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.

Quarter 1
Quarter 2
Quarter 3
Quarter 4
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.
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.
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.
Continue as needed.

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.

Increasing Rigor

  • 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

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.
Show grids and number lines.

The Illustrative Mathematics Project task below demonstrates expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

VDW3-5.png

Teaching Student-Centered Mathematics (Grades 3-5)

pg. 191-* Activity 7.9 Line 'Em Up, * Figure 7.11
pg 202-203 Expanded Lesson- Friendly Fractions to Decimals


Pick It, Shade It
  • Have students pick 2 digit cards from a deck.
  • Have students make a decimal (to the hundredths place) with their digit cards and record it below a blank grid.
  • Have students shade their grid to match their decimal.
  • Have students repeat this for the second grid.
  • Have students compare the two models using < , > , or = in the circle between the grid.
  • Bring the class together to share student ideas.


Human Number Line Race
  • Have students pull 4 digit cards from a pile to make a number with no more than 2 digits in their whole number.
  • Have students record their number on a sticky note or index card.
  • Have students put themselves in order from least to greatest without talking.
  • Measure the amount of time it took the students to put themselves in order and record the time on the board.
  • Challenge the students to beat their first time with new numbers. Tell students that there will be a penalty for breaking silence or numbers out of order.
  • Have students create a second number and put themselves in order.
  • Record the time and compare to see which was faster.

Greater Than / Less Than the Teacher’s Number Challenge
  • The teacher creates a 5 digit number that goes to the thousandths place
  • Have students guess the number by asking questions about the number. (For example, is there a 9 in the number? If there is write the number on the board and let the students ask another question). Continue until the students discover the teacher’s number.
  • After finding the teacher’s number, have students create a number that is greater than the teacher’s number and a number that is less than the teacher’s number and record it on a sticky note. Each number created has to have 5 digits and go to the thousandths place.
  • Collect numbers from students. Share a number with the class and have them identify if the number should be placed to the right of the teacher’s number (greater than the number) or to the left of the number (less than).
  • The challenge is to get all of the numbers placed without making any mistakes. If so, the teacher creates a new number and tries to place the number cards with the students without making any mistakes.

Learnzillion Video Resources (4 Lessons)

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Select image for lesson set.


Print Resources:

hands_on_standards_cc_fractions_4.jpgHands-On Standards, Common Core Fractions, Gr 4

Compare and Order Fractions Lesson 4, pg 42
braincompatible4-5.pngBrain-Compatible Activities for Mathematics 4-5 (57-60)
hands-on_standards.png
Hands on Standards (Grades 3-4), pgs. 60-61 (Comparing Decimals)
numbersense.pngNumber Sense 3-4 (116-120)

Web Resources:

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lessons.jpg
student_resources.jpg
video_segments.jpg
Games and Centers
Lessons
Student Resources
Video Segments
Comparing and Ordering Decimals
Choose "Decimal Hundredths"
Comparing Decimals
(lesson seed)
Virtual Manipulatives

Teacher guide for Virtual Manipulatives 4.NF.6 & 4.NF.7
Learnzillion Video Resources
(4 lessons)
Compare Money Amounts
StudyJams
Decimal Sort
(lesson seed)


Ordering Decimals Balloon Pop
(online game)
Trashcan Basketball
Decimal Chart


Expanding Decimals with Money



Grammy Dotty's Quilt
Cache Public Schools, Utah



Comparing and Ordering Fractions and Decimals



Comparing Decimals using Money



Decimal Fraction Number Line
Georgia Dept. Of Ed, pg.13



Money Exchange
Georgia Dept. of Ed., pg.63



In the Paper
Georgia Dept. of Ed, pg.106



Planning a 5K
Georgia Dept. of Ed, pg.112



Cell Phone Plans
Georgia Dept. of Ed, pg.116


Questions/Comments:
Contact John SanGiovanni at jsangiovanni@hcpss.org.


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Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.