Teaching to the Next Generation

Sunshine State Standards

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

Grade Level Old GLE’s NGSSS

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

Original FCAT

Original FCAT

(FT Items)

New FCAT

SF (2004) SF (2004) New Adoption

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. 1Subject

GradeLevel

Body of Knowle

dge

Big Idea/

Supporting 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.

Cognitive Complexity

Low ComplexityRelies heavily on the recall and recognition; computation

Moderate Complexity Involves flexible thinking and usually multiple operations; problem solving

High Complexity Requires more abstract reasoning, planning, analysis, judgment, and creative thought; multiple representations

Topics not Chapters

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

NCTM Process Standards Problem Solving

– Developing perseverance– Examples by grade level, Model

drawing– Teacher’s role

Reasoning and Proof– Mathematical conjectures– Examples and counterexamples– Examples by grade level

NCTM Process Standards Communication

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

– Tool for understanding and explaining

– Increased use of math vocabulary– Examples of rich problems by

grade level

NCTM Process Standards Connections

– Equivalence: fraction/decimal, cm/m

– Other content areas, science– Real World contexts

Representation– Model Drawing

Number Sense

= 5

The importance of developing number sense in a gradual sequence

Activities that build upon one another for students to gain a better sense of number relationships

Counting, which involves the skills of orally reciting numerals, matching and writing numerals to identify the quantity and understanding the concepts of more than, less than and equal to

Participants will explore …

Students Receive Information

Students Apply Their Learning

Active Learning Pyramid

Instructional Strategies

NCTM Math Process Standards:– Problem Solving– Representation– Communication– Connections- Reasoning and Proof

Cooperative learning, emergent literacy instruction, the use of manipulative materials, and think-pair-share will be highlighted

Examining the Standards

MA.K.A.1.1

Represent quantities with numbers up to 20, verbally, in writing, and with manipulatives. (Moderate)

Examining the Standards

MA.1.A.1.1

Model addition and subtraction situations using the concepts of “part-whole”, “adding to,” “taking away from”, “comparing,” and “missing addend”. (Moderate)

Examining the Standards

MA.2.A.2.1 Recall basic addition and related subtraction facts. (Low)

MA.2.A.1.1 Identify relationships between the digits and their place values through the thousands, including counting by tens and hundreds. (Moderate)

Write down the last two digits of the year you were born. (A)

Divide that number by 4 and ignore any remainder. (B)

Write down the day of the month you were born. (C)

Which Day of the Week Which Day of the Week Were You Born?Were You Born?

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Sunday 1 Jan/Oct 1

Monday 2 May 2

Tuesday 3 August 3

Wednesday 4 Feb/Mar/Nov 4

Thursday 5 June 5

Friday 6 Sept/Dec 6

Saturday 0 Apr/July 0

Find the number of the month you were born from the Month Table. (D)

Add A + B + C + D

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Divide this total by seven and use the remainder to see which day you were born on from the table

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Sunday 1 Jan/Oct 1

Monday 2 May 2

Tuesday 3 August 3

Wednesday 4 Feb/Mar/Nov 4

Thursday 5 June 5

Friday 6 Sept/Dec 6

Saturday 0 Apr/July 0

What are your thoughts about this activity?

Were you amazed at the outcome?

What would be the depth of knowledge for this activity? Justify your answer.

Which Day of the Week Which Day of the Week Were You Born?Were You Born?

Foundational Number Concepts

Inclusion-If you ask a child to bring you 5 toy trucks and he brings you the fifth truck that he counts, he may not understand that all 5 trucks are included in the entire set of trucks. The fifth truck is only part of the set.

One-to-One Correspondence -The matching of one number to one object. Children who call numbers at a faster or slower rate than they are able to point to, may not yet have mastered the skill.

Conservation of Number -Children have acquired conservation of number when, for example, they recognize that a group of objects clustered tightly together still contains the same number of objects when spread over a larger area.

Number Sense and Relationships - Just

like learning to read, learning to count requires numerous opportunities for purposeful counting.

Foundational Number Concepts

Table Talk Activity:

What do you know about five?

The answer is 5, what is the question?

