4.NF.7 - About the Math, Learning Targets, and Rigor
Grade 4 Decimals (4.NF.7)
About the Math, Learning Targets, and Rigor
Full Standard
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions( e.g., by using a visual model).
Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Learning Targets
- Compare decimals using representations (decimal grids, base ten models, and number lines).
- Compare decimals using benchmarks (0, 0.5, and 1.00)
- Compare decimals using place value.
- Explain how decimals are compared.
- Estimate decimals relative to the benchmarks and compatible numbers.
- Record comparisons using >, <, or =.
About the Math
When comparing decimals, students should use models (such as hundredths grids) and number lines. When locating decimals on a number line the smaller numbers are farther to the left and the greater number is farther to the right. Often students are able to better understand comparing decimals if the problem is in context such as comparing scores or records of athletes. Students need to understand that some decimals are equivalent. Sharing examples with models to show that .4 = .40 will help students see the equivalency. Decimal numbers are rational numbers and so we can use them to indicate quantities that are less than one or between any two whole numbers. In between any two decimal numbers, there is always another decimal number.
Progression of Standard within Grade 4
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
| Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
|---|---|---|---|
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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.
| Grade 3 | Grade 5 |
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Preferred Tasks
These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.
Compare decimals:
- Snack Attack Links to an external site. +++
- Pet Store Links to an external site. +++
- Comparing Decimals on a Number Line Links to an external site. +++
- Comparing Train Times Links to an external site. +++
- Using Place Value Links to an external site. (Illustrative Math)
Lesson Seeds (Prompts for Rigor)
Rigorous mathematics instruction balances the teaching and learning of conceptual understanding, procedural understanding, and the application of mathematics standards. Below are prompts for applying rigor in your classroom. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning. See the Increasing Rigor page for more information.
- How does your knowledge of fractions and/or place value help you compare decimals? Use the comparison of .6 and .36 in your response.
- Write four decimals that are in between .3 and .67?
- What decimal could be less than .7 but have a 9 in it?
- How can you arrange the digits 5,3,0 to create the smallest/largest decimal possible? How can you arrange these digits to create a decimal between .5 and .9?
- Megan has a collection of dimes and pennies and Jennifer has 64 pennies. Megan is arguing that she has more money even though she less coins. What coins could Megan have that would make Megan correct? What coins could she have that would make Megan incorrect?
- How do you know that 0.04 < 0.40?
- When could .6 be smaller than .3? (e.g., .6 of a meter vs. .3 of a kilometer)
- What digits could be placed in the blank to make the number sentence true? 0.43 > 0.__9
+++ Indicates recently created HCPSS instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.
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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.
| Book Thumbnail | Book Title | Grade | Pages |
|---|---|---|---|
| Teaching Student-Centered Mathematics | 3-5 | Line 'Em Up, Activity 7.9, Page 191 Expanded Lesson Friendly Fractions to Decimals, Page 202 |
|
| Hands-On Standards, Common Core | 4 | 42 (Lesson 4) |
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| Hands-On Standards | 3-4 | 60-61 (Comparing Decimals) | |
| NumberSense |
4-6 |
116-120 | |
| Brain-Compatible Activities for Mathematics | 4-5 | 57-60 | |
|
Math In Practice Teaching Fourth-Grade Math |
4 | Module 10 |
Additional Tasks and Lesson Seeds
These links provide ideas for lessons connected to this standard. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning.
- Grammy Dotty's Quilt (rtf) Download Grammy Dotty's Quilt (rtf) (Utah Core Academy Lesson)
- Which Piece Do You Want (docx) Download Which Piece Do You Want (docx) (Utah Core Academy Lesson)
- Decimal Fraction Number Line Links to an external site. (Georgia Dept. Of Ed, pg.13)***
- Double Number Line Decimals Links to an external site. (Georgia Dept. of Ed. pg. 60)
- Money Exchange Links to an external site. (Georgia Dept. of Ed., pg.63)***
- In the Paper Links to an external site.(Georgia Dept. of Ed, pg.106)***
- Planning a 5K Links to an external site.(Georgia Dept. of Ed, pg.112)***
- Cell Phone Plans Links to an external site.(Georgia Dept. of Ed, pg.116)***
*** These lessons are all contained in the same file. ***
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Student-Facing Centers
These links provide online and print resources to engage students during independent or center time. These resources could also be used as lesson seeds.
- Comparing Decimals with Coins Download Comparing Decimals with Coins (HCPSS-adapted print resource)
- Close to 0, 1/2, or 1: Sticky Decimal Edition Download Close to 0, 1/2, or 1: Sticky Decimal Edition (HCPSS-adapted print resource)
- Dice Decimals Download Dice Decimals (HCPSS-adapted print resource)
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Comparing and Ordering Decimals
Links to an external site. (student-facing resource, pictured, choose hundredths)
- Compare Money Amounts Links to an external site. (student-facing resource)
- Ordering Decimals Balloon Pop Links to an external site. (student-facing resource)
- Fruit Splat Compare Links to an external site. (student-facing resource)
- Balloon Pop Math Links to an external site. (student-facing resource)
Independent Practice
These resource sheets can be used for independent practice or homework. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
- Comparing to Hundredths Links to an external site.
- Determining Greater / Less Than Value Links to an external site.
- Number Sentences with Decimals Links to an external site.
- Finding Decimals on Number Line Links to an external site.
- Ordering (hundredths) Links to an external site.
- Ordering #2 (hundredths) Links to an external site.
- Comparing with Money Links to an external site.
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Learning Targets
- Compare decimals using representations (decimal grids, base ten models, and number lines).
- Compare decimals using benchmarks (0, 0.5, and 1.00)
- Compare decimals using place value.
- Explain how decimals are compared.
- Estimate decimals relative to the benchmarks and compatible numbers.
- Record comparisons using >, <, or =.
Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. The recording sheet can be used to collect data. The rubric can be applied to any task. Select the preview icon to preview the task before downloading.
Recording Sheet
Download Recording Sheet (docx)
Rubric
Download Rubric (docx)
Assessment Tasks
These tasks align with the learning targets for the standard. They can be combined with other tasks for extended assessment opportunities. Teachers/students are not expected to complete all these tasks.
- Evaluate Inequalities Using a Given Model Links to an external site.
- Compare Decimals with a Model and in Writing Links to an external site.
- Compare Decimals with a Model and in Writing_2 Links to an external site.
- Compare Decimals with a Model, Inequality, and Written Explanation Links to an external site.
- Compare Decimals with a Model, Inequality, and Written Explanation_2 Links to an external site.
- Compare Decimals with a Number Line, Inequality, and Written Explanation Links to an external site.
- Compare Decimals with a Number Line, Inequality, and Written Explanation_2 Links to an external site.
- Compare Decimals without a Provided Model and Justify Comparison Links to an external site.
- Compare Decimals without a Provided Model and Justify Comparison_2 Links to an external site.
PARCC Released Items
These items are PARCC released items. They can be used for assessment or instruction. See notes at the bottom of each slide for more information.
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Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.