Proportional Relationships and Area

This lesson covers identifying proportional and non-proportional relationships using tables. It includes exercises on typing speed, state parks visited, and square area to determine proportionality. The lesson concludes with a summary of how to identify proportional relationships and answers the essential question about their importance in understanding quantities.

What is the essential question discussed in the introduction of the lesson?

• What is the relationship between speed and time?

• How many words can be typed in a minute?

• What is the formula for calculating the area of a square?

• How can understanding proportional relationships help in solving climate-related questions?

If a person types at a constant rate of 42 words per minute, how many words will they type in 5 minutes?

• 240 words

• 220 words

• 200 words

• 210 words

In the typing example, why is the relationship between words typed and time considered proportional?

• Because the typing speed changes over time.

• Because the number of words typed increases by a constant amount each minute.

• Because the number of words typed decreases over time.

• Because the typing speed is inconsistent.

How many months does it take Mark to visit 23 state parks?

• 10 months

• 15 months

• 8 months

• 12 months

Why is the relationship between the number of parks visited and months not proportional?

• Because Mark visits parks at random intervals.

• Because the number of parks visited does not increase by a constant multiplier each month.

• Because Mark visits the same number of parks every month.

• Because the number of parks visited decreases over time.

What is the area of a square with a side length of 4 units?

• 20 square units

• 8 square units

• 16 square units

• 12 square units

Why is the relationship between the side length of a square and its area not proportional?

• Because the side length and area are unrelated.

• Because the area increases by the square of the side length, not a constant multiplier.

• Because the side length and area are equal.

• Because the area decreases as the side length increases.

What is the key step to determine if two quantities are proportional?

• Check if the ratio of the two quantities is constant.

• Check if the quantities are unrelated.

• Check if the quantities are different.

• Check if the quantities are equal.

According to the summary, what can be substituted for 8 ounces?

• Four cups

• Two cups

• Half a cup

• One cup

What is the final conclusion about proportional relationships in the lesson?

• A pattern in numbers always indicates a proportional relationship.

• Proportional relationships are always non-linear.

• Proportional relationships are always linear.

• A constant multiplier or ratio indicates a proportional relationship.