There will surely be a child who says, 'The remainder is 3!' — Summer vacation lesson preparation is about anticipating children's voices
5100 ÷ 600
How would you solve this calculation?
For those who thought, 'Cross out two zeros each, and you get 51 ÷ 6 = 8 remainder 3.'
Actually, this 'remainder 3' is not correct.
And in the second semester, in my classroom too, there will surely be a child
who energetically declares, 'The remainder is 3!'
Right now, I am doing my summer lesson preparation while imagining that moment.
Today, I will show you a little bit of what is on my desk.
During summer vacation, I want to build up as much of a lesson bank as possible
Do you know what teachers do during summer vacation?
Of course, there is professional development.
There is also administrative work.
But for me, the most important job during summer vacation is
preparing lessons for the second semester.
What I am currently planning is division for fourth graders. Division of large numbers with zeros at the end, like 4800 ÷ 600.
To be honest, if I just wanted to teach this, I could do it in five minutes.
'Let's cross out the same number of zeros and calculate. Yes, 48 ÷ 6 = 8' — and that's it.
But is that really okay?
When I face the task of creating a math lesson, I
The fun of the teaching material
The moments where children struggle and think
I especially value these two things.
A child who only learns 'it's easy if you cross out the zeros'
will come to a standstill when asked about the meaning behind it.
And above all, thinking about 'why is it okay to cross them out?' is
the most rewarding part of this teaching material.
Lesson preparation is about anticipating children's comments
There is something I always do in my lesson preparation.
It is to anticipate the children's comments while looking at the teaching material.
'If I present this problem, what will that child say?'
'Where will they stumble?'
'What kind of "incident" will occur?'
I try to imagine the classroom scene as concretely as possible.
Actually, I wasn't able to do this when I was a young teacher.
A single comment from someone changed the way I approach lesson planning.
(I wrote about that story in a recent article)
Now, for the division lessons in the second term.
I am thinking of starting with a game.
It is a game where you create an equation of '□□00 ÷ □00' using number cards,
and the one with the smaller remainder wins.
(This is a powered-up version of the number card game 'Make the Remainder Small!' that I released previously)
As I imagine this game and anticipate the children's remarks—
I have a premonition that a certain 'incident' will occur.
The 'Remainder 3' incident that hasn't happened yet
As the game progresses, there will surely be teams that create equations like this, for example.
5100 ÷ 600
They must verify whether it divides evenly.
Children who have discovered how to cancel out the zeros will likely calculate it like this.
'51 ÷ 6 = 8 remainder 3. Remainder 3! It's small, I might win!'
At this point, if it were the children in my class, someone would probably say this.
'Wait, hold on. Isn't a remainder of 3 a bit strange?'
I believe this sense of discomfort is important.
The calculation method isn't wrong, but something doesn't feel quite right.
This is where the children's time for thinking begins.
This is a situation where you are dividing 5100 yen into groups of 600 yen.
If you distribute 600 yen to 8 people, that's 4800 yen.
What remains is—300 yen. Not 3 yen.
Even if you cancel the zeros to calculate, the quotient '8' does not change.
However, the remainder '3' actually meant 'three 100s'.
Therefore, you must return the zeros you canceled to the remainder, making it '8 remainder 300'.
The child who said 'The remainder is 3!' was not wrong.
They simply followed the equation with the zeros canceled out honestly.
That is precisely why this 'mistake' becomes a perfect entry point
for the whole class to return to the question,
'What did canceling the zeros actually mean?'
Whether the prediction comes true or not
…And that is my 'prediction' so far.
Will I be right?
Or will the children go beyond my expectations?
To be honest, it is most interesting when my predictions are wrong.
Even in the bar graph lesson I published in July,
the children went above and beyond my expectations.
I believe that exhausting all possibilities in curriculum research is not to get it right,
but to broaden the range of how I can accept children's comments.
I will report back on how this lesson went in the second semester.
But if a child appears who says, 'The remainder is 3!'—
I want to cherish that moment not as a failure,
but as a signal that the lesson is coming to life.
