Sunday, February 21, 2016

Klee Art Projects

Paul Klee was a Swiss painter who spent most of his life living in Germany. He was a talented musician as well, and often tried to capture the feeling of musical rhythm and movement in his paintings, especially his abstract color studies. Klee explored balance, geometry and color, and the warm red, yellow and orange colors he experienced on a trip to Tunisia show up in much of his work.

The first work we'll explore is Cat and Bird. This is a great example of balance versus symmetry in art. The cat's face is not symmetrical (exactly the same on either side), but it is balanced. If you divide the composition into thirds, either horizontally or vertically, you can see that there is a point, counter point or weight to balance the planes. This could definitely lead to some math work in symmetry or fractions, homeschool moms!

Point out to your kids that the face is composed of two tear drop shapes that overlap in the middle like a Venn diagram (oh, that math again!), with a u shape for the mouth and that same tear drop shape, pulled out on either side, for the eyes. Add a heart nose, whiskers, and whatever is on the cat's mind! Trace over your picture with Sharpie, then erase the pencil lines.

We did our pictures with chalk pastels, choosing three colors for the cat's face and a few additional for the background. The key to working with pastels is blending and layering, blending and layering.

Our next project was inspired by Castle and Sun.

In this painting, Klee works with more rigid geometric shapes, appropriate for a strong castle. You could have your kids draw a castle free hand, with a ruler, or even pull out classic wood blocks and trace around them. Once they have a satisfactory castle, trace with Sharpie and erase the pencil. Make sure you use a waterproof ink to trace with, not Crayola markers!

Next, wet the paper with a brush dipped in water and apply squares of colored tissue paper, then go over the tissue once more with a wet brush. The dye from the paper will bleed onto the paper after a few minutes. Please test your tissue ahead of time - some papers have fixative that prevents bleeding, and some colors are so light that they don't leave much on the page.

After a few minutes, remove the paper and it looks like watercolor!

Since Klee uses such strong, identifiable geometric shapes, this is a great project to do with a geometry unit!

The last project is inspired by the painting Senecio. In this painting, Klee combines the organic, balanced elements from Cat and Bird with the hard geometry of Castle and Sun. 

We followed the same steps as above with drawing in pencil then Sharpie, tracing a paper plate for the head and adding a center line to divide the face and aid with drawing in the features. Next, grab an old gift card or one of those fake credit cards that come in the mail, and a little tempera or acrylic paint. Load a little on the edge of the card and scrape it down the paper.

Create the background the same way, then cut out the face and glue it on your background:

Max chose to color his face with oil pastels instead. I must say that I have not been inspired by the kid's art books about Klee that I have seen, but there may be some good ones floating around out there. However, there are some great internet resources, including this video for grade school kids, and this slide show for any age. You can catch my Periscope about these projects and my thoughts on instruction vs. creativity here. Great art, math and music tie ins - you can't go wrong with Paul Klee!

Friday, February 19, 2016

Birthday Drawing

Happy birthday to my talented, kind, hard working, sensitive, funny, creative inspiring daughter!

Tuesday, February 16, 2016

Any Easier Way To Do Long Division

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.