ALEX Learning Activity

  

Comparing Fractions: Race to the Number Line

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  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2537
Title:
Comparing Fractions: Race to the Number Line
Digital Tool/Resource:
Fraction Cards
Web Address – URL:
Overview:

Students will work in groups to put fraction cards on a number line.  They will need to use strategies based on fraction models and benchmarks to determine the proper placement.  This can be done as a race between groups.

This activity results from the ALEX Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 4
14. Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, ½, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.

a. Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Compare two fractions with different numerators and different denominators using concrete models, drawings, and benchmarks (0, 1/2, 1).
  • Recognize that comparisons are valid only when the two fractions refer to the same whole.
  • Record the comparisons of two fractions using symbols >,<, or =, and justify the conclusions.
Teacher Vocabulary:
  • Compare
  • Equivalent fraction
  • Numerator
  • Denominator
  • Benchmark fraction
  • Concrete model
  • Visual model
  • Length model
  • Area model
Knowledge:
Students know:
  • Comparing two fractions is only valid if they refer to the same whole.
  • Meaning of comparison symbols,<, >, or = .
  • Fractions can be represented by a variety of visual models (length and area).
Skills:
Students are able to:
  • Use concrete models, benchmarks, common denominators, and common numerators to compare two fractions and justify their thinking.
  • Explain the comparison of two fractions is valid only when the two fractions refer to the same whole.
Understanding:
Students understand that:
  • When comparing fractions they must refer to the same whole.
  • Benchmark fractions can be used to compare fractions.
  • Fractions can be compared by reasoning about their size using part to whole relationship.
  • Fractions can be compared by reasoning about the number of same-sized pieces.
  • Fractions can be compared by reasoning about their size when there are the same number of pieces.
  • Fractions can be compared by reasoning about the number of missing pieces.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.4.14.1: Identify fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts and size 1/b.
M.4.14.2: Identify a fraction as a number on the number line; represent fractions on a number line diagram.
M.4.14.3: Recognize a fraction as a number on the number line.
M.4.14.4: Represent fractions on a number line diagram.
M.4.14.5: Recognize fractions as numerals that may represent division problems.
M.4.14.6: Label numerator, denominator, and fraction bar.
M.4.14.7: Identify parts of a whole with two, three, or four equal parts.
M.4.14.8: Distinguish between equal and non-equal parts.

Prior Knowledge Skills:
  • Recognize fractions as lengths from zero to one.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
  • Identify a number line.
  • Recognize whole numbers as lengths from zero to one.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
  • Identify a number line.
  • Label the fractions on a pre-made number line diagram.
  • Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2…, and represent whole-number sums and differences within 100 on a number diagram.
  • Recognize a number line diagram with equally spaced points.
  • Compare length using non
  • standard units to determine which is longer.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.13 Identify and compare models of a whole (1), one-half (1/2), one-third (1/3), and one fourth (1/4) using models, manipulatives, numbers lines, and a clock.
Learning Objectives:

Students will be able to compare fractions with different numerators and denominators using models and benchmarks.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

  • Begin by putting students in groups of 3-4. Each group will need a set of fraction cards and a set of anchor cards.

  • Each group will need plenty of room to spread out on the floor or a group of desks. They will place their anchor cards (0, 1/2, 1, and 2) in order to create a number line. They must work together as a group to put their fraction cards in the correct spot on the number line.

  • Tell students that some fractions may be equivalent and will need to be on the same spot on the number line. They need to make sure that all cards are visible, even if they are at the same spot.

  • As students are working, walk around and question students on their placement of the cards on the number line. If students need help, encourage them to draw a model or use strategies based on benchmarks or comparing the size of the pieces.

  • If you want to make the activity a race, the first group to have all of their fraction cards in the correct spot on the number line wins.
Assessment Strategies:

Observe and question students to assess their ability to compare fractions using benchmarks, models, or the size of the pieces. You can use a checklist to keep track of which students are struggling or need enrichment.
Advanced Preparation:

You will need a set of fraction cards and anchor cards for each group of students. The students will need room to spread out to make the number line, so plan to give each group some space. (Consider going outside if the weather is nice!)
Variation Tips (optional):

  • You can have each group check the work of the other groups after everyone is finished.

  • You can accommodate the activity by removing some of the fraction cards or limiting the number line to between 0 and 1. 

  • Another option is to complete the number line as a whole class -- give each student a fraction card and have them place it in the correct spot.
Notes or Recommendations (optional):

14. Compare two fractions with different numerators and different denominators using concrete models, benchmarks (0, ½, 1), common denominators, and/or common numerators, recording the comparisons with symbols >, =, or <, and justifying the conclusions.
a. Explain that comparison of two fractions is valid only when the two fractions refer to the same whole.
  Keywords and Search Tags  
Keywords and Search Tags: benchmark fraction, compare, fraction, fraction model, greater than, improper, less than, mixed number, number line