And the number of baby food containers we have in the Trees Class is...
(drum roll please)
... Just wait.
It took a while to get there.
It took a while to get there.
While it seems that counting baby food cereal would be simple
and straightforward, it is quite a bit more complicated than one
might think, especially if you are a preschooler.
One of the things that we hope for children is that when they
encounter a “knot” or difficulty, that they realize it, name it, and
then begin to work through it. When we puzzle through and work hard
to figure something out, it can help us to learn more. Counting
our many boxes of baby cereal turned out to be quite a big knot!
It certainly provided many, many challenges to work through!
One of the things that we hope for children is that when they
encounter a “knot” or difficulty, that they realize it, name it, and
then begin to work through it. When we puzzle through and work hard
to figure something out, it can help us to learn more. Counting
our many boxes of baby cereal turned out to be quite a big knot!
It certainly provided many, many challenges to work through!
And that's the best kind of work...
First, we began talking and thinking about how to tackle the
task at hand. How could we possibly count all of these boxes?
It was so many! But children quickly began to think of
strategies for counting. First, children thought that it would be
a good idea to sort the boxes by color.
They had had some prior experience sorting...
task at hand. How could we possibly count all of these boxes?
It was so many! But children quickly began to think of
strategies for counting. First, children thought that it would be
a good idea to sort the boxes by color.
They had had some prior experience sorting...
 |
Sorting buttons by size
Max thought that if we sorted everything by color, we could count each color, and “mix the numbers together to see how much there are all together.”
 |
| Sorting by color |
A small group of older children began to really work on puzzling
through this problem, and though everyone helped in some
way and all children heard about the ideas they were
developing, these older children took the lead and worked on it
throughout the counting process.
 |
| Sorting by color and seeing how many blue we have! |
They knew quickly that “blue is the most.” (We had more blue
than any of the other colors.) But as Max pointed out, “We
still don’t know how many blues.” As they were trying to count,
the children realized that it was really hard to keep track of
which ones had been counted and which ones were still left
to count, so Hugh suggested that each box get tipped over
as it was counted so they could keep track of which ones had
been counted.
This became a strategy that worked very well for all children
(and it was fun!).
than any of the other colors.) But as Max pointed out, “We
still don’t know how many blues.” As they were trying to count,
the children realized that it was really hard to keep track of
which ones had been counted and which ones were still left
to count, so Hugh suggested that each box get tipped over
as it was counted so they could keep track of which ones had
been counted.
This became a strategy that worked very well for all children
(and it was fun!).
 |
| Using Hugh's tipping strategy |
The children also realized that once a group of boxes was
counted, it was hard to remember how many total of each
color they had counted. Another child suggested that after
counting each color, we record how many they had counted.
A fantastic idea! “We need your help,” one child said to me.
(It is great to realize when you need help.) And so I wrote down
the count for each color.
counted, it was hard to remember how many total of each
color they had counted. Another child suggested that after
counting each color, we record how many they had counted.
A fantastic idea! “We need your help,” one child said to me.
(It is great to realize when you need help.) And so I wrote down
the count for each color.
 |
| Counting colors |
Green proved to be a tricky color because there was more of it
than most of the other colors. As children worked to count the
green containers, some of them noticed that as the numbers got
into the teens, sometimes a child would skip a number or two
(very typical for pre-schooler’s development to get confused
when counting into the teens). They began observing and
listening to each other and helped each other notice when a
number got missed.
than most of the other colors. As children worked to count the
green containers, some of them noticed that as the numbers got
into the teens, sometimes a child would skip a number or two
(very typical for pre-schooler’s development to get confused
when counting into the teens). They began observing and
listening to each other and helped each other notice when a
number got missed.
It was a great discovery to realize that sometimes we
run into difficulty or make mistakes, and that is okay. When we
are able to recognize that we are experiencing a problem, that is
huge!
This laser-focuses on a wonderful moment of metacognition
(or, thinking about thinking) that happens with many children
at this age:
It is difficult to solve a problem if you don’t know you are
having one!
 |
| So many green to count! |
Another major discovery was realizing that often, you need to count things more than once to make sure you have the right answer. They kept getting different results when they tried to count the green boxes. But once they landed on the number 15 three times children knew that we had the correct number of greens. The children found it astounding that they had to count the green containers 5 times to finally know how many there were!
Then it came time to try to count the blue boxes. What a task!
Again, children tried many different ways of lining them up
(in a circle, in a line, all over the place, etc.) They were
continuing to try their hands at using different strategies.
With the blue boxes, again they discovered that it was very
hard to keep track and when numbers got bigger it was really tricky!
In the course of working through the counting, children realized
that it is easier to count smaller groups of things than it is to
count bigger groups...
This led them to group the blue boxes in groups of 10s!
Again, children tried many different ways of lining them up
(in a circle, in a line, all over the place, etc.) They were
continuing to try their hands at using different strategies.
