Topic Four: Dividing by 1-Digit Divisors


Desired Results


Transfer:

1. Makes sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals:
  • 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.

I Can Statements:
  • I can divide four digit dividends by two-digit divisors.
  • I can illustrate and explain a division problem using equations, arrays, and/or models.

Pre-Requisite Standards:
  • 4.NBT.6: 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 calculations by using equations, rectangular arrays, and/or area models.
  • 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote power of 10.
  • 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.
Big Ideas:
  • Patterns, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. For some relationships, mathematical expressions and equations can be used to describe how members of one set are related to members of a second set.
  • Basic Facts and Algorithms: There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
  • Estimation: Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. Some measurements can be approximated using known referents as the unit in the measurement process.
  • Equivalence: Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.
  • Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems.
Essential Question:

  • What is the standard procedure for division and why does it work?
Students will know...

  • Basic facts and place value patterns can be used to divide multiples of 10, 100, and so forth by one-digit numbers.
  • There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.
  • Answers to problems should always be checked for reasonableness and this can be done in different ways. Two ways are to use estimation and to check the answer against the question in the problem.
  • The sharing interpretation of division and money can be used to model the standard division algorithm.
  • Different numerical expressions can have the same value.
  • Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.

Vocabulary: dividend, divisor, quotient

Students will be skilled at...

  • Finding the quotient of a division problem whose dividend is a multiple of 10, where division involves a basic fact.
  • Rounding and compatible numbers to estimate quotients of whole numbers.
  • Checking problems for reasonableness by using various methods, including estimation and checking their final answer.
  • Finding quotients using the model of sharing money.
  • Dividing three-digit whole numbers by one-digit divisors.
  • Dividing with zeros in the quotient.
  • Using pictures and equations to help them represent remainders in a problem.


  • Assessment Evidence
Performance Assessment:
Performance Assessment Task-5.NBT.6-Fruits and Vegetables

Other Evidence:

  • Learning Plan

Learning Activities:

4-1: Basic facts and place value patterns can be used to divide multiples of 10, 100, and so forth by one-digit numbers.
4-2: There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.
4-3:Answers to problems should always be checked for reasonableness and this can be done in different ways. Two ways are to use estimation and to check the answer against the question in the problem.
4-4: The sharing interpretation of division and money can be used to model the standard division algorithm.
Different numerical expressions can have the same value.
4-5:The sharing interpretation of division and money can be used to model the standard division algorithm.
4-6:The sharing interpretation of division and money can be used to model the standard division algorithm.
4-7:Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.
Resources:

Home-School Connection:


Problem of the Month:
5.NBT.6-Through the Grapevine

Centers:
5.NBT.6-Division Strategy-Partial Quotients
5.NBT.6-Division Strategy-Partition the Dividend
5.NBT.6-Division Strategy-Multiplying Up
5.NBT.6-Estimating Quotients
5.NBT.6-Creating and Solving a Division Problem