I started the unit by presenting containers of beans. The object was to play with the concept that once you have 10 ones, you have one ten. If you have 11 ones, you have one ten plus one one.The teaspoon held about ten beans. The cap, 100 beans, etc. He got that pretty quickly. He asked if he could draw it in his MLB, which was a total surprise. (I'm coming to learn that he'd much prefer to draw a picture of a concept than write about it.)
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| Using beans to "show" place value |
I then moved to naming the place values. The chalkboard illustration below shows one of our morning warmups. I placed tally marks in each place value box. His job was to read across and tell me what the number would be, in standard form. (Example: the orange would be 3,205,230). I also worked that conversely by giving him standard form and he had to make the tally marks. And we worked in extended form. (Ex. three million, two hundred five thousand, two hundred thirty).
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| Place Values |
This part of the block went quickly. He was already familiar with place value, due to an introduction in third grade. We finished place value by observing that as you move left, the number gets 10x larger.
Then I asked the question, what if we wanted to move right? Candy bars work great for this lesson, especially for my little chocolate lover. I used a mini Toblerone and showed him one candy bar. "Now, what if you, Daddy, and I each want a piece? How do we make a singular object into something smaller." "We break it into 3 pieces, Mom." (In fractions that would be? Thirds!). In decimals we break it into ten pieces and each of us gets 3 and 1/3 pieces.
We talked about how decimals show us pieces, just like fractions. But unlike fractions, the pieces are always parts of ten. We learned that a decimal point shows us "AND." One candy bar AND three pieces out of ten. (Such a simple concept, but not one I ever learned.) And we observed that as we move to the right of the decimal point, the numbers get 10x smaller. From there we named the place values for the decimals and our morning math warmup centered on that skill.( It was great review for me, as I've gotten lazy and say things like "two point four three" instead of "two AND fourty three hundredths")
Once I was sure he had a good grasp of what a decimal is, we started with the operations. Division has been the most challenging for him, which is just an overflow of his work with whole numbers. He wants to get finished so quickly that he misses steps, such as bringing down the next digit or moving decimal points over. With practice, I'm sure he'll get it.
We ended the block by working on word problems, having him use all four operations. One of the more difficult exercises was one where I had a list of produce and prices (4 oranges/$1.25, two pounds of bananas/$.75, etc.) But then asked him how much 3 oranges and half a pound of bananas would cost. He was a little stumped at first, then I gently reminded him that he needed to figure out what each orange cost. He was able to take it from there.
We've moved into our study of India now. It's so dreamy with the imagery of mighty gods, lush jungles, and wild animals. So opposite of math!
