A quick overview of the first math domain and first cluster found in Grade 6 Common Core State Standards. It contains a mere 3 standards based on the domain of Ratios and Proportional Relationships...so as you would guess, it has a lot of lead in points to Algebraic concepts and is therefore a critical domain to cover with students.
The following question is a standards-aligned model question from New York for Gr. 6 Domain 1 / Cluster 1.
Students answering parts a-c of this question will utilize many elements of standards 1-3 that make up the cluster: Understand ratio concepts and use ratio reasoning to solve problems.
Challenge 1: Aside from noodling through parts a & b of this question. Take a moment and type up your own approach to solving part c and identify what you'd expect a student to "show" in order to demonstrate they not only solved part c, but understood a viable approach to its solution. (when you've finished, go to the next activity to compare your notes on this problem versus that of a proficient student's)
Source: New York Department of Education
Ahhh, the classic tree trunk problem as adored by Forestry Science Majors, Arborists, and Middle School Math teachers alike. This is a model question taken from the California High School Exit Exam as related to CCSS Math, Gr.6 Domain 1 / Cluster 1.
*Consider which of the three standards for Cluster 1 are tied to the skills students would need to solve this problem.
Source: California Department of Education - PD-ROM (www.pdrom.coursepath.org)
Let's assume you would like to make an instructional video available to your students the night before covering these standards and specifically the concepts of Rate and Common Ratios.
Of the following two video tutorials below, which do you think would be most effective for your students and why?