Introduction to Linear Polynomials: common misconceptions

If your child says… “The middle coefficient is 3.”

Ask together

Does the middle term add three times x times y, or subtract it?

What’s true

Subtracting three times x times y means adding a term whose coefficient is −3.

If your child says… “The first term decides the degree.”

Ask together

Which power stays highest if you move the constant to the end?

What’s true

The highest power decides the degree wherever its term appears.

If your child says… “I can leave out the input’s minus sign.”

Ask together

Are you multiplying two by negative one or by positive one?

What’s true

The minus sign stays attached to the input during substitution.

If your child says… “The starting value is 4.”

Ask together

How many sticks were there before the first square?

What’s true

The starting value is 1, before any square has been built.

If your child says… “The falling line has positive slope because y is still positive.”

Ask together

On the falling line, does y increase or decrease as x increases?

What’s true

The direction of change decides the slope’s sign, regardless of the output’s sign.

If your child says… “Lines are parallel when their added numbers match.”

Ask together

Do the lines sharing a vertical-axis crossing also rise by the same amount?

What’s true

Different lines are parallel when their slopes match, even with different y-intercepts.