ALEX Classroom Resource

  

Grade 5 Mathematics Module 1, Topic E: Multiplying Decimals

  Classroom Resource Information  

Title:

 Grade 5 Mathematics Module 1, Topic E: Multiplying Decimals

URL:

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

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

A focus on reasoning about the multiplication of a decimal fraction by a one-digit whole number in Module 1, Topic E provides the link that connects Grade 4 multiplication work and Grade 5 fluency with multi-digit multiplication. Place value understanding of whole-number multiplication coupled with an area model of the distributive property is used to help students build direct parallels between whole-number products and the products of one-digit multipliers and decimals (5.NBT.7). Once the decimal has been placed, students use an estimation-based strategy to confirm the reasonableness of the product through place value reasoning. Word problems provide a context within which students can reason about products.

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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