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Grade 5 Mathematics Module 1, Topic D: Adding and Subtracting Decimals

  Classroom Resource Information  

Title:

 Grade 5 Mathematics Module 1, Topic D: Adding and Subtracting Decimals

URL:

 https://www.engageny.org/resource/grade-5-mathematics-module-1-topic-d-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 1, Topics D through F mark a shift from the opening topics of Module 1. From this point to the conclusion of the module, students begin to use base ten understanding of adjacent units and whole-number algorithms to reason about and perform decimal fraction operations—addition and subtraction in Topic D, multiplication in Topic E, and division in Topic F (5.NBT.7).

In Topic D, unit form provides the connection that allows students to use what they know about general methods for addition and subtraction with whole numbers to reason about decimal addition and subtraction (e.g., 7 tens + 8 tens = 15 tens = 150 is analogous to 7 tenths + 8 tenths = 15 tenths = 1.5). Place value charts and disks (both concrete and pictorial representations) and the relationship between addition and subtraction are used to provide a bridge for relating such understandings to a written method. Real-world contexts provide opportunities for students to apply their knowledge of decimal addition and subtraction as well in Topic D.

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
4. Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

Example: 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on the meaning of the digits in each place, using >, =, and < to record the results of comparisons.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a decimal number in one form (words, base-ten numerals, expanded), identify the number in another form.
  • Read decimals with number names.

    • Example: Read 4.023 as "four and 23 thousandths."
  • Write decimals using base-ten numerals and expanded form.

    • Example: 4.023 as 4 x 1 + 2 x 1/100 + 3 x 1/1000 or 4 x 1 + 2 x 0.01 + 3 x 0.001.
  • Use place value understanding to compare two decimals.
Teacher Vocabulary:
  • Compare
  • Decimal
  • Thousandths
  • Hundredths
  • Tenths
  • Symbol
  • Greater than
  • Less than
  • Equal
  • Place value strategy
  • Expanded form
  • Expanded notation
Knowledge:
Students know:
  • How to read and write whole numbers in standard form, word form, and expanded form.
  • How to compare two whole numbers using place value understanding.
  • Prior place value understanding with whole numbers is extended and applied to decimal values.
  • Recognize and model decimal place value using visual representations to compare.
Skills:
Students are able to:
  • Read and write decimal values in word form, standard form, and expanded form.
  • Compare decimals to thousandths using <, >, or = .
Understanding:
Students understand that:
  • the adjacent place value relationship in the base ten system extends to decimals and is used to write decimals in expanded form and compare decimals.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.4.1: Recognize decimals as parts of a whole.
M.5.4.2: Compare whole numbers.
M.5.4.3: Write whole numbers in words and expanded form.
M.5.4.4: Read whole numbers.
M.5.4.5: Define expanded notation and standard form.
M.5.4.6: Convert a number written in expanded to standard form.
M.5.4.7: Define hundredths and thousandths.
M.5.4.8: 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.5.4.9: Identify comparison symbols.
Examples: >, =, and <.

Prior Knowledge Skills:
  • Read and write decimal values in word form, standard form, and expanded form.
  • Compare decimals to thousandths using <, >, or = .
  • Understand rounding decimals using place value.
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
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, baseten, compare, decimals, digits, divide, expanded form, hundredths, multiply, pattern, place value, subtract, thousandths, unit form
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Author: Hannah Bradley
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