Answered

A school held a candle fundraiser to raise money to buy toys for children who live in a group home. The Candle Fundraiser table shows how many candles each class sold.



Beehive candles sell for $20 each. The class raised $12 for each candle sold.



Soybean candles sell for $22 each. The class raised $14 for each candle sold.




\multicolumn{3}{|c|}{Candle Fundraiser}

Teacher		Number SoldAmount Raised for Each

Mr. Li		32\$12

Ms. Schmidt		25\$14

Ms. Picard		18\$14

Ms. Goldwasser		47\$12





  1. About how much money did the fourth-grade students raise? Explain.


  1. The school secretary needs to know exactly how much money was raised.



Part A

How much money did Ms. Schmidt's class raise? Use an area model and partial products to find the product.

Verified Answer :

  • Estimate the total money raised by rounding candle sales and multiplying by earnings per candle: \(\$360 + \$600 + \$350 + \$280 \approx \boxed{\$1590}\).
  • Calculate the exact amount for Ms. Schmidt's class using partial products (\(20 \times 10, 20 \times 4, 5 \times 10, 5 \times 4\)) to get \(\boxed{\$350}\).

Explanation

  1. Estimating the Total Money Raised

To estimate the total amount of money raised, we first group the classes by the amount they raised per candle. Mr. Li and Ms. Goldwasser raised \$12 per candle, while Ms. Schmidt and Ms. Picard raised \$14 per candle.
The number of candles sold is:

  • Mr. Li: 32 candles
  • Ms. Goldwasser: 47 candles
  • Ms. Schmidt: 25 candles
  • Ms. Picard: 18 candles

For a quick estimate, we can round these numbers to convenient values:

  • Mr. Li sold approximately 30 candles at \$12 each: \(30 \times 12 = \$360\).
  • Ms. Goldwasser sold approximately 50 candles at \$12 each: \(50 \times 12 = \$600\).
  • Ms. Schmidt sold approximately 25 candles at \$14 each: \(25 \times 14 = \$350\).
  • Ms. Picard sold approximately 20 candles at \$14 each: \(20 \times 14 = \$280\).

Summing these estimates:
\(\$360 + \$600 + \$350 + \$280 = \$1590\).
Thus, the fourth-grade students raised approximately \(\$1590\).

  1. Calculating Exact Earnings for Ms. Schmidt's Class

To calculate the exact amount raised by Ms. Schmidt's class, we multiply the number of candles sold (25) by the amount raised per candle (\$14). We use an area model by decomposing both numbers:
25 = 20 + 5
14 = 10 + 4

The area model (partial products) calculation is:

  • \(20 \times 10 = 200\)
  • \(20 \times 4 = 80\)
  • \(5 \times 10 = 50\)
  • \(5 \times 4 = 20\)

Summing the partial products:
\(\$200 + \$80 + \$50 + \$20 = \$350\).
Ms. Schmidt's class raised exactly \(\$350\).

Examples

In real life, this method of estimation and exact calculation is vital for organizing community events or fundraisers. Whether you are selling cookies, candles, or tickets, being able to quickly estimate your total revenue helps you set realistic goals and manage budgets. Precise calculation using partial products is then used for final accounting to ensure every dollar is accounted for. This balance of estimation and exact math is a fundamental skill for managing projects and resources efficiently.

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