Curriculum  /  Math  /  3rd Grade  /  Unit 6: Fractions  /  Lesson 11

Fractions

Lesson 11

Math

Unit 6

3rd Grade

Lesson 11 of 24

Objective

Place various fractions on a number line where the given interval is not a whole.

Common Core Standards

Core Standards

  • 3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  • 3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Criteria for Success

  1. Given a unit fraction on a number line, plot the whole by making a certain number of copies of the unit fraction adjacent to one another (e.g., to create the whole given $$ \frac{1}{5}$$, make copies of the unit fraction so that there are 5 equal pieces adjacent to one another).
  2. Given a non-unit fraction on a number line, construct the whole by partitioning the given fraction into the appropriate number of equal pieces so that they represent the unit fraction, and then add copies of the unit fraction so that they make a whole (e.g., to create the whole given $$ \frac{3}{5}$$, partition the given interval into 3 equal pieces so that they each represent $$ \frac{1}{5}$$, then make copies of that unit fraction so that there are 5 equal intervals adjacent to one another).
  3. Given a fraction greater than 1 on a number line, construct the whole by partitioning the given fraction into the appropriate number of equal pieces so that they represent the unit fraction, and then count the number of unit fractions that make a whole (e.g., to create the whole given $$\frac{5}{3}$$, partition the given interval into 5 equal pieces so that they each represent $$\frac{1}{3}$$, then plot a point at $$\frac{3}{3}$$ by counting up 3 intervals).
  4. Given a fraction on a number line, plot another fraction of the same whole by using any of the strategies above to find the whole, then partition the whole into the relevant fractional pieces (e.g., to plot $$\frac{2}{3}$$ given $$\frac{3}{4}$$, partition the interval into three equal pieces, then make a fourth copy of it to construct a whole; then partition that whole into thirds and plot a point at $$\frac{2}{3}$$ by counting up 2 intervals).

Tips for Teachers

This lesson provides many opportunities for students make sense of problems and persevere in solving them (MP.1). Each task pushes students to make sense of the meaning of fractions and their numerators and denominators and use that understanding to relate them to the whole as well as other fractions of the same whole.

Fishtank Plus

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

Anchor Tasks

25-30 minutes

Problem 1

Iskra is running a race as shown on the number line below. Iskra is $$\frac{1}{3}$$ of the way from the starting line to the finish line. Where is the finish line? Locate and label it on the number line below.

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

Locate 1 on each number line below. Label the point. Be as exact as possible.

a.   

b.   

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Find 1 — Part b

Find 1, accessed on March 19, 2019, 9:45 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 3

Locate $$\frac{5}{6}$$ on the number line. Label the point. Be as exact as possible.

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Find 2/3

Find 2/3, accessed on March 25, 2019, 12:08 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

15-20 minutes

Discussion of Problem Set

  • Look at #1. How can you tell just by looking at the numerator and denominator that $$\frac{3}{2} $$ would be to the right of 1?
  • Look at #4. Did anyone solve it without locating where 1 was? How did you know to do that?
  • Look at #6. What number corresponds with the point Anna mislabeled?
  • Look at #3 and #7. What do you notice about these number lines? What do you wonder?
  • How did you decide to create 5 fractions in #8? How did you know how to place fractions in relation to one another on the number line? Where would you place a fraction with 1 as the denominator, such as $$\frac{5}{1}$$? Where would you place the fraction $$\frac{4}{2} $$ on the number line? Why?

Target Task

5-10 minutes

Problem 1

The number line below shows two numbers, 0 and $$\frac{6}{5}$$.

Where is 1 on this number line?

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

The number line below shows two numbers, 0 and $$\frac{1}{2}$$.

Where is $$2\over 3$$ on this number line?

Student Response

Upgrade to Fishtank Plus to view Sample 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.

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.

Next

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

Lesson 12
icon/arrow/right/large

Lesson Map

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

Topic A: Understanding Unit Fractions and Building Non-Unit Fractions

Topic B: Fractions on a Number Line

Topic C: Equivalent Fractions

Topic D: Comparing Fractions

Topic E: Line Plots

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?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free