5.NBT.3 - About the Math, Learning Targets, and Rigor

Grade 4 G/T Place Value and Decimals

5.NBT.3

About the Math

Full Standard

Read, write, and compare decimals to thousandths.

  1. 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).
  2. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

 

Learning Targets (I can)

  • Read and write decimals to the thousandths place in word form, base-ten form, and expanded form.
  • Represent decimals with base ten models and number lines.
  • Estimate decimals to a near benchmark.
  • Decompose decimals in varied ways (5.61 = 5.00 + 0.60 + 0.01; 5.61 = 5.50 + 0.11)
  • Compare two decimals to the thousandths using benchmark comparisons or place value.

 

About the Math

Our number system extends beyond the ones to decimal place values. These numbers represent values that are less than one and show parts of wholes. The value to each place to the right of the decimal point is found by dividing the previous value by ten. This is similar to how values to the left of the decimal point are found.

  • Read and write decimals to the thousandths place in word form, base-ten form, and expanded form.

Decimals can be written in several ways. Standard Form: 8.634 Expanded Form: 8 + 0.6 + 0.03 + 0.004 Word Form: Eight and six hundred thirty-four thousandths. The decimal point is always read as AND.

  • Represent decimals with base ten models and number lines.

Decimals can be represented in a variety of ways. Base ten models and number lines are essential. One can modify a hundred chart to show the relationship between 0.00 and 1.00 or other decimals. Note that reliance on money can be problematic as place values are expanded. 

  • Estimate decimals to a near benchmark.

Estimating decimals is similar to estimating whole numbers and fractions. Students should use number lines to justify estimations at first. Students should also estimate with benchmarks of 0, 0.5, and 1.0. In time, this is expanded to 0, 0.25, 0.5, 0.75, and 1.0. Students should note how the benchmarks of 0, 0.5, and 1.0 are related to numbers like 66, 66.5, and 67. 

  • Decompose decimals in varied ways (5.61 = 5.00 + 0.60 + 0.01; 5.61 = 5.50 + 0.11)

Decomposing decimals by place value supports develop of advanced computational strategies and the standard algorithm. Students should also decompose decimals in non-standard ways to further develop their number sense and computational fluency.

  • Compare two decimals to the thousandths using benchmark comparisons or place value.

Comparing decimals can become too dependent on procedure and less dependent on understanding. It is important that students understand how to compare decimals. They should make connections to how whole numbers are compared. Students should use relationships on number lines and other models to justify their comparisons. Students should also estimate to compare. 

Essential vocabulary for this standard includes: decimal, decimal place, expanded form, word form, >, <, and =.

 

Progression of Standard within Grade 4 G/T

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Read and write decimals to the thousandths place in word form, base-ten form, and expanded form.
  • Represent decimals with base ten models and number lines.
  • Estimate decimals to a near benchmark.
  • Decompose decimals in varied ways (5.61 = 5.00 + 0.60 + 0.01; 5.61 = 5.50 + 0.11)
  • Compare two decimals to the thousandths using benchmark comparisons or place value.

 

  

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 4 Grade 5
  • Read, write, and compare multi-digit whole numbers (4.NBT.2)
  • Compare two decimals to hundredths (4.NF.7)
  • Use place value understanding to round decimals to any place.. (5.NBT.4)

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

  • How would you compare 7,822.562 and 7,822.82? Explain how you know which number is larger or smaller?
  • How is comparing whole numbers similar/different than comparing decimals?
  • Why is 3.3 > 3.2999 even though 3.2999 has more digits?
  • Using expanded form, explain why 3.14 is larger than 3.014?
  • Write three decimals that are in between .4 and .675?
  • What decimal could be less than .7 but have a 9 in it?
  • What could the missing digit in 0.43 > 0._9 if the statement is true?
  • What is a number less than 0.245? Use expanded form to justify and explain your answer.
  • Jerome is a candy maker. He has three different pieces of fudge. The chocolate fudge weighs 4.562 pounds, the white fudge is 4.872 pounds, and the peanut butter fudge weighs 4.572 pounds. Taylor is really hungry for fudge, which piece of fudge should she pick? Explain your reasoning.

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 6 • Decimals

Read, Write, and Compare Decimals; Show Decimals on Number Lines:

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 3-5 Line 'Em Up, Activity 7.9, Page 191
  Hands-On Standards 5-6 26-27 "Decimal"
28-29 "Equivalent Fractions and Decimals"
30-31 "Compare and Order Fractions and Decimals"
Brain-Compatible Activities for Mathematics 4-5 57-60 "Put the Dot on the Spot"
63-65 "A Portrait of Parts"
   Number SENSE 4-6 102-106 "Sorting Decimals"
107-110 "Which Is Bigger?"
184-187 "Name a Decimal"

Math In Practice

Teaching Fifth-Grade Mathematics

 5 Module 1

 

 

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

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Assessment

Learning Targets

rubric

  • Read and write decimals to the thousandths place in word form, base-ten form, and expanded form.
  • Represent decimals with base ten models and number lines.
  • Estimate decimals to a near benchmark.
  • Decompose decimals in varied ways (5.61 = 5.00 + 0.60 + 0.01; 5.61 = 5.50 + 0.11)
  • Compare two decimals to the thousandths using benchmark comparisons or place value.

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

 

 

 

 

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