Filling up on Apples is a problem created for fifth graders on fraction addition and comparing fractions. In the task, two people eat multiple fraction amounts of apples and students are to use equivalent fractions and knowledge of fraction addition to determine how many apples were eaten. Scaffolding is used to break down the fractions and allow students to work on the problem one step at a time. Students are asked, through argumentation language, to critique the response on who ate more apples and show justification.
Microsoft Word version: 5_NF_FractionsAdditionComparing_Problem_Critique_FillingUpOnApples
PDF version: 5_NF_FractionsAdditionComparing_Problem_Critique_FillingUpOnApples
I used this task in my 5th grade classroom. It involves adding three fractions with unlike denominators. When the fractions are added, the sum is greater than one. The students also need to compare two mixed numbers to decide which mixed number is greater. The task requires them to decide who ate the most pie based on their comparison of two mixed numbers.
Microsoft Word version: 5_NF_FractionsAdditionComparing_Problem_Critique_EatingPies
PDF version: 5_NF_FractionsAdditionComparing_Problem_Critique_EatingPies
The task, Comparing Decimals, is created for fifth graders working on reading decimals and learning about place value of decimals. Students are asked to compare two decimals. The task offers two different variations: students are asked to either critique the correct answer or critique an incorrect answer. The incorrect response addresses a common error in which students believe a number to be larger based on the number of digits visible or based on larger digits after the decimal point. The task includes argumentation language including claim and warrants.
Microsoft Word version: 5_NBT_DecimalsComparing_FamilyOfTasks_Critique_ComparingDecimals
PDF version: 5_NBT_DecimalsComparing_FamilyOfTasks_Critique_ComparingDecimals
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
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
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
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
Different Ideas is a task designed for third graders to understand how to compare two fractions with the same numerator but different denominators. Students must critique Penelope’s idea that the bigger fraction is the one with the bigger denominator. Argumentation language is used when reminding students to provide a claim, evidence, and warrants.
Microsoft Word version: 3_NF_FractionsComparing_Problem_Critique_DifferentIdeas
PDF version: 3_NF_FractionsComparing_Problem_Critique_DifferentIdeas