This problem was used by students after working visually and conceptually to explain division with fractions. They use this problem as a transition to dividing fractions using the mulitplicative inverse. Students benefitted from constructing a diagram that showed the fence sections. Constructing the diagram on graph paper, using 20 squares for the length helped students divide equally and find the fraction they needed. Explaining the connections between the diagram and the equation are very important for constructing the argument.
Microsoft Word version: 6_NS_FractionsDivision_Problem_Critique
PDF version: 6_NS_FractionsDivision_Problem_Critique
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
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
Dividing by a Decimal is a family of tasks on decimals to help fifth graders understand decimal division. Students are given a statement where a whole number is divided by a decimal and are to critique the provided answer. Different variations of the question are provided with scaffolding and argumentation language to promote stronger critiques of the response that include a claim and evidence.
Microsoft Word version: 5_NBT_DecimalsDivision_FamilyOfTasks_Critique_DividingByADecimal
PDF version: 5_NBT_DecimalsDivision_FamilyOfTasks_Critique_DividingByADecimal
This task is used with third grade students. The task is an application of single digit division, but encourages students to draw a picture in order to construct an argument. The application asks students to distribute cookies to 5 people, given 15 cookies. Students must construct an argument by stating a claim and providing evidence. Students are then encouraged to engage in a pair-share and understand a partner’s thinking.
Microsoft Word version: 3_OA_DivisionSingleDigit_WordProblem_Construct
PDF version: 3_OA_DivisionSingleDigit_WordProblem_Construct