Divide with Remainders

10 min

Narrative

This Warm-up prompts students to analyze patterns and look for structure in division expressions and equations (MP7), and to reinforce their understanding of factors and multiples. This Notice and Wonder prepares students to work with division situations that have remainders later in the lesson.

Launch

  • Groups of 2
  • Display the table.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

division expression multiplication equations
100÷5100\div5 100=20×5100=20\times5
101÷5101\div5 101=20×5+1101=20\times5+1
102÷5102\div5 102=20×5+2102=20\times5+2
103÷5103\div5 103=20×5+3103=20\times5+3
104÷5104\div5 104=20×5+4104=20\times5+4
105÷5105\div5 105=20×5+5105=20\times5+5

Sample Response

Students may notice:

  • All the division expressions have a dividend of 5.
  • 100 and 105 are the only dividends that are multiples of 5.
  • Each time the dividend goes up one, you add one more in the equation.
  • In each row, the total in the equation is the same as the dividend.

Students may wonder:

  • Why do some equations have addition and some don’t?
  • Why is it adding more each time?
  • What do the equations have to do with the expressions?

Synthesis

  • “Today, we are going to work with dividing numbers that don’t have a whole number quotient.”
Standards
Addressing
  • 4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.
  • 4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.
  • 4.OA.4·Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
  • 4.OA.B.4·Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

25 min

10 min