We used this task for sixth graders. The objective was for students to use proportional thinking to reason out which recipe was more concentrated. Students selected one of two solutions in order to state a claim, provide evidence and state a warrant. Many students would find a common denominator in order to demonstrate a higher value ratio of corn syrup to water or total amount (sweeter) or lower value (less sweet). Students might also show how one mixture is sweeter with visual representations such as circles or a drawing of a pitcher with labeled portions.
Microsoft Word version: 6_RP_ProportionalReasoning_Problem_Critique_WhichIsSweeter
PDF version: 6_RP_ProportionalReasoning_Problem_Critique_WhichIsSweeter
I used this task with a group of 5 students that I selected for my evaluation. When I started with this group in mid/late January they were chosen by the teacher and myself to receive intervention as well. This year the students were learning about ratios and proportions. I tried to build their understanding of ratios by doing Number Talks before giving them this particular task. The students were required to use a rubric I found on the Exemplars website to help guide them in solving and writing an argument for this problem. The students were instructed to use more than one model to solve this task
Microsoft Word version: 6_RP_ProportionalReasoning_Problem_Critique_CarlylesPlants
PDF version: 6_RP_ProportionalReasoning_Problem_Critique_CarlylesPlants
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
We used this task for sixth graders later in the year after working with argumentation for several months. As students became proficient with providing evidence and warrants for their own arguments, we transitioned to explaining others’ reasoning. This task required students to provide warrants to explain the evidence provided. Students needed to understand the distributive property, commutative property, and how to simplify equations. Some struggled with explaining why each step was “warranted.”
Microsoft Word version: 6_EE_ExpressionsSimplifying_ArgumentFrame_Critique
PDF version: 6_EE_ExpressionsSimplifying_ArgumentFrame_Critique
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 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