Answer to Question #131044 in Algebra for Thembeka

Question

Solution for x and y:

Y =× + 4 and

Y = 2ײ+ 6× − 8

Classify the problem as either routine and non-routine based on the procedure and skills required to solve the problems. Write brief notes to explain your classification of problems

Answer 1

$$\begin{matrix} y=x+4 \\ 2y=2x^2+6x-8 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ 2(x+4)=2x^2+6x-8 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ x+4=x^2+3x-4 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ x+4-x-4=x^2+3x-4-x-4 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ x^2+2x-8=0 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ x^2-2x+2x+2x-8=0 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ x(x-2)+4(x-2)=0 \end{matrix}$$ $$\begin{matrix} y=x+4 \\ (x-2)(x+4)=0 \end{matrix}$$

$$\begin{matrix} y=x+4 \\ x+4=0 \end{matrix}$$

Or

$$\begin{matrix} y=x+4 \\ x-2=0 \end{matrix}$$

Then

$$\begin{matrix} x=-4 \\ y=0 \end{matrix}$$

Or

$$\begin{matrix} x=2 \\ y=6 \end{matrix}$$

$\big(-4, 0 \big), \big(2, 6 \big)$

Routine problems

Do not require students to use High-order Thinking (HOTS).

Use clear procedures.

Non-routine problems

Require students to use High-order Thinking (HOTS).

Use clear procedures.

Increase the reasoning ability.

Use answers and procedures that are not immediately clear.

Encourage more than one solution and strategy.

Expect more than one answer.

Challenge thinking skills.

Produce creative and innovative students.

Require solutions that are more than simply making decisions and choosing mathematical operations.

Require a suitable amount of time to solve.

Encourage group decision in finding the right solution.

Then our problem is the routine roblem.