Teaching to the Next Generation SSS (2007) Elementary Pre-School Inservice August 17, 2010

Teaching to the Next Generation SSS

(2007)

Elementary Pre-School Inservice August 17, 2010

Next Generation Sunshine State Standards Eliminates:

Mile wide, inch deep curriculum

Constant repetition

Emphasizes:

Automatic Recall of basic facts

Computational fluency

Knowledge and skills with understanding

Comparison of Standards Grade Level Old GLE’s New

Benchmarks

K 67 11

1st 78 14

2nd 84 21

3rd 88 17

4th 89 21

5th 77 23

6th 78 19

7th 89 22

8th 93 19

Implementation

Schedulefor

NGSSS

2008 - 2009

2009 - 2010

2010 - 2011

FCAT 1 FCAT 1 FCAT 2

SF (2004) SF (2004) enVisionMATH

K - 2nd 2007 Standards

2007 Standards

2007 Standards

3rd 2007 Standards

w/ transitions

2007 Standards

w/ transitions

2007 Standards

4th 1996 Standards

2007 Standards

w/ transitions

2007 Standards

5th 1996 Standards

1996 Standards

2007 Standards

MA. 3. A. 2. 1

Subject

GradeLevel

Body of Knowledg

e

Big Idea/ Supportin

g Idea

Benchmark

Coding Scheme for NGSSS

MA.3.A.2.1

Intent of the Intent of the StandardsStandards

The intent of the standards is to The intent of the standards is to provide a “focused” curriculum.provide a “focused” curriculum.

How do we make sense of How do we make sense of teaching deeply?teaching deeply?

Think of a swimming pool. Think of a swimming pool.

What is Rigor?

What Rigor is NotWhat Rigor is Not a measure of the quantity of

content to be covered.

a special program or curriculum

for select students.

about severity or hardship.

only about higher-order thinking.

RigorRigor

Rigor is quality instruction that focuses on the depth of the learning not the breadth. It’s not more work; it’s meaningful, respectful work that requires the student to think deeply and critically to accomplish the assigned tasked. Eric Bergholm, Hillsborough County Public Schools, Florida

What are the NCTM Process Standards?

– Problem Solving

– Reasoning and Proof

– Connections

– Communication

– Representation

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NCTM Process Standards

Problem Solving– Developing perseverance and critical

thinking– Teacher’s Role: Allowing students to

struggle Is multiplying by four the same as doubling and then doubling again. Does it always work? Why?

COUNT THE SQUARES!

How many are in the figure?

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Reasoning and Proof– Mathematical conjectures– Examples and counterexamples

Connections– Math: fraction/decimal, cm/m – Other content areas, science– Real-world contexts

NCTM Process Standards

NCTM Process Standards Communication

– Read, write, listen, think, and communicate/discuss

– Tool for understanding and explaining thinking

– Increased use of math vocabulary

NCTM Process Standards Representation

– Useful tools for building understanding

– Tables, describe in words, draw a picture, write an equation

– Concrete-Representational-Abstract

– Model DiagramExample of Model Diagram from enVisionMATH

Topics not Chapters

Daily Review WB

Problem of the Day

Interactive Learning

Quick Check WB

Center Activities

Reteaching WB

Practice WB

Enrichment

Interactive Stories (K-2)

Letters Home

Interactive Recording Sheets

Vocabulary Cards

Assessments

Resources with enVisionMATH

Four-Part Lesson

1. Daily Spiral Review: Problem of Day

2. Interactive Learning: Purpose, Prior Knowledge

3. Visual Learning: Vocabulary, Instruction, Practice

4. Close, Assess, Differentiate: Centers, HW

Conceptual Understanding

Conceptual Understanding

Conceptual Understanding

Old Instruction vs New Instruction

Old Instruction vs New Instruction

Focus on Fractions!

Fractions as a window into depthFractions as a window into depth

Using sharing situations to Using sharing situations to introduce fractionsintroduce fractions

Representing fractions with flexible Representing fractions with flexible wholeswholes

Estimating fraction sums and Estimating fraction sums and differencesdifferences

Adding and subtracting fractions Adding and subtracting fractions through storiesthrough stories

Teaching for Depth

MA.3.A.2.1 Represent fractions, including fractions greater than one, using area, set and linear models.

MA.3.A.2.2 Describe how the size of the fractional part is related to the number of equal sized pieces in the whole.

MA.3.A.2.3 Compare and order fractions, including fractions greater than one, using strategies and models.

