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Teaching to the Next Generation Sunshine State Standards

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August 17, 2010

- Eliminates:
- Mile wide, inch deep curriculum
- Constant repetition

- Emphasizes:
- Automatic Recall of basic facts
- Computational fluency
- Knowledge and skills with understanding

MA.3.A.2.1

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.

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

Topics not Chapters

Daily Spiral Review: Problem of Day

Interactive Learning: Purpose, Prior Knowledge

Visual Learning: Vocabulary, Instruction, Practice

Close, Assess, Differentiate: Centers, HW

Conceptual Understanding

Conceptual Understanding

Conceptual Understanding

Old Instruction vs New Instruction

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

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

Connections

Equivalence: fraction/decimal, cm/m

Other content areas, science

Real World contexts

Representation

Model Drawing

5

=

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

Active Learning Pyramid

Students

Apply Their

Learning

Students ReceiveInformation

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

MA.K.A.1.1

Represent quantities with numbers

up to 20, verbally, in writing, and

with manipulatives. (Moderate)

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)

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)

26

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

Add A + B + C + D

27

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

28

- 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.

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.

Table Talk Activity:

What do you know about five?

The answer is 5, what is the question?

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

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 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.

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?

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.

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

40

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

index cards

black dots

Materials

Instructions

- number word
- numeral
- corresponding dots

- 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?

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?

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?

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

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

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?

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

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)

27

+ 46

You’re not allowed to use it today

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

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

