Jake’s Idea is a problem for fifth graders on division with remainders. Students are given a statement that a four-digit number will have a remainder when being divided by 4 and must take a stance. Through argumentation language, students must critique the statement and give evidence to support their claim.
Microsoft Word version: 5_OA_DivisionRemainders_Problem_Critique_JakesIdea
PDF version: 5_OA_DivisionRemainders_Problem_Critique_JakesIdea
Dot Pattern is a scaffolded task in which students must create an expression to represent the number of dots in a figure at any given point in a pattern. Students are given a visual representation of the first three figures and asked to think about how the figures change each time, and how the next figures would look. Ultimately, students will generate an algebraic expression to represent any figure. Students must construct an argument in order to explain why an expression works and where it comes from.
Microsoft Word version: 5_OA_AlgebraPatterns_Problem_Construct_DotPattern
PDF version: 5_OA_AlgebraPatterns_Problem_Construct_DotPattern
Getting There is a problem created for fifth graders on adding numbers in different combinations. Students are given a distance a frog hops in three hops and a set of questions asking them about three numbers that will add up to the distance. The task provides a variation to include more argumentation language, specifically to explain their thinking, as they construct a response.
Microsoft Word version: 5_OA_AdditionCombinations_Problem_Construct_GettingThere
PDF version: 5_OA_AdditionCombinations_Problem_Construct_GettingThere
Fraction differences is a task designed for fifth graders to critique a comparison of two differences of fractions. The task highlights the skills of finding a common denominator, finding equivalent fractions, subtracting fractions, and comparing fractions. Students must agree or disagree with the student’s comparison of the differences, and explain his or her answer.
Microsoft Word version: 5_NF_FractionsSubtraction_Problem_Critique_FractionDifferences
PDF version: 5_NF_FractionsSubtraction_Problem_Critique_FractionDifferences
Making Hot Cocoa is a task on fraction multiplication and division for a fifth-grade classroom. Students are given a certain amount of cocoa powder and the fraction amount needed for each cup. Through a series of questions containing argumentative language, students are asked to construct a response to how many cups of cocoa they can make. Students are to construct a solution through a variety of methods, including pictures, mental thought, multiplication, and division. Sample solutions and commentary are provided.
Microsoft Word version: 5_NF_FractionsMultiplicationDivision_Problem_Construct_MakingHotCocoa
PDF version: 5_NF_FractionsMultiplicationDivision_Problem_Construct_MakingHotCocoa
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Turkish Delight is a task developed for fifth graders working on multiplication of fractions. Students must understand how to take a fraction of a fraction by using multiplication. Students are then asked to compare the resulting fraction with a given fraction and critique a student’s comparison. The task asks the student to explain reasoning. When making the comparison, students must either convert fractions to decimals, or find common denominators, because the fractions will have different denominators, which may be an area for discussion with the class.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_TurkishDelight
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_TurkishDelight
Harvesting Corn is a problem on fraction multiplication for fifth graders. Students are given the number of acres harvested and amount of days in a mixed number. The questions are scaffolded to require transformation of the mixed number to improper fraction, subtraction, and the final multiplication question that asks students to critique the thinking of a worker through argumentative language.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_HarvestingCorn
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_HarvestingCorn
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This task is created for fifth-grade students learning how to multiply fractions. Students are asked to critique the statement that half of a quarter is the same as a quarter of a half through multiple questions allowing for the problem to be visualized and broken down. A modification to the problem is presented to contain specific argumentation language, including as claim and evidence.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_5-11
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_5-11
This is a task designed for fifth graders learning how to multiply mixed numbers. Students are asked to critique a student’s strategy to multiply mixed numbers, which ends up addressing a common misconception in multiplication of mixed numbers. Students must determine if adding the product of the whole numbers to the product of the fractions is equal to multiplying the two mixed numbers. Students are asked to decide if this is a rule that works, and explain their answer.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Critique_5-32
PDF version: 5_NF_FractionsMultiplication_Problem_Critique_5-32
This task was used with 4th and 5th graders because it focused on multiplying fractions by whole numbers and converting common measurements. The main objective was to use a real world situation so that students would develop a deeper understanding of multiplying fractions by whole numbers as well as converting ounces and cups.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Construct
PDF version: 5_NF_FractionsMultiplication_Problem_Construct
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