Thursday, March 22, 2018

Math Memes and Order of Operations

Ok guys, you've seen these, you've likely commented on them...and every once in a while you actually hoped that the majority would get them right, only to be disappointed. What am I talking about?

Math Memes that broke the internet. They seem to be everywhere, Instagram, Facebook, Twitter, and the rest. And they always seem like a simple math equation or expression that everyone (at least everyone who made it passed 6th grade) should be able to answer with ease...but they DON'T. I even recently saw one posted in a Math educator's group, and even THEY couldn't agree on the right answer.

I have no idea who the original poster was, but it's on Facebook somewhere!

Most people today blame the "New Math" or "Common Core," they say things changed...But we all know they didn't. SO what really is the problem? Why do some arrive at the answer 24 while others get 6? And more importantly, how can we nip this problem in the bud before no one can get to the right answer?

We all learned the acronym in school, we know how to do this! The letter stand for: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction....That means we just work the problem in that order. So it look like this:
P first = 60/5(2)
M next = 60/10
D last = 6
Problem Solved!

Not so fast! Remember, some got the answer 24...But how? These math minds are remembering a part of the rule that many tend to forget. We drill that acronym into students  minds, so they think its static...but it's NOT! No. The sub-rule is a left to right order...Yes, the inverse operations are worked TOGETHER in the order they appear in the equation/expression. So Multiplication and division are worked together and addition and subtraction are worked together. So for this particular problem, the acronym would be more accurate if it were written PEDMAS. Sometimes you might even do multiplication, division, then multiplication AGAIN ;) Here's a more accurate image to help sort this out: 

P first = 60/5(2)
D next because it's first = 12*2
M last = 24
That's it! Now we have it!

Here's another one that blew up the internet about 3 years ago...

Again, no idea who the original poster was, but this is everywhere now.
Can you solve it? Leave your explanation in the comments.
Have questions? Ask them in the comments and I'll try to help you sort it out. 

Want to help me clear this confusion up, once and for all? Download the free poster and practice page by clicking the image above. OR, head over to my store and grab a copy of the full unit. It doesn't matter what age you are teaching, or tutoring, no one is "too old" for this lesson. Clearly, otherwise the internet would have solved it years ago! If you and your students would like a little more practice you can pop over to my store and gab a copy of How to Use PEMDAS. Thank you for your support!

 Order of Operations Made Simple

Saturday, February 3, 2018

Homeschooling 101: What is a Homeschool Co-Op?

Guys, I've been away for too long! I had to take care of some medical issues, some family things, and carve out some me time to recuperate. But I'm back and ready to start delivering some great content again! During my hiatus I had some time to rethink my plans and goals, for myself as well as my business...That led me to the conclusion that I have a wide variety of educators in my audience. The first teachers I encountered on the internet were homeschoolers such as myself. Then I met many classroom educators while I was working on my degree. Soon, while figuring out how I wanted to use that degree, I connected with many tutors and special education teachers and specialists. Years later I found a fabulous group of teacher authors....That means I need to find a way to provide meaningful content for each of you! That's not a small order you know? That being said, I'm going to start a monthly series called Homeschooling 101. I'm going back to my roots friends! Today's topic is Co-Ops...oh boy is that a loaded subject!

Let's start by defining exactly what a Homeschool Co-Op is, and what it is not.
The word "Co-Op" is short for cooperative, a popular dictionary defines this as an adjective, meaning "involving mutual assistance in working toward a common goal" and as a noun meaning, "a farm, business, or other organization that is owned and run jointly by its members who share jointly in its profits or benefits" (Google Dictionary). These two definitions give us the answers to our two first questions!

How do homeschool co-ops operate? They operate as a collective, one voice for the group.

Smaller co-ops (of 2-10 families) will likely all have a say in any plans and procedures. They typical hold regular meetings to discuss how things are going and where they want them to go. Then the group will vote to make decisions. Occasionally, the group will nominate or elect a head or leader to make tough calls when the group doesn't agree.

Larger co-ops (of 10-hundreds of families) usually have a board of directors or a leadership committee. This committee works as a sort of representative government for the rest of the members, they are usually chosen because of their experience or expertise, either as homeschoolers, certified teachers, business leaders, or religious authorities. The members who participate and work "under" this leadership head typically know, trust, and respect their committee members. They feel comfortable enough to talk with them about their goals and concerns, and have faith their voice will be heard during the committee's meetings.

Who pays for what? If the co-op functions as one unit equally profiting or benefiting from the arrangement, that means the costs are typically shared evenly among the members.

Again, this arrangement may very from group to group and according to the size of the group. But most co-ops (especially ones that meet regularly and maintain a wide variety of classes) meet this need with a basic monthly, quarterly, semesterly, or yearly, membership fee. These fees are typically called dues, just like Boy Scouts or Awana Clubs. Some co-ops I've been involved with over the years held regular fundraising events to help share the cost without putting the burden on low-income families. Others offered discounts to larger families if they took on more duties to help spread the work load for others. And still others required tuition for classes each child would attend, therefore if a family opted out of a term, they didn't loose their membership, but also didn't have to pay to keep it active.

