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 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
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
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