Module 3 for Second Grade has under the suggested materials one set of large place value card for the teacher and a set of small place value cards for the students 1-500 (pg 1) Here are some templates of small place value cards that you can use. The only difference between the sets is that the first document has plain cards and the second set shows the value of the digits. You only need the first page for this module. The template is set to print on 8 1/2 x14 paper.
A number path is a tool that young children (up to 2nd grade) can use to model addition, subtraction and comparison problems. You can find an explanation of a number path and a template you can print at this site
This model provides a bridge between concrete manipulatives and abstract numeric symbols. If you laminated the number paths, the students could mark out problems on their number path and then erase it. For comparison problems it may be useful to have two number paths so students can easily see how the two quantities compare. Use this model to lay the foundation for the use of the bar model and the number line to solve problems with a larger range of numbers in the later grades.
The link above takes you directly to the information on number paths, but the Mathematically Minded website has a number of printable resources that are worth checking out. http://www.mathematicallyminded.com/book1.html
The bar model helps students visualize the relationships between the numbers given and the amount you are looking for in a word problem. What's great about this tool is that the model starts in elementary school with addition and subtraction problems and then can be expanded to work with multiplication and division problems, fractions, ratios, and percents. This model is incredibly
useful when you need to make sense of the given information and figure out how to attack a complex problem (MP1). Once students know how to create and apply these models, all they need is a surface to write on and a writing utensil.
This model shows how the part and whole are related through multiplication and division. I could show that if I had 15 stickers and I divided them evenly among 3 kids, each kid would get 5 stickers. Later we can use this diagram to model fraction relationships. This picture shows that the part is 1/3 of the whole.
So what can you do with these basic models? Check out these two articles for some examples of problems that can be solved using the bar model. The first article quotes Scott Baldridge a professor at LSU and the mathematics expert who is overseeing the development of the NY Math Modules.
Technology and Bar Models-
I haven't decided what I think about using computer or iPads to create bar models (Erin). I love the simplicity of just being able to draw a quick sketch anytime anywhere. The best argument for using a program to create a bar model is a situation that requires you to split a bar into equal pieces. You'll see how easily that was done in the video.
The Youtube video below shows a solution modeled using the "Modeling Tool" on the Thinking Blocks website.
The rekenrek (rek- en- rek) is a tool that was developed in the Netherlands to support the development of number sense in young children. The picture shows a homemade rekenrek that I created with string, beads, and the bottom of a shoebox. This rekenrek has 20 beads. Much of your work with students in grades PK-2 could be done with a rekenrek of this size. You will also see larger versions that have 10 rows of beads to work on numbers within 100. The larger version is great for counting patterns within 100. The larger version would also be useful for 3rd grade teachers because you can easily create arrays on the rekenrek that model multiplication.
If you are looking for a rekenrek app for the iPad, I like the one called
"Number Rack" You can adjust how many strings of beads you have showing up to 10 strings. The movement of the beads is pretty similar to the actual rekenrek. It's nice that I can pull beads to the right at the same time I'm sliding beads to the left. It also lets me slide a whole group of beads over at once. It has a screen, but I can't seem to be able to move the beads under the screen like I could with a real rekenrek. However, you could use the screen to decompose a number. If 3 beads are showing, how many beads in the string of 10 are hidden under the screen, etc.
Want to see the rekenrek in action? Check out this video on Youtube created by Bill Davidson. He was one of the presenters that came to Albany to share information about the upcoming math modules. In less than 5 minutes you can see many ways to use a 20 bead rekenrek... enjoy :)
Why Would I Want to Use That?
With so many mathematical models and tools, how do you decide which ones are worth investigating? We have created this blog to help faciliate that discussion.