edison common core

7/28/2019 Edison Common Core

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Enriching the Mathematics Classroom


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Agenda

Time

on

Task

Mathematical Practices

Vertical Alignment

Visual Learners

Chunking

Self Discovery

Activity

Thingswork outbest for

those who

make thebest of how

thingswork out.

-John Wooden


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MathematicalPractices

Increased Student Engagement Increased Student

Understanding Students who are

College/Career Ready

Math Content Math Practices =+


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Make sense of problems and

persevere when solving them.

Mathematically proficient students start by explaining to themselvesthe meaning of a problem and looking forentry points to its solution.They analyze givens, constraints, relationships, and goals. They makeconjectures about the form and meaning of the solution and plan a

solution pathway rather than simply jumping into a solution attempt.They consider analogous problems, and try special cases and simplerforms of the original problem in order to gain insight into its solution.They monitor and evaluate their progress and change course ifnecessary. Older students might, depending on the context of theproblem, transform algebraic expressions or change the viewingwindow on their graphing calculator to get the information theyneed. Mathematicallyproficient students can explaincorrespondencesbetween equations, verbal descriptions, tables, and graphs or drawdiagrams of important features and relationships, graph data, andsearch for regularity or trends. Younger students might rely on usingconcrete objects or pictures to help conceptualizeand solve a problem.Mathematically proficient students check their answers to problems

using a different method, and they continually ask themselves, Doesthis make sense?They can understand the approaches of others tosolving complex problems and identify correspondences betweendifferent approaches.

Mathematically proficient students start

by explaining to themselvesthe meaning of a problem and looking for entry points to its solution.They analyze givens, constraints, relationships, and goals. They makeconjectures about the form and meaning of the solution and plan a

solution pathway rather than simply jumping into a solutionattempt. They consider analogous problems, and try special casesand simpler forms of the original problem in order to gain insightinto its solution. They monitor and evaluate their progress andchange course if necessary. Older students might, depending on thecontext of the problem, transform algebraic expressions or changethe viewing window on their graphing calculator to get theinformation they need. Mathematically proficient students canexplain correspondences between equations, verbal descriptions,tables, and graphs or draw diagrams of important features andrelationships, graph data, and search for regularity or trends.Younger students might rely on using concrete objects or pictures tohelp conceptualize and solve a problem. Mathematically proficient

students check their answers to problems using a different method,and they continually ask themselves, Does this make sense? Theycan understand the approaches of others to solving complex problemsand identify correspondences between different approaches.


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Explain theirthinking

Analyze giveninformation

Makeconjectures

Try simpler/

special cases

Plan a solution

path

Monitor their

progress

Check using adifferent

method

They ask, Doesthis make

sense?

Understand theapproaches of

others


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Activity

Read through your

math practice,

highlighting key

words.

With your group,

design a student-

friendly poster

about your mathpractice.

Be prepared to

share your math

practice and poster

with the group.


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Common Core

StandardsAn excerpt from Appendix A

Watered-down courses which leave students to learn,

to their peers and in postsecondary

courses or for entry into many skilled professions upon graduation fromhigh school are neither necessary nor desirable. The results of not

providing students the necessary supports they need to succeed in high

school are well-documented. Too often, after graduation, such students

attempt to continue their education at 2-or 4-year postsecondary

institutions only to find they must take remedial courses, spending time

and money mastering high school level skills that they should have already

acquired.

Furthermore, research shows that allowing low-achieving students to

take low-level courses is not a recipe for academic success (Kifer, 1993).


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CCSSthe Content

Where do we go from here?

What do we need to knowabout the changes to the

content standards?

How do we start preparing?


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Step 1:Vertical Alignment

Know what was

required of studentsin previous grades

and they

were exposedto

that information.

Make references to

what they learned

before. Take time tofind out how

students learnedkey information sothat you can make

connections forthem.

Know how what

youre teaching/notteaching impacts

future learning.


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Common Core

Standards are

listed by grade

level for k-8 and

also by DOMAIN.


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www.illustrativemathematics.org offers a similaralignment by DOMAIN. This site makes the connectionbetween k-5 and 6-8 standards.
http://www.illustrativemathematics.org/http://www.illustrativemathematics.org/


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Group examples together to make connectionsamong problems.

Group sections in a chapter together to make

connections within the chapter.

Group sections throughout the text to show therelationship between concepts.

Step 2:Chunking

We dontchunk with the intention of getting more in ortalking faster.

We chunk in order to make connections between concepts

we previously taught as individual unconnected sections.


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Math for College

Readiness Academic Plan

2 Days

Add/Subtract/Multiply/Divide Fractions

Add/Subtract/Multiply/Divide Decimals

1 Day

Evaluate Algebraic Expressions

Determine Solutions of Equations & Inequalities

1 Day

Absolute Value, Order of Operations

Opposites, Reciprocals

1 DayCombining Like Terms


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What We Know

None of the material in these firstdays is new.

In fact, a portion of it has beentaught as isolated lessons sinceelementary school.

Students have most likely beenformally taught each of thesetopics a minimum of four times.

Is this approach working?


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What We Know

If secondaryschools are seeingminimal results

What could wedo differently tomaximize results?

Whatapproachhavent we tried?


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What We Know

Give them Algebra TilesVisual/Hands

On

Give visual examples. Let students figure out how to collect like terms without the

technical terms.

Work with Combining Like TermsChunk

Material

Once students are comfortable with the manipulatives, apply it to mathematics. Be

cautious about moving on too quicklystudents need to commit the hands-on

activities to memory! Once its there, toggle back and forth between the

mathematics until they make the connections.

Apply this to a real world situationGo Deeper

Can Students apply the use of the manipulative to real world situations?


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What We Know

Evaluating Expressions

ApplyKnowledge

Once students are comfortable with the tiles and expressions, begin to use the

tiles to evaluate. When evaluating, include fractions and decimals. If needed

revisit fraction strips and decimal grids.

Include Relevant Information

AddAdditionalMaterial

Take the time to ensure students understand the importance of order of

operations in expressions, that they understand key concepts, and that they

make the connections among the concepts.

Be careful not to include extra information.


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Step 3:Visuals, Movement, Hands On

Integer Chips forVisual Connections

to Numbers

Highlighting KeyFacts

Alternating TextColors to ShowRelationships

Algebra Tiles toShow Properties

and PerformOperations

Equation Balances Human Graphing

Fraction Strips

Notall students are auditory learners.Being able to touch,see, andact out

math concepts will help studentsunderstand why things are the way

they are.

St 4


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Step 4:Experiment & Grapple

Why is it importantto allow time forstudents to attemptthe problemindependently?

How does thediscussion betweenstudent pairs allowstudents to revisetheir thinking?


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Activity

Look throughthe standards/academic plan

for collegereadiness.

Find materialthat could be

chunked

together.

How will youchunk it?

How will youpresent thematerial?

Whatconcrete/visual

material will youuse to introduce

the topic?


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Wrap Up

Try one new thing at a time andmaster it before tryingsomething else.

Math Talk, Chunking, VerticalAlignment, Ways to makeConnections

Questions?

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