# Counting without Seeing (Age 5)

## The Activities

1. Topic: Zero, Multiplication, Addition. Book: A Place for Zero by Lopresti. This book covers the additive and multiplicative properties of zero in a very flavorful and engaging way.
2. Topic: Counting. We used the Base 10 Blocks to count to 100 by 10s, and 1000 by 100s and 10s.
3. Topic: Search, Pan Balances, Inference. I showed the kids a box that contained some number of plastic leaves.  I asked them to figure out how many leaves were in the box without opening the box.  I gave them a pan balance, and an identical, empty box.

## How did it go?

There were only 3 kids at circle this week due to Thanksgiving travel.  It was a really good, focused circle.  All three kids paid attention and took turns very nicely.

#### A Place for Zero

The kids really enjoyed this book, about poor Zero who has no place in numberland. One kid predicted that Zero would be paired with a One to make 10 (which turned out to be true).

The book first shows how any number + Zero = the number.  Next Zero headed off to multiplication land to try to multiply himself.  At this point, I paused the book, and used Base 10 Blocks to teach the kids about multiplication.  Two of the kids had not done multiplication before, but I explained that 2 * 3 means you make 2 groups with 3 items in each group, and then count how much you have.

We did a couple small problems like that, and then I asked how much would 0 * 7 be? Two kids thought it should be 7.  My son said it would be 0.  I said, well, if we make Zero groups each with seven cubes, how may cubes do we have?  The kids agreed that would probably be zero, but were not super convinced.  I figured that 7 * 0 was probably easier to explain.

I said, “If I give you 7 bags which each have 0 pieces of candy in them, how much candy did you get?” All three kids immediately saw that they would have no candy.  After circle, I quizzed one girl, in front of her mother: “What’s 1,000,000 times 0?” and she instantly said “0”, and went on to explain that 1 million bags, each with no candy, makes 0 pieces of candy. 🙂

After we got a bit of intuition about multiplication, I finished the books, and the kids were all excited to see that 0 multiplied by any number made 0.  They also loved seeing 0 and 1 pair up to make 10 and lots of other big numbers.

#### Base 10 Blocks

After the book, I had the kids try out some big addition problems, like 22 + 33, using base 10 blocks.  First you make 22 by getting two 10-bars, and 2 unit cubes.  Then make 33, and combine the two piles and count the result.  All three kids were able to do this.

My son looooves addition and multiplication, so these problems were too easy for him, but he was thankfully very patient during this activity.  He begged the other kids to give him a hard problem, and the hardest one they thought of was 100 – 2.  My son said 98, and we all checked that he was right by counting 2 higher than 98.

Next we used 100 squares to count by 100 to 1000.  Then we used 10 bars to count by 10s to 1000. The kids each made 100 out of 10 bars, and I carefully added it to our stack, so in the end we had a block of 10 bars the same size and shape as the 1000 cube.

#### Counting Without Seeing

Next I showed the kids the pan balance, and said they should use it to figure out how many plastic leaves were in a treasure box (without opening it). If they could get it right, they would each earn a treasure.

They quickly got the idea of putting a handful of leaves in the empty box and weighing it vs the treasure box. They were very good at interpreting the result, knowing that if their box weighed more than the treasure box, then they should take out some leaves.  They even understood that they should only adjust it by a few leaves if the boxes were close in weight.

At one point, it looked like the boxes weighed the same, but the kids wanted to test to make sure, so they first added one leaf (too heavy), then took away two leaves (too light), then added back a leaf to get a match.

To find our answer, we opened up the kids’ box and made piles with 5 leaves in each. We had 41 leaves.  We then checked the treasure box, and found 41!! Everyone cheered!