Sunnyside School District

Math Training Module 5Kinder and First GradeConcept Development

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?

• Fluency Standard: K---Add/Subtract within 5• Fluency Standard 1st grade – Add/Subtract within 10

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

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?

Penny Plate

Math Practice 3 Suggestions

Critique the reasoning of others:

1. Show solutions or methods for a problem.

2. Have students identify if the solution is correct and why.

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

Penny Plate

We started with 10 pennies.

Jose says that there are 6 pennies under the plate.

Do you agree or disagree with Jose? Why?

12

Initial Instruction

Balance BetweenConcepts 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. (March PD- Module 6)

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

• Think about the DOK of:• 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?

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

DOK of Questions

Level 1 Questions:1. Show 6 counters on the ten frame.2. How many more counters are needed to make a ten?

Level 2 Questions:3. Represent this word problem with a drawing and

equation or act out your steps to solve the problem.4. How do you know your answer is correct?

Level 3 Questions: 5. Create another solution for the problem (open ended).6. Can you use a different strategy to solve the problem?

DOK Questions

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

DOK 1: Is that a 2D or 3D Shape?

DOK 2: Is that a 2D or 3D shape and how do you know?

DOK 3: How is a 2D shape the same or different from a

3D shape?

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?

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

Wait Time Guidelines• DOK 1: 10 seconds- quick and move on

• DOK 2: 1-2 minutes- think time and time to talk

• DOK 3: 5 minutes- give kids time to process to

Reflection

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

How can you increase the level of your questions?

Where can you find higher level questions?

Create DOK Questions

K.MD.A.1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

What are some of the concepts we are working on in this standard? What would be some examples of DOK 1, 2, and 3 level activities/questions?

Activity

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

K: K.MD.1-3

1st: 1.MD.1-4