# Empty Number Lines-Bridging Through Ten

Even though I retired last school year, I am still working with students in the schools. I volunteer and also do math clubs. The other day, one former student said, “I thought you retired. Why are you here so much?”

To which I answered, “Because I love working with children!”

I have been working with a group of students on strengthening their basic multiplication facts. One area we worked on was counting by multiples. We were doing an activity, Count Around, where we were counting by 7s and each person in the circle had to say the next number in the sequence.

The first few students quickly counted 7, 14, 21, 28, and then there was a pause. The next student’s hands went under the table and it appeared he was counting on by ones to get the answer. When he answered with 35, I asked him how he figured it out. He told me he counted by ones.

I asked the other students how they figured it out. One student said, “I know 28 plus 2 is 30 and then 5 more is 35.” I immediately pulled out my white board and showed that student's thinking on an empty number line (ENL). We discussed “bridging through 10” or “bridging through multiples of 10”.

We quickly reviewed the counts so far saying 7, 14, 21, 28, 35, and then the next student paused and after a few seconds said 42. In the past, I have noticed him using his fingers to count and using strategies of counting by one. When I asked him how he figured it out, he said, “I tried what you just showed us. We have been talking about that in class. Now I get it. I took 5 from the 7 and added it to 35 and that makes 40. Then I took the 2 left and added that to make 42.” Again I showed his thinking on an ENL.

I started using empty number lines to record student thinking back in 2011. The ENL 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:

Subitizing

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 1^{st} and 2^{nd} grade using the group and array models for subitizing/strategy practice.

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