This task was used with fourth graders to develop reasoning skills with multiplication of a fraction and a whole number. It also requires students to solve a two-step problem by comparing their solution to data given in the problem.
Microsoft Word version: 4_NF_FractionsMultiplication_Problem_Critique_HeightOfSunflowers
PDF version: 4_NF_FractionsMultiplication_Problem_Critique_HeightOfSunflowers
This task was used with fourth graders. It requires students to understand the meaning of multiplication in relation to the value of the factors. The task emphasizes fractional number sense and the relationship of a fraction to 1.
Microsoft Word version: 4_NF_FractionsMultiplication_Problem_Critique_ComparingProducts
PDF version: 4_NF_FractionsMultiplication_Problem_Critique_ComparingProducts
Agreeing or Disagreeing with Sally is a task designed for fourth graders working on fraction fluency. Students are asked to compare two fractions with different numerators and different denominators. Students must critique an argument that states that two fractions are equivalent by agreeing or disagreeing and explaining the decision. The task will also allow students to demonstrate ability to create equivalent fractions.
Microsoft Word version: 4_NF_FractionsEquivalence_Problem_Critique_AgreeingOrDisagreeingWithSally
PDF version: 4_NF_FractionsEquivalence_Problem_Critique_AgreeingOrDisagreeingWithSally
Students were able to come up with more than one way to solve the problem and then compare the work of other students. The task also allowed students to argue about the reasoning of others.
Microsoft Word version: 4_NF_FractionsDecimals_Problem_Construct
PDF version: 4_NF_FractionsDecimals_Problem_Construct
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Running Out of Gasoline is task designed for fourth graders comprehending how to compare fractions. Students are given the amount of gas left in two different car tanks as a fraction with different numerators and denominators. The task is scaffolded through multiple questions that contain argumentative language asking the students to break apart the fractions, use equivalent fractions, and ultimately critique a response and provide justification.
Microsoft Word version: 4_NF_FractionsComparing_Problem_Critique_RunningOutOfGasoline
PDF version: 4_NF_FractionsComparing_Problem_Critique_RunningOutOfGasoline
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I used this task in the beginning of the school year with 6th graders who were struggling with fractions. I had 2 main objectives for this task. One was to give students more practice with equivalent fractions, and two was to introduce the Talk Frame to the students.
Microsoft Word version: 4_NF_FractionsComparing_Problem_Critique_WhoAteMore
PDF version: 4_NF_FractionsComparing_Problem_Critique_WhoAteMore
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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
We used this task to teach teachers about how to use a Talk Frame in their instruction to begin lessons that support argumentation. The main objective was to develop teachers’ understanding of how to use the Talk Frame in order to give students the opportunity to first work independently, then as a group, then for groups to present 3 distinct approaches/strategies to problem solving and finally to critique each other’s mathematical argument. This task required teachers to experience participating in a Talk Frame from the lens of the student. They needed to work with their groups to select a strategy, provide evidence of how the strategy got them to their solution, and finally to come away with some understandings either about Talk Frames or around the actual content of the problem.
Microsoft Word version: 4_NF_FractionsAddition_Problem_Construct
PDF version: 4_NF_FractionsAddition_Problem_Construct
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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
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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