2y – 2x = 8Number sense is the ability to understand and manipulate quantities. A number line provides the spatial representation that is the key to number sense. Using linking cubes on the number line helps students understand the concept of quantity. Use different colored linking cubes when adding and subtracting with the number line, for example: 3 red cubes plus two yellow cubes equals five total cubes. Have students use language and “say” what they are doing. This will significantly increase their understanding.
When teaching multi-step subjects, like mathematics, the process in every lesson should be broken down for students step by step. Every step should be covered individually, and the students should have sufficient practice with each stage, even when the math problem itself hasn’t been entirely solved. Do NOT proceed to a new step until there is mastery of the current step. When students have mastered the individual steps to a specific type of problem, there is a much greater understanding of the problem as a whole and how to solve variations of it.
Example: One Step at a Time: Algebra
Do the first step of multiple problems involving the same concept. When step one is mastered, add step two. When step two is mastered, add step three and so on. Do not move on to the next step until there is mastery.
Instructions: Rewrite the equation by changing it to slope-intercept form.
2y – 2x = 8
Steps to solve: (Only show students one step at a time.)
1. Add x variable to both sides of equation: 2y – 2x + 2x = 8 + 2x
2y + 0 = 8 + 2x
2y = 8 + 2x
2. Divide both sides by the y coefficient: 2y = 2x + 8
2 2 2
y = x + 4
3. Clean up final equation; box your answer: y = x + 4
Practice with multiple variations of individual steps:
Original equations: → Perform Step 1:
a. 5y + 10x = 10
b. 3y – 7x = –15
c. 2x + 6y = 18
d. 9y + x = –27
e. x – 2y = –14
From Step 1: → Perform Step 2:
a. 5y = –10x + 10
b. 3y = 7x – 15
c. 6y = –2x + 18
d. 9y = –x – 27
e. 2y = x + 14
Step 3: Clean up equations; box final answers:
a. y = –2x + 2
b. y = 7/3x – 5
c. y = –1/3x + 3
d. y = –1/9x – 3
e. y = 1/2x + 7