Author: Tutita Casa

Gr 6_EE_ExpressionsOrderOfOperations_Problem_Construct

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This problem is meant for students developing their understanding of the distributive property in algebraic representations. A number trick is a series of calculations in which the person giving the directions always knows what number the players will end up with. When the students are asked to represent Step 3 in a different way, they will use the distributive property. When students use parentheses, the outside number is the number of groups. The expression inside the parentheses is what is in one group. When they write the expression without parentheses, they are saying how many total x tiles and total 1 tiles they have. Switching between these two representations gives a concrete, visual, and abstract expression of using the distributive property to group and ungroup terms in an expression.

Microsoft Word version: 6_EE_ExpressionsOrderOfOperations_Problem_Construct

PDF version: 6_EE_ExpressionsOrderOfOperations_Problem_Construct

Gr 6_EE_ExpressionsEquivalence_Problem_Critique

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This task is designed for sixth grade students developing skills with geometric formulas for area while also working on algebraic interpretations of expressions and equations. Students are given the formula for the area of a triangle, written in two different ways. Students must use logic and algebraic knowledge to determine if the two expressions are equivalent, and why. This task highlights the relationship between multiplying by a fraction, and dividing. Students are critiquing a student interpretation.

Microsoft Word version: 6_EE_ExpressionsEquivalence_Problem_Critique

PDF version: 6_EE_ExpressionsEquivalence_Problem_Critique

Gr 6_EE_Expressions_Problem_Critique

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This task is for sixth-grade students learning algebraic expressions. Students are asked a series of questions on how many tiles are needed to frame a picture, given a set side length. Misconceptions on these algebraic expressions are addressed in part c, when students are asked to critique the mistake made by a customer. Combining in the second extension problem brings in argumentation, as students are asked to explain how they arrived at their answer.

Microsoft Word version: 6_EE_Expressions_Problem_Critique

PDF version: 6_EE_Expressions_Problem_Critique

Gr 6_EE_AlgebraRateOfChange_Problem_Construct

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This task is designed for sixth graders developing skills with rate of change. The task provides students with a distance travelled along with the amount of time taken. Students must use this information to determine how far someone could get in a given amount of time. Students must recognize that a rate of change is necessary. Students may solve the problem using a rate and creating an expression, or by creating equivalent fractions, which may open the class to discussion about different methods. Students are asked to provide an explanation and evidence for why a rate is necessary, which provides an opportunity for students to create a solid argument.

Microsoft Word version: 6_EE_AlgebraRateOfChange_Problem_Construct

PDF version: 6_EE_AlgebraRateOfChange_Problem_Construct

Gr 5_OA_Rounding_ArgumentFrame_Critque

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This task is an argument frame for fifth graders on rounding decimals. Students are given a problem on the price of roast beef per pound and two sample answers on rounding either the price or number of pounds bought to estimate a final cost. Through the graphic organizer, students have a place to provide the details of their decision of which of the given students are closer to the actual price through the argument frame.

Microsoft Word version: 5_OA_Rounding_ArgumentFrame_Critque

PDF version: 5_OA_Rounding_ArgumentFrame_Critque

Gr 5_OA_PropertyOddEvenSums_ThinkPairShare_Critique

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This task is a think-pair-share activity designed for fifth graders learning about properties of numbers, specifically odd numbers. Students are given a statement about odd numbers and must determine whether they agree or disagree with the statement. A template is given for students to make a claim and provide an argument to back the claim. Students must then consult with a partner and compare arguments. Students will use knowledge of the properties of both odd and even numbers.

Microsoft Word version: 5_OA_PropertyOddEvenSums_ThinkPairShare_Critique

PDF version: 5_OA_PropertyOddEvenSums_ThinkPairShare_Critique

Gr 5_OA_PropertyAssociative_Problem_Critique

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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

Gr 5_OA_MultiplicationMultiDigitAlgorithm_Problem_Critique_KellysSolution

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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

Gr 5_OA_Multiplication_ArgumentFrame_Critique

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This task is an argument frame for fifth graders on multiplication. Students are given a problem on collecting a number of acorns a day for a week and two solutions, one solving the problem by using groups and multiplying by seven and the other by adding the number of acorns collected a day seven times. Through the graphic organizer, students have a place to provide the details of their critique of the solutions, such as their claim, evidence, and warrants.

Microsoft Word version: 5_OA_Multiplication_ArgumentFrame_Critique

PDF version: 5_OA_Multiplication_ArgumentFrame_Critique

Gr 5_OA_EstimationDivision_Problem_Critique_TedAndJP

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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