I recently was working with a first grade teacher meeting with a student who was struggling with recognizing numbers on the 100 rack when flashed on Dreambox (see picture). While the teacher was working with her, it became apparent that the tool was not automatic for her in subitizing numbers to ten. When she was flashed a two-digit number, she had no idea what to pay attention to in the few seconds she had to look at the image. She was not seeing the structure that the rack provides. It became apparent that she needed some strategies to apply structure and meaning to the tool in order to be successful at subitizing large numbers.
I recently ordered 100 racks for teachers to use in small group with students. The teacher pulled that out and was working with her to build the number that she saw.
I thought we might need to pull her back to the 20 rack and work on showing numbers to 10 with one pull, but I thought we would stay with the 100 rack for now and do the same. When she started to pull over the beads a few at a time. I asked her to stop and think of what 6 might look like? What did she know about the beads that could help her? She wasn’t sure how they could help, but when I asked her how many red beads were on top and how many white beads, she said 5 of each. I then said, what do you think 6 might look like? She quickly pulled over 6 beads.
We tried a few more numbers within 10 and then I asked her to show me 16. She stared blankly at me for a minute and then pulled over 6 and stopped. I said, Hmm, let’s think about what the number 16 looks like, can you find it on the number line for me? She pointed to it and I said, you’re right! There are 6, but what does the one tell us? She said one ten. I said now show me that one ten very quickly on the rekenrek. She did and then I said and what would 6 more look like. She showed me and looked at me for praise:) I said, hmm, what is 10 and 6 is that 16? She looked puzzled and said no.
I pulled out the place value arrows. I said find the arrow that shows 10, now find the arrow that shows 6. Slide them together. What number is that? She said 16 with a big grin on her face. I asked, were you right? She said yes:)
I asked if she wanted to try some more and she did! We worked on several numbers in the teens and then I asked her if she wanted a challenge. She nodded. She was able to show me several numbers to 100 with the rekenrek and place value arrows. I started by having her pull over numbers in the 20’s and she was very quickly able to do so. We continued with a few more numbers while also making the numbers with place value arrows.
We had a brief discussion about why she thought the colors on the rack might change halfway down. She said because the top is 5 tens or fifty. I asked her why they might change at fifty. She said so we can see how many tens.
This student was missing just a few pieces that kept her from connecting her knowledge to the setting on the math rack. With a few simple questions and the right tools, she was able to be confident and successful working with 2-digit numbers.
Scaffolding math instruction can be very challenging for teachers. Not because they aren’t great teachers, but because they lack the knowledge of early numeracy acquisition and the tools for connecting concepts. In my next blog post, I will share some of my favorite math tools and manipulatives that I think every teacher should use regularly to scaffold instruction.
So why is subitizing important for place value concepts? Students need these opportunities in order to visualize numbers. This is especially important as students start to add a 2-digit number plus a multiple of ten and as they add a 2-digit number and a 1-digit number. If a student is able to visualize a number (67) on the math rack (see picture) it becomes very easy for them to visualize how many more to get to the next decade (3 are missing) or to 100 (33 are missing). This leads to more advanced addition strategies by decomposing numbers instead of relying on finger counting and number lines to count on.
For example if I want to add 67 + 8, I know that 3 more will get me to 70, and then I can add the left over 5 to get to 75. Likewise, If I visualize 67 and I want to add 20, I simply imagine what two more rows of ten might look like.
Dreambox offers great teacher tools that are free for instructional use. These can be used
for students to gain practice subitizing numbers to 10, 20 and 100. If you do not have access to rekenreks, they are very inexpensive and easy to make using pony beads, foam, and pipe cleaners.