With the blue boxes, again they discovered that it was very
hard to keep track and when numbers got bigger it was really tricky!
In the course of working through the counting, children realized
that it is easier to count smaller groups of things than it is to
count bigger groups...
This led them to group the blue boxes in groups of 10s!
 |
| Counting a group of 10 |
Once they were able to see the groups of tens, many of them
found that they could visually see and know right away that
there were 10 containers if the containers were sorted into two
rows of 5s (“Because I know that 5 and 5 is 10!”).
found that they could visually see and know right away that
there were 10 containers if the containers were sorted into two
rows of 5s (“Because I know that 5 and 5 is 10!”).
 |
| Two groups of 5 make 10! |
It was a great discovery to understand that sometimes you have
to count each item, but sometimes you can know how many
objects there are, simply by looking; having things grouped or
organized (into groups of 5s or 2s) can help with visual
recognition of quantities. Max told us, “Sometimes I look for a
while and I know how many there are. But if I don’t know the
number, then I know that I have to count them.”
Grouping in other ways was an idea that children used as the
process continued. Henry suggested that we give each child in
the class the same number of blue boxes of cereal and then we
could figure out how many there are all together. So, we passed
out blue cereal and each person wound up with 3 boxes.
Even though we had done some sorting, grouping and counting,
we still didn’t know how many blue boxes we had or how many we had in total! What complicated
work!
process continued. Henry suggested that we give each child in
the class the same number of blue boxes of cereal and then we
could figure out how many there are all together. So, we passed
out blue cereal and each person wound up with 3 boxes.
Even though we had done some sorting, grouping and counting,
we still didn’t know how many blue boxes we had or how many we had in total! What complicated
work!
 |
| We have all these groups, but how many all together? |
Hugh referred to this as "The Number Problem". With a huge
swish of his arms in front of him, he said, "We need to
de-number the problem!"
swish of his arms in front of him, he said, "We need to
de-number the problem!"
Along the way, a few other strategies that children suggested
were:
then the great count of blue cereal began.
were:
- to use tally marks
- to ask someone who knows more about bigger numbers for help
- to use a card with each number written on it and put the card next to the cereal container as it was counted.
then the great count of blue cereal began.
Children were organized and orderly in taking each number off
the 100s chart and placing it on each cereal box. Some
children noticed when the numbers got out of order and
changed them. We practiced counting while looking at the
numbers on the boxes and saw that we got to 42! We had 42
total blue cereal boxes!
the 100s chart and placing it on each cereal box. Some
children noticed when the numbers got out of order and
changed them. We practiced counting while looking at the
numbers on the boxes and saw that we got to 42! We had 42
total blue cereal boxes!
 |
| Using written numbers to help with the count. |
Next, they lined up all of the other groups that they had counted
and kept going.
And going ...
And going ...
In the end, the numbers showed that there were ...
78 boxes of cereal!
Very exciting!
 |
| Working together to put down numbers and count everything! |
The children were very excited about this ... but ...
They had learned (through counting the green boxes) that it is
really important to check your answers more than once.
And so started the final stage of our counting. They invited an
expert: Josh, our middle school intern. He was pleased to be
summoned to come help with the process. And they thought
he might have some other ways to count. He’s coming, they said,
“To re-count. Just to make sure.”
They had learned (through counting the green boxes) that it is
really important to check your answers more than once.
And so started the final stage of our counting. They invited an
expert: Josh, our middle school intern. He was pleased to be
summoned to come help with the process. And they thought
he might have some other ways to count. He’s coming, they said,
“To re-count. Just to make sure.”
Josh listened carefully to the children's information. Then he used the information they gathered when each child had been given an equal number of blue boxes. He explained how multiplication is counting groups and he showed them what this looks like (they had counted 14 groups of 3). Josh confirmed that there were in fact 42 blue boxes when he checked it using multiplication.
 |
| Counting groups of 3 (multiplication!). |
He also took the information that the children had already gathered from their counting of all of the groups of different colors and he showed them how to do addition by putting all of those numbers together.
 |
| Josh showing how to use addition. |
And guess what? Josh’s addition-work-re-count got to a total of ...
Our counting project is finally finished! This was a project of
problem-solving, flexible thinking, team-work and perseverance!
When the older children presented their findings, the rest of the children cheered. There
were many questions and comments about counting in groups
and about the 100s chart from other children. Together they
reflected, not only on their counting but all the good work they
each had done to earn their baby food.
It's not often you can quantify exactly how much good you have
done. But when you can (twice, just to be sure) it feels very, very
good.
78 boxes of cereal! So exciting!
 |
We de-numbered the problem!
problem-solving, flexible thinking, team-work and perseverance!
When the older children presented their findings, the rest of the children cheered. There
were many questions and comments about counting in groups
and about the 100s chart from other children. Together they
reflected, not only on their counting but all the good work they
each had done to earn their baby food.
It's not often you can quantify exactly how much good you have
done. But when you can (twice, just to be sure) it feels very, very
good.
