Much of primary math is about establishing benchmarks of 5 and 10, but have you ever stopped to wonder why those are good numbers to use? Here are a few reasons:
Benchmarks of 5:
We have 5 fingers (if we count the thumb!) on each hand, so a hand-y (ha!) benchmark to start with is the number 5. For young children, it is concrete, visual and accessible, thus making it a good starting point. Children as young as 2 or 3 can easily recognize one hand as 5 fingers, thus showing their ability to subitize 5 in that arrangement.
Benchmarks of 10:
Benchmarks of 10 is a natural progression (two hands); but there is a more important reason for why we want to establish 10 as an anchor. Our place value system is a base 10 system. That means every time we have a group of 10, we regroup it as 1 of the next place value. As a result, encouraging students to have 10 as a benchmark is crucial to their understanding of the place value system. And where does it start? Pre-school!
Establishing anchors of 5 and 10:
There are 3 great manipulatives you should use:
- Fingers: first and foremost fingers!
- 5 and 10 frames. Start with 5 frames and once students are comfortable with them, move to 10 frames. Once students are using 10 frames fluently, there is no need to go back to 5 frames. You will know they are ready when they recognize that a 10 frame is two 5-frames put together.
- The Rekenrek: this tool is designed to help students subitize groups of 5. It is a concrete manipulative with 5 white beads next to 5 red beads. This makes it easy to see benchmarks of 5, as well as to begin seeing how many more or less to make 5 or 10. To learn more about the rekenrek, see my earlier post here.
Oliver is 4 years old (pre-school) and to introduce him to 5 and 10 frames we played a game: ‘About how many?’. The purpose of this game is to teach estimation; establish the benchmarks of 1, 5 and 10; practice subitizing and finally to work on 1:1 correspondence. Wow! Pretty impressive that one game can do all that!
In week one, Oliver had never seen 5 or 10 frames so we introduced this manipulative and the benchmarks of 5 and 10. I found it fascinating that no matter how many objects were hiding, Oliver would never estimate there were 10. Perhaps he is not developmentally ready to use 10 as a benchmark, or perhaps he just needs more practice.
By week two, Oliver knew exactly what a 5 and 10 frame were. He easily identified the benchmarks of 5 and 10 using all three manipulatives (fingers, frames and a rekenrek). He still had trouble estimating something that was close to 10, although he did guess 10 if it was a lot over 10. When I did this lesson with kindergarten, they were much better at guessing if something was closer to 10.
For week three, I would like to change the game to hiding 10 frames that are filled out with different numbers (like 6) and then seeing if he can recognize it as being closer to 5 or 10. If he did, this would show he is beginning to understand the benchmarks of 5 and 10 and can demonstrate his knowledge with 10 frames. It would also indicate improvement in his estimation skills.
How can I help Oliver solidify his learning? Practice, practice, practice! More work with fingers, 10 frames and the rekenrek will help him begin to recognize the difference between a group of 5 and a group of 10. And playing ‘About how many’ is a fun way to do it!
What things do you do to reinforce benchmarks of 5 or 10? Share them in the comments section below!