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.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

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.

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.

TASKS

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

• Write decimals on index cards. Students choose two decimal cards and represent the decimals using manipulatives or on a number line. Students should explain which decimal is greater/less and justify their answers using the decimal representation they created.
• Provide students with an open number line. Using the decimals on the index cards, students should place the cards, in order, on the number line. After all cards have been placed, allow students to justify their thinking using the word bank vocabulary words (greater than, less than, hundredths, tenths, ones, value)
• Create a list of decimals that all fall between two consecutive whole numbers. Students should used models to order numbers from greatest to least. For students who are struggling, encourage them to evaluate each place value position. For example, if the decimals is 4.264 begin by asking students if the number is closer to 4 or 5. Then repeat with tenths, hundredths, and thousandths. At each place value, ask students to defend their choices with the use of a physical model or other conceptual explanation.
• 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

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.

Additional Tasks 

  These links provide instructional ideas connected to this standard. 

• Using Place Value Links to an external site. (Illustrative Math)
• 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. ***

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 Expanded Lesson Friendly Fractions to Decimals, Page 202
	Hands-On Standards, Common Core	4	42 (Lesson 4)
	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

Centers

  These print resources can be used 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)

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.

• Compare Decimals a Links to an external site.
• Compare Decimals b Links to an external site.

• 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.

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. This rubric can be applied to tasks and observations for assessment and/or grading. 

Rubric for Tasks Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.