Common Core State Standards for Mathematics: Shifts and Implications for Mathematics Instruction

Common Core State Standards for Mathematics:

Shifts and Implications for Mathematics Instruction

Schedule 11:00-11:30 Auditorium- ALL 11:30-2:00 Break-out rooms

Group A- Amy Room 108 A (Science comes 1:00-1:30) Group B- Marilyn Room 108 B (Science comes 1:30-2:00) Group C- Susan Room 209 (Science comes 12:30-1:00) Group D- Drew Room 112 (Drew’s group stay in auditorium 11:30-12:00

for Science, then move to room 112

Morning Session

Focus, Coherence, and Rigor; Realizing the Common Core in

Elementary Mathematics Understand how the Common Core influences

our Instruction Identify the 3 major shifts in math education

Last week, I was at a restaurant with a group of friends. The bill came and this is what was

said…

“I’m not good at math, have Drew

figure it out.”

Out to lunch…

Next time we go…“I’m not good reading, can you read this

to me?”

Same Reaction?

Illiteracy Innumeracy

Why is it socially acceptable to be

innumerate?

Innumeracy21% of Americans possess numeracy skills at the lowest level . . . [which] means that

people cannot . . . work out the change from $2 when buying

goods worth $1.58.

(Murray, 2000. p. 2)www.lausd.net/District_8/math/secmath/0607/math_anx_ncsm.ppt 

Making Banners

You have 9 yards of fabric.You need 2 of a yard to make a banner.How many banners could you make?

We have number lines, graph

paper, and blank paper available.

Approaches? Now let’s change the numbers…

Making Banners

You have 9/4 yards of fabric.You need 1/2 of a yard to make a banner.How many banners could you make?Solve 2 ways– number line/picture AND then computation

We have number lines, graph

paper, and blank paper available.

Under every other chair there is a solution to this problem. With a partner, show how how

a student might arrive at this solution.

Making Banners

Find your group4 ½ 4 2 9/8

How are your solutions the same?How are they different?

Making Banners

Listen as groups share what they noticed4 ½ 4 2 9/8

A Lesson in the “old” DaysWhat did math class look like when you were a student?

First, invert the 1/2 so you now have 9/4 x 2/1

Next, multiply 9x2 to get 18, then 4x1 to get 4.Now we need to reduce so you take 18 divided by 4 to get 4 r 2 or 4 2/4 that needs to then be reduced to 4 1/2

4 ½ 4 2 9/8

Which answer does method this lead to?

“Don’t Ask Why, Just Invert and Multiply!”

During and after reading a selected text, we ask…

“What do you notice in the text?”

“Do you agree with the characters decision

to…/why?”

After solving a math problem, we ask…

“Did you get the right answer?”

Numbers….9 divided by 2???

How did changing the numbers influence the “difficulty” of the task?

9/4 divided by 1/2

Procedures = Understanding

17- 6

10- 6

How did changing the numbers influence the “difficulty” of the task?

Procedures = Understanding

17- 6

By place value…start at the right…Ones column: 7- 6 = 1. Tens column: Bring down the 1.I have a 1 in both places. Answer is 11.

Procedures = Understanding

10- 6

By place value…start at the right…Ones column: I can’t do 0 minus 6.

Go next door… change the 1 to a 0 in the tens

Change the 0 to a 10 in the ones.Ones: 10 – 6 = 4Tens: 0 – 0 = 0.I have 0 tens and 4 ones. My answer is 4.

Do they understand?

Turn and TalkThink of a mathematical procedure

you learned as a student.

How does that make it difficult for you to explain your mathematics behind your solution?

FoilButterflyStandard Algorithm for …Change mixed numbers to improper fractions

Break

Welcome BackWhat is MOST

IMPORTANT at your grade level?

Answer by placing one sticker on the chart.

The Three Shifts in Mathematics

Focus specificity and concentration on fewer “big ideas”

Coherence: Think across grades and link to major topics within grades

Rigor: Require conceptual understanding, fluency, and application

Shift One: Focus strongly where the Standards focus

Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom

Focus deeply only on what is emphasized in the standards, so that students gain strong foundations

It starts with Focus

The current U.S. curriculum is ‘a mile wide and an inch deep.’

