1. Understanding New Expectations for Rigor in Mathematics
Elementary Level (Grades 3 – 5)

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
To help students meet the standards, educators need to pursue, with equal intensity the three aspects of rigor in the major work of each grade.

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. In elementary rigor includes:
Conceptual Understanding:
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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. In elementary rigor includes:
Procedural Skill and Fluency:
Fluently multiply multi-digit whole numbers using the standard algorithm.

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. In elementary rigor includes:
Application:
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem

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

11. Analyzing a Task to Better Understand Rigor
Fraction Model

12. Sub-Claim C: Highlighted Practices MP
Sub-Claim C: Highlighted Practices MP.3,6 with Connections to Content3 (expressing mathematical reasoning)
The student expresses grade/course level appropriate mathematical reasoning by constructing viable arguments, critiquing the reasoning of others, and/or attending to precision when making mathematical statements..
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
Sub-Claim C includes Major, Additional and Supporting Content.
CCSS.Math.Practice.MP6 Attend to precision.

13. Understand decimal notation for fractions, and compare decimal fractions.
CAS 1.1.b.i (CCSS.Math.Content.4.NF.C) Understand decimal notation for fractions, and compare decimal fractions.
5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

14. Evidence Table Evidence Statement Key Evidence Statement Text
Clarification MP
4.C.4-5
Base arithmetic explanation/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in their response), connecting the diagrams to a written (symbolic) method.
Content Scope: Knowledge and skills articulated in 4.NF.C
Tasks have “thin context” or no context.
Tasks are limited to denominators 2,3,4,5,6,8,10,12, and 100 (CCSS footnote, p. 30).
2,3,5,6

15. How is this task rigorous?
How are conceptual understanding, procedure fluency, and/or application emphasized in this task?

16. Does the item address this claim?

17. Does the item address this standard?
Understand decimal notation for fractions, and compare decimal fractions.
CAS 1.1.b.i (CCSS.Math.Content.4.NF.C
5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

18. Can we gather this evidence?
Evidence Statement Key
Evidence Statement Text
4.C.4-5
Base arithmetic explanation/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in their response), connecting the diagrams to a written (symbolic) method.
Content Scope: Knowledge and skills articulated in 4.NF.C

19. 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.

20. Does the item address these standards of mathematical practice?
CCSS.Math.Practice.MP3 Construct viable argument and critique the reasoning of others.
CCSS.Math.Practice.MP6 Attend to Precision