Long division is not fun. At least according to my 11 year old.  However, there is an approach to make  it more accessible, especially for kids who look at the problem and have no idea where to start. Division is often taught to young kids as the process of partitioning an amount into smaller groups. We give them ten Lego guys and ask them how many groups of two they can make. As kids get a little older, we point out that division is the inverse of multiplication, which usually works well with facts. But if multiplication is just repeated addition, wouldn't the inverse of that be repeated subtraction? Yes! Viewing division as repeated subtraction can remove the deer in the headlights stare we often see when a child faces a long division problem. Let's start with a simple example:

 If we start with 10÷5, we can subtract 5 once from 10, leaving us with 5, then subtract 5 once again and we have 0. We subtracted 2 fives, so the answer is 2. Follow?

Now for bigger problems. Kids are usually comfortable with doubling a number or multiplying it by 10. Multiplying by 5 is just halving ten, so that's not usually a problem, either. We will work with multiplying the divisor by 1, 2, 5, or 10, using repeated subtraction, to solve the problem. That's it. Let's look at my super high tech example:


 The numbers on the right side indicate whether I multiplied the divisor by 1, 2, 5 or 10.  Once I get to 0 (or less than the divisor), I add the numbers on the right to get my answer. Note that you are always subtracting from the whole dividend, not portions of it as in the standard algorithm. Here's another example:

When kids get comfortable with this method, they start seeing that doubling the double is times 4, or if times ten is slightly too big, they will subtract one divisor to get times 9, and that's exactly the reasoning we are looking for! Conversely, some kids are only able to start with doubling and multiplying by ten, and that's okay, too. The problem may take awhile to finish, but the calculations are easy, which reduces anxiety.

I did show my kids the standard approach later, after they had mastered this one, and allowed them to choose what made the most sense to them. They both thought this way was easier, and allowed them to tackle the problem right away with confidence. Once your kids understand the concept of long division and can accurately solve problems, do them a favor and move on. Calculation is a small portion of mathematics, and in reality, nobody does long division by hand. Of course you and I will grab a calculator, but even people who use math in their careers every day use a computer or calculator to do computations. Math is reasoning, patterns, problem solving, spatial thinking; get to the good stuff once they have basic competency and stop beating a dead horse with pages of long division. Here's a link to my periscope about this strategy.

I have a guest post today about planning for the school year over at the Waldorf Essentials blog. Please pop over and check it out!

I spent an afternoon binge listening to the NPR TED Radio Hour podcast while I sorted through our bookshelves and homeschooling supplies recently.  If you've never heard them, you must subscribe; seriously, do it right now. You won't regret it. For the podcast, they pick a theme, then play portions of TED talks which relate to that theme, and also interview the presenters. A talk, 5 dangerous things you should let your kids do, caught my attention. Granted, the notion that you should allow your children to take risks or try activities that might not be approved by the AAP is not a new idea, but this talk sparked a little more reflection than usual on my part. The older kids were spending a week with their grandparents, and during a FaceTime call my son showed us the sewing machine he had just made a project on. My first reaction was surprise and a little thrill, since he really enjoyed sewing (hooray!). My husband's first reaction was something like, "Wow, be careful using that." He saw danger. I did not.

The next day my father in law called to ask how to cook the allergy friendly mac and cheese I sent up. After talking him through the steps I mentioned that Madeline could help, since she had made it before at home. He noted his concern about boiling water. He saw danger. I did not.

While camping, my husband taught Max how to make a camp fire. He let him build it, feed it and stoke it. It was a pretty big fire. I saw danger. He did not.

Upon reflection, I realized how intimately connected the risk we allow our kids is intertwined with our own feeling of expertise. My mother in law and myself are completely comfortable with kids using a sewing machine because we both sew. I sewed on machines at ten years old. I started cooking around that age, too. Baking actually - from scratch, the whole nine yards. So I feel comfortable with teaching my kids to use the stove and oven. My father in law, and my husband for that matter, see the risk, because they are not comfortable in the kitchen. Just as I saw the risk with the camp fire, which is not part of my responsibilities when we camp.

Of course, now the question becomes how do we get comfortable with risks that are outside our areas of expertise? Oh, that is the catch, isn't it? How did my mother feel comfortable with me using the oven when she'd never made a cookie from scratch in her life? While I'm pretty good at letting my kids use tools and appliances to create what they wish, I'm much more protective with physical risks. Climb that towering tree? Jump off of high places? That's much harder for me to approve. And yet we know that's exactly what we should be doing, within reason. We should be allowing for wings to expand, for space to explore, for challenges that just might cause injury, but definitely will cause pride and a sense of accomplishment.

It's still an open question for me. I am making more of a conscious effort this year to allow more risks in areas I feel comfortable with (more sewing!!!) but also encouraging my husband to expose the kids   to things he feels confident in (power tools, anyone?). And those dangerous things that scare me? Well, for now, once in awhile, I will try to smile and say, "sure, but be careful." Try.

Do you allow your kids to do "dangerous things"?

Well, it's that time of year again, when we homeschoolers don't go back to school.  We started our day with a walk to the park, and unfortunately, the timing was just wrong on this shot so I didn't capture their sweet hand in hand stride.

Over the next few weeks I added the bushes, some felted animals, a rubber frog to represent some we found in the creek, and  sun and moon gnomes. There is a little summer sign with a hand cut stamp, and I used a Scrabble tile holder as the base.

He likes to play with the pieces (as I knew he would), and sometimes they migrate to other places, but that's okay with me. He enjoys them, I didn't have to purchase anything, and they look cute on the bookcase!

