical student loses 1 to 3 reading levels in just 2 months of summer break.  This is something that plagues the hearts and minds of every educator I know.

Much to my dismay, I can’t make my students exercise their brains over the summer. However, much to their dismay, I have begun to take a look at my own children. : ) I could just enforce a certain amount of time they must spend reading a book every day. That goes a long way to helping maintain their educational progress, so I’m not slinging mud a that!  If my students’ grown-up(s) would just do that I’d be on cloud nine!  I have to reign on my own kids like a Spring storm all summer long to make daily reading happen.  So if that’s what I have to do anyway, this year I’m trying something a little different.

I gave the boys a few weeks to relax while I furiously wrote four really intense papers on cognitive development in order to finish up my own college term after my last day of work.  I told the boys to read something every day; I watched to see what they would do without me riding them.  They didn’t pick up a book; not once.  So, today I assigned a research project to each of them.  One child laughed at me; the other one cried.

I’ll tell you a little secret; there are things kids think they hate but once you get them to start doing it, you can’t get them to stop.  PowerPoint is a fun program.  It has progressed to the point that it is pretty easy to use.  And you can make things spin, wobble, fly around, and explode complete with sound effects.  Kids like that.  Kids LOVE that.  And it’s an extremely valuable skill for a vast array of jobs!

So, my 9th grader is researching political parties.  His goal is to find out how and when they started, what they believe, who leads them, a few famous (or infamous!) members, what they use as their symbol and why.  By the time he enters college, it is imperative that he know the difference between education and indoctrination.  High school is his opportunity to ask questions and build on this foundation, so he needs to know what questions to ask.

My 6th grader is gathering all of the base data on every US President since 1960.  I have given him a list of what I want him to find out about them; it isn’t brain surgery and it’s easy to find. I want to know: their name, the names of their wives and children, date of birth/death, dates in office, President # i.e. Obama is our 44th President, political party, and one or two things that we remember about their Presidency.  He has to include a picture of each of them.

Let me repeat, there are things that kids think they hate until they start doing it; then you can’t get them to stop.  Whenever I assign my students a Venn Diagram they moan and groan and the mentors look at me like I’m nuts.  Then they start comparing and contrasting.  When class is over I can’t pry them away from the thing.  “OK, Mrs. W, hold on. I just remembered that this is different and I don’t have it on here.  Can I take this with me?! Can we do this again tomorrow? PLEEEEEASE??”  Everyone is laughing and communicating and comparing and contrasting and learning.  The kids don’t hate me anymore. The mentors stop to thank me on their way out the door for making the time so fun.  It’s all in how you set up a task.

So my sons have to give this one hour per day, only on the week days.  All of their research can be done on the internet.  Do you know how fast an hour goes when you’re Googling and scanning for facts?  Do you know how many skills and brain activities are being used and developed here?  Their final presentation is to be in PowerPoint which they both LOVE.  I expect to see things floating and flying, sizzling and spinning.  They have to create one artifact that is tangible.  It can be anything that relates to their topic–something they draw, or cut out, or glue together, or find somewhere.  This project is due the day before I go back to work (July 29th), so they have plenty of time.

Last night they reluctantly started their research.  Guess what.  They found facts!  They came to me with lists and they were proud of what they had.  They had questions!  When a kid has questions, they’re interested.  So they don’t hate me anymore, they’re not laughing at me, and they’re not crying. Best of all, they’re thinking.  One of them just came to where I’m sitting and writing this with news on in the background, and started asking me intelligent questions about the public figure being interviewed on the TV.  It’s someone he recognizes as a former Vice Presidential candidate.

I believe that this summer project will wind up being interesting for them, and will help maintain their education level, while not sucking all of the fun out of their summer.

Balance.

LW

Happy Mother’s Day, Mom

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Dear Mom, I know I wasn’t an easy kid to raise.  I think that’s why God gave me to you; He knew you could do it.  And you did!  I’m far from perfect, but I’m way better than just OK.  You taught us what truly matters in life–love, loyalty, family, faith, education, and moral standards.  All things no amount of money could ever buy.  You led us by example. You ARE the Grandma you set out to be.  Their sun rises and sets in you.

Thanks, Mom.  I love you.  Happy Mother’s Day.

(Click the “Play Button” on the bottom right)

A New Life With A Fifth Family Member

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The Fifth Wormald

Emma grows with us…

The only dogs I’ve ever had are ones I raised from tiny puppies, or one we inherited from a family member, that was raised right, and at 16 years old left very large paws to fill. : (  Emma is my first foray into taking on someone else’s neglected pet with ingrained bad habits.  It’s been a road…

Keep in mind that I have that mojo…y’know, the one that if I go bragging too much, LOOK OUT LAURA, it will bite you in the butt!  This said…

4 mos down this road, she’s family now.  She gets the trust she’s earned.  This now means most nights she gets to sleep on a bed with a person.  Mess around–in the crate you go!  She likes the bed, so I think she really tries to be worthy.

They’re like little kids in so many ways.  She’s developed some coping skills for some of her bad habits.  We’ve found a type of bone she really likes that is made for power chewers.  We keep about three of them around.  I can actually see her use her bone to cope with the stress of wanting to eat a shoe, or a piece of furniture, or a door.  Do I trust her? NOT A CHANCE! But we’re getting there.

She still has a trash fetish, particularly bathroom trash (ew).  I want to choke whoever paper trained her, but great progress is being made.  Weeks go by, then we have a day of scrubbing carpet all over the place, then more weeks go by.  Baby steps…

I could not have imagined what Emma was going to do for my sons.  There are places in some children’s world where dogs can go that people just can’t.  The value is immeasurable and I am blown away by what she has brought to this family…

All of Emma’s training comes from humanely but firmly commanding respect, and rewarding it with love–NOT TREATS!!!  She gets treats every day, but not as blackmail for good behavior.  She is made to behave because that’s required.  She is never hit.  Never chained up.  The crate is her safe haven–not jail unless it’s for her own safety or someone else’s.  Yes, she’s in there when we’re not home–for our safety and hers.  She can’t be allowed to eat my house. I can’t take a chance she gets into trouble she can’t get herself out of safely.  But we go to great lengths to make the days OK for her.  I come home for lunch a few days a week.  She gets a limited amount of treats because we love her.  Have you ever read the ingredients on the average dog treat package?  They’re horrifically unhealthy.  I buy healthy dog treats (Newman’s Peanut Butter Heart-Shaped).  She also gets some cheese, or peanut butter, and believe it or not she likes carrots!

I wasn’t too sure about this back in December.  Now we’re the Wormald 5 and we wouldn’t have it any other way.

LW