What do you see?

Three Musicians by Pablo Picasso

Educator Enhancement Academy

3rd Grade

Mathematics

Day 1

Thinking is a requirement for learning mathematics.Visible Thinking in Mathematics

Welcome & Introductions

Goals for Conference

• Develop an understanding of the Standards for Mathematical Practice

• Develop an understanding of the structure of the Next Generation CSOs

• Develop an understanding of the mathematical content within the 3rd grade Next Generation Mathematics CSOs

Visible Thinking

• Teachers explain their thinking out loud.• Students orally articulate their thinking.• Students listen to other students articulate

their thinking.• Students engage in discussion while forming

their understanding.

Visible Thinking in the K-8 Mathematics ClassroomHull, Balka Miles

What’s in the Bank?

• Determine all possible combinations of coins for your piggy bank. Provide justification for your solution.

• How do you know that you have found all possible combinations?

Most Professional Development is based upon strategies for teaching, this Professional Development will focus on getting to know the standards/using the standards for instruction.

Setting the Stage•Teachers need to become students of the

standards with his or her collaborative team in their school.

•Focus on teaching the entire cluster, not standard by standard.

“…the standards define what students are expected to know and be able to do, not

how teachers should teach.” CCSS authors

In our schools, we prioritize teacher development over curriculum development. You do not make teachers better by handing them a packaged curriculum and sending them to a few days of training. Instead, teachers need time to analyze the standards, practice different teaching strategies, learn from mentors, collaborate with colleagues, observe one another, look at student work together, reflect on why certain approaches work better than others, learn from mistakes and continually improve. None of this is fast or easy, But it is how teachers become great.

Deborah Kenny founder of Harlem Village Academies

Shift in Professional Development

How much mathematics a third grader in the United States learns, and how deeply he or she learns it, in many schools is largely determined by the student’s school and, even more directly, the third-grade teacher to whom the student is assigned. Sometimes, the inconsistencies teachers develop in their isolated practice can create gaps in curriculum content with consequent inequities in students’ instructional experiences and learning (Kanold, 206)

One of the characteristics of high-performing elementary schools that are successfully closing the achievement gap is their focus on teacher collaboration as a key to improving instruction and reaching all students. (Education Trust, 2005; Kersaint, 2007)

The world’s highest-performing countries in mathematics or sustained educational improvers—Singapore, Hong Kong SAR, South Korea, and Japan—allow significant time for elementary school mathematics teachers to collaborate and learn from one another. (Mourshed, Chijioke, & Barber, 2010)

Nxt Gen vs Other

Knowing Standards

Using Standards for Instruction

CCSS Shifts

Processes

Strategies

The Structure is the StandardsPhil Daro, Bill McCallum, Jason Zimba

3 – things you learned2 – questions you have1 – reaction to what you’ve read

Next Generation Content Standards and Objectives for Mathematics in

West Virginia Schools

• Standards for Mathematical Practice• Content Standards and Objectives

Standards for Mathematical Practice

1. Make sense of problems and persevere in 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.

Standards for Mathematical Practice

• Read and study resources related to your assigned Standard for Mathematical Practice.

• Think about:– What is the intent of the Mathematical Practice?– What teacher actions facilitate this Mathematical Practice?– What evidence is there that students are demonstrating this

Mathematical Practice?• Create a poster illustrating the key elements of the

Standard for Mathematical Practice.• Connect SMP to “What’s in the Bank?” task. How did you

use it? (Be ready to share evidence.)• Prepare a 2 minute presentation highlighting the

important elements of this Mathematical Practice? (Be Creative!) Make sure everyone in your group is ready to share.

