ALEX Classroom Resource

  

Grade 5 Mathematics Module 1, Topic C: Place Value and Rounding Decimal Fractions

  Classroom Resource Information  

Title:

 Grade 5 Mathematics Module 1, Topic C: Place Value and Rounding Decimal Fractions

URL:

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

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 1, Topic C, students generalize their knowledge of rounding whole numbers to round decimal numbers to any place. In Grades 3 and 4, vertical number lines provided a platform for students to round whole numbers to any place. In Grade 5, vertical number lines again provide support for students to make use of patterns in the base ten system, allowing knowledge of whole-number rounding (4.NBT.3) to be easily applied to rounding decimal values (5.NBT.4). The vertical number line is used initially to find more than or less than halfway between multiples of decimal units. In these lessons, students are encouraged to reason more abstractly as they use place value understanding to approximate by using nearest multiples.

Naming those nearest multiples is an application of flexibly naming decimals using like place value units. To round 3.85 to the nearest tenth, students find the nearest multiples, 3.80 (38 tenths 0 hundredths) and 3.9 (39 tenths 0 hundredths), and then decide that 3.85 (38 tenths 5 hundredths) is exactly halfway between and, therefore, must be rounded up to 3.9.

Content Standard(s):
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
5. Use place value understanding to round decimals to thousandths.
Unpacked Content
Evidence Of Student Attainment:
Students:
When given a decimal number,
  • Use place value vocabulary and models to justify the rounding of the number to a specified place value.
  • Rounded to a specified place value, identify a number that could have resulted in that rounding.
Teacher Vocabulary:
  • Round
  • Place value
  • Tenths
  • Hundredths
  • Thousandths
  • Decimal
  • Number line
  • Midpoint
Knowledge:
Students know:
  • how to use place value understanding to round multi-digit whole numbers to any place.
Skills:
Students are able to:
  • Round decimals using place value understanding.
Understanding:
Students understand that:
  • in the base ten system, the adjacent place value relationship extends to decimals and is used to round decimals.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.5.5.1: Round multi-digit whole numbers to any place.
M.5.5.2: Round whole numbers to the nearest 10 or 100.

Prior Knowledge Skills:
  • Use the standard algorithm to find a product.
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 (<, >, =).
Tags: baseten, compare, decimals, digits, expanded form, number names, place value, round, thousandths, unit form
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Author: Hannah Bradley
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