Vintage image created by Tirachard -
Since a homeschool co-op is education based, rather than a farming co-op or purchasing power co-op, the need for good teachers is at the root of their existence. This fundamental concept of homeschooling co-ops brings us to our third question, and again can be answered using in part using the definition we started with.

Where do homeschool co-ops find teachers? Remember, they work together to reach a common goal...that means their most powerful teachers are already among them!

Yes, as homeschooling parents, members of the co-op already have a core belief that they can provide the best available education for their children, so why wouldn't they want to assist each other to reach that common goal? Typically speaking, each member has an area of education that they feel passionate about, have a lot of background knowledge in, or have trade experience with. That makes it very easy for that member to provide classes for other members and their families. The skills of one offset the needs of others. That's why homeschool co-ops work!

Occasionally the need arise for a more qualified, out-side teacher. Say a few high schoolers want to get certified in a trade, they need a registered, licensed tradesmen to apprentice them, otherwise their time spent will not actually help them reach their goal. In some states or territories, core subjects must be taught by a certified, licensed teacher. In this case, those core subjects are often outsourced to a local teacher, perhaps a retired teacher or substitute that has the time available. In either case, or others that are particular to the co-op's needs, the group as a whole will use their local resources and personal connections to find a qualified teacher that meets their standards and their needs. These teachers rarely come free, so that tends to be another expense the group has to decide how to fund.

Where do co-ops meet? There is no specific answer for this one! Where-ever works best for the group.Of all of the co-ops I've been a part of over the past 20 years, there have been 4 basic meeting places.

Large co-ops often rent a facility, usually a church or religious building, sometimes a private school gym or cafeteria and a few classes during off school hours. Many of these local organizations provide a discount to the co-op because of the nature of their organization. Again, this incurs costs the committee has to account for.

Smaller groups can often find suitable meeting places in their area for free or very low cost. I've meet in coffee shops, libraries, book stores, pavilions in the park, and food courts in the mall! Yes, all of those are viable free meeting places. Each one presents its own issues however.

Intimate co-ops of just a few families often meet in each others' homes. One home (usually the most centrally located and/or the one with the most room) will serve as the meeting hub, then each satellite home serves as the specific classroom for the classes that family cares for. This worked for groups of 3-10 families and was really nice for working parents because they could drop off their kids on their way to work, knowing they would be continuing their studies under the supervision of a trusted adult!

A newer, more tech-aged meeting place is online in social media groups! I absolutely LOVE the possibilities with this last meeting option. Families can now connect with other like-minded homeschooling families, free from the limitations of distance! I am part of virtual homeschool co-op now that has members in several different countries, and it's such a beautiful thing to share culture and heritage in that way! No school on the planet can give our kids this kind of real life education :) These co-ops are free from room rentals and that kind of overhead, but they come with their own financial burden. Virtual meeting rooms that offer the tools needed for a quality classroom don't come free. And all members, obviously, must maintain tech equipment and internet service to participate fully. There is another issue of scheduling across time zone differences.

People vector created by Freepik

The last two questions are answered again by that definition we used. A co-op is a an organization made of individuals who share a common goal.

Where do homeschool co-ops find members? Short answer--people they already know.

The size of the co-op is relative to the number of people each founder knows directly who share their ideals and goals for organizing the group. Often times these are members of other organizations they belong to; their church, social club, neighborhood, family or close friends. Each person likely knows another person with the same goal, in turn that person knows another...and so continues the word-off-mouth invitations to be a part of something bigger than yourself. 

Occasionally new members are found through advertising streams. There are many co-ops listed on websites for people to find, and they may host community events to get the word out. The idea with such groups is "it takes a village," so they work hard to create the kind of village they want raising their child with them. 

So who can start a homeschool co-op? Again, short answer--any two or more, like-minded individuals.

There may be some local registration or licensing that has to be taken care of. But for the most part, it just takes to great minds, and often that starts with 1, who put the wheels in motion. From that point on its up to the member body to keep the co-op moving and growing.

I hope that answered some of the questions you've been asking about homeschool co-ops, and please, if you have any more, post them in the comments section below, I will do my best to either answer from my experience or find others' experiences to share! Come back next month to explore the topic, Homeschooling 101: What to Worry About and What to Let Go. See you then!

Saturday, January 14, 2017

Virtual Field Trips For Middle Schoolers

Budget cuts. This time they hit you personally. Those fabulous field trips your students used to look forward to are now off the table. How are you going to replace them?

Thankfully, we live in the digital age. Virtual field trips are not a new concept, but the options and availability are growing and changing as I type this. As a thrifty homeschooling parent, virtual field trips have always been a part of my teaching world, but I realize that the idea may be new for some. SO. How about I share with you 3 of my top picks for virtual field trips perfect for Middle School classrooms. I also am just learning how to use Google Earth to create my own virtual field trips that I can share with my tutoring students, so I'll share what I've learned so far. 

