Using tape diagrams to solve one and two-step equations makes the procedures more visual and concrete. Tape diagrams show that the values on each side of the equal sign are equal. Tape diagrams make the operation needed to solve an equation more obvious. The concrete foundation can lead to a more solid foundation on which to build future lessons based on inverse operations.
Modeling Equations Using Tape Diagrams:
One-step equations
Solving 4x=36 requires one step to solve. By creating a tape diagram, we can see that 4 groups, each x in size, are equal to 36. To solve, we need to think about the number of items in each group.
What to do next becomes clearer. Since 36 is being split evenly between 4 groups, it makes sense that division is the operation that will be used to solve for x.
4x=36 so x=36/4 and x=9
Two-step equations
A solid foundation in using tape diagrams for one-step equations can be extended to also make two-step equations more concrete.
Solving 4x+24=36 requires two steps. This time 4 groups, each x in size, plus 24 are equal to 36.
The diagram helps make it clear that the 24 is in the way of figuring out the number in each group. Subtracting 24 makes sense, but the tapes will only remain equal if we subtract 24 from both tapes.
4x+24 – 24 = 36 – 24
The tapes remain equal in length and we are left with 4x= 12
What remains is that 4 groups, each x in size, are equal to 12. Once again, the division is the operation that will be used to solve for x.
4x=12 so x = 12/4 and x=3
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Also read: Modelling Equations With Hangers
Frequently Asked Questions on Modeling Equations Using Tape Diagrams
1. What are tape diagrams?
In simple words, tape diagrams are a visual representation that can help students understand number operations in a simple manner.
2. What type of equations can we solve using tape diagrams?
You can solve one-step and two-step equations using tape diagrams.
3. Where can I find worksheets on modeling equations using tape diagrams?
You can find math worksheets on modeling equations and more exclusive math worksheets, click here.
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