Fractions

Gr 4_NF_FractionsComparing_Problem_Critique

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This task asks fourth grade students to critique a student’s comparison of two fractions. The task asks student to agree or disagree and provide an expanation. Students must compare fractions with different denominators. This addresses the common error of students only looking at the numerators and comparing them. The task may also require students to create equivalent fractions by finding common denominators in order to compare the fractions.

Microsoft Word version: 4_NF_FractionsComparing_Problem_Critique

PDF version: 4_NF_FractionsComparing_Problem_Critique

Gr 4_NF_Fractions_Problem_Critique_DifferentDenominators

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This task was used with fourth graders to develop reasoning skill with fractional equivalence related to adding fractions. The task requires students to demonstrate an understanding that unlike fractions must be converted to equivalent forms to be added.

Microsoft Word version: 4_NF_Fractions_Problem_Critique_DifferentDenominators

PDF version: 4_NF_Fractions_Problem_Critique_DifferentDenominators

Gr 4_NF_Fractions_Problem_Critique

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I used this task during a fourth grade unit on fractions. I wanted to measure students’ understanding of equivalence. The objective was for students to demonstrate their understanding of equivalent fractions using a graphic organizer for a mathematical argument. Students struggled to figure out how they could fill in the evidence section of the graphic organizer.

Microsoft Word version: 4_NF_Fractions_Problem_Critique

PDF version: 4_NF_Fractions_Problem_Critique

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Gr 4_NF_Fractions_Problem_Critique_CarlosThoughts

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Carlos’ Thoughts is a task created for fourth graders working on fractions. The task asks students to crtique a comparison of a mixed number to an improper fraction. The task uses argumentation language including claim, evidence and warrant. This task gets at a common error in reading mixed numbers versus improper fractions in which students see a whole number in front of a fraction and assume it is larger than the improper fraction. The task may also display a student’s ability to convert between mixed numbers and improper fractions.

Microsoft Word version: 4_NF_Fractions_Problem_Critique_CarlosThoughts

PDF version: 4_NF_Fractions_Problem_Critique_CarlosThoughts

Gr 4_NF_Fractions_Problem_Critique_AShadedRectangle

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A Shaded Rectangle is a fractions problem involving a picture for fourth graders. Students are given a rectangle divided into sections, with some sections shaded, and a given student response stating how much of the rectangle is shaded. Argumentation language is used when asking students to critique the response, create a claim, and explain their thinking on whether the student response is correct.

Microsoft Word version: 4_NF_Fractions_Problem_Critique_AShadedRectangle

PDF version: 4_NF_Fractions_Problem_Critique_AShadedRectangle

Gr 4_NF_Fractions_BriefArgument_Construct

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This task was intended for grade 4 students. The main objective was to have the students demonstrate understanding of equivalent fractions. The task required them to construct an argument which would help explain whether they agreed or disagreed with the claim.

Microsoft Word version: 4_NF_Fractions_BriefArgument_Construct

PDF version: 4_NF_Fractions_BriefArgument_Construct

Gr 3_NF_FractionsEquivalence_ThinkPairShare_Critique

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I used this task in my 3rd grade classroom as an introduction to equivalent fractions. Students were given a visual, as well as a written description of 2 different ways that students split a pizza. The idea was for students to shade in fraction pieces and see that the 2 fractions were equivalent, however students were not told how to go about solving the problem. The task gives students a place to write their claim and argument, as well as a place to write what their partner thinks.

Microsoft Word version: 3_NF_FractionsEquivalence_ThinkPairShare_Critique

PDF version: 3_NF_FractionsEquivalence_ThinkPairShare_Critique

Gr 3_NF_FractionsEquivalence_Problem_Critique_WhatDoYouThink

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What Do You Think is for third graders to understand the concept of fraction equivalence. Students are given a square divided into sections, with some of them shaded, and two responses as to the amount of squares shaded. Argumentation language is used when asking students to critique the given responses and explain their own thinking.

Microsoft Word version: 3_NF_FractionsEquivalence_Problem_Critique_WhatDoYouThink

PDF version: 3_NF_FractionsEquivalence_Problem_Critique_WhatDoYouThink

Gr 3_NF_FractionsComparing_Problem_Critique_ComparingFractions

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This task was used with third graders to develop fractional number sense. It emphasizes the relationship of the denominator to the size of a unit fraction. Students struggle with this fundamental understanding of fractions because it contradicts the relationship of whole numbers that they are familiar with (i.e. as the number in the denominator gets larger, the value of the unit fraction gets smaller). This task requires students to realize that the denominator signifies the number of equal parts in the whole. Consequently, the more equal parts there are in the whole, the smaller each fractional part becomes.

Microsoft Word version: 3_NF_FractionsComparing_Problem_Critique_ComparingFractions

PDF version: 3_NF_FractionsComparing_Problem_Critique_ComparingFractions