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
Students were able to come up with more than one way to solve the problem and then compare the work of other students. The task also allowed students to argue about the reasoning of others.
Microsoft Word version: 4_NF_FractionsDecimals_Problem_Construct
PDF version: 4_NF_FractionsDecimals_Problem_Construct