Standard

Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 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 meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Student Language:

"I can read, write, and compare decimals to thousandths."

Explanation

About the Math, Learning Targets, and Rigor

This standard references expanded form of decimals with fractions included. Students should build on their work from Fourth Grade, where they worked with both decimals and fractions interchangeably.

They read decimals using fractional language and write decimals in fractional form, as well as in expanded notation. This investigation leads them to understanding equivalence of decimals (0.8 = 0.80 = 0.800).

5.NBT.3a example

Base-Ten Numeral (standard form): 34.802

Number Name (written form): thirty four and eight hundred two thousandths

Expanded form: 3 x 10 + 4 x 1 + 8 x 1/10 + 2 x 1/1000

5.NBT.3b example

• Comparing 0.25 and 0.17, a student might think, “25 hundredths is more than 17 hundredths”. They may also think that it is 8 hundredths more. They may write this comparison as 0.25 > 0.17 and recognize that 0.17 < 0.25 is another way to express this comparison.
• Comparing 0.207 to 0.26, a student might think, “Both numbers have 2 tenths, so I need to compare the hundredths. The second number has 6 hundredths and the first number has no hundredths so the second number must be larger.
• Comparing 0.451 to 0.49, a student might think, “I know that 0.451 is 451 thousandths (and may write 451/1000). 0.49 is 49 hundredths (and may write 49/100) but I can also think of it as 490 thousandths ( 490/1000). So, 490 thousandths is more than 451 thousandths.
• A common misconception that is directly related to comparing whole numbers is the idea that the longer the number the greater the number. With whole numbers, a 5-digit number is always greater than a 1-, 2-, 3-, or 4-digit number. However, with decimals a number with one decimal place may be greater than a number with two or three decimal places. For example, 0.5 is greater than 0.12, 0.009 or 0.499.

Resources

Videos

• Instructional Video (7:53 - 10:50)
• Khan Academy
  • Scroll to 5.NBT.3, click on skill, find videos on left side of each skill
• Learn Zillion
  • 5.NBT.3a
  • 5.NBT.3b
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 5th grade at bottom, then 5.NBT.3
• Common Core Sheets
  • 5.NBT.3a
  • 5.NBT.3b

Released Assessment Questions

PARCC

Common Core State Standards

5.NBT.3a

Read, write and compare decimals to the thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

• Tasks have “thin context” or no context.
• Tasks assess conceptual understanding, e.g., by including a mixture (both within and between items) of expanded form, number names, and base ten numerals.

5.NBT.3b

Read, write and compare decimals to the thousandths. b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

• Tasks have “thin context” or no context.
• Tasks assess conceptual understanding, e.g., by including a mixture (both within and between items) of expanded form, number names, and base ten numerals.

Performance Indicators: 5.NBT.3a, 5.NBT.3b

Level 5: Exceeds Expectations

Reads, writes and compares decimals to any place using numerals, number names, expanded form and symbols (>, <, =); rounds to any place and chooses appropriate context given a rounded number.

Level 4: Meets Expectations

Reads, writes and compares decimals to the hundredths using numerals, number names, expanded form and symbols (>, <, =), and rounds to any place.

Critiquing/Reasoning Standards

5.C.3

Reason about the place value system itself.

(Content Scope: Knowledge and skills articulated in 5.NBT.A)

• Tasks do not involve reasoning about place value in service of some other goal (e.g., to multiply multi-digit numbers). Rather, tasks involve reasoning directly about the place value system, in ways consistent with the indicated content scope.

Performance Indicators: 5.C.3

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on place value system including:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning, and providing a counterexample where applicable.

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response based on place value system including:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning.