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Sunnyside District Day One Math TrainingFocus 1 & 2; Mathematical Shifts & Practices; June 2014

2+Anticipatory Set

1. When you fully implement the common core in math, what do you think will be the biggest challenge?

1. For Teachers2. For Students

3+Activity

Fast Fingers---Fast Mind

4+Something to Ponder…..

“Mathematics can be defined simply as the science of patterns.” David Sousa

“The brain is a pattern-making machine.” Peter Diamandis

5

Are you………

Good at Math?OR

Bad at Math?

What evidence do you have to support

your answer?

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Math is in our nature!

“Because we are born with number sense, most of us have the potential to be a lot better at arithmetic and mathematics than we think.” David Sousa

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The common core standards demand a balance between procedural skill and conceptual understanding.

Rate your knowledge of the Common Core State Math Standards

“Common who? Common what?”1“I’ve heard something about those…didn’t we adopt them in CA?”2“I’ve scanned through the documents.”3“I know what my grade specific Critical Areas, Domains, and Mathematical Practices are.”

4“I know these standards backwards and forwards; transitioning to these new standards will be a breeze!”

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9+Why the need for change in instruction?

Common Core Content Standard:

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

10+ What’s different in the new standards?

Arizona (3rd)-- Compare and order benchmark fractions.

CC 3rd Grade—3.NF.2a Represent a fraction a/b on a number line diagram by marking a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

11+How are the standards different?First Grade:

PO 3. Represent a word problem requiring addition or subtraction facts using an equation.

1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

+Common Core Math

Standards

Content Standards

What students should know and be

able to do

Math Practice Standards

How students should do the

content

+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.

14+Math Practice 3

Read Math Practice 3 and consider the following:

1. What would this look like in a classroom?

2. How could you assess this practice?

15+Math Practice 6

Read Math Practice 6 and consider the following:

1. What are all of the ways that students need to be precise when doing mathematics?

2. Why do you think Math Practice 6 often connected to Math Practice 3?

16+PARCC Assessment Given in 2014-15 for accountability

Given every year 3rd grade through 11th grade

Testing Window of 20 days for each test

Results returned within weeks

2 sections: Performance Based Component

Given at 75% of school year Includes both short and extended response questions

End-of-Year Component Given at 90% of school year Mostly short answer questions

17+PARCC Sample Questions

+CCSS Math Shifts

1. Focus

2. Coherence

3. RigorProcedural Skill and FluencyConceptual UnderstandingApplication of Math Standards

+Shift of Rigor

This is how instruction should be different. There should be a balance of these in all classrooms:

1. Procedural Skill and Fluency

2. Conceptual Understanding

3. Application (problem solving)

+Procedures and Fluency

Procedures: Practicing previously learned skills often and strategically.• Teachers need a system to spiral in skills for

practice.

Fluency: Doing something quickly and accurately.• One fact in 3 seconds.

Both of these take TIME!

+Procedural Skill & Fluency

Concepts Procedure Fluency

Progression of Math Skills

22+Procedural Skill and Fluency

Daily Spiraled Review

Daily Mental Math

Weekly Fluency (Mastery of Math Facts)

5 components of Balanced Math—Ainsworth/Christianson

23+ Mental Math

Purpose: Use strategies to calculate mentally.

3-5 questions daily

Multi-step

Discuss strategies

24+Daily Spiraled Review

Purpose: Review and practice of previously learned math skills.

3-5 questions daily

Each question is a different skill

2 week cycleReview Quiz at end (2 questions per

skill)

Processing is the most important part!

25+Math Review Example

1. Use the algorithm to find the difference

50-19= ________

2. 59 x 4 = _______

3. Find the area and perimeter of a rectangle with a length of 6 cm and a width of 2 cm.

Bonus:

Simplify the expression: 7 + 6 (31-18) - 28

26+Math Review Sample

1. 5 + ____ = 18

2. Draw a picture to solve: 8 – 6 = _____

3. What is this shape?

Bonus: One student brought 3 cookies and another student brought 6 cookies. How many cookies is that all together?

27+Math Review Processing

Error Analysis

Reasonableness of answers

Multiple ways to solve

+Procedural Skill & Fluency

Concepts Procedure Fluency

Progression of Math Skills

+Common Core Fluency

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

+Where are the Fluency Standards?

3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. *Up to 1,000,000

+Division Skill Progression3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret

56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

32+Closure

1. How can teachers incorporate Math Practice 3 when spending time on procedural skill and fluency?

2. What 2-3 things can you look for in classroom walk-throughs based on what we discussed today?

33+Common Core Content Standards3rd Grade Standards:

1. Independently read through 3.OA.1 to 3.OA.4 and determine the meaning of each standard.

2. Discuss in depth what standard 3.OA.2 and 3.OA.3 mean. What are the key concepts in teaching

these standards? How are these different from how we

currently teach multiplication and division?

3. Read 3.MD.7 and discuss how this relates to the 3.OA standards that you read.

34+Dissecting a Standard

1. Read 3.NF.1 and think about what this means.

2. Discuss with your group.

3. Come up with two ways in which students can show mastery of this standard.

4. How can you help teachers understand these standards?

35+Working Lunch Activity

You will complete a PARCC practice test:

1. Chose a partner and a grade level 3rd-8th.

2. Go to parcconline.org and find the practice tests.

3. Take the test for your grade level. 1. If you want to check your answers, you can

open up the answer key in another window while to take the test.

4. While taking the test, fill out the questionnaire provided.