Exhale. The combination of a toddler and technical issues with Google has left this blog quiet for far too long. There are many posts in the works, if the tech gods continue to be on my side;) For now I leave you with this week's chalkboard drawings, my favorite Waldorf obsession:

Soldiers' Tree

Wish

Baa Baa Black Sheep

Circles from rectangular building blocks? Am I crazy? No, I did not give the kids the task of creating circles from Legos, but we did create tools from Legos to make circles! The bricks pictured above are the ones we found in our collection that worked the best, but sort through yours and see what you can find.

Math is not a favorite subject for either of my children, even though it comes so easily to Max. I am always looking for a way to make it more fun, more appealing, and nothing is more appealing to my kids than Legos. So, when we started a geometry unit, I thought it would be a perfect pairing. I sorted through the Lego baskets and pulled pieces that would work well with line segments and angles, our first lessons. I mostly selected the thin, single row Legos you see above, in different lengths. I introduced the concept of lines and line segments using the pieces, then we made parallel and perpendicular lines using the bricks.

Taking those line segments and perpendicular lines, we snapped them together (or pivoted them, in the case of perpendicular lines) to create angles. We opened them to different widths to show acute, right and obtuse angles.


We traced them in our math journals and labeled the three different kinds of angles. You need to trace the inside of the angle, not the outside. It also helps if someone holds it, because they have a tendency to shift on you while you are tracing!
                             
                            

The next day I told the kids to create five different angles and trace them in their notebooks. I expected that they would make five individual angles, but they both surprised me with their approach. Max made one angle, then just pivoted it to create different degrees. Madeline took the right brain approach and created the structure on the right, then laid it in her notebook and traced the different angles it creates. I love their creative problem solving!

We have several museum trips coming up, thanks to free and reduced homeschool days, and I love using scavenger hunts to help focus the kids' energy when we are there. However, I do not love carrying a clipboard around, or trying to write against a wall or knee, or searching through the backpack for a pen. My solution? A book! I printed pre-made scavenger hunts from the Monterey Bay Aquarium website (many museums have them listed under the teacher resources, or you could make them yourself from pictures from the website) and bound them in a sturdy chipboard book, sort of following Angry Chicken's directions here. Instead of stapling the pages together, I folded each page in half and glued them back to back. Then I glued the first and last pages to the covers which made end pages and at the same time, secures all of the pages to the book.
This allowed the whole page to fold down for viewing, and the floating spine enables you to fold the whole book backwards. The hard chipboard covers (I took mine from the back of a sketchpad) provide a perfect surface for writing.
To keep track of the elusive pen, I added an elastic loop between the back page and the cover. To add extra hold insurance, I glued it down and then covered the edge with gaffer's tape.
That's all there is to it! Now I have a pint sized book of fun to focus our attention and our energy, and maybe discover something we hadn't noticed before. Now if I could only make our lunch bags and water bottles pint sized...

Learning kit number two - the geology basket. We are studying geology along with space, and we like to get hands-on with our work. I used a recycled basket (once the home to Numi teas), and added an extra clasp and handle to make it more portable. The handle is simply a corrugated cardboard  tube with raffia threaded through and tied on the underside of the lid.  A button and cord provided extra security to the front of the basket.
I gathered materials we had around the house for supplies. I included a magnifying glass, rock guide, notebook, pencils, colored pencils, a sharpener and eraser, small tape measure, paint brushes and a specimen box (i.e. recycled scrapbooking flower tin). It's easy to take outside for a little backyard geology, and while I don't tote it on hikes, it's nice to have it all in one place so I can throw the supplies in my backpack as we head out the door.

Science on the go

Time to take a hike!

I was browsing the Playful Learning and Imagine Childhood websites this weekend, and their products reminded me how much I love kits. The passion started early, when I would walk into those Sanrio mall stores and salivate over the little boxes filled with Hello Kitty stationary, stickers, and miniature pencils. Years later, I loved walking the aisles of Papyrus, lingering over the beautifully packaged cards and wrappings. Oh, and gift baskets, with all of those special little treats all bedecked with ribbons? Sigh.

Educational kits are fabulous, but often expensive. Why not make them myself? I could tailor them to what we are studying this year, use up some of those craft supplies that seem to breed in our home, and maybe motivate the kids in the process? Introducing....
Yes, the entire solar system in a can. Actually, it's a bunch of wool roving in a decorated coffee can. I chose bits of roving in colors to match the planets, then packaged each in a baggie (to protect it from the coffee smell that still filled the inside of the canister). The kids first had to decide which baggie was which planet (with the help of a book we read on the solar system), and then we tried turning the wool into felted balls. We used a You Tube tutorial at first, but it didn't go so well. Darling son said the wool made his hands itch and promptly left the activity. Considering he's allergic to everything, I didn't argue. Then I recalled that Amanda Soule had a tutorial in The Creative Family. I knew it would be kid friendly and easy, and it was. We used the kitchen sink instead of bowls outside (it was ninety degrees, after all), but the balls came together much better. I highly recommend the book, by the way. It's full of great projects and packed with good old fashioned inspiration.

Interest lasted for about two balls (it is time consuming), so I ended up doing the rest. I loved the process - very meditative. We set them outside to dry:
The kids have checked on them several times now, and are more excited about putting together a mobile with them when they are done. I haven't decided what to make the rings out of yet. Felt? Colored wire? I'll probably let the kids have the final say. Overall, they enjoyed most of it. I liked using up some supplies and having a project wrapped and ready to go. I have one other kit done that I will share next week, and more in the planning stages. Maybe I need to make a few adult ones as well. Who says that kids are the only ones allowed to have fun?