9-15-06

Bring 8 glue sticks and 2 baskets to the rug.

“One of the jobs teacher have at the beginning of the year, when they get ready for school to start, is to organize the supplies, things like pencils, glue sticks, scissors, etc. Here are some glue sticks to organize. How many glue sticks are there? Show me on your fingers and try not to look at each other’s fingers.”

Put 4 glue sticks in each basket, lined up so the kids can still see each individual glue-stick (not in a clump).

“How many //groups// of glue sticks are there? How many baskets with glue sticks in them?” Repeat the questions like the day before, alternating between how many glue sticks there are and how many groups of glue sticks.

Other things may come up, such as 4 + 4 = 8, in which case I mentioned that yes, that is a //double//, and doubles are very important. I also modeled writing a few equations on the board, which some children will follow and others won’t, and I wrote both addition and subtraction equations on the board because so often subtraction is overlooked.

Then bring out 13 pencils and 2 cups. Lie the pencils down in a big pile on the rug (so they can’t be counted).

“Let’s organize the pencils now. Who can make an //estimate// of how many pencils there are? Who can make a good guess of how many pencils there are?” I write the estimates on the board with the child’s name next to the them.

“Let’s put the pencils in groups. Who can come put 5 pencils in one cup? Now who can come put 5 pencils in the other cup?” I also draw the cups with 5 pencils in each one on the board, and 3 extras outside the cups. “Can we make another group of pencils? Do we have enough pencils to fill another cup if each cup has 5 pencils in it?” Children answer no.

“How many pencils are there?” Discuss different ways to count: by ones, by fives to ten and then by ones, or some children just know that 5 +5 = 10 and then they count on 3 more. Count all the ways and make sure you always get the same answer. Look back at the estimates to see who was close.

“How many groups of pencils are there? Remember these ones on the floor are not in a group, they are extras. How many groups of 5 pencils are there? How many cups with pencils in them are there?”

“Now, how many //extras// are there? How many pencils are there that don’t fit in a group?”

Again, repeat the questions, alternating between how many pencils, how many groups, and how many extras.

It might be a good idea to begin a chart that has heading of Total, Groups, Extras that you can fill in as you continue to do problems like these. Teach the games Staircases and Double Compare. Children with less experience comparing numbers should do Staircases; those who have a solid understanding of number under 12 don’t need to do it and can practice Double Compare. When you demonstrate Double Compare, count on, and see if they try it out when they play, instead of counting all.