Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

[divider] [/divider] Students are able to… 

  • Use a variety of models, manipulatives and equations to represent multi-digit division.
  • Understand the role of place value in division strategies.
  • Make connections between multiplication and division strategies.
  • Understand that in some division problems there will be remainders.

[divider] [/divider] Students are able to…because teachers:

  • Provide a variety of different division scenarios for students to make sense of.
  • Promote the use of a variety of strategies and facilitating discussion that helps students connect different representations.
  • Make connections between models and written strategies.

[divider] [/divider] Questions to ask students:

  • What is a reasonable estimate for quotient of this division problem?
    • Sample answer that indicates understanding: Before I divide I look at the number and estimate. In the problem 463 ÷ 6 I know that 420 ÷ 6 is 70 and 480 ÷ 6 is 80. My answer should be somewhere between 70 and 80.
  • Using the problem 56 ÷ 7 = 8:  What does the 56 represent?  What does the 7 represent?  What does the 8 represent?  How do those number relate to the story problem?
    • Sample answer that indicates understanding:  Student can describe that the 56 represents the total, 7 is either how many equal groups or the number in each group and the 8 represents the quotient or number in each group/number of groups.  Student can also relate the equation back to the story problem accurately.
  • What multiplication problem would relate to your division problem?  How that would help you determine the quotient?
    • Sample answer that indicates understanding: I can always use multiplication to help me solve a division problem because they are opposite. I can think of division as an unknown factor multiplication problem.  Example:  42÷6=? is related to 6x?=42.
  • Looking at the dividend, Which number are you going to divide by the quotient?  What is the value of that digit?  What happens if that digit is less than the divisor?
    • Sample answer that indicates understanding: If I don’t have enough hundreds to divide I can regroup those hundreds and make tens. Then I can divide the tens.
  • Referring to partial quotients:  Why is it easier to subtract larger multiples of the divisor rather than just continuously subtracting the divisor itself? 
    • Sample answer that indicates understanding:  If you subtract larger multiples, you will arrive at the quotient quicker.  Example: 72 ÷ 6… I could subtract 10 groups of 6 or 60.  Then I would subtract 2 groups of 6 or 12.  The quotient  of 72 ÷ 6 is 12 because that’s how many groups of 6 I subtracted.

[divider] [/divider] FSA Notes

Cognitive Complexity Level: 2 – Basic Application of Skills and Concepts

Achievement Level Descriptors:

2- divides a whole number (of up to three digits) by a single-digit whole number, using strategies based on place value

3- divides a whole number up to four digits by a single-digit whole number (including remainders), using strategies based on place value, properties of operations, and/or the relationship between multiplication and division; illustrates and explains calculations by using equations, rectangular arrays, and/or area models

4- determines the equation that represents a base-ten model; makes connections between different division strategies

5- analyzes and describes an error in a strategy and shows the correct solution

Assessment Limits:

Items may not require finding a quotient within the factor pairs of 10 x 10.

Context: No Context

[divider] [/divider] Additional Resources:

Additional in depth content knowledge

Blog Post: Division Progression

Video: Divide Two Digit Dividends Using Friendly Multiples

[divider] [/divider] Sample Formative Assessment Tasks:

 

Resources/Tasks to Help Your Child at Home: 

Using a spinner, dice or cards create or pose different division problems with 1-digit divisors for your child to model using base ten blocks or a quick picture. Then encourage them to also use an area model. Make connections between the two models by asking, “How are the strategies similar? How are they different?”  Extend to have your child use partial quotients by subtracting larger multiples of the divisor.

Khan Academy: Division with Area Models https://goo.gl/fpFuLR

Khan Academy: Division Using Place Value https://goo.gl/ve85qJ

When your child solves any division problem, having them use estimation before solving to determine reasonableness of the answer. After they have determined the quotient, have them use multiplication to check their answer.

Video: Estimate the Quotients Using Multiples https://goo.gl/KGTY14

Use the same division story scenario with different questions to explore all the different ways to interpret a remainder. Discuss similarities and differences of each solution. Encourage your child to draw models to show their thinking.

Khan Academy: Intro to Remainders https://goo.gl/udhZ2B