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Place Value

We continued on playing games representing placement value. I introduced on day three, a carnival style game that I took from a wonderful book called “Games for Math” by Peggy Kaye. Using 3 dixie cups, I numbered each with 1, 10 and 100. Evan got 10 beans to play. The idea is to try and get the highest score by throwing beans into the cups. After throwing all 10 beans, he got a second try with those that did not make their target. Afterwards he had to tally his score onto the tree in the right order. We played for 5 rounds. Then he added up his score. This evidently lead to carrying numbers into the tens and hundreds compartment. He seem to get it right but later this past week I have noticed some gaps in his understanding.

So far everything that I was showing him seem to be well understood until I came to carrying. It was not part of this particular block but I felt that Evan seemed to be progressing in leaps and bounds so I thought that challenging him couldn’t hurt.

I had to understand what was triggering his confusion. Instead of using the sticks and pine cones as place holders, I followed Donna’s advice about using small boxes. Having no small boxes on hand but hundreds of dixie cups, I used the latter. In the first compartment of ‘ones’ I placed seeds. At first, I kept the total below 10. In the ‘tens’ compartment I placed 10 seeds in each cup and kept the number of cups below 10 yet again, in order to keep it simple for now. So far, there were no confusion. I then went on to explain that each compartment can hold no more then 9 of its kind, whether be seeds or cups.

While placing a higher number of seeds into the ‘ones’ compartment, say 15. I asked Evan to count them and make as many groups of ten that he could make. He then placed the group of ten into a cup. I then ask him to carry the cup into the tens compartment to be added to the other five cups that were already there. Adding was simple once this step was accomplished, but I was not convinced that he really understood why he was carrying the cup into the tens column. At this point I felt it was time to let it simmer over the week-end before coming back to it by Monday morning. If by then he still did not understand the reasoning then we will shelve it for a few months before coming back to it.

After contemplation, I decided on shelving the lesson on carrying and borrowing for several months before coming back to it. It’s important to note that any newly acquired skill takes time to ripen. You’ll notice this very clearly by using block lead learning. One of the fundamentals of Waldorf education is the individual blocks tailoring to one topic at a time for a few weeks, putting it aside and coming back to it 6 to 8 wks. later. Magic happens when the topic is left dormant for a time, a child having difficulty understanding it in prior circumstances has ‘ripened’ his cognitive skills when you revisit it later on.

This is exactly what happened with Evan. Something was missing in his understanding why he had to carry cups over. I tried different formats for him to understand, yet it did not seem to help. He was simply immature on the subject. Just a few weeks back in late April, I reintroduced him to the squirrels, he dreaded it. (clearly I had pushed a little too much!) But this time instead of using beans and cups, I decided to go the monetary route. I did not approach the subject this way yet only because of the third grade block on money. I wanted to keep it fresh and interesting for next year. But since we were coming to the end of second grade, I figured a sneak peak couldn’t hurt him. Using the same numbered cups as before; 1-10-100, I placed piles of pennies, dimes and loonies (Canadian dollar for those who don’t know the term) in front of them. I gave him a small chalk board with an addition equation to solve. Before he could solve it on the board, I wanted him to use the money manipulatives. It was instantaneous, I could almost see the light bulb turn on. Next I gave him a subtraction equation to solve, this time he had to place the top number into the cups and subtract from it. Sure enough, he got it right. So I was curious to see if it was my new approach with money that clarified his understanding, so I went back to beans and cups. It wasn’t the case, he was capable of accomplishing any equation I set up for him, whether it be with beans or money.

He even replied “this is so easy, it’s for babies!” Incredible…. isn’t it?

5 Responses to Place Value

  1. Kimberly Moore

    Beautiful! I also started from scratch to help my children learn the four processes. I ended up taking it all pretty far by creating a little program called “arithmetic village”. Your pictures are stunning and your children lucky to have a dedicated teacher. Blessings, Kimberly

    • Stephanie

      I’d love to hear about your Arithmetic village, sounds fun and creative. Thank you for your kind words, I love the lessons we do, normally inspired by many other wonderfully creative people. It’s wonderful to be able to share what we do with people around the earth, it makes our world seem more interconnected.

  2. tara jansen

    Thanks so much Stephanie!
    You are an inspiration. I am going to go make one the best I can right now! I hope things are going your way in the New Year!

  3. tara jansen

    I love this game!!!!! Do you sell it? How did you make it. I absolutely need one!


    • Stephanie

      Thank you Tara! I don’t sell it but you can make it easily with household items around the house. I drew the tree with the three compartments and plastified it. Using a deck of cards or dice, you can add a series of numbers. Starting by just counting out a double or triple digit number on to the tree with beans. To selecting several numeral cards to add up vertical style which will lead to learning about placement value. The squirrels were cut out of pine and painted in watercolour paint. To make the carnival style game all you would need is three dixie cups numbered 1,10 and100 with a handful of beans to throw into the cups. Have fun!

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