MA.3.A.2.4 Use models to represent equivalent fractions, including fractions greater than one, and identify representations of equivalence.

NGSSS: Fractions (3NGSSS: Fractions (3rdrd))

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MA.4.A.2.3 Generate equivalent fractions and simplify fractions.

MA.4.A.2.4 Compare and order decimals, and estimate fraction and decimal amounts in real-world problems.

NGSSS: Fractions (4NGSSS: Fractions (4thth))

MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties.

MA.5.A.2.2 Add and subtract fractions and decimals fluently, and verify the reasonableness of the results, including in problem situations.

MA.5.A.2.3 Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding.

NGSSS: Fractions (5NGSSS: Fractions (5thth))

When asked to compare 4/5 When asked to compare 4/5 and 2/3, a student said…and 2/3, a student said…

““I know that 4/5 is greater than 2/3.”I know that 4/5 is greater than 2/3.”

How would you respond?How would you respond?

Hopefully you would ask the Hopefully you would ask the student how he or she knew.student how he or she knew.

Perspective…Perspective…

The student said…The student said…

I made both fractions using manipulatives. I made both fractions using manipulatives.

I knew that 4/5 was bigger because 4/5 has I knew that 4/5 was bigger because 4/5 has

4 pieces and 2/3 only has 2 pieces and since4 pieces and 2/3 only has 2 pieces and since

4 is greater than 2 then 4/5 is greater than 2/3.4 is greater than 2 then 4/5 is greater than 2/3.

Perspective…Perspective…

QUIZ: Which Fraction is QUIZ: Which Fraction is Greater?Greater?

1. 3/7 and 5/8

2. 4/7 and 4/9

3. 9/10 and 5/4

4. 3/8 and 5/8

5. 6/7 and 8/9

Think about this…Think about this…

Alex and Jessica are racing their bicycles. Alex and Jessica are racing their bicycles.

Alex is Alex is 3/7 3/7 of the way to the finish line of the way to the finish line

and Jessica is and Jessica is 2/32/3 of the way to the finish of the way to the finish

line. Which racer is closer to the finish line. Which racer is closer to the finish

line? line? How do you know?How do you know?

Think about this…Think about this…

Marc and Larry each bought the same Marc and Larry each bought the same

type of energy bar. Marc has type of energy bar. Marc has 1/81/8 of his of his

energy bar left, Larry has energy bar left, Larry has 1/101/10 of his of his

energy bar left. Who has more energy energy bar left. Who has more energy

bar left? bar left? How do you know?How do you know?

Think about this…Think about this…

Riley and Paige each bought a small Riley and Paige each bought a small

pizza. Riley ate pizza. Riley ate 5/65/6 of her pizza, and of her pizza, and

Paige ate Paige ate 7/87/8 of her pizza. Who ate more of her pizza. Who ate more

pizza? pizza? How do you know?How do you know?

Let’s Talk About Why!Let’s Talk About Why!

1. 3/7 and 5/8

2. 4/7 and 4/9

3. 9/10 and 5/4

4. 3/8 and 5/8

5. 6/7 and 8/9

A new perspective…A new perspective…

At what grade level would you At what grade level would you ask a student to compare ask a student to compare 22/23 and 26/27?22/23 and 26/27?

According to the intent of the new According to the intent of the new standards, this question is appropriate standards, this question is appropriate for a student in Grade 3. for a student in Grade 3.

Why Fractions?Why Fractions?

Because sometimes they’re the Because sometimes they’re the only way to get your fair share…only way to get your fair share…

This is particularly important This is particularly important

when it comes to when it comes to

and .and .

And the doorbell rang…And the doorbell rang…

Share 2 cookies among Share 2 cookies among 4 people.4 people.

Share 4 cookies among Share 4 cookies among 3 people.3 people.

Share 4 cookies among Share 4 cookies among 5 people.5 people.

Sharing Cookies

Teaching Children Mathematics, March 2007

Share 3 candy bars Share 3 candy bars among 6 people.among 6 people.

Share 3 candy bars Share 3 candy bars among 6 people.among 6 people.

How much of a candy bar will each person need to give the newcomer if a 7th person comes along?

Consider telling the “whole” Consider telling the “whole” story with story with pattern blockspattern blocks..

The whole is The whole is important…important…

Use the Use the yellow yellow hexagon hexagon as the whole.as the whole.

What fraction is represented What fraction is represented by 5 by 5 greengreen triangles? triangles?

Consider telling the “whole” Consider telling the “whole” story with story with pattern blockspattern blocks..

