Understanding Ratios and Proportions

This lesson teaches how to represent proportional relationships algebraically. It explains that a proportion is an equation showing two equal ratios, using examples like candy bars and cookies. The lesson emphasizes that ratios are proportional if they represent the same comparison and can be simplified to the same unit rate. It demonstrates solving a real-life problem involving students and rows using proportions, highlighting the importance of maintaining equal ratios. The lesson concludes with an algebraic approach to solving proportions using cross products.

What is a proportional relationship?

• A relationship where two ratios are different.

• A relationship where two quantities are different.

• A relationship where two ratios are equal.

• A relationship where two quantities are equal.

In the example given, what is the ratio of candy bars to cookies?

• 1 to 2

• 2 to 3

• 1 to 3

• 2 to 4

Why can the ratios 1:2 and 2:4 be considered proportional?

• They simplify to the same fraction.

• They simplify to different fractions.

• They have different unit rates.

• They represent different comparisons.

What must be true for a set of ratios to be proportional?

• They must be in different forms.

• They must represent different quantities.

• They must have different unit rates.

• They must have the same unit rate.

How can proportions be used in real life?

• To solve problems involving non-proportional relationships.

• To solve problems involving proportional relationships.

• To solve problems involving different quantities.

• To solve problems involving equal quantities.

What is the initial ratio of students to rows in the given problem?

• 3 students to 1 row

• 6 students to 2 rows

• 12 students to 4 rows

• 18 students to 6 rows

How do you represent the ratio of students to rows as a fraction?

• Students over rows

• Rows over students

• Rows plus students

• Students minus rows

What is the equation set up to solve for the number of students?

• 2s = 6 / 12

• 2s = 6 x 12

• 2s = 6 - 12

• 2s = 6 + 12

What is the final number of students that can fit in 12 rows?

• 36 students

• 24 students

• 42 students

• 30 students