Groups of three

Next Generation Standards Progression

Pre-K K 1 2 3 4 5 6 7 8 HS

Number-Counting & Cardinality

Counting & Cardinality

Number and Operations in Base TenRatios and

Proportional Relationships Number &

QuantityNumber and Operations –

FractionsThe Number System

Number-Operations and the Problems

they Solve

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry Geometry

Measurement & Data

Measurement and Data Statistics and ProbabilityStatistics & Probability

• The Mathematics Standards: How They Were Developed and Who Was Involvedhttp://www.youtube.com/watch?v=dnjbwJdcPjE

Final Thoughts

What do you see?Paint the Red Town by:Maeve Wright

Day 2

Next Generation Content Standards and Objectives for Mathematics in

West Virginia Schools

• Counting and Cardinality--Kindergarten Only• Operations & Algebraic Thinking• Numbers & Operations Base Ten• Number & Operations Fractions--Shows up third

grade• Geometry• Measurement & Data

The Importance of Coherence in Mathematics

• http://www.youtube.com/watch?v=83Ieur9qy5k&list=UUF0pa3nE3aZAfBMT8pqM5PA&index=17&feature=plcp

Three Shifts in Mathematics

• 1. Focus: Focus strongly where the standards focus.

• 2. Coherence: Think across grades, and link to major topics.

• 3.Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.

DIGGING DEEPER IN THE STANDARDS

Next Generation Common Core Standards

• Read and study resources related to Measurement and Data and Geometry – What are the grade level priorities?– Which Objectives in the Cluster Are Familiar?– What is New or Challenging in these Objectives?

• Complete the Analysis Tool• Be ready to share with other groups.

Connect the standards to the “Piggy Bank” task. Be ready to share evidence that supports the standards.

45 minutes

RIGOR: CONCEPTUAL UNDERSTANDING, PROCEDURAL SKILL AND FLUENCY, AND APPLICATION

Fluency: Simply Fast and Accurate? I Think Not!

• Individually read this article.• Use the Triangle, Square, Circle Reporting

Strategy

What I Learned?

Something I knew and or I agree with.

Things I am still not sure

about.

Adding It Up The National Academies Press

“Procedural Fluency- skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.”

Rigor-Fluency

• The standards require speed and accuracy in calculation.

• Teachers should structure class time and/or homework time for students to practice core functions.

Adapted from Achieve

Rigor-Application

• Student use appropriate concepts and procedures for application

• Provide opportunities for students to apply math concepts in “real world” situations

• Outside of math students are using grade –level-appropriate math to make meaning of and access content

Adapted from Achieve

Required Fluencies in K-6K K.OA.5 Add/subtract within 5

1 1.OA.6 Add subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20Add/subtract within 100 (paper & pencil)

3 3.OA.73.NBT.2

Multiply/divide within 100Add/subtract within 1000 (paper & pencil)

4 4.NBT.4 Add/subtract within 1,000,000 (paper & pencil)

5 5.NBT.5 Multi-digit multiplication (paper & pencil)

6 6.NS.26.NS.3

Multi-digit division (paper & pencil)Multi-digit decimal operations (paper & pencil)

Developing Fluency

1. Help children develop a strong understanding of number relationships within the operations.

2. Develop efficient strategies for fact retrieval through practice.

3. Then provide drill in the use and selection of those strategies once they have been developed.

John A. Van de Walle & LouAnn H. Lovin

From Memory ≠ Memorize

M.2.OA.2 fluently add and subtract within 20 using mental strategies and by end of Grade 2, know from memory all sums of two one-digit numbers.

M.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 and by the end of Grade 3, know from memory all products of two one-digit numbers.

Number Talks

• Number talks are short conversations centered around purposefully crafted computation problems.

Strategies

Addition Subtraction Multiplication DivisionCounting All/Counting On

Adding Up Repeated Addition or Skip Counting

Repeated Subtraction or Sharing/Dealing Out

Doubles/Near-doubles Removal or counting Back

Making Landmark or Friendly Numbers

Partial Quotients

Making Tens Place Value and Negative Numbers

Partial Products Multiplying Up

Making Landmark or Friendly Numbers

Adjusting One Number to Create an Easier Problem

Doubling and Halving Proportional Reasoning

Breaking Each Number into Its Place Value

Keeping a Constant Difference

Breaking Factors into Smaller Factors

Compensation

Adding Up in Chunks

Teaching Basic Facts

What to do---• Ask students to self-

monitor• Focus on self-improvement• Drill in short time

segments• Work on facts over time• Involve families• Make drill enjoyable• Use technology• Emphasize the importance

