### Which is the BEST Hands-On Tool for Teaching Decimals?

5th-grade teachers are set with a difficult task. Your students previously spent the majority of their time working with whole numbers in the base ten system. Now, you are supporting your students to build numbers that may be very difficult to model and conceptualize.

Thinking CRA is helpful but what tools do you have at your disposal to model a number like 4.315?

#### Not All Manipulatives Are Created Equally!

When thinking about place value manipulatives you have 3 main options:
1. Groupable, Proportional Models
2. Pre-Grouped, Proportional Models
3. Pre-Grouped, Non-Proportional Models
As you move down this list of materials, the manipulatives themselves are more abstract to work with.

To model the number 1.5 with a groupable, proportional model, I may consider linking cubes. Tell your students that each cube represents one-tenth and ask them if they could use them to build the number 1.5.

To model that same number with a pre-grouped, proportional model, you may consider using base ten blocks. Again, you would designate the whole to your student (perhaps a flat is considered a whole in this case) and you would ask your students to create the number.

Lastly, when using a pre-grouped, non-proportional model such as place value disks, you will see that your students will be able to create a number such as 1.5 incredibly easily. You are losing a bit of conceptual work (If a whole looks like this... what does a tenth look like?) but you are affording yourself the opportunity to build much more complex numbers that you couldn't readily build using base ten blocks or linking cubes.

When moving through this variety of hands-on materials, the most powerful thing you can do for your students is to ask them to use multiple materials alongside each other and ask LINKING QUESTIONS.

• Show me the part in your [manipulative #1] model that matches the "0.5" your [manipulative #2] model?
• What does your whole look like in [manipulative #1]? How is it different than the whole in [manipulative #2]?
• How would it look different if you built 3.4 with these different materials?
• Which manipulative do you think would be easier to use to build a number such as...

#### FREE Printable

I have created a free printable for you. Keep this handy on your desk or taped inside of your math manual. Keeping in mind the different types of place value manipulatives will allow you to quickly and easily differentiate for the variety of learners you have in your classroom.

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