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
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
Agreeing or Disagreeing with Sally is a task designed for fourth graders working on fraction fluency. Students are asked to compare two fractions with different numerators and different denominators. Students must critique an argument that states that two fractions are equivalent by agreeing or disagreeing and explaining the decision. The task will also allow students to demonstrate ability to create equivalent fractions.
Microsoft Word version: 4_NF_FractionsEquivalence_Problem_Critique_AgreeingOrDisagreeingWithSally
PDF version: 4_NF_FractionsEquivalence_Problem_Critique_AgreeingOrDisagreeingWithSally
I used this task in my 3rd grade classroom as an introduction to equivalent fractions. Students were given a visual, as well as a written description of 2 different ways that students split a pizza. The idea was for students to shade in fraction pieces and see that the 2 fractions were equivalent, however students were not told how to go about solving the problem. The task gives students a place to write their claim and argument, as well as a place to write what their partner thinks.
Microsoft Word version: 3_NF_FractionsEquivalence_ThinkPairShare_Critique
PDF version: 3_NF_FractionsEquivalence_ThinkPairShare_Critique
What Do You Think is for third graders to understand the concept of fraction equivalence. Students are given a square divided into sections, with some of them shaded, and two responses as to the amount of squares shaded. Argumentation language is used when asking students to critique the given responses and explain their own thinking.
Microsoft Word version: 3_NF_FractionsEquivalence_Problem_Critique_WhatDoYouThink
PDF version: 3_NF_FractionsEquivalence_Problem_Critique_WhatDoYouThink