4.NF.6 - About the Math, Learning Targets, and Rigor
Grade 4 Decimals
4.NF.6
Full Standard
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Note: Grade 4 expectations include decimals greater than 1 through 100 (i.e. 74.62).
Measurement Topic
This standard is reported on the report card in these quarters as follows:
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Report Card Measurement Topic: Demonstrates understanding of number, fraction, and decimal concepts.
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Quarter 1 | Quarter 2 | Quarter 3 | Quarter 4 |
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Report Card Measurement Topic: Demonstrates understanding of number and fraction concepts. |
Learning Targets
- Explain the relationship between a fraction and a decimal.
- Represent a fraction with a denominator of 10 or 100 as a decimal.
- Identify the tenths and hundredths place.
- Represent a decimal on a number line with varied endpoints (ticked number line and open number line).
About the Math
Students need to understand that decimals are an extension of our whole number base ten system. Decimals and fractions both represent parts of a whole. Students need to understand the value of the place and the relationship between place values so that 0.7 is ten times larger than 0.07. When reading decimals the decimal point is read as AND which separates the whole number from the decimal. Having students read decimal names out loud helps them make connections to fractions. When we see 0.4 we say, “Four-tenths” and 0.07 is read as “Seven Hundredths.”
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.
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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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TASKS
These tasks can be used with small group or whole group instruction.
- Begin the module by giving students the opportunity to share what they already know about decimals. Write one question on a piece of poster paper and hang them around the classroom. Give each group of students a different color marker. Groups should circulate around the room answering the different prompts and adding their ideas to the posters. After each group has had a chance to visit each question, share the responses with the entire class and facilitate a discussion about decimals. Questions ideas: I am thinking of some numbers between 1 and 2. What might they be? Write any number less than one. Where do you see decimals in your community? List as many places as possible. Where do you see fractions in your community? List as many places as possible. What do you know about decimal numbers? List the place values you remember.
- Use the resources Links to an external site.to create a visual representation of the relative size of tenths and hundredths. Students should work together to build the model of ten, one, tenths, and hundredths. After the model is constructed, ask students to represent decimal numbers (less than 20). Once students have a solid understanding of the relative size of tenths and hundredths, you can transition to using place value disks to build decimal numbers. Encourage students to use a place value mat when building numbers with the place value disks. Once a number is created using the manipulatives, students should write the numbers in expanded from to help solidify their understanding of the value of each digit.
- Use the zoomable number line Links to an external site. to investigate decimals on a number line. Navigate the number line while students notice, wonder, and observe the location of decimals on a number line.
- What is the relationship between decimals and fractions?
- Is it easier to convert a fraction to a decimal when the denominator is a multiple of 10? An even number? An odd number?
- Rewrite this number sentence using decimals : 40/100 + 2/100 = 42/100.
- Write three decimals that are in between ¼ and ¾? How do you know your answer is correct?
- Name two decimals that occupy the same point on a number line.
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 11 • Decimals
Read, Write and Represent Decimals (on a number line as well):
Additional Tasks
These links provide instructional ideas connected to this standard.
- Expanded Fractions and Decimals Links to an external site. (Illustrative Math)
- Dimes and Pennies Links to an external site. (Illustrative Math)
- How Many Tenths and Hundredths? Links to an external site. (Illustrative Math)
- Expanding Decimals with Money Download Expanding Decimals with Money (Georgia Dept. of Ed, pg.53) ***
- Base Ten Decimals Links to an external site. (Georgia Dept. of Ed, pg.21)***
- Decimal Designs Links to an external site. (Georgia Dept. of Ed, pg.33)***
- Converting Rainfall Data Download Converting Rainfall Data (Utah Core Academy Lesson)
- Aliens vs Robots Download Aliens vs Robots (Utah Core Academy Lesson)
*** 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.
Book Thumbnail | Book Title | Grade | Pages |
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Teaching Student-Centered Mathematics | 3-5 | Base-Ten Fractions to Decimals, Activity 7.2, Page 186 Calculator Decimal Counting, Activity 7.3, Page 187 |
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Hands-On Standards, Common Core | 4 | 22 Equivalent Fractions and Decimals Lesson 4 |
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Beyond Pizzas and Pies | 80-87 | ||
Hands-On Standards | 3-4 | 56 (Fractions as Decimals) | |
NumberSense |
4-6 |
185-187 223-225 |
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Math In Practice Teaching Fourth-Grade Math |
4 |
Module 10 |
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Centers
These print resources can be used during independent or center time. These resources could also be used as lesson seeds.
- Decimals Detectives Download Decimals Detectives (HCPSS-adapted print resource)
- Decimal Representation Download Decimal Representation (HCPSS-adapted print resource)
- Decimal Chart Download Decimal Chart (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.
- Read and Write Decimals a Links to an external site.
- Read and Write Decimals b Links to an external site.
- Represent as a Visual Model, Fraction, and Decimal Links to an external site.
- Identify Decimal Fractions and Decimals Represented by a Given Model Links to an external site.
- Explain Relationship Between Equivalent Fractions and Decimals Links to an external site.
- Evaluate Equations that Relate Decimal Fractions and Decimals Links to an external site.
- Match Decimal to Labeled Point on a Number Line Links to an external site.
- Plot Decimals and Decimal Fractions on a Number Line Links to an external site.
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Learning Targets
- Explain the relationship between a fraction and a decimal.
- Represent a fraction with a denominator of 10 or 100 as a decimal.
- Identify the tenths and hundredths place.
- Represent a decimal on a number line with varied endpoints (ticked number line and open number line).
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.
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This course content is offered under a CC Attribution Non-Commercial Share Alike
Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.