In mathematics, an equation is a math sentence that shows two expressions that are equal. Understanding that these two expressions must stay equal is foundational as kids begin to learn Algebra. It is also important and useful as kids begin to write proofs or solve more difficult problems, because sometimes an expression is not written in a convenient way. But re-writing it in a way that is still equal (i.e. doesn’t change the problem) is an incredibly useful technique and one that I think is often not taught or explained well in high school math classes. This equal or not equal place value sort is intended to help kids practice writing in expanded form, as well as reinforce the idea that expanded form is just another way to write the number. It is not something new or different.
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Understanding place value is an essential math concept for early math learners. It’s important as students begin to add and subtract larger numbers, compare quantities and make sense of more complicated math.
But it is equally important that kids understand that expanded form is just another representation of the same number.
As kids get older and the math more complicated, they will be better able to problem solve and think outside the box if they are able to think of numbers and expressions in other ways.
As a high school teacher, I often saw kids struggle with factoring. They wanted to memorize a procedure, or just guess random numbers based on examples they saw, without actually understanding what they were doing.
I tried to explain over and over again that factoring is just writing an expression another way. Re-writing it as two things multiplied together, just as 15 is equal to 5×3.
This is also good practice for students to get in the habit of checking their work. Most kids, once they have completed a problem, are done. Solving it was so much work, who wants to go back and actually check to see if it’s right?!
But checking for accuracy is a habit we should encourage from an early age. This activity will allow students to look for mistakes and practice “checking their answers.” They have to use what they know about numbers and evaluate what is written and determine if they actually are equal.
To Use the Equal or Not Equal Place Value Sort:
Very little prep is required for this super-hero themed lesson! Simply print the “equal” and “not equal” mats, as well as the equation cards. For durability, I suggest printing on card stock and laminating the pieces.
Then, cut out the mats and cards and let your students sort them based on whether or not the equations are equal!
I would encourage you to discuss the problems together (either as a class or in small groups) and be sure to ask students to explain why something is equal or not equal. This will allow them to explain in their own words what they understand about place value and expanded form.
A great way to get kids talking? Ask them to prove it. “Oh really? Those are not equal? Prove it!”
This would also be a fun partner activity. Have students split the set of equation cards and take turns sorting them, explaining their decision to each other as they go.
If you’d like to use this activity with your students, download it free below! Included in the download are the equal/not equal mats as well as 18 equation cards to sort (including numbers to the thousands place).
I hope this is a useful and meaningful activity for your students, and helps them understand the importance of place value, and checking their work!
For more place value activities, check out one of the following posts:
- Expanded Number Puzzles
- Place Value Lessons to use with the book, Sir Cumference and All the King’s Tens
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