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Grade 5 Mathematics Module 2, Topic G: Partial Quotients and Multi-Digit Decimal Division

  Classroom Resource Information  

Title:

Grade 5 Mathematics Module 2, Topic G: Partial Quotients and Multi-Digit Decimal Division

URL:

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

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 2, Topic G uses the knowledge students have accumulated about whole number division with double-digit divisors and extends it to the division of decimals by double-digit divisors (5.NBT.7). Parallels between sharing or grouping whole number units and sharing or grouping decimal units are the emphasis of Topic G. Students quickly surmise that the concepts of division remain the same regardless of the size of the units being shared or grouped. Placement of the decimal point in quotients is based on students’ reasoning about when wholes are being shared or grouped and when the part being shared or grouped transitions into fractional parts. Students reason about remainders in a deeper way than in previous grades. Students consider cases in which remainders expressed as whole numbers appear to be equivalent; however, equivalence is disproven when such remainders are decomposed as decimal units and shared or grouped.

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
8. Add, subtract, multiply, and divide decimals to hundredths using strategies based on place value, properties of operations, and/or the relationships between addition/subtraction and multiplication/division; relate the strategy to a written method, and explain the reasoning used.

a. Use concrete models and drawings to solve problems with decimals to hundredths.

b. Solve problems in a real-world context with decimals to hundredths.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use strategies based on place value, properties of operations, and relationship between addition and subtraction to find sums and differences of decimals.
  • Use strategies based on place value, properties of operations, and relationship between multiplication and division to find products and quotients of decimals.
  • Use models to justify the sum, difference, product or quotient of decimals.
  • Solve real-world problems with decimals to hundredths.
Note: Products are limited to thousandths and quotients are either whole numbers or decimals terminating at the tenths or hundredths place.
Teacher Vocabulary:
  • Decimal
  • Tenths
  • Hundredths
  • Place value
Knowledge:
Students know:
  • Strategies based on place value understanding, properties, and relationship between operations to find the sum, difference, product, and quotient of whole numbers.
  • How to write decimal notation for fractions with denominators of 10 or 100.
  • Use estimation strategies to assess reasonableness of answers.
Skills:
Students are able to:
  • 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.
Understanding:
Students understand that:
Problems involving operations with decimals
  • Can be solved using a variety of strategies based on place value, properties of operations, or the relationship between the operations.
  • Can be illustrated using concrete models or drawings.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.8.1: Use decimal notation for fractions with denominators 10 or 100.
M.5.8.2: Multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations.
M.5.8.3: Add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
M.5.8.4: Apply properties of operations as strategies to multiply and divide.
M.5.8.5: Identify that 100 can be thought of as a bundle of ten tens, called a "hundred".
M.5.8.6: Identify that the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
M.5.8.7: Recall basic addition, subtraction, multiplication, and division facts.

Prior Knowledge Skills:
  • Use fraction equivalence to add and subtract fractions and mixed numbers with unlike denominators.
  • 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.
  • 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.5.8 Add decimals to tenths using concrete models, drawings, and manipulatives without regrouping.


Tags: add, addition, decimal, divide, exponents, hundredths, multiply, operations, patterns, place value, powers of 10, subtract, subtraction, zeros
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Comments

There are four lessons in this topic.

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Author: Hannah Bradley