This task was designed for 6th graders working on condensing their writing to make their argument completely and quickly. The content is scaling figures, using proportional reasoning to prove similarity. Students who struggled with mulitiplying decimals struggled to find a multiplier. Students also struggled with providing sufficient reasoning in the brief space.
Microsoft Word version: 6_RP_ProportionalReasoning_BriefArgument_Construct
PDF version: 6_RP_ProportionalReasoning_BriefArgument_Construct
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 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