Sunnyside School District

Math Training

Conceptual Lessons

Good Afternoon

1. Where is your classroom in regards to the year-long fluency expectations? What’s working well and what challenges have come up?

2. Have you tried a performance task with your students? What challenges came up and how did you handle them?

3. What comes to mind when you think about teaching conceptually? What would this look like in a math classroom?

Year-long Fluency Standards

K---Add/Subtract within 5

1st—Add/subtract within 10

2nd—Add/subtract within 20; Add/subtract within 100 (includes regrouping)

3rd—Multiply/divide within 100; Add/subtract within 1000

4th—Add/subtract within 1,000,000

5th—Multi-digit multiplication using standard algorithm

6th—Multi-digit division; All operations with decimals

7th—Two-step equations

Rigor MeasurementWebb’s Depth of Knowledge (DOK)

• Four Levels

• Based on the cognitive demand of a task or question

• Process more important than product

• Used to write the new standards and assessments

• Teachers should think about the DOK of:• Their questions• Student activities• Classroom assessments

DOK Review

Read pages 1 and 2 in the document on Math DOK and come up with a statement about the difference between a DOK 2 and a DOK 3 activity.

How can you see the difference in a classroom?

DOK Questions

Think about the math that you are teaching right now and create a question at each DOK level (1-3).

Percentage of questions on AzMERIT at each DOK Level:

Level 1: 10-20%

Level 2: 60-70%

Level 3: 12-30%

Level 4: 0%

How do these compare to the activities and questions in your classroom?

DOK on AZMerit

CCSS Math Shifts

1. Focus

2. Coherence

3. RigorProcedural Skill and FluencyConceptual UnderstandingApplication of Math Standards

Math Practice Standards

1. Make sense of problems and persevere is solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Math Practices 3 and 5

Read Math Practices and discuss:

1. How would these look in a classroom?

2. What are all of the types of tools in MP 5?

3. What are the two parts to MP3? How can you give students an opportunity to practice these?

Math Practice 3 Suggestions

Critique the reasoning of others:

1. Show two or more solution methods for a problem.

2. Have students identify which is correct and why.

3. Create a common phrase or word to identify the common mistakes we make (oops!, pitfall, misconception, etc.)

Joe’s Solution:

2/3 + 1/3 = 3/6

Liz’s Solution:

2/3 + 1/3 = 3/3

12

Initial Instruction

Balance

Between

Concepts Procedures

13

Concepts and Procedures

Doing something correctly, in itself, does not indicate understanding.

Conceptual Understanding

• Students can explain HOW the math works.

• Students can explain why THEY are using a specific strategy.

• Students can derive formulas and/or shortcuts on their own.

• Students can explain the meaning of math symbols and numbers.

Teaching Conceptually

Two Methods:

1. Increase the depth of teacher questioning in your classroom during lessons AND REQUIRE all students to answer them.

2. Create conceptual activities where students discover an understanding.

Rigor (DOK) of Teacher Questions

Level 1 Questions:

1. Simplify using the order of operations.

2. Solve: 5x + 3 = 168

Level 2 Questions:

3. Represent this word problem with an equation or drawing.

4. Write (in words) your steps to solve the problem.

Level 3 Questions:

5. How do you know that your answer is correct?

6. Why can’t you add fractions with unlike denominators?

From Teacher Questions

Consider this:

• Did one student answer the question?

• Did the teacher answer the question?

• Did ALL of the students answer the question?

Reflection

What level of questions to you ask most often in your classroom?

How can you increase the level of your questions?

Create DOK2/3 QuestionWe Do

2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Activity

For an upcoming standard, identify concepts in the standard and create questions (DOK 2 or 3) that you will ask students to ensure they have the understanding.

Closure

1. How can you ensure that all students answer a high level question that you ask? Brainstorm as many strategies as you can.

Standards Study

K: K.MD.1-31st: 1.MD.1-42nd: 2.MD.1-63rd: 3.MD.1-44th: 4.MD.1-75th: 5.MD.1-56th: 6.G.1-4