Give Me Five!

Sets of FiveSets of Five

Write the number 1 on an index card

Place the card on the table

Place one counter above the card

Write another number card that is one more than the first number

Place the appropriate number of counters above that card

Continue until you have sets of 1-5

Developing “Five-ness”

Read the article, “ Developing ‘Five-ness’ in Kindergarten” and highlight the meaningful points.

Discuss highlighted points with table partners.

Compare learning experiences identified in the article, with your past instructional strategies.

How does the depth of knowledge in the ‘Five-ness” activities compare to the ‘Day of the Week” activity?

Create a Picture

Create a picture using up to 5 colors.

Complete the sentence below and write it on the bottom of the picture.

I used _______different colors in my picture.

Five Frame

Word Problems: Compare

Sally has 4 apples. Jimmy has the same. How many apples does Jimmy have?

Sally has 4 apples. She has 3 more than Jimmy. How many does Jimmy have now?

Game

Dot Cards 1-5 Shuffle the cards and give a set to

each group. One person takes a card, the

others find a card that is fewer or more than.

Repeat so every one gets a turn.

Marilyn Burns, 2005Marilyn Burns, 2005

The standard for mathematics should be the same as the standard for reading-bringing meaning to the printed symbols. In both situations, skills and understanding must go hand in hand. The challenge is how do we help students develop meaning and make sense of what they do?”

Discuss Marilyn Burns’ purpose in the statement above.

Why Connect Mathematics and Literature?

Mathematics and literature bring order to the world around us

Math and literature classify objects Math and literature emphasize problem

solving skills Math and literature involve relationships

and patterns

Literacy, Libraries and Literacy, Libraries and LearningLearning

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Read the text aloudDraw a number line on chart paper sequenced from 0 to 10

Place the appropriate amount of sticky dots above the line to represent each counting number

Count the number of sticky dots above each number

Ten Black DotsTen Black Dotsby Donald Crewsby Donald Crews

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Make Ten Black Dots Book

index cards black dots

Materials

number word numeral corresponding dots

Instructions

Create a foldable book similar to the one in the story

Complete this on a separate sheet of paper– We each needed _____ dots.– I got my answer by _____.– The entire class needed ____ dots.– I know that because _______.

What are the different ways that young learners will complete these tasks?

Ten Black Dots BookTen Black Dots Book

Find a partner from another group

Count the number of dots together

Explain how your books are similar and different

In what ways might you revise current instructional strategies to incorporate the in-depth understanding intended by the Next Generation Sunshine State Standards?

Ten Black Dots BookTen Black Dots Book

one

1

two

2

three

3

four

4

five

5

six

6

seven

7

eight

8

nine

9

ten

10

Ten Black Dots

Ten Frame Grid

“Show Me” 10 Frame Activity

Show me 4 objects on the 10 frame. How many counters are on the 10 frame? Show me 2 more, what is the number now? How many more to make 10?

Show me seven. Show me 1 more, what is the number now? Show me 2 less, what is the number now? How many more to make 10?

Using 2 ten frames, show me 13. Show me 5 more, what is the number now? Show me 6 less, what is the number now/ How can you make 20?

How does the depth of knowledge in the “Show Me” activity compare to the “Five-ness” activity?

Make a “Ten Bead” Bracelet

How are the process standards of problem solving, representation, communication, reasoning and proof, and connections addressed in the previous activities?

How will allowing students to think for themselves impact their computational fluency?

Debriefing:Debriefing:

4949

Looking back at the benchmarks discussed, what background knowledge must children know in order to meet the requirements of this standard?

How might you utilize manipulatives to support conceptual depth and understanding?

Debriefing:Debriefing:

50

Debriefing:Debriefing:

How will you assess students’ understanding of the benchmark, MA.K.A.1.1?

What other benchmarks in grades K-2, are related to this benchmark?

In what ways might you revise current instructional strategies to incorporate the in-depth understanding intended by the Next Generation Sunshine State Standards?

