ALEX Learning Activity

  

Comparing Fractions: Build Your Own Models

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

You may save this Learning Activity to your hard drive as an .html file by selecting “File”,then “Save As” from your browser’s pull down menu. The file name extension must be .html.
  This learning activity provided by:  
Author: Samantha Wallace
System:Limestone County
School:Cedar Hill Elementary School
  General Activity Information  
Activity ID: 2531
Title:
Comparing Fractions: Build Your Own Models
Digital Tool/Resource:
Fraction Model Templates
Web Address – URL:
Overview:

Students will work in groups to create cards using templates. Each card will have a model of the fraction, mixed number, or improper fraction. After making the cards, students will answer questions during a whole-class discussion to compare fractions with different numerators and denominators using visual models or benchmarks.

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:
Before/Engage
Activity:

  • Begin by drawing a rectangle on the board. Invite a student volunteer to shade in three-fourths. As the student works, invite the other students to ask questions. If no one asks, ask the student how they know they have three-fourths.

  • Repeat the same process with the fraction three-eighths, one and one-third, and five-fourths, making sure students have seen a model for both an improper fraction and a mixed number. It’s okay if the students are not completely comfortable with drawing these models because they will have a chance to practice in the activity.

  • Put the students in groups of 3-4. Give each group a fraction list, a fraction template sheet, and 3 sheets of copy paper. It’s helpful to give each group a different color of copy paper to keep the cards from getting mixed up, but it’s not necessary.  Each group will also need scissors, glue, and something to write with.

  • Students should fold and cut their blank paper into fourths so that they have 12 cards. Their job is to create a model for the 12 fractions on their list. They should shade in the required number of pieces on the fraction templates and then glue the model onto the card. The last step is to label the models on the card with the fraction.

  • Rotate around to each group, helping and encouraging participation as needed. If a group finishes early, they can try to sort their cards into groups: less than one/more than one, fraction/mixed number/improper fractions, etc.

  • After each group gets finished making their cards, have them come back to sit together as a whole group with their groupmates. Explain that you are going to ask a question and the group will have to decide which card to choose as their answer. They should discuss with their groupmates before picking a card and they will need to be prepared to defend their answer.

  • Ask the students to find a card that fits the following statement:

    • Show me a fraction that has more than one whole.

    • Show me a fraction that is less than one half.

    • Show me a fraction that has an even number of pieces.

    • Show me a fraction that is bigger than one third.

    • Show me a fraction that is bigger than seven-eighths.

  • After each group has chosen a card, choose a group to defend their answer. Be sure to call on groups that are both correct and incorrect to point out any misconceptions. If you have time, choose two groups that chose different cards (both correct) and ask the class to decide which one is correct.  

  • Encourage students to use benchmarks and comparisons about numerators and denominators. For example, students might say that two-thirds is bigger than two-fifths because they both have two pieces but thirds are bigger than fifths. Another possible strategy to highlight is that four-fifths is smaller than seven-eighths because they are both only one piece away from being a whole but the missing fifth is bigger than the missing eighth. It might be helpful to draw/show the models on a document camera to further illustrate these ideas as they are discussed.
Assessment Strategies:

Monitor the students as they are building the cards and answering the class discussion questions to ensure students are able to correctly compare fractions with different numerators and denominators. Student conversations will give insight into the strategies that students are using to compare the fraction models.  You can use a checklist with student names to keep track of who needs extra help or enrichment.
Advanced Preparation:

You will need to make copies of the fraction lists and fraction template sheet for each group. Each group will also need copy paper (white or colored), scissors, glue, and something to write with.
Variation Tips (optional):

One option is to turn the discussion at the end into a competition.  As each group chooses a card, they can earn a point for their team if it matches the description. The winning team is the group that has the most points.
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