Teaching to the next generation sunshine state standards
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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

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Teaching to the next generation sunshine state standards

Teaching to the Next GenerationSunshine State Standards

August 17, 2010


Next generation sunshine state standards

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


Coding scheme for ngsss

Coding Scheme for NGSSS

MA.3.A.2.1


Teaching to the next generation sunshine state standards

Intent of the Standards

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

  • How do we make sense of teaching deeply?

  • Think of a swimming pool.


Cognitive complexity

Cognitive Complexity

Low ComplexityRelies heavily on the recall and recognition; computation

Moderate ComplexityInvolves flexible thinking and usually multiple operations; problem solving

High Complexity

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


Teaching to the next generation sunshine state standards

Topics not Chapters


Four part lesson

Four-Part Lesson

Daily Spiral Review: Problem of Day

Interactive Learning: Purpose, Prior Knowledge

Visual Learning: Vocabulary, Instruction, Practice

Close, Assess, Differentiate: Centers, HW


Teaching to the next generation sunshine state standards

Conceptual Understanding


Teaching to the next generation sunshine state standards

Conceptual Understanding


Teaching to the next generation sunshine state standards

Conceptual Understanding


Teaching to the next generation sunshine state standards

Old Instruction vs New Instruction


Nctm process standards

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 standards1

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 standards2

NCTM Process Standards

Connections

Equivalence: fraction/decimal, cm/m

Other content areas, science

Real World contexts

Representation

Model Drawing


Number sense

Number Sense

5

=


Teaching to the next generation sunshine state standards

Participants will explore …

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


Teaching to the next generation sunshine state standards

Active Learning Pyramid

Students

Apply Their

Learning

Students ReceiveInformation


Instructional strategies

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

Examining the Standards

MA.K.A.1.1

Represent quantities with numbers

up to 20, verbally, in writing, and

with manipulatives. (Moderate)


Examining the standards1

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 standards2

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)


Which day of the week were you born

Which Day of the Week Were You Born?

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)

26


Teaching to the next generation sunshine state standards

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

Add A + B + C + D

27


Teaching to the next generation sunshine state standards

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

28


Which day of the week were you born1

Which Day of the Week Were You Born?

  • 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.


Foundational number concepts

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.


Foundational number concepts1

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


Give me five

Table Talk Activity:

What do you know about five?

The answer is 5, what is the question?

Give Me Five!


Sets of five

Sets 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

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

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

Five Frame


Word problems compare

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?


Teaching to the next generation sunshine state standards

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 2005

Marilyn 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.


Literacy libraries and learning

Literacy, Libraries and Learning

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

40


Ten black dots by donald crews

Ten Black Dotsby Donald Crews

Read the text aloud

Draw 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

41


Make ten black dots book

Make Ten Black Dots Book

index cards

black dots

Materials

Instructions

  • number word

  • numeral

  • corresponding dots


Ten black dots book

Ten Black Dots Book

  • 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 book1

Ten 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 intendedby the Next Generation Sunshine State Standards?


Ten black dots

Ten Black Dots


Ten frame grid

Ten Frame Grid


Show me 10 frame activity

“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

Make a “Ten Bead” Bracelet


Debriefing

Debriefing:

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?

49

49


Debriefing1

Debriefing:

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?

50


Debriefing2

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 subtraction strategies

Addition and SubtractionStrategies

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

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

The Standard Algorithm

27

+ 46

You’re not allowed to use it today


Problem 1

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

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

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

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 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

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

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

Base-10 Blocks as a Model

Problem 1: 27 + 58

1

1

1

1

1

1

1

1

10

10

10

10

10

10

10

+

1

1

1

1

1

1

1

  • Problem 2: 24 + 46

  • Problem 3: 17 + 34


Partial sums

Partial Sums

32

+2911

+50

61

32 + 29 = (30 + 2) + (20 + 9) = (2 + 9) + (30 +20) = 11 + 50 = 61


Partial sums focus on place value

Partial Sums: Focus on Place Value

32

+2911

+50

61

32 + 29 = (30 + 2) + (20 + 9) = (2 + 9) + (30 + 20) = 11 + 50 = 61


Partial sums1

Partial Sums

3276

+ 4785

7000

900

150

+ 11

8061


Using base 10 blocks for subtraction

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

Partial Differences

73

-26

73 – 26 = (70 + 3) – (20 + 6) = (60 + 13) – (20 + 6)= (60 – 20) + (13 – 6)= 40 + 7 = 47

60

13

7

+ 40

47


Jigsaw strategy the empty number line

Jigsaw Strategy: The 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

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


Studying the standards

Studying the Standards

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)?

70


What can i do tomorrow morning teaching the content

What can I do tomorrow morning?Teaching the Content

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?

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