Sunday, March 27, 2022

Trouble with Times

In Waldorf schools, all four mathematics operations are introduced at once in First Grade: addition, subtraction, multiplication, and division.

Addition and subtraction are very intuitive for children; however, some students have a hard time with "times" when they first encounter it.

You can say, "Here are 12 gems. Each gem is a cabbage. How can the farmer plant his garden so that each row has the same number of cabbages in it?" and that is fairly intuitive. And, in truth, that's actually a division problem. You are starting with the whole and sharing it out fairly. When you get to the phrasing "make three gems four times" is when it becomes confusing.

When someone says to you, "three gems four times," you hear two numbers. 3. 4. If you don't understand multiplication, you get stumped. Which one of these numbers am I supposed to make? So you pick the first one the teacher says (which seems safest) and you make a row of three gems and you stop. You have no idea what to do with that second number.

Four is not the number of gems. Four is the number of groups.

You're doing the same thing over and over. And you need to know how many times. So I've been thinking about different ways to get children used to this terminology. I think it's useful to relate it to movements. Can we go from "clap your hands six times" and "pat your head six times" and "run around the tree six times" to "make two gems six times?"

What if you used glass gems (or translucent counters or water beads) on the light table (to keep it fun and interesting) and worked with them in groups instead of rows of cabbages in a garden?

They can be fish that swim in the sea and when the groups get too big the fish become worried they will lose someone, so they make a rule to limit the size of the groups. Make three groups of four fish. Make two groups of eight fish. Make seven groups of two fish.

If your child needs the groups to have firm boundaries, you could lay a piece of paper on the light table and draw circles on it, or you can use something like the rings from canning jars.

You could also let your child trace several circles on transparency film and then overlay them onto construction paper. You could draw on the construction paper, too, but the transparency film would last longer and be reusable (if you will be homeschooling multiple children for first grade).

Or buy Swedish fish and group them (and then eat them)!

You could also work with the idea of groups with bowls, baskets, etc. on your living room floor. Sort pinecones or acorns into them. If you are outside at a stump playground, put the items on the tree stumps.

You can really use almost any nature treasure (shells) or craft supply (popsicle sticks, peg dolls) or art supply (crayons) that you have on hand. You can use stuffed animals and lay down playsilks on the floor to be their picnic blankets...

wooden animals fit well on handkerchief silks

Or take apart your sofa and use the sofa cushions... pretend they are tents and the animals are going camping. Can you set up four tents with two animals apiece?

If your child loves stickers, you can get index cards and scatter them around the floor and let your child stick a certain number of stickers on each. You could also create a bunch of index cards with stickers on them in advance, put them in a basket, and then quiz your child. Can you find and lay down the cards to go with "4 groups of 3 stickers" and/or "3 stickers 4 times"?

I think it would be good to go from something like that and circle back around to an array. Once you know what multiplication is talking about, can you see the groups even when they are all pushed together? Oh, aha! Each row (or column) is a group!

If your child struggled with the concept of times and you have other suggestions, please share them!

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