## Thursday, September 18, 2014

### Math problems of the week: more Common Core-inspired math problems

A continuing series...

From a site called the Mathematics Common Core Toolbox, which advertises itself as

a resource designed to support districts working to meet the challenge and the opportunity of the new standards. Here you will find tools and instructional materials that help you to better understand and to implement the CCSSM.
Here are two (part A and part B) of its 7th grade tasks, designed to align with the following math Standards:
MP.3    Construct viable arguments and critique the reasoning of others.
7.RP    Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.EE    Use properties of operations to generate equivalent expressions.

According to the site's explanation:
This two-part task integrates content from across the grade level and calls for students to apply proportional reasoning and properties of operations as they critique others’ reasoning. The idea of critiquing the reasoning of others (MP.3) is a new demand in the CCSSM not typically addressed on most current state assessments. This is an important feature of the task, thus making it a “practice forward” task.
According to the CCSSM, students in grade 7 use their understanding of ratios and proportionality to solve a wide variety of percent problems and use properties of operations to generate equivalent expressions. In this task, students must also evaluate two different forms of reasoning and justify their analysis.
In Part a, students engage in a multistep percent scenario; they must deal with both discount and sales tax. This fairly traditional assessment item provides an entry point to set up the reasoning and understanding required in Part b, in which students are presented with two lines of reasoning and must evaluate whether the two are equivalent. The crux of the reasoning rests in their ability to apply properties of operations to algebraic equations.