Focus is necessary in order to achieve the rigor set forth in the standards

The following graphs refer to mathematics instructionWith a partner, predict what these represent

Mathematics topics intended at each grade

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

By at least 2/3 of US States By at least 2/3 of A+ Countries

The Shape of

Math Instruction

Comparing Charts

Compare our school chart to this one

What do you notice?

K 12Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach

Complete the Diagram Below

Algebra

K 1 2 3 4 5 6 7 8 High School

-Number and Operations—Fractions

-Expressions and Equations

-Operations and Algebraic Thinking

-Number and Operations—Base Ten

-The Number System

Focusing attention within Number and Operations

Operations and Algebraic Thinking Expressions and Equations

Algebra

Number and Operations—Base Ten

The Number System

Number and Operations—Fractions

K 1 2 3 4 5 6 7 8 High School

How do they compare?

Content Emphasis-Released by Achieve.org-Non-profit group of educational leaders who have committed to provide resources at no cost.-Designed to help teachers focus on what is most important at each grade level.

Focus

Sample Content Emphases

What do you notice?What’s missing?

Focus – your grade levelWith your grade level team

Look at the Content Emphasis

In YOUR copy of the Common Core –highlight areas of focus at your grade level.

Focus

What is vital at my grade level?

Complete this sentence with only one mathematical concept;

“By the end of ___ grade, if my students knew _____ they would be

considered mathematically proficient.”

Focus

Walk and Trade

Shift Two: Coherence Carefully connect the learning within and across

grades so that students can build new understanding onto foundations built in previous years.

Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new set of events, but an extension of previous learning.

Coherence Within GradeLook within your grade and find where

important concepts are connected across domains.

Create a product that communicates your findings

Coherence Within GradeGrade Levels Share

Shift Three: Rigor

The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations

This requires balanced intensity in time, activities, and resources in pursuit of all three

Rigor

Hundreds, Tens, and Ones

Hundreds, Tens, and Ones

Compare the two Hundreds, Tens, and Ones activities thinking about how each provides…Solid conceptual understandingProcedural skill and fluencyApplication of skills in problem solving

situations

DPI 3-5 Released Item

Mrs. Gregory assigned a project that required each of her 20 students to use 36 toothpicks. How many toothpicks did the students use?

A 72B 620C 720D 7,200

Common Core

Rigor

Compare the two items, which provides for…Solid conceptual understandingProcedural skill and fluencyApplication of skills in problem solving

situations

Three Mathematical Shifts

Which shift will have the greatest impact on student learning?

Decide with your team and be prepared to share!

Realizing the Promise of the Common Core

It will take hard work on our part to move a society from this…

10 - 6

To This!

Afternoon SessionEnsuring the Standards for

Mathematical Practice at the student level.

Illustrating the Mathematical Practices

Afternoon SessionEnsuring the Standards for

Mathematical Practice at the student level.

A pen for Great Danes is shown below. Amy wants to add a safe place for her Chihuahua to run around the great Danes (and not get stepped on!). If she adds 2 ½ feet from the perimeter of the Dane’s pen shown below,

how much fencing will she need?

7 ¼

3 5

2

Solutions

Standards for Mathematical Practice

4 and 5 In pictures and words, show how you

used either mathematical practice 4 or 5 as you solved this task

(you might have to pull these out and re-read )

An Experience with Students

The following slides are from DPI.

The Task

What would that look like…

With our students?

Step 1: Introduce/Review Standards for Mathematical Practice # 4 and #5

Date:

Briefly describe how you will introduce/review Standards for Mathematical Practice # 4 and #5

Step 2: Apply Standards for Mathematical Practice # 4 and #5 to a math lesson.Select a lesson that provides students the opportunity to choose appropriate tools strategically and model with mathematics.

Briefly describe lesson chosen:

Toward the end of the lesson, ask students to illustrate how they used mathematical practice #4 OR #5 in their work today.

Step 3: Bring illustrations to math planning.As a team, choose 2 illustrations (one that shows a solid understanding and one that shows minimal understanding). Send illustrations in to Amy and Marilyn (use envelope provided).