Empty Number Lines-Bridging Through Ten #2

By on Nov 22, 2015 in Blog, Blogs about Empty Number Lines | 0 comments


I am working with a group of students on a volunteer basis, and we are working on creating a zoo. In one activity, students had to figure out how much space their animals would need in an enclosure. The students were adding up the space needed for trees, a large rock, a cave, a pond, etc.


One student was trying to figure out what 16 plus 8 was. She thought and thought, and seemed stuck. I asked her, “What is a strategy you could use to figure that out?”


She thought for a moment longer and said, “I could count by twos.”


“Okay, show me,” I said.


She said 16 and counted up by twos keeping track on her fingers. “It’s 24.” 


Many of the students were working on similar problems depending on what they wanted to include in their animal’s enclosure. I wanted to teach the strategy of “bridging through ten”, so I called them all over.


I used the example of 16 plus 8 and asked all the students to solve that problem mentally.  Then the girl who solved it showed us what she did to solve it.


I showed the group her thinking on an ENL like this:


ENL 16 + 8 #1.jpg CROP


Then I asked the rest of the students how they solved it. One boy said, “I added 16 and 5 first because I know that is 21. Then there were 3 left, so I added that and it is 24. I showed that on the ENL:


ENL 16 + 8 #2.jpg CROP


Then I asked another student how he solved it. He said, “I split the 8 in half and got 4 and 4. I added 4 to 16 and got 20. Then I added the other 4 and got 24.” Here’s that strategy on the ENL:


ENL 16 + 8 #3.jpg CROP


We discussed that strategy as “bridging through ten”.


Then I asked them to use that strategy to solve 17 plus 6. After one of the students explained how she did it, I showed her thinking on the ENL:


ENL 17 + 6.jpg CROP


Then I sent them back to work on their projects. A few minutes later, the original girl who counted by twos said, “I used the strategy you just showed us. That worked really well. It was a lot easier and faster.”


I do believe showing the visual model on the empty number line is such a beneficial way to show students thinking. I often hear from students comments like:


“Oh, now I get it.”


“Oh, I see that now.”


“That’s so much easier.”


I started using empty number lines to record student thinking back in 2011. The empty number line has been a powerful visual model to show students’ thinking during mental computation.


To read another one of my blogs about using empty number lines, click here to check out Hero Zero and the Mental Math Mystery


For more information about this topic, click here to read What is an Empty Number Line? through K-5 Math Teaching Resources LLC.  


Our Flip Flop Math products are a great tool to use to help students build the following critical numeracy concepts to help them with their mental math strategies. Click here to check out my Math Path  for combining and partitioning numbers up to twenty:


Math Path for Combining and Partitioning Numbers up to Ten:


Combinations of 5

5 and Some More

Combinations of 10

Doubles to 10

Near Doubles to 10


Math Path for Combining and Partitioning Numbers up to Twenty:

10 and Some More

Doubles to 18

Near Doubles to 18

9 and Some More

Combinations of 20


Click here to check out the Teacher Toolkit for Number Sense to 100 for K-2 numeracy concepts. 


Click here to check out the Multiplication Decks that can be used at a variety of levels, even 1st and 2nd grade using the group and array models for subitizing/strategy practice.  



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