Oh, and btw, this post is linked with a little group of teacher bloggers who are all sharing fresh ideas for teachers, and we are giving away a camera to one of our readers to use in his/her classroom!
1. History/Geography: Beringia

7th and 8th grade students across the country learn about the Beringia Land bridge and how it allowed the first people to find the North American continent. But it seems like ancient history, and no one cares! At least that was the song my 8th graders were singing this year. What if we could bring them there today? What if they could interact with the people and see their customs? Ok, we know we can't, but we can bring the Iditarod Dogsled Race to them!

Start the field trip off with a little geography overview, and add in a little math while you're there!
Under the "Curriculum" drop-down menu, you chose which direction to take this field trip. Learn how the Iditarod race route has been changed and shaped over time by selecting "Breaking the Trail." Help your History students connect their geography brain to their math brain by clicking "Fastest Team Ever." Or, you may want to help your students personally connect by discovering how people develop a connection to their homeland, by choosing "A Sense of Place."

Each of the pages under Curriculum will provide questions for discussion and extension activities, projects, or videos to help your students dive right into the subject.

2. STEM: Architecture and Design

Students of all ages constantly bemoan math, wondering, "When will I ever use this?" A virtual field trip into the world of various designers and architects quickly answers the question and may open students eyes to some interesting careers. 
You can organize this journey in a number of ways. I start off on the road, at This interactive website allows students to explore several careers, but it also provides teachers with tools to promote discussion and extend the experience with activities. Once you've "entered the building" you can decide whether to view videos (each are around 4-5 minutes, covering careers such as a cake designer, sculptor, architect, urban planner, and landscape architect), or try your hand at designing either your own park or environmental center. 

3. Geology: Explore the layers of the Grand Canyon

Our budding scientists either love geology or hate it, I haven't figured out why but there doesn't seem to be much middle ground. Bringin the layers of rock to life will help those disconnected students engage, if even only for a few minutes at a time. And being right there at the base of a 3,000 foot cliff will no doubt encourage your geology-loving students to dig deeper.
This interactive virtual tour offers 3 options. Each option includes pictures, video, and audio. The two guided tours also included quiz-like questions along the way.

DIY with Google Earth

There is a definite learning curve to using Google Earth to create your own virtual field trip. I already said I am just figuring this out, so I'm not quite there yet, I will absolutely share with allI learn along the way!

The first thing I've discovered is that it's really all about the story. The "tour guide" really has to have a definite plan, and be willing to spend some time recording ahead of time. A key component to setting up your virtual field trip is knowing where you want to "pin" your images. There's a tool that looks like the Pinterest pin (only it's yellow), and when you insert the pin you are given a box to label and describe the location. You can include as many images as you'd like at that location. 

Once you've added all of the locations, you can reorganize them into the desired order, and then start moving along the route. As you move along the route, you'll record your commentary (if you want to include it in the tour). As I was playing around with this, creating a field trip of a recent vacation I wanted to share with my extended family, I thought that this might be a great way to prepare for a lesson you really want to teach, but know you'll be unable to teach yourself. A homeschooling, tutoring momma has no need for sub plans, so if any of you have ever done this, or venture in this direction, I'd love to hear all about it!

Mrs. Russell's RoomELA BuffetKirsten's KaboodleAmy MezniCinnamon's ClassroomThe Room MomStudy All KnightBrittany WashburnInteractive Learning with Miss StefanyMeredith AndersonImage HTML map generator

Do you have a favorite virtual field trip you've used before, and plan to use again? Please share it with the rest of us in the comments below.

Sunday, May 8, 2016

Hidden Gems: A Fair Bear Share

I found this month's hidden gem in a little book called "A Fair Bear Share" by Stuart Murphy. Murphy weaves counting beyond ten, adding groups of ten, adding 2-digit numbers using place value, and making new groups of ten, all while telling a cute story that also teaches the value of working hard.

Mama Bear is known for her Blue Ribbon Blueberry pie, and her four cubs LOVE it! Mama promises to make the bears her famous pie if they work together to gather the needed ingredients. If they can get enough nuts, berries, and seeds, each will get their fair bear share! To teach a lesson to young readers, Murphy tells of a slacking off little bear not doing her share, which of course results in Mama not having enough ingredients to make the pie.

After a day of gathering ingredients, the cubs must count them up. They quickly find that pilling their hoards together and counting groups of ten is the fastest and simplest way to find the totals. They add up their groups and count by tens, then add up the remaining piles, to come to totals such as 37 and 28.

When the youngest cub realizes she must do her part for all to enjoy Mama's famous Blue Ribbon Blueberry Pie, she gets to work, and collects enough of each ingredient. BUT, the cubs must add her collection to theirs, and thus we find a new strategy of adding, making new tens!

Since I have several first and second graders who are working on these skills right now, it was a fantastic find to come across this little gem of a math mentor text! It even inspired me to create a follow up activity for my students. I decided I'd share a sample of it with you for free, the complete set is in my store now (and 50% off for the first 10 buyers)!

Click HERE to grab: A Fair Bear Share Math Center Free Sample

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