Why do the Rules Make Sense?

This is a long overdue blog post! This year has gotten off to a great start, but like any other teacher it's been so busy! My energy is lacking due to some nasty germs invading my body, but I'm too excited to share this post to care!

Let me be honest, I have never really loved teaching math. I struggled with math as a child and still find certain mathematical concepts challenging, but this year has changed my mathematical mindset.

Here's why.

When I was in school, I was taught mathematical rules, such as how to borrow in subtraction, carrying in addition, looking at the digit before when rounding.  I used these rules to accurately, sometimes painstakingly, solve mathematical problems. But I never knew WHY the rule worked, why it made sense.

This year, my students are learning WHY certain mathematical rules make sense and HOW to represent these rules in different ways - and so am I!

Today was a particularly remarkable day in math class because I observed students representing 'carrying' using their place value charts.

We began by reviewing our objective (above) and exploring our Launch together in table groups. 

At this point, I did not tell them what a tape diagram was, I just asked them to use the figure below when they solved. I noticed most students using the  3 sections for the 3 numbers, those smarties!

As students worked collaboratively on the problems, I circulated  and observed some students rounding to the nearest thousand, and some to nearest ten thousand. When we came back together to share out, I had two students who rounded to different place value model their work. 

Students came to a concensus that rounding to the nearest thousand gave a more accurate estimation!

Next, we read the addition statement together and represented it on a tape diagram, labeling our unknown with the letter 'w'

Then we modeled it on our place value chart - here's where the magic started to happen. 

As we were adding up our number disks, we realized that there were more than 10 in our tens place. To represent the rule of carrying, we bundled a group of ten tens and drew an arrow to make one hundreds. Here is where students could visually make the connection between carrying when adding multidigit numbers! 

They had some practice with partners, and I was really impressed - check out this awesome, smart mathematical thinking!

Tomorrow, I'm excited to have my students dig deeper into word problems using tape diagrams!

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