Thank Goodness for Math!

It is much easier to say don’t worry about the time, worry about quality. That is until you see how long it takes some 6th graders to cut paper and glue things into a notebook

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It is much easier to think of how to engage students in meaningful learning, but then you start the lesson and you realize…you still need to get to know your students more.

It is much easier to envision a remake of the classroom in which students are the ones talking the most, and then all you keep hearing is your own voice.

It hasn’t been a bad start. In fact we have done some amazing things. The students have been great: working hard, responding and trying. It is just…not where I want to be.

But…thank goodness for math!

We did our first visual pattern during our first full week from Lesson 1-3 of our CPM Book.  

Students thought, processed, were encouraged to use color to look for how the pattern was growing and then we shared their ideas.

“I saw boxes. The first shape has 1 box. the 2nd figure has 2 boxes. the 3rd figure has 3 boxes.”

photo 3-22

I saw the pattern growing because they added 1 dot to the middle of the shape and 2 on the top right and 2 on the top left.”

“I saw the pattern growing by adding 5 to each one.”

photo 1-30

“They look like backwards Cs”, said a student after I circle the 5 dots the student had pointed to.

We started seeing Cs and backward Cs. Seeing the 5 dots that were added to the previous figure in different places.

“But the first figure has 8.” said one student.

Then…” I see that there are the same number of boxes as the number of the figure.” says one student.

Yes! Somebody saw the relationship between the figure and dots. Best part, it was a student that doesn’t typically have all the answers.

“Wait, look. The first figure has a C of 5 dots too! Plus 3 extra dots.”

photo 5-5

” Wait, there are the same number of Cs as the number of the figure.”

So then, I helped them write what they said algebraically. So, what is the same in all the figures? I asked

“3 dots”

What do we add to the 3?

“A C”

“5 dots”

“the figure number times 5.”

photo 2-30

Ok, so figure 2 is 3 +  2 times 5. and Figure 3 is 3 + 3 times 5. So what would Figure x be? ” 3 + x times 5″

We test it. Then we write an equation for the first way of seeing the pattern. 5 (x-1) plus the original 8. How can they both be true? We review the distributive property using area models and see that 5(x-1) + 8 is equal to 5x -5 +8 and that is equal to 5x + 3 which is equal to 3 + 5x

photo 4-9

That was our Warm Up! Ok, it took the entire hour. Should I have spent all that time? Did they all understand? I’m sure not. Did a large group of them? Yes. Did they all see a pattern and see some type of growth? Yes! Everyone had success.

Were there things I could have done better? Umm….yes! I hadn’t thought about how I would record everything and the space I needed, soI was writing on 5 different pieces of paper and drawing each figure. Waste of time!!!!

But, thank goodness for week 2! I had my board planned, pre-drew three sets with space underneath each for space to write the equation. I had multiple colors ready and had thought about how I would circle or notate when students shared their strategies. What was the result?

photostars

Understanding! Lesson learned…plan your board! Now I just have to teach them what the equal sign means!  Stay tuned for that one!

One thought on “Thank Goodness for Math!

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