Different Ideas is a problem designed for fifth-grade students to understand rounding decimals to the nearest hundredth. Two responses are given as to what a decimal rounded to the nearest hundredth is and students are to critique the response and choose a side. The task uses argumentation language when specifically asking for the claim and evidence.
Microsoft Word version: 5_NBT_DecimalsRounding_Problem_Critique_DifferentIdeas
PDF version: 5_NBT_DecimalsRounding_Problem_Critique_DifferentIdeas
Ordering Decimals with Zero Digits is a family of tasks on decimals to help fifth graders understand if decimals with more zero digits are greater than those without zero digits. In the first example given, the zeros are in the hundredths and thousandths place values, and the decimals to be ordered have the same number in the tenths place. In the second example, the ones, tenths, and hundredths place values are the same, while the zeros lie in the thousandths and ten-thousandths place. Both examples provide multiple variations and extensions to enforce stronger critiques of the given responses and to contain argumentation language.
Microsoft Word version: 5_NBT_DecimalsOdering_FamilyOfTasks_Critique_OrderingDecimalsWithZeroDigits
PDF version: 5_NBT_DecimalsOdering_FamilyOfTasks_Critique_OrderingDecimalsWithZeroDigits
This task is designed for fifth graders and uses a visual picture of a 100% block. It asks students to critique two student responses that state how much of the block is shaded. Each student takes a different approach, but essentially states equivalent answers. One student looks at all of the pieces individually, as 23 ones, and the other student looks at the pieces like place values, as 2 tens and 3 ones. Students must recognize that these are two different ways to arrive at the same answer. Students are asked to draw pictures and use words to explain how the two students came about the answer in different ways.This task is an excellent example of how students may use different interpretations and methods to solve the same problem.
Microsoft Word version: 5_NBT_DecimalsEquivalence_Problem_Critique
PDF version: 5_NBT_DecimalsEquivalence_Problem_Critique
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
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
This argumentation problem was designed for fifth graders understanding measurement and the relationship between area and volume. Students are given a visual representation of a floor plan, as well as the area and volume, and must critique the reasoning of the given response by investigating if the floor plan will always have the equal area and volume. This task provides a modification to simplify what is being asked of the students and contains argumentation language when asking students to create a claim, state evidence, and work through misconceptions.
Microsoft Word version: 5_MD_MeasurementAreaVolume_Problem_Critique
PDF version: 5_MD_MeasurementAreaVolume_Problem_Critique
This task is designed for fourth grade students learning about how to classify odd and prime numbers. Students are asked to critique a statement made by a student regarding odd and prime numbers. The task addresses a common misconception that all odd numbers are also prime numbers. Students are asked to use diagrams to help support answers and also provide a counter example in order to prove a statement is false.
Microsoft Word version: 4_OA_PropertyPrimeNumbers_Problem_Critique
PDF version: 4_OA_PropertyPrimeNumbers_Problem_Critique
Running a Race is a task designed for fourth graders working on multiplying fractions by a whole number. The task is an application problem that asks students to compare which answer will be larger. Skills necessary to complete this task sufficiently may include multiplying a fraction by a whole number, finding common denominators, and comparing fractions. Students are asked to make a claim and support it with an explanation.
Microsoft Word version: 4_NF_FractionsMultiplication_Problem_Critique_RunningARace
PDF version: 4_NF_FractionsMultiplication_Problem_Critique_RunningARace
Lemonade is a task for fourth-grade students learning how to multiply fractions, specifically a mixed number in this problem. Two responses are given as to how many lemons are needed, but no work is shown as to how an answer was determined. Through argumentative language, students are asked to critique given responses, provide evidence, and explain their thinking.
Microsoft Word version: 4_NF_FractionsMultiplication_Problem_Critique_Lemonade
PDF version: 4_NF_FractionsMultiplication_Problem_Critique_Lemonade
This task was used with fourth graders to develop reasoning skills with multiplication of a fraction and a whole number. It also requires students to solve a two-step problem by comparing their solution to data given in the problem.
Microsoft Word version: 4_NF_FractionsMultiplication_Problem_Critique_HeightOfSunflowers
PDF version: 4_NF_FractionsMultiplication_Problem_Critique_HeightOfSunflowers