Fairly early on in the school year, most primary students know number names beyond 10. Maybe they can even count beyond 10 objects accurately. However, this ability doesn’t guarantee that they can think about and manipulate larger numbers properly, as their knowledge may represent linguistic skills more so than math skills. When it comes to numbers above 10, place value is a critical concept to master. Early understanding of place value is an important milestone for your students as they advance in numeration and operations.
In this post, we share key lessons to help your students to move toward this milestone as well as links to exercises that build prior knowledge.
All of the exercises mentioned here are part of the HappyNumbers.com course and are presented along with exercises using other representations.
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Before digging into place value using two-digit numbers, your students should have a solid foundation of numeracy, addition, and subtraction skills up to ten. For more information on building these skills, please see our posts Number Sense Step by Step, Reinforce +/- Facts to Ten, and 7 Classroom Ideas for Building +/- Fact Fluency.
Tens and Ones
Maybe the most important step in studying place value is to understand that numbers above 10 are composed of tens and ones. Manipulating and sorting arrays of visually distinct objects into groups of tens and ones is a great place to start. And this is what our Numeration 11-20 topic is based on.
For example, packing fruit into a box (or 10-frame):
Followed by a more abstract model using cubes and rods:
This exercise is especially effective if used on tablets, as the touch screen provides students with a very similar experience to using actual cubes. However, HappyNumbers.com is not limited to a touch screen as it is compatible with most internet-enabled devices, such as IWBs, PCs, Macs, iPads, and Android tablets.
The exercises above lend themselves easily to a discussion with your students about the properties of the 10-frame/rod and the relationship between 2-digit numbers and objects grouped into tens and ones.
To support this discussion, the next activity in the topic Numeration 11-20 uses the same objects as above to help students visualize 2-digit numbers through animation:
Example of the animation relating a 2-digit number to objects grouped into tens and ones
From here, students are provided the opportunity to practice this new skill. A great way to strengthen skills and understanding of new concepts is to explore them from different angles. Our lessons on place value are specifically designed to do just that.
Here are some examples.
Write the number for the given array of tens and ones:
Represent the given number with tens and ones:
If a student responds incorrectly, a hint will help them understand how to correct it:
Then we remove the 10-frame:
But it reappears if the student makes a mistake:
Changing the position of the box is a great way to extend students’ thinking:
Place value is one of those topics that crops up again and again across grade levels as students move through increasingly advanced concepts in math. What we’ve shown here is only a small sample of the many exercises we’ve developed to help address that topic (using number lines, equations, etc.). If you are inspired by these exercises, head over to HappyNumbers.com to see many more.
Thanks for visiting our blog. We’re looking forward to see you here again!
Happy Numbers Team