Addition and SubtractionAddition and SubtractionStrategiesStrategies

Participants will explore …

–The use of invented strategies to solve multi-digit addition and subtraction problems

–The use of Base 10 blocks, partial sums, and differences to solve multi-digit addition problems

–The empty number line as a method to focus on place value when solving subtraction problems

Invented Strategies Overview

These strategies are personal and flexible for the students

Students will solve the same problem in different ways that make sense to them

“There is mounting evidence that children both in and out of school can construct methods for adding and subtracting multi-digit numbers without explicit instruction.” (Carpenter, et al., 1998, p. 4)

The Standard Algorithm

27+ 46

You’re not allowed to use it today

Problem 1

The two scout troops went on a field trip. There were 46 girl scouts and 38 boy scouts. How many scouts went on the trip?

–Van de Walle, 2007, p. 223

Problem 2

Sam had 46 baseball cards. He went to a card show and got some more cards for his collection. Now he has 73 cards. How many cards did Sam buy at the card show?

–Van de Walle, 2007, p. 223

Problem 3

There were 84 children on the playground. The 37 second-grade students came in first. How many children were still outside?

–Van de Walle, 2007 p. 225

Problem 4

Tommy was on page 67 of his book. Then he read 58 more pages. How many pages did Tommy read in all?

–Van de Walle, 2007, p. 222

What do you think?

What are the advantages of using invented strategies?

What are the disadvantages of using invented strategies?

What depth of knowledge does this activity lead to?

Getting Students to Invent Their Own Strategies

Utilize word problems

-Notice the wording involved in the previous problems

Allow plenty of time Listen to different strategies Have students explain their methods Record verbal explanations for others to model Pose problems to be solved mentally

Transitioning to “New” Standard Algorithms

Using Base -10 Blocks for Addition

–For each problem, one person of the pair should be the “doer” and the other person the “recorder.”

–Keep a “written record” to translate what you do with the blocks into a paper-and-pencil algorithm.

Base-10 Blocks as a Model

10 10 1

11

1 11

1 1 1

11

1

1

1

110 10 10 10 10+

Problem 1: 27 + 58

Problem 2: 24 + 46

Problem 3: 17 + 34

Partial Sums

32

+29 11

+50 61

32 + 29 =

(30 + 2) + (20 + 9) =

(2 + 9) + (30 +20) =

11 + 50 = 61

Partial Sums: Focus on Place Value

32

+29 11

+50 61

32 + 29 =

(30 + 2) + (20 + 9) =

(2 + 9) + (30 + 20) =

11 + 50 = 61

Partial Sums

3276+ 4785 7000 900 150+ 11 8061

Using Base-10 Blocks for Subtraction

Using Base-10 blocks and place-value charts to develop the traditional algorithm for subtraction.

Problem 1: 73 – 26

Problem 2: 60 – 32

Partial Differences

73 -26

73 – 26 =

(70 + 3) – (20 + 6) =

(60 + 13) – (20 + 6)=

(60 – 20) + (13 – 6)= 40

+ 7 = 47

1360

7+ 40 47

Jigsaw Strategy: Jigsaw Strategy: The Empty Number LineThe Empty Number Line

Divide into dyads Read your half of the article (5 min.)

Highlight important ideas When ready, share your ideas with your partner

What was surprising or interesting within your group discussion?

Developing Two-Digit Subtraction Using the Empty

Number Line Be ready to describe the child’s strategy to your

partner

What depth of knowledge is exhibited in this strategy?

Video Link:http://www.teachertube.com/view_video.php?viewkey=05f243646d6f1e199f0b

Examine the Big Ideas related to the Base-10 Number system across Grades K - 2.

– How is the content across the grade levels related? How does the content progress to a deeper level of understanding?

– How does the content prepare students for more advanced mathematics?

– How do the prior activities support children to get to the depth of knowledge identified by the State (Moderate – DOK2)?

Studying the StandardsStudying the Standards

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How might you use the strategies/methods discussed today in your classroom?

What do you expect your students to find challenging about invented and standard methods for addition and subtraction?

What misconceptions might students hold about addition and subtraction that you will need to address?

What can I do tomorrow What can I do tomorrow morning?morning?

Teaching the ContentTeaching the Content

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