I recently saw a post on social media with a fun place value activity. The teacher was using saltine crackers as a hundred, thin pretzel rods as a ten and marshmallows as ones. Students would use these materials to build a variety of three-digit numbers.
In general, I don’t hate it!
…. except that in this case I did.
This activity was going to be used to introduce place value.
**Major Disclaimer… If you have done an activity like this, no worries. No judgment. I used to be convinced that base ten blocks were the end-all of 2nd-grade place value tools. My thinking changed only after I learned more about math tools and how kids learn. This post does NOT come from a place of “Shame on you! How dare you use pretzels to teach math!” it comes from a place of “I was there too. Let me share what I learned!”
3 Types of Place Value Manipulatives
When choosing a place value manipulative you want to start with a model that will show students how units can be put together or taken apart to create other units. These groupable and proportional models allow your students to explore with place value. Linking cubes are an example of a groupable model.
Next, a pre-grouped proportional model allows your students to explore with more efficiency because, as the name suggests, groups of 10, 100, etc have been pre-grouped so your students are not constructing from scratch. Base ten blocks are an example of a model that can not be physically put together or broken apart but that IS to scale.
A pre-grouped, non-proportional model allows students who have a grasp of unit and scale to explore how place value impacts numbers on a much larger scale. Using place value discs, for example, students can easily explore with numbers in the thousands or even higher without the material becoming too cumbersome. This type of model also helps students move toward more abstract understandings.
Groupable Place Value Manipulatives
Students’ first exposure to place value concepts comes in studying teen numbers. A double ten frame with counters is an ideal groupable model because your students can see the teen numbers as “a ten and some ones” and are physically building the ten each time they construct a new number.
A number bond or part/whole diagram paired with this activity helps your students to build a web of understanding between the manipulatives they are using and the numbers they represent.
Linking cubes are another groupable option. When using linking cubes your students can physically put together (or decompose!) a group of ten.
Remember, you can be fluid with your hands-on tools and place value manipulatives! Perhaps your students were building 2-digit numbers comfortably with linking cubes so you moved ahead to a pre-grouped model such as base ten blocks.
You can always go “back” to a groupable model as you progress to a more complex topic such as comparing 2-digit numbers.
Moving between groupable, pre grouped proportional and pre grouped non-proportional models is an easy way to differentiate and add scaffolding to your instruction.
Pre-Grouped Proportional Place Value Manipulatives
When your students are comfortable working with a groupable model, you can move to a pre-grouped proportional model.
Base ten blocks are the most common pre-grouped proportional model available. In these models, a ten is the same size as ten ones, but the manipulative is already grouped together for your students.
This model is advantageous because it is less cumbersome for students to use. Your students can quickly build the number 248 using base ten blocks compared to the amount of time it would take to represent this number using individual counters.
Additionally, using a pre-grouped proportional model offers slightly less support than a groupable model so it is a step in the right direction toward the ultimate goal of eliminating manipulatives.
Pre-Grouped Non-Proportional Place Value Manipulatives
A pre-grouped non-proportional place value manipulative is the tool to choose if you are ready to decrease the level of hands-on support your students need.
If your students are working with larger numbers than could be managed with a proportional model, this is also a tool that can be helpful to your students in your instruction.
Place value disks, coins and dollars, and yes, even saltine crackers and pretzel rods are an example of pre-grouped non-proportional place value manipulatives.
Troubleshooting Place Value
Keeping these three types of manipulatives in mind can be helpful when it comes to troubleshooting and differentiating your place value instruction.
Ex: You are working on comparing 2-digit numbers with your students using base ten blocks. You have a student who continues to struggle with this concept. Try this:
- Change to a groupable model such as linking cubes. Ask your student to build each of the 2-digit numbers by building sticks of 10 using linking cubes and to compare. Then, ask your student to take the ten sticks back apart so that they have 2 piles of cubes. Compare again.
- Consider changing the numbers your student is working with! Perhaps the class is working on comparing 2-digit numbers to 99. Linking cubes might be cumbersome to use when building larger numbers such as 87 or 93. Instead, ask your student to only work with numbers to 30. As they become comfortable comparing numbers to 30 using linking cubes, try to move them again to base ten blocks before increasing their comparisons to larger numbers.
Ex: Your students are adding decimal numbers to the hundredth using a pencil/paper method. You have a student who is consistently having difficulty in combining ten hundredths to create a tenth. Try this:
- Add in a manipulative. Place value disks are a pre-grouped model that will allow your students to model decimal numbers. Try building on a place value chart to organize the manipulative.
- If your student is still not successful, take a step back and move to a tool such as base ten blocks that are still pre-grouped but are proportional. A flat can stand for “1”, a ten stick can represent tenths and the unit cube can represent hundredths.
- If your student is still not successful, try changing numbers! Is your student able to successfully add whole numbers together when regrouping is involved? Perhaps it’s a “place value and operations” problem rather than a “decimal” problem your student is experiencing.
Being thoughtful about your place value manipulatives can provide your students with exactly the level of support they need and can be a powerful tool in terms of troubleshooting and differentiation as well.