IM Alg1.2.7 Lesson: Explaining Steps for Rewriting Equations
Is 0 a solution to each equation?
Here are some pairs of equations.
While one partner listens, the other partner should:- Choose a pair of equations from column A. Explain why, if is a number that makes the first equation true, then it also makes the second equation true.
- Choose a pair of equations from column B. Explain why the second equation is no longer true for a value of that makes the first equation true.
Noah is having trouble solving two equations.
In each case, he took steps that he thought were acceptable but ended up with statements that are clearly not true. 1. 2. Analyze Noah’s work on each equation and the moves he made. Were they acceptable moves?
Why do you think he ended up with a false equation? Discuss your observations with your group and be prepared to share your conclusions. If you get stuck, consider solving each equation.
We can’t divide the number 100 by zero because dividing by zero is undefined.
Instead, try dividing 100 by 10, then 1, then 0.1, then 0.01. What happens as you divide by smaller numbers?
Now try dividing the number -100 by 10, by 1, by 0.1, 0.01. What is the same and what is different?
In middle school, you used tape diagrams to represent division.
This tape diagram shows that .
Draw a tape diagram that shows why .
Draw a tape diagram that shows why .Try to draw a tape diagram that represents . Explain why this is so difficult.