1. Understanding New Expectations for Rigor in Mathematics
Middle School Level (Grades 6 – 8)

2. Turn and talk to the person next to you…name three aspects of rigor
So What is Rigor?
Turn and talk to the person next to you…name three aspects of rigor

3. 3 Aspects Conceptual Understanding Procedural Skill and Fluency
Application:
……which means

4. Rigor includes:
Conceptual Understanding: Students need a conceptual understanding of key concepts, such as place value and ratios. Teachers support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than just a set of mnemonics or discrete procedures.

5. Middle school rigor includes:
Conceptual Understanding:
Understand ordering and absolute value of rational numbers.

6. Rigor includes:
Procedural Skill and Fluency: Students need to have speed and accuracy when performing calculations. Teachers should structure class/homework time for students to practice core functions such as single-digit multiplication so students have access to more complex concepts and procedures.

7. Middle school rigor includes:
Procedural Skill and Fluency:
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently…

8. Rigor includes:
Application: Students need to be able to use math flexibly for applications. Teachers should provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content.

9. Rigor includes:
Application: Students need to be able to use math flexibly for applications. Teachers should provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to make meaning of and access content.

10. Middle school rigor includes:
Application:
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real world and mathematical problems.

11. And… 8 Mathematical Practices Application to real‐world Modeling
Multiple approaches

12. What is evidence of aspects of rigor?
What do students “say and do” in the classroom?
Turn and talk.

13. Analyzing a Task to Better Understand Rigor
Proportion of Instruments

14. Mr. Ruiz is starting a marching band at his school
Mr. Ruiz is starting a marching band at his school. He first does research and find the following data about other local marching bands.
Part A. Type your answer in the box. Backspace to erase. Mr. Ruiz realizes that there are brass instrument player(s) per percussion player.
Part B. Mr. Ruiz has 210 students who are interested in joining the marching band. He decides to have 80% of the band be made up of percussion and brass instruments. Use the unit rate you found in part A to determine how many students should play brass instruments. Show or explain all your steps.
Band 1
Band 2
Band 3
Number of Brass Instrument Players
123 42
150
Number of Percussion Instrument Players 41 14 50

15. Sub-Claim A: Major Content1 with Connections to Practices
The student solves problems involving the Major Content1 for her grade/course with connections to the Standards for Mathematical Practice.
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. CCSS.Math.Practice.MP6 Attend to precision

16. Understand ratio concepts and use ratio reasoning to solve problems.
CAS 1.1.c (CCSS.Math.Content.6.RP.A) 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables or equivalent ratios, tape diagrams, double number line diagrams, or equations.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

17. Evidence Table Evidence Statement Key Evidence Statement Text
Clarification MP
Calculator
6-C.8.1
Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as
1 + 4 = = 12 , even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 6.RP.A
i) Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p42.) The initial numerator and denominator should be
whole numbers.
2, 3, 6
yes

18. How do we know if students are successful?
How are conceptual understanding, procedure fluency, and/or application emphasized in this task?
How could evidence for math content be demonstrated in student work?
How could evidence for the standards of mathematical practice be demonstrated in student work?
Hand out/project item along with these questions so teachers can analyze the item through the lens of these questions.

19. Does the item address this claim?
The student solves problems involving the Major Content1 for her grade/course with connections to the Standards for Mathematical Practice.

20. Does the item address this standard?
Understand ratio concepts and use ratio reasoning to solve problems.
CAS 1.1.c (CCSS.Math.Content.6.RP.A) 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables or equivalent ratios, tape diagrams, double number line diagrams, or equations.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

21. Can we gather this evidence?
Evidence Statement Key
Evidence Statement Text
6-C.8.1
Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as
1 + 4 = = 12 , even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions. Content Scope: Knowledge and skills articulated in 6.RP.A

22. WARNING
The evidence tables are meant to clarify the details of assessment items. Within a standard there may only be a portion that needs clarification and that is the only part addressed in the evidence tables. The tables are only a supplementary document.

23. Does the item address these standards of mathematical practice?
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively. CCSS.Math.Practice.MP6 Attend to precision