Size Model extensions
If you and your students have been exploring Size Models for a while with great discussions about number relationships, you might wonder if there is more you can do with them—and the answer is YES! I’ll share three extensions here to give you some ideas for going further with this powerful model and then you might be inspired to create more on your own!
First up is something I like to call “Put a lid on it” because we double a Size Model we have already been using and then unite them by drawing a bar across both of them on top. I like to point out to the students that this is like a ‘copy and paste’ computer command and we are simply creating the same model over again, right next to it. This activity focuses on the idea that all factors of one number will naturally be factors of multiples of that number. You can easily see that if 10 is a factor of 40, then it has to also be a factor of 80, which is just double 40. We can also see that there will be twice as many groups of 10 in 80 as there were in 40, thanks to that ‘copy and paste’ metaphor. This is a fun extension to explore with kids and you can ask many prediction questions as prep!
2. Next up is building the Size Model from the ground up as well! With Size Models, we are often focused on breaking numbers down from the top, with the largest number occupying the top row. (Side note: there is no hierarchy that has to be followed, as each bar is equal to the others.) So sometimes it’s a good idea to start with the smallest numbers in the bottom row and ask students to fill in the row on top. This emphasizes the inverse relationship of multiplication and division and assists with those really important half-double relationships in a nice, structured way.
3. The last extension I’ll mention is trying out different divisions of the cells in each model. Remember, for it to be a Size Model, the cells in each row have to be the same, as we’re showing same-sized parts. If students are feeling confident with whole-half-quarter decomposition, you can move on to add eighths to the bottom, or try whole-third-sixths, or try to find all the equal parts (factors) of a number, such as 12. Once you’ve found all the ways to break up 12, try extension #1 from above and double it to 24 and then 48, 96, etc, to see the relationships between the number of parts and the number in each part. This is a wonderful, natural way to learn about factors and multiples and kind of ‘condense’ the number system by focusing on connections. Have fun!
