standards for mathematical practice 1. make sense of complex problems and persevere in solving them....

Standards for Mathematical Practice

1. Make sense of complex problems and persevere in solving them.2. Reason abstractly and quantitatively3. 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.

Grouping the SMP’s

Common Core State Standards for Mathematics:

Shifts and Implications for Mathematics Instruction

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, you 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 

Procedures = Understanding

17- 6

Explain to your partner how you would use the traditional algorithm to solve this

Procedures = Understanding

Now explain to your partner how you would use the traditional algorithm to solve this 10

- 6

Procedures = Understanding

17- 6

10- 6

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

Procedures = Understanding

10- 6

https://www.teachingchannel.org/videos/subtraction-as-a-confidence-builder?fd=1

Do they understand?

SMP IntegrationTraditional U.S. ProblemWhich fraction is closer to 1: 4/5 or 5/4 ?

Same problem with SMP integration4/5 is closer to 1 than is 5/4. Using a number line, explain why this is

so…

Discuss the shift with this question…

Procedures & Algorithms

At your table, fill your large paper with examples of algorithms/procedures you learned as a student. Examples:Foil method in algebraButterfly to compare fractionsStandard Algorithm for multiplication or division

AlgorithmsChoose one procedure or algorithm

that you learned as a student.E.g., Finding common denominator,

FOIL, Butterfly to compare fractions, multiplication or division algorithm, dividing fractions

Do a sample problem using it… Then explain it to your neighbor –

explain the process and why it works

AlgorithmsWhat algorithms did you explain?

How does understanding the math relate to following the steps of the algorithm?

BreakWhen you come back, please sit in

grade level groups.

Welcome BackAccording to the

Common Core, What is MOST IMPORTANT at your grade level?

Answer by placing one sticker on the chart.

The Three Shifts in Mathematics

Focus Coherence Rigor

Authors of the Common Core Math

Standards have emphasized 3 shifts

from old state standards

(like the NCSCOS)

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

Why Focus?

The U.S. curriculum before the Common Core was known as ‘a mile wide and an inch deep.’What did this look like in the NCSCOS?

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

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

Teach Less, Learn More!

https://www.teachingchannel.org/videos/common-core-state-standards-for-math?fd=1

How will teaching fewer “topics” in each grade change your planning?

Content Emphasis

Designed to help teachers focus on what is most important at each grade level.

Focus

Content Emphases by Cluster

Not all of the content in a given grade is emphasized equally in the standards.

Some clusters require greater emphasis based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness.

An intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice.

Focus does not mean neglecting certain standards. Neglecting material will leave gaps in student skill and understanding and may leave students unprepared for the challenges of a later grade.

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

With your grade level team, discuss…

K-2 Teachers Look at the supporting

standards at your grade level.

Generate specific examples of how each supporting standard relates to major standards

3-5 Teachers Identify major changes

within your grade level. How has the focus

changed from the 2003 NCSCOS?

Focus

FocusWould you

change where you placed your sticker?

Focus

Break!~

Coherence Within GradeUse the handout of your Grade Level

ClustersAnalyze how these clusters are classified

How do these clusters overlap or address similar “larger concepts”?

How do Supporting Clusters align with Major Clusters.

CoherencePick a unit from Investigations that

incorporates multiple clustersWhat are the pre-requisite skills you

hope students have before this unit starts?

As students are doing the work in the unit, what is the Major Cluster?What other clusters are also

incorporated?

CoherenceMove and group with teachers from

multiple grade levels

Exchange ideas and discuss what your grade level came up with

Coherence Wrap-up When teaching the Common Core, teachers should: 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.

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

Place Value…

Why do we need rigor when we work with place value concepts?

Hundreds, Tens, and Ones

In groups with teachers from different grade levels, analyze the two Hundreds, Tens, and Ones activities. How does each provide…Solid conceptual understandingProcedural skill and fluencyApplication of skills in problem solving

situations

Hundreds, Tens and OnesDo these promote Conceptual

Understanding?Why or why not?

Hundreds, Tens and OnesDo these promote Procedural Skill and

Fluency?Why or why not?

Hundreds, Tens and OnesDo these promote skill application in

problem solving situations?Why or why not?

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)72 B)620 C)720 D)7,200

Common Core

Rigor

Compare the two previous multiplication items, and discuss how each does/does not provide the opportunity for students to demonstrate…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!

C.C. Item ExamplesInside Mathematics

http://insidemathematics.org/index.php/home

Tools for Educators Choose your grade level Mars Tasks

These should be similar to future Common Core assessment Items…

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!

Choose 3 Ways!

4 Teachers $20.00

Burrito - $4.12 Soda - ?

February 21Ensuring the Standards for

Mathematical Practice at the student level.

Illustrating the Mathematical Practices

February 21Ensuring the Standards for

Mathematical Practice at the student level.

A pen for Aramis and Elise (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 a fence that is 2½

feet from the current perimeter, how much fencing will she need for the Chihuahua’s run?

7 ¼

3 5

2

The Chihuahua run must be built 2½ feet from the edge of the Great Dane pen!

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 )

Solutions

Linking Content and Practice

Numbers and Operations in Base Ten (NBT) K-2: 1.NBT.5 and 1.NBT.6

3-5: 4.NBT.5 and 4.NBT.6

Practice 4Model with Mathematics…

What fraction of this shape is red? https://www.teachingchannel.org/videos/what-fract

ion-of-this-shape-is-red?fd=1 Explain how the students engaged in one of the 3

shifts? (Focus, Coherence, Rigor) How could Mr. D extend this lesson to develop

students thinking around adding and subtracting fractions or decomposition of fractions?

Practice 5Use Appropriate Tools Strategically…

On the count of 3, you have 30 seconds to find as many colored tiles as possible. When the time is up, please bring them back to your group.

Complete the tally chart with your groups tiles. Then construct a bar graph with your data. Combine group data to make a class bar graph. Range, Median, Mode What conclusions can you draw?? How might the data relate to

animals in the wild? How does hiding the tiles around the room affect the lesson?

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).