Decimal Fractions

Lesson 6

Math

Unit 6

4th Grade

Lesson 6 of 13

Objective


Locate decimals on a number line and explain their placement.

Common Core Standards


Core Standards

  • 4.NF.C.6 — 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.

Foundational Standards

  • 3.NF.A.2

Criteria for Success


  1. Represent decimals to tenths on a number line marked in tenths (MP.5).
  2. Represent decimals to hundredths on a number line marked in tenths (MP.5) by reasoning about its relative location between two tenths (MP.5).
  3. Begin to understand the magnitude of decimals based on their location on a number line (i.e., understand that two decimals are equivalent if they are at the same point on a number line or that the farther to the right a decimal is on the number line, the greater it is).

Tips for Teachers


  • This interactive number line is a neat way to build students’ understanding of a decimals’ relative location on a number line and its magnitude. You could play around with this applet as a warmup to the lesson or after the Anchor Tasks to help build students’ estimation. The first page of the applet shows decimals to the tenths place and the second page shows decimals to the hundredths. Later pages are neat extensions of these ideas into smaller places.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks


Problem 1

a.   Label each tick mark on the number line with the number it represents.

b.   Here are eight numbers.

0.10 0.30 1.0 0.75 1.05 0.53 0.3 0.88
  1. Locate and label each number on the number line. 
  2. Nigel says two numbers above are located at the same point. Do you agree? Explain your reasoning. 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Illustrative Math Grade 4 Unit 4 Lesson 3Activity 1

Illustrative Math Grade 4 Unit 4 Lesson 3, accessed on July 24, 2023, 10:42 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

Determine the location of the points Q and T on the number line below.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Smarter Balanced Assessment Consortium: Item and Task Specifications Math Item Specifications - Claim 1, Grade 4 (G4_1H_NF_Spec_v4)Task Model 4c, Example Stem

Math Item Specifications - Claim 1, Grade 4 (G4_1H_NF_Spec_v4) from Development and Design: Item and Task Specifications made available by Smarter Balanced Assessment Consortium.  © The Regents of the University of California – Smarter Balanced Assessment Consortium. Accessed June 1, 2018, 2:32 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Here is a number line with two points on it.

a.   Name the decimal located at point A.

b.   Is the decimal at point A less than or greater than 0.50? Explain or show your reasoning.

c.   Is the decimal point at point B greater or less than 0.06? Explain your reasoning.

d.   Estimate the decimal at point B.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Illustrative Math Grade 4 Unit 4 Lesson 3Activity 2

Illustrative Math Grade 4 Unit 4 Lesson 3, accessed on July 24, 2023, 10:42 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

  • Vivian thinks that the decimal represented on the number line in #1c is 0.3. Zach says it is 0.30. Who is correct? How do you know? 
  • What did you notice about the number line in #1e? 
  • Look at #3. What endpoints did you choose to plot each number? Could you have chosen other ones?
  • Look at the first row in #3. How would you represent this number using only tenths? With your partner, use the number line or centimeter ruler to prove that 39 tenths is the same as 3 ones and 9 tenths. 

Target Task


a.    Plot the point $${{{76\over100}}}$$ on the number line below. Make sure to label the endpoints.

b.   What is $$\frac{76}{100}$$ written as a decimal?

Student Response

Create a free account or sign in to view Student Response

Additional Practice


The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Answer Keys

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

icon/arrow/right/large copy

Lesson 5

icon/arrow/right/large

Lesson 7

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Tenths

Topic B: Understanding Tenths and Hundredths

Topic C: Decimal Comparison

Topic D: Decimal Addition

Topic E: Money as a Decimal Amount

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free