Topic Seven: Dividing Decimals

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.2: I can explain patterns when a decimal is multiplied or divided by a power of 10.
  • 5.NBT.7:I can add, subtract, multiply, and divide decimals to hundredths. I can use concrete models or drawings to explain the method used.

Pre-requisite skills:
  • 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 calculation by using equations, rectangular arrays, and/or area models.
  • 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

Student Friendly "I Can" Statements
  • I can read and write larger whole numbers using numerals, words and in expanded form.
  • I can compare two large numbers using symbols to show the comparison.
Big Ideas:
  • The Base-Ten Numeration System: The base-ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value.
  • Comparison and Relationship: Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways.
  • 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 Questions:

What are the standard procedures for estimating and finding quotients involving decimals?
Students will know...
  • Place value patterns can be used to mentally divide decimals by 10, 100, or 1,000.
  • Estimating quotients for whole number divisors and dividends can be applied to calculations with decimal dividends and divisors. Substituting compatible numbers can be used in most cases.
  • The location of decimal points in decimal division calculations can sometimes be decided by reasoning about the relative size of the given numbers.
  • The standard division algorithm involving decimals is an extension of the standard algorithm for dividing whole numbers.
  • A number divided by a decimal can be represented as an equivalent calculation using place value to change the divisor to a whole number.
  • Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem.

Vocabulary: dividend, decimal, divisor, quotient
Students will be skilled at...
  • Mentally dividing decimals by 10, 100, or 1,000.
  • Estimating quotients involving decimals, and using reasoning to understand how the size of the quotient relates to the dividend and divisor.
  • Learning how to use reasoning to correctly place the decimal point in a quotient.
  • Finding quotients where the dividend and/or the quotient is a decimal.
  • Dividing whole number by decimals.
  • Finding quotients of two decimals.
  • Using multiple steps to solve a variety of problems.

Assessment Evidence

Performance Assessment:
Other Evidence:

Learning Plan

Learning Activities:

7-1: Place value patterns can be used to mentally divide decimals by 10, 100, or 1,000.
7-2: Estimating quotients for whole number divisors and dividends can be applied to calculations with decimal dividends and divisors. Substituting compatible numbers can be used in most cases.
7-3: The location of decimal points in decimal division calculations can sometimes be decided by reasoning about the relative size of the given numbers.
7-4:The standard division algorithm involving decimals is an extension of the standard algorithm for dividing whole numbers.
7-5: A number divided by a decimal can be represented as an equivalent calculation using place value to change the divisor to a whole number.
7-6:A number divided by a decimal can be represented as an equivalent calculation using place value to change the divisor to a whole number.
7-7:Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem
Resources:

Problem of the Month:
Problem of the Month-Got Your Number
Problem of the Month-Diminishing Return

Centers:
Dividing a Decimal by a Power of Ten
Decimal of the Week