I used this task to continue our 5th grade discussion about multiplying fractions. Prior to this talk frame, our class discussed the difference between multiplying whole numbers and multiplying fractions, and explored why fractions multiplied together result in a fraction that contains smaller pieces. Students struggled with the deeper conceptual understanding of why, and this talk frame supported that discussion.
Microsoft Word version: 5_NF_FractionsMultiplication_Problem_Construct_AngelasIdea
PDF version: 5_NF_FractionsMultiplication_Problem_Construct_AngelasIdea
This task is a multi-digit multiplication problem addressing the associative property for fifth-grade students. Students are given the statement 22 x (36 x 5) = (22 x 36) x 5, and after examining both expressions, are given two questions to critique. Scaffolded questions are provided with argumentation language to break down the problem and address the associative property.
Microsoft Word version: 5_OA_PropertyAssociative_Problem_Critique
PDF version: 5_OA_PropertyAssociative_Problem_Critique
Kelly’s Solution is a multi-digit multiplication problem in which fifth grade students are asked to crtique the work of a student. The student work highlights a common error of forgetting to leave a place holder when multiplying by the ten’s place during multiplication. Students must recognize the student’s error by examining the work shown, correcting the error, and providing the correct answer to the problem.
Microsoft Word version: 5_OA_MultiplicationMultiDigitAlgorithm_Problem_Critique_KellysSolution
PDF version: 5_OA_MultiplicationMultiDigitAlgorithm_Problem_Critique_KellysSolution
Ted and JP is a task designed for fifth graders in working on division and estimation. A problem is presented in which students must estimate a quotient, and students must critique two estimations and decide which is better. This requires students to critically think about how to make a good estimation. Students must state which estimation is better and explain the answer.
Microsoft Word version: 5_OA_EstimationDivision_Problem_Critique_TedAndJP
PDF version: 5_OA_EstimationDivision_Problem_Critique_TedAndJP
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
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