of quick recall of facts

What NOT to do---• Don’t use lengthy timed

tests• Don’t use public

comparisons of mastery• Don’t proceed through all

facts all at once• Don’t move to

memorization too soon• Don’t use facts as a barrier

to good mathematics• Don’t use fact mastery as a

prerequisite for calculator use

Mad Minute Math Activity

• Scenario: Students have just completed their latest 3 minute math drill.

• Each person will start with a different student.

• Using a sticky note write down what you notice about the students.

“Designer” Flashcards

• Create a set of 20 “Designer” flashcards based on student assessments.• Personalized according to individual student needs• Repeated practice of targeted facts

.

Given: Students in 2nd grade have an understanding of addition and students in 3rd grade have an understanding of multiplication.

Where is the standard algorithm?

• The standard algorithm for addition and subtraction doesn’t appear in the standards until 4th grade.

NUMBER AND OPERATIONS-FRACTIONS

Which is larger?Explain Your Answer

56

78

Taking Fractions to the Number Line

Who is Winning?

The friends are playing “Red Light-Green Light.” Who is winning? The fractions tell how much of the distance they have already moved. Can you place these friends on a line to show where they are between the start and finish?

Mary Harry Larry

Sam Michael Angie

34

12

56

58

59

23

How Far?Mark lives of a mile from school on the same street as his best friend David. David’s house is a mile from the school

They both participate in an afterschool program and sometimes ride the public bus to a stop which is halfway between their two houses. But they aren’t sure how far this bus stop is from each of their houses or from school. Help Mark and David figure out the distance from the school to the bus stop, and the distances from the bus stop to each of their homes.

Use the number line to help you figure out the problem.Great Tasks for Mathematics (NCSM)

4 10 8

10

Day 3

What do you see?

ADDITIVE/MULTIPLICATIVE STRUCTURES

Write a short typical addition “word” problem.

Structure vs. Key Words

• Encourages students to ignore the meaning and structure of the problem

• Key words may be misleading• Problems may not have key words• Key words don’t work with two-step problems

Elementary and Middle School MathematicsTeaching Developmentally

Problem SortAdditive/Multiplicative

Structures• Read each problem.• As a group decide which structure it

represents.

• Using the priorities, clusters, and objectives identify the structures that are required at your grade level.

What Makes a Great Math Task

• Revolves around an interesting problem• Is directed at essential mathematical content

as specified in the standards• Requires examination and perseverance• Begs for discussion• Builds student understanding• Warrants a summary look back

NCSM Great Tasks for Mathematics

Mathematical Task

• Non-routine problems• May be solved

individually and collaboratively

• Encourages communication among students

• May evolve into an entire lesson

• Develops or reveals mathematical understanding.

• Routine problems• Practice procedures with

words• Focuses on getting the

answer

Typical Word Problem

Typical Word Problem

Lia has 13 pencils. Thomas has 6 pencils Nate has 7. How many pencils do they have in all?

Answer 13 + 6 + 7 = 26 pencils

Mathematical Tasks

Lia, Thomas and Nate have 26 pencils. How many pencils could each student have?

Your Turn

PULLING IT TOGETHER

Looking at Student Work

How Many Windows?Look at the building in the picture. How many windows do you see in the picture? Share your mathematical thinking.

•Identify Cluster, Objectives, and Standards for Mathematical Practice supported by this task.

Complete the task as:•A student at the novice level•A student on grade level•A student above grade level

Looking at Student Work

• Evaluate student work samples:– Novice– Grade Level– Above Grade Level

• How will you as a classroom teacher support students at the various levels of understanding? What are your next steps?

SMARTER BALANCED ASSESSMENT

http://www.smarterbalanced.org/

Smarter Balanced Practice Test