The whole is The whole is important…important…

Use the Use the yellow yellow hexagon hexagon as the whole.as the whole.

What fraction is represented What fraction is represented by 1 by 1 blueblue rhombus? rhombus?

Now use 2 Now use 2 yellowyellow hexagons hexagons as the as the wholewhole..

The whole is The whole is important…important…

What fraction is represented What fraction is represented by 4 by 4 blueblue rhombuses? rhombuses?

Now use 1 red trapezoid and 1 blue Now use 1 red trapezoid and 1 blue rhombus combined as the whole.rhombus combined as the whole.

The whole is The whole is important…important…

What fraction is represented What fraction is represented by 2 red trapezoids?by 2 red trapezoids?

Stories should be told in more than Stories should be told in more than one way.one way.

The whole is The whole is important…important…

Consider using two-color counters to Consider using two-color counters to tell your story beginning at the end.tell your story beginning at the end.

Determine the whole given the parts.Determine the whole given the parts.

The whole is The whole is important…important…

If 6 counters represent 2/3 of the whole set, If 6 counters represent 2/3 of the whole set, how many counters are in the entire set?how many counters are in the entire set?

Determine the whole given the parts.Determine the whole given the parts.

The whole is The whole is important…important…

If 8 counters represent 4/5 of the whole set, If 8 counters represent 4/5 of the whole set, how many counters are in the entire set?how many counters are in the entire set?

Determine the whole given the parts.Determine the whole given the parts.

The whole is The whole is important…important…

If 10 counters represent 2/9 of the whole set, If 10 counters represent 2/9 of the whole set, how many counters are in the entire set?how many counters are in the entire set?

Creating a Fraction Kit

Paper Strips Scissors Pencil or Pen

Whole

Marilyn Burns: Marilyn Burns: Cover and Cover and Uncover!Uncover!

How can we help students to make sense How can we help students to make sense of fractions and fraction operations?of fractions and fraction operations?

Picture this…Picture this…

Through estimation!Through estimation!

When asked the following question, only When asked the following question, only 24% of 13-year olds and only 37% of 17 24% of 13-year olds and only 37% of 17 year olds could estimate correctly.year olds could estimate correctly.

Number Sense…Number Sense…

Estimate 12/13 + 7/8.Estimate 12/13 + 7/8.

a)a) 11 b) 2b) 2

c) 19c) 19 d) d) 2121

Consider the highly technical paper plate…Consider the highly technical paper plate…

How do we address How do we address this?this?

Show me 1/2Show me 1/2

Show me less than 1/2Show me less than 1/2

Show me more than 1/2Show me more than 1/2

How do we address How do we address this?this?

What other fraction can you What other fraction can you show me?show me?

What fraction should I show What fraction should I show you?you?

Can we use this for decimals Can we use this for decimals and percents?and percents?

1/2 + 2/51/2 + 2/5

Estimate the following:Estimate the following:

2/6 + 3/112/6 + 3/11

2 1/13 + 6/72 1/13 + 6/7

3 4/5 + 1 1/33 4/5 + 1 1/3

It’s About Time

1. Fraction Bar Graphs– Part of the Whole– Equivalent Fractions

2. Clock Model– Fraction Tool– Addition and Subtraction

1 hour = 60 minutes

1/2 hour = 30 minutes

1/6 hour = 10 minutes

1/12 hour = 5 minutes

1/4 hour = 15 minutes

1/3 hour = 20 minutes

Fractions to Minutes

Inch by Inch

http://illuminations.nctm.org/LessonDetail

Manipulatives

Learning Stages

Concrete

RepresentationalPictorial

Abstract

Jim ate 1/4 of a medium cheese pizza then he at 1/8 of a medium pepperoni pizza. What fractional part of a pizza did Jim eat?

Let’s get back to Let’s get back to stories…stories…

Jean had 2 1/2 yards of ribbon. She gave

2/3 yard of her ribbon to Matt. How much

ribbon did Jean have left?

Let’s get back to Let’s get back to stories…stories…

Jessica just built a fishpond. Seven-tenths of

the fish in the pond are goldfish and 1/5 of the

fish in the pond are catfish. What fraction of

Jessica’s fish are goldfish or catfish?

Let’s get back to Let’s get back to stories…stories…

How would this problem change if the catfish came first?

Write a story to support 3/4 + 5/8.

Now it’s your turn to Now it’s your turn to tell the story…tell the story…

Write a story to support 4/5 - 1/2.

Now it’s your turn to Now it’s your turn to tell the story…tell the story…

Thank You!