I typically teach grade 5 and 6, so when I helped out in a grade one/two class and the students were asked to represent a 2-digit number four different ways, I drew a little bit of a blank. I immediately thought of representing the number with base 10 materials, and then thought of using tally marks, but that was as far as I got! What are four different ways to represent a two-digit number?
Using some of my own ideas, and watching and learning with the kids, here are some representations we came up with:
1. Drawing Shapes in a One-to-One Correspondence
Most students started with representing their number using shapes; one picture or shape until they reached their two-digit number.
It was a lot of drawing, and a lot of counting, and some kids found it challenging to count what they were drawing accurately. Most students drew their shapes in rows, which was easier than counting 30 or more shapes randomly arranged on the page, but there were still some counting errors. We talked about strategies for counting accurately, but some students still found this difficult.
There were also a number of students who thought that drawing squares and then drawing triangles counted as two different ways to represent their number. It opened up discussion that representing a number with a one-to-one shapes or drawings was one strategy, and choosing a different shape did not change the strategy.
2. Tally Charts
The second-most popular representation students used was the tally chart. I could tell that this was a representation they had been practicing. Almost all students used this representation, and used it confidently.
Many students checked their work by counting the groups and skip counting by 5s, but some counted each tick individually if they lost where they were or wanted to double check.
3. Ten Frames
Students had only very recently been introduced to the ten frames. Some students shied away from using it because they weren’t confident enough to try it even thought they identified as a representation that could be used. Others got stuck on trying to draw the ten frames, drawing a 10 frame with only 8 squares.
If they made mistakes drawing their ten frames, they typically did not catch their error because they checked their work by counting by ones instead of tens. They did not realize that a 10 frame holds ten. A rather interesting error. I thought some students might count their 10-frame as 10, but not a single student did.
4. Groups of Ten
Students made the connection to this activity and grouped shapes into sets of 10.
5. Number Sentences
Before students set off to task, the children participated in a class brainstorm and discussion to come up with some ideas about the different ways a number could be represented. One of the ideas that was shared was that number could be represented as an addition or subtraction sentence. Very few students used this representation, although many students had not finished the task before it was time for me to go. They got so caught up in the counting I think, that they forgot about number sentences.
Some students were not able to come up with 4 different representations. Some students represented them inaccurately because they mis-counted, or drew their 10-frames with only 8 squares.
How do we get students comfortable with all of these ways of representing number? And how do we get them representing number accurately so they don’t make mistakes counting or drawing 10 frames?
I created a chart to summarize the ways that grade 2 students can represent number. Feel free to use it in your classroom.