Unit 6, Lesson 3
Reasoning about Equations with Tape Diagrams
Grade 7
3.2
Activity
Match each equation to one of the tape diagrams. Be prepared to explain how the equation matches the diagram.
Student Lesson Summary
We have seen how tape diagrams represent relationships between quantities. Because of the meaning and properties of addition and multiplication, more than one equation can often be used to represent a single tape diagram.
Let’s take a look at two tape diagrams.
We can represent this diagram with several different equations. Here are some of them:
- , because the parts add up to the whole.
- , because addition is commutative.
- , because if two quantities are equal, it doesn’t matter how we arrange them around the equal sign.
- , because one part (the part made up of 4 ’s) is the difference between the whole and the other part.
Here are some equations that represent this diagram:
- , because multiplication means having multiple groups of the same size.
- , because multiplication is commutative.
- , because division tells us the size of each equal part.
Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.
For example, is equivalent to .
- When is 3, both expressions equal 21.
- When is 10, both expressions equal 70.
- When is any other number, both expressions still have equal value.