why does 50+7=57? working with accelerated kindergartners

Working on decomposing and composing numbers into their groups of tens and ones is a key standard in kindergarten. Kinders are expected in Common Core standard K.NBT to work within numbers 11-19, but what about students who are ready for an accelerated pace? Here's a glimpse into a portion of a guided math lesson from our classroom to yours. We are focusing on moving into expressing this standard with equations. This is a follow up from the first two posts in this series,

• Decomposing and Composing Numbers- Part 1 and
• Tips for Working on Decomposing and Composing Numbers in Kindergarten - Part 2

Decomposing and Composing With Accelerated Students

Now, I know that we often call this "place value" as teachers, but really it is number sense because they truly have to understand what these numbers are in quantity, number form, numeral and in comparison to their surrounding numbers (like where they fall on the one hundreds chart for example). It's all intertwined. No matter what number or skill you're working on - it can be connected to it's value in tens and ones.

Why does 50+7=57?

The Question
I am about to revisit the lesson in my math groups to ask my students, "Why does 10+6=16?" Just like when I asked earlier this year, "Why do teens have a 1?" I know that I might face blank stares and we might be headed into murky water discussion.

Maybe.

We've worked intentionally to practice understanding teens and other numbers and their value in tens and ones. Yet, that was with pictures and words like "group of tens and ones." I've found that a big misconception comes into place when transitioning to equations because they are used to seeing or representing 16 as 1 group of ten and 6 ones. What if they were to just take what they've always done and put it into an equation?

The "Stuck" Point

Whether we are working on level or numbers to 100... I apply this question... Will writing 1+6=16? Does that make sense?

Well, of course not... because equations don't have words in them, right? So how else can we show 1 group of ten in order to show that it's ten? If we get stuck, this is usually where it happens - the "stuck" point.

Drawing Out Their Thinking

This is where we will be exploring. I usually ask my students to draw or write about their thinking whenever I pose questions like this. Why draw? Because they have a harder time sometimes verbalizing their thinking.

Give 'em a drawing to talk about and they are much more successful.

Pre-Assessing Groups

Last week I began to pre-assess my two highest math groups on this concept to see if we'd need practice or need to address any misconceptions. With these groups of students {and I'll be totally honest that I have an exceptionally high number of students that have these skills this year in comparison to any other year} I know that their number sense is stronger and can apply the same concept, just deeper. So we're exploring, "Why does 50+7=57?"

I simply asked them to "show their thinking" {they must seriously hear that 12 times a day} and handed them a white board.

Their responses gave me great insight as to where we can work next and that making the transition to equations will be a natural next step for them.

Guided Practice - Small Groups

So no blank stares this year when it came time to approaching equations, though I did find that when we practiced it more in our booklets that we had to work through the common misconception with two students. With enough practice and learning to self check by asking like, "Can 8+1=81?" we are figuring it out and moving on!

Follow Up - Independent Practice

As the natural follow up after I've seen we've made good progress in a skill area I'm sure to put materials into our practice zone. For decomposing and composing using equations I'll be adding our equation cards for our magna doodle boards, I SPY tools into our independent practice zone to improve accuracy and fluency (and I have a game in the works).

Previous Step: Understanding Composing and Composing Part 1
Previous Step: Tips for Composing and Decomposing Part 2

More on Decomposing Numbers

How to Teach Counting by Tens, Then Adding Ones
A Sample Decomposing LessonWhy Does 10+6=16?
Learning Decomposing with Words
Creating Decomposing/Composing Manipulatives

I hope you enjoyed this series as I enjoyed thinking through what I've learned about working with kinders on this standard. Did I mention that I had nooo clue what it even meant when I first read it? We all learn and grow. {wink}

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- Leslie

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