Forming and Solving Equations

This lesson focuses on solving equations using mental math and tape diagrams, particularly those involving parentheses. Students learn to form equations from word problems and solve them step-by-step. The lesson includes examples and a summary, preparing students for their assignments.

What is the main focus of the lesson on tape diagrams and equations?

• Solving equations with parentheses

• Understanding geometry

• Drawing tape diagrams

• Learning about fractions

If 6 minus 1 equals 5, what is the solution to the equation 'what minus 1 equals 5'?

• 7

• 6

• 5

• 4

In the gift bag problem, if each bag contains x pencils and 3 more are added, what equation represents the total pencils in 5 bags?

• 5x + 3 = 20

• x + 5 = 20

• x + 3 = 20

• 5(x + 3) = 20

For an equilateral triangle with side length 5 inches, increased by x inches, what equation represents a perimeter of 20 inches?

• 5 + 3x = 20

• 3(5 + x) = 20

• 5x + 3 = 20

• x + 5 = 20

In the art class problem, if each student pays $3 plus a fee, what equation represents the total collected from 5 students?

• 5(3 + x) = 20

• x + 5 = 20

• 3x + 5 = 20

• 5x + 3 = 20

If Elena ran 20 miles, which is three times as far as Claire, and Claire ran 5 more miles than last week, what equation represents this?

• 20 = 3(x + 5)

• 20 = x + 5

• 3x + 5 = 20

• x + 3 = 20

What is the first step in solving the equation 5(x + 3) = 20?

• Subtract 3 from both sides

• Multiply both sides by 5

• Divide both sides by 5

• Add 3 to both sides

In the summary example, if 10 baskets contain a total of 140 toys after adding 2 items to each, what equation represents the toys per basket?

• 10x + 2 = 140

• x + 2 = 140

• x + 10 = 140

• 10(x + 2) = 140

How many workers were originally on each team if 10 were added to each, making a total of 140 workers across two teams?

• 50

• 80

• 60

• 70

What is the main challenge in forming equations from word problems as discussed in the lesson?

• Understanding the problem context

• Identifying the variables

• Drawing diagrams

• Solving the equations