Using the chart paper, draw a square with an area of area 40 units2I circulated around the class and recorded the conversations. I didn't answer any questions but I did repeat, 'it has to be a square' a few times.
I hadn't even asked a question yet and this is what I got in return.
What I heard and what I saw:
Wait, how big is that?
Can we use a calculator?
Does it have to be a square…can it be a rectangle?
I know what it is! ~ (…what does he mean by it?)
But 40 is not….
Is 40 a perfect square!
Points…we have to use points… point 5
6 x 6 = 36.
40 is not a perfect square.
It must be between 6 and 7
What's 40 divided by…
What’s 40 divided by… (not sure how to complete this sentence)
Does it have to be a perfect square?
What can be divided by 40 so that it makes a perfect square?
What number by what number will get us 40…but it has to be the same number.
Does it have to be a square?
No rectangles?…is a rectangle a square?
It has to be times by the same number
(found written on a page)
6.6 x 6.6
7.5 x 7.5
6 x 7 =42
What’s 40 divided by…
Can we do point 5’s
HAS TO BE A SQUARE RIGHT?
Factors of 40
40 is NOT A PERFECT SQUARE!
6 is closest to 36.
Guys, it’s 40 divided by 15
Wait, 40 isn’t a square.
20 x 20 that’s it...no wait.
20 x 20 is not equal to 40...it’s like...400
Let's find something that = 40
Something that multiplies to give 40
What times itself = 40, let’s start with that....
Has to be lower than 6.5
Try multiplying 6.5, 6.8, 6.7
More than 6, because 6 x 6 is 36.
6.3 is too low.
A rectangle is a square
When you say a square what do you mean?
Area is 40 units (2)
Rectangle is a square or a square a rectanlge?
2 of the same...numbers
Something times something....= 40
It needs to be squared
Can we go to decimals
Definitely not 7, no wait, definitely not 6
6 x 6 = 36
6.5 x 6.5
What’s on these sides? (points to the sides of the square)
It’s a decimal point!
8 x 5 = 40
6.3 x 6.3
Some End Results
I also noticed a surprising amount of reluctance at not being exactly at 40 units2. So much so that some groups were paralyzed and did not show any numbers, like this:
And, to be honest, I even saw some of these (despite work being done somewhere on the side.)
And then, after all that, I mentioned square roots.
I feel like my return on investment is very high here.
Which of these student comments stands out for you?
Are there some comments worth noting more than others?