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!

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.

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!

In our homeschool, games are a regular part of the curriculum. With an ADD daughter and a son who dreads math worksheets, games are a fun way to liven up a sometimes dull subject. I was inspired by this marble arch game on Pinterest, but made a few changes to make it more versatile.

I used a whole box, minus the lid, so the marbles wouldn't run everywhere. The top and sides are covered with scrapbook paper, because I'm lazy and didn't want to wait for two or three coats of paint to dry. I painted the front with chalkboard paint (sigh, how I love chalkboard paint!), so I can change the numbers depending on what each child is working on. For the example above, you shoot two marbles through the arches and then multiply the numbers. Of course you could add, subtract, or divide the same way. But why stick with whole numbers? You could use fractions, decimals, or negative numbers. You could play with fraction bars, so the child collects the corresponding fraction bars until they have made a whole. You could use pattern blocks to practice geometry and/or cover a pattern block card with a design. You could use coin amounts and have the child collect the corresponding coins until they reach a dollar (or other specified amount). I love having wipe-off games that I can customize to whatever skill is needed!