I was asked to come in and work with small groups (4-5 students) in Kindergarten today using ten-frames. The teacher wanted students to unitize by 5, 10, and 15, counting on the rest by ones. For example, if I asked a student, “How many do you see? How do you see them?”, she wanted the students to understand that you could find the value in a variety of ways. Here are a few of the anticipated answers she wants them to give by the end of the year:

- I counted them all. One, two, …twelve, thirteen, fourteen (Level 1)
- I saw two- 5’s, so 5, 10, 11, 12, 13, 14 (Level 2)
- I saw a ten, so 10, 11, 12, 13, 14 (Level 2)
- I saw 5’s and 1 missing. 5, 10, 15, (counting backwards) 14 (Level 3)

I had a deck of ten- and double ten-frame cards, so I decided to do some “quick shows”. I would show a card to the kids for about 5 seconds, and they had to ‘think’ about their value (versus just shouting out the number). We rotated who gave the value first, but every child had to give the value they thought was on the card. I chose a** different** student to explain how they got the value, then gave every other student a chance to share their thinking. We did this for about 15 minutes per group of 4-5 students.

Here are our ah-ha’s:

- Out of the 4 groups, only one group stayed within the single 10-frame. I was getting answers from this group that were bigger than 10 every time. For example, when I showed them a card with 8 dots, one said 8, one said 12, and the other two were still counting by ones. I quickly drew a double (or triple) 10-frame and grabbed some counters (plastic circle thingies) and would show them their answer, then the original card. That worked for all but one student. For him, I kept on the table the card with the ten-frame filled in, then did the quick show. That clicked for today, but I need to do some hands-on work with this group. I also need to go back to a 5-frame and really focus on 5+ values before moving beyond 10.
- Students needed to be convinced that the two cards below each showed a value of 5. Great for starting the discussion about the commutative property! We rotated the card over and over until someone said,
*“It is just the same thing! You didn’t put more on or take any off. Geez!”*

- The sequencing of the quick show was instrumental in students building strategies beyond counting one-by-one. The order that seemed to work the best today was as follows: 3, 5, 5 (again, upside down), 4 (to see it was 1 less than 5), 6, 8, 10, 9, 11. Notice we kept them seeing 1 more/less so they could use that strategy as well.
- For the groups that could “just see” the ten-frame, I worked up to 20. Here is the order we used with those groups: 3, 5, 5 (upside down), 8, 10, 12, 15, 14, 20, 18. 18 was tough (see the number of dots), as students really needed to push to 5’s versus counting 10 then by ones.
- One group finished about 5 minutes early, so we played war. That way, they each had a different card and had to tell me their value before determining who had the most dots.
**This was interesting, as they had the cards to touch and many reverted back to one-to-one counting.**We will need to think about that for next time.

What I loved about this activity was that I had 15 solid minutes to informally assess each child. I heard what they understood and where they struggled. I was able to note for the teacher which cards each child got quickly, and which he/she reverted back to counting by ones (or guessed). Every child was engaged and had to listen to their friends as each shared out their strategy. And most important to me, **every child left my group smiling**, asking when I was coming back to do more “quick thinking”.

For large ten-frame cards: https://lrt.ednet.ns.ca/PD/BLM/pdf_files/five_and_ten_frames/ten_frames_large_with_dots.pdf

For double ten-frame cards: We made them by cutting/pasting two ten-frames together. I am sure you can buy the cards, but this was cheapest for us.

Thanks for sharing the number strings you used. Found it a really helpful connection as read about your take-always and next steps.

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