Drawing multiples on graph paper. Knowing that bright pink crosses the middle at intervals of eight, can you find where 24 is?
homeschooling,  mathematics

Math, both coursework and recreational

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Reason #124 for loving homeschooling is that we can stop schoolwork in May and June when the weather is beautiful and we long to be outside and then start it up again in late July and August when it feels to hot to venture out anyway.multiplearches

I’m back into schoolwork mode. Right now that means insisting that the boys each do some math, writing and piano every day. With my oldest I am trying to finish up Level D of Rightstart mathematics within the next few months. In the early spring I was doubting we would continue on to Level E. I had felt frazzled and I was tending to just hand my son a worksheet instead of sit down and doing the lesson proper with him. The worksheets on their own are too difficult for him. They’re meant to practice the strategy and without taking the time to help him find the strategy it was like throwing him into the deep end of a pool. Now I’m making a point of sitting down and really looking at what the lesson is meant to teach and I’m thinking we will continue to use the program.


We’re doing recreational math too. I showed my seven year old the basics of using a slide rule to do multiplication. I need to learn more about how to use it, because I’m really rough on it. Then today I found this stunning little interactive illustration of multiples and I decided to try drawing it on graph paper. Here’s two versions, one in which I used random colors and the other where I tried to make a rainbow.

This picture is not hard to make. Draw a straight line across a piece of graph paper. Start at one side and mark all the multiples of two. Then draw a wavy line connecting the multiples. Imagine the wavy line like a collection of half circles, one above then one below and so on. You could use a compass and get it much more exact but even just using graph paper and approximates the picture was fun to make and explore. For each arc there is the half-way place where you would put a compass, if you were using it. After marking all the multiples of two, move on to the next multiples. Trying to remember to have the peak in the middle of a square, not at an intersection, for the odd numbers was a challenge for me. Prime numbers either have only one color flowing through them or are empty.

At some point I want to go through and draw the wave and spiral like patterns that you can get if you draw just the lines for the divisors of a specific number.

Using graph paper it is easy to create draw a brickwall to study multiples and factors.

Then I wanted to see which other ways I could illustrate the multiples and so I came up with this brick wall. The brick wall picture gave my seven year old some practice multiplying as I asked which number certain lines stood for. He kept wanting the wall to come out even at the end, but of course there isn’t one number which is a multiple of all the other numbers. We stopped at forty-two, which is a multiple of several of the numbers and a neat and tidy ending point. If the left is the start, the first set of vertical lines makes a very clear diagonal. I challenged my son to explain to me why the later ones don’t. When I next get his attention with this I want to see if he can find a pattern for predicting when neighbouring rows will first match up their lines.

I’ve been working with my four year old on math too. To him games don’t have to be competitive so some of the best games are very simple ones. Today we sat down with an abacus and took turns rolling the die and recording the roll on the abacus. I gave commentary sometimes, pointing out that my roll of a one and his roll of a four made five or that seven was five and two, etc. We’re using an abacus that came with the RightStart math program so the beads are colored so groups of five are visible. I’m trying to give him lots of time to play with the numbers and resist teaching too much.

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  • Jackie H.

    I have a four year old too so we’re more on that level. I like how you add some commentary of higher level skills even while he is “playing” with math!

    • christyk

      After three days of playing that abacus game, he stopped counting the beads! Instead of counting he’s moving the beads in groups. Six is 3 + 3. Five is 3 + 2. The game really works well for teaching that skill because depending on what the previous rolls were there might be places where he has to add a larger number but there’s less beads than he needs on the one line and he has to move to the next, so he’s forced to break the larger number up and think of it in terms of smaller numbers.

    • christyk

      Thank you for the compliment! I feel embarrassed sometimes about my blog because I’m writing about teaching the kids stuff and yet I don’t really have any teacher’s qualifications or anything, I’m just making stuff up as I go along and learning along with the kids.

  • Tonya Dirksen

    I love that you are not stuck in the traditional school year but do school to fit your family. That is what we do too. My girls don’t know what summer vacation is! Learning is a life time process, not something you do Sept-May!

    • christyk

      I went one year working right through the summer with the kids, but then the next year they learned about summer holidays from a friend. We don’t really stop learning during that time, I just stop insisting on them practicing the things there less willing to do.

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