Do your students struggle with common linear equations and inequalities mistakes? I know mine did before I started using these strategies in my classroom. Here are my strategies for combating the top four linear equations and inequalities mistakes that I see students make!
Linear Equations and Inequalities Mistake #1
With linear equations and inequalities, students confuse m and b when the order is switched in slope-intercept form.
Solution: Tell your students that m(slope) and x go together like: shoes and socks, bees and honey, toothbrush and toothpaste, etc. (you can even have students come up with their own analogy to help them remember!) And because of this the b feels left out and says WHY(Y)?? This will help them remember the b represents the y-intercept!
So whether you have have:
y= 5x – 6 OR y=-6+5x
The slope is 5 and the y-intercept is -6
Linear Equations and Inequalities Mistake #2
Assuming that horizontal lines are represented by x= while vertical lines are represented by y= in linear equations and inequalities.
Tip: Use a mnemonic device to help students remember that horizontal lines are represented by y= because they are parallel to the x-axis AND vertical lines are represented by x= because they are parallel to the y-axis.
Use y= for the equation
Use x= for the equation
Linear Equations and Inequalities Mistake #3
Students use the reciprocal instead of the negative reciprocal when finding perpendicular lines.
Tip: First, make sure that students know the meaning of perpendicular. Then use a visual example to show that one slope must be positive and one negative for them to intersect at a 90 degree angle. This can save a lot of headaches down the road! See the example below.
Linear Equations and Inequalities Mistake #4
Students shade the wrong side when graphing inequalities.
Tip: Have students solve each inequality for y. Have them shade BELOW the line if the inequality symbol is < or ≤. If the inequality symbol is > or ≥, have them shade ABOVE the line. Then if the equation is in standard form, use a test point and SHADE where the point is TRUE for the inequality.
By using these strategies, I have decreased the number of errors students make with linear equations and inequalities significantly! Which tip will you use in your classroom? Let me know in the comments!
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