The Standard Long-Division Algorithm

The Standard Long-Division Algorithm

Compare Solutions

Opening

Compare Solutions

Jason, Denzel, and Martin solved the division problem 5,512 ÷ 32.

All three students started out using the steps shown, but all three got different answers.

Here are their answers:

Jason’s answer: 172 R8
Denzel’s answer: 17214
Martin’s answer: 172.25

  • Which answer is correct, and why?
  • Discuss this question with your partner, and then with your class.

Math Mission

Opening

Solve real-world problems by dividing whole numbers.

Solve Real-World Division Problems

Work Time

Solve Real-World Division Problems

Choose one of the following problems. Solve the problem and show your work.

  • Twelve friends went on a camping trip. The total cost for the campsite, food, supplies, and gas was $693. If the friends split the cost evenly, how much did each person pay?
  • The student council is planning a school sweatshirt sale. The council members found a supplier who charges $12 per sweatshirt, but they have to pay the money up front. If they have $693, how many sweatshirts can they buy?
  • Each cabin at a summer camp can hold 12 campers. If 693 students sign up for the camp, how many cabins will be needed?
  • An employee at a bakery packaged 693 scones in boxes that each hold 12 scones. Her boss told her that she could keep any extra scones for herself. How many scones did the employee get to keep?

Ask yourself:

  • Camping Trip Problem: How can you represent the amount left over in this situation?
  • Sweatshirt Problem: Can you buy a fraction of a sweatshirt?
  • Cabin Problem: Where will the “leftover” campers sleep?
  • Bakery Problem: Will the answer be the number of boxes the employee packed or the number of scones left over?

 

Prepare a Presentation

Work Time

Prepare a Presentation

  • Prepare your problem solution to share with your classmates.
  • Include a drawing and an explanation of what you did to solve the problem.

Challenge Problem

  • Write two word problems that you would solve using the same whole-number division expression, but that have different solutions.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ approaches to solving the problems.

As your classmates present, ask questions such as:

  • Explain each step in your long division procedure.
  • Is your answer reasonable? How do you know?
  • How does your answer make sense in the context of the problem situation?
  • What do the whole number and the remainder each represent in this situation?

Divide Whole Numbers

Formative Assessment

Summary of the Math: Divide Whole Numbers

Write a summary about dividing with whole numbers.

Check your summary.

  • Do you explain how to represent problem situations with whole-number division expressions, and include examples?
  • Do you describe and provide examples of the different forms that the answer to a whole-number division problem can have?
  • Do you discuss why different problem situations can be represented by the same division expression, and have different solutions?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Two everyday situations that involve dividing whole numbers are …