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Grade 5 Mathematics Module 2, Topic E: Mental Strategies for Multi-Digit Whole Number Division

  Classroom Resource Information  

Title:

Grade 5 Mathematics Module 2, Topic E: Mental Strategies for Multi-Digit Whole Number Division

URL:

https://www.engageny.org/resource/grade-5-mathematics-module-2-topic-e-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 2, Topics E through H provide a parallel sequence for division to that offered in Topics A to D for multiplication. Topic E begins concretely with place value disks as an introduction to division with multi-digit whole numbers (5.NBT.6). In Lesson 17, 420 ÷ 60 is interpreted as 420 ÷ 10 ÷ 6. Next, students round dividends and 2-digit divisors to nearby multiples of ten in order to estimate single-digit quotients (e.g., 431 ÷ 58  420 ÷ 60 = 7) and then multi-digit quotients. This work is done horizontally, outside the context of the written vertical method.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 5
5 ) 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 powers of 10. [5-NBT2]


NAEP Framework
NAEP Statement::
4A1b: Given a pattern or sequence, construct or explain a rule that can generate the terms of the pattern or sequence.

NAEP Statement::
4NPO3d: Describe the effect of operations on size (whole numbers).

NAEP Statement::
4NPO6a: Explain or justify a mathematical concept or relationship (e.g., explain why 15 is an odd number or why 7-3 is not the same as 3-7).

NAEP Statement::
8NPO1a: Use place value to model and describe integers and decimals.


Mathematics
MA2019 (2019)
Grade: 5
3. Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and 1/10 of what it represents in the place to its left.

a. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, using whole-number exponents to denote powers of 10.

b. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10, using whole-number exponents to denote powers of 10.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use models to illustrate the relationship between two successive place values in whole numbers and decimals.
  • Explain that a digit in one place represents 1/10 of what it represents to its left or the place value is 10 times the place value on the right.
  • Use strategies to find products and explain patterns when multiplying by powers of 10.
    Example: The product of 420 x 200 = 42 x 10 x 2 x 100 is the same as (42 x 2) x (10 x 100) = 84 x 1000 = 84,000 shows multiplying by three powers of 10 shifts the digits in the product three place values greater (to the left.)
  • Use strategies to find products and quotients and use place value understanding to explain patterns in the placement of the decimal point when involving a power of 10.
  • Write powers of 10 in standard form and using exponential notation.
Teacher Vocabulary:
  • Digit
  • Decimal
  • Decimal point
  • Thousandths
  • Hundredths
  • Tenths
  • Base-ten
  • Expanded form
  • Place value
  • Power of 10
  • Factor
  • Base
  • Exponent
  • Product
Knowledge:
Students know:
  • Each place value position represents 10 times what it represents in the place to its right.
    Example: In 433, the underlined 3 represents 3 tens and has a value of 30 which is ten times the value of the 3 ones to its right.
  • Place value understanding is extended to apply reasoning that a place value position represents 1/10 of what it represents in the place value to its left.
    Example: In 433, the underlined 3 represents 3 ones and has a value of 3 which is one-tenth of the value of the 3 tens or 30 to its left.
  • A given number multiplied by a power of 10 shifts the digits in the given number one place value greater (to the left) for each factor of 10. -A given number divided by a power of 10 shifts the digits in the given number one-tenth of the value (to the right) for each factor of 10.
Skills:
Students are able to:
  • Reason and explain the relationship between two successive place values.
  • Explain patterns of zeros of the product when multiplying by powers of 10.
  • Explain patterns in placement of decimals when multiplying or dividing by power of 10.
  • Write powers of 10 using exponential notation.
Understanding:
Students understand that:
  • The relationship of adjacent places values in the base ten system extend beyond whole numbers to decimal values.
  • Multiplying or dividing by a power of 10 shifts the digits in a whole number or decimal that many places to the left or right respectively.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.3.1: Use place value understanding to round whole numbers to the nearest 10 or 100.
M.5.3.2: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits using >, =, and < symbols to record the results of comparisons.
M.5.3.3: Identify that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

Prior Knowledge Skills:
  • Reason and explain the relationship between two successive place values.
  • Explain patterns of zeros of the product when multiplying by powers of 10.
  • Explain patterns in placement of decimals when multiplying or dividing by power of 10.
  • Write powers of 10 using exponential notation.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.3 Compare base-10 models up to 99 and whole numbers up to 100 to determine symbols (<, >, =).


Mathematics
MA2019 (2019)
Grade: 5
7. Use strategies based on place value, properties of operations, and/or the relationship between multiplication and division to find whole-number quotients and remainders with up to four-digit dividends and two-digit divisors. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Choose strategies based on place value, partial quotients, properties of operations, or the relationship between multiplication and division to find whole number quotients and remainders.
  • Solve word problem situations involving division.
  • Justify solution path for quotients using equations, arrays or area models.
    • Note: Standard algorithm for division is not an expectation at grade 5.
Teacher Vocabulary:
  • Quotient
  • Dividend
  • Divisor
  • Divide
  • Multiply
  • Equation
  • Remainder
  • Multiple
  • Area model
  • Decompose
  • Partial quotient
  • Equation
Knowledge:
Students know:
  • Efficient strategies to find a whole number quotient when a multi-digit number (up to 4-digit dividend) is divided by a single-digit divisor.
  • How to justify quotients using an illustration or the relationship between multiplication and division.
Skills:
Students are able to:
  • Find whole number quotients and remainders using a variety of strategies based on place value and properties of operations.
  • Illustrate and explain the calculation using equations, arrays, and area models.
Understanding:
Students understand that:
  • Strategies for division by a one-digit divisor are extended to two-digit divisors.
  • Visual models are used to illustrate division.
  • Remainders may be written as a fraction or decimal and interpreted based on context of the problem situation.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.7.1: Construct a division equation with an example of the division algorithm.
M.5.7.2: Illustrate the division algorithm using a one-digit divisor and a 2-digit dividend.
M.5.7.3: Identify the place value of a division problem.
M.5.7.4: Restate the inverse process of division as multiplication.
M.5.7.5: Recall basic multiplication facts.

Prior Knowledge Skills:
  • Use concrete models, drawings, and strategies to add, subtract, multiply, and divide decimals.
  • Relate strategies for operations with decimals to a written method and explain reasoning used.
  • Solve real-world context problems involving decimals.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.5.6 Model multiplication with two digit whole numbers by one digit whole numbers with regrouping using strategies such as arrays, decomposition, and manipulatives.


Tags: arrays, decimal, divide, dividend, divisors, equations, exponents, multidigit, multiply, operations, patterns, place value, powers of 10, quotient, zeros
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There are three lessons in this topic.

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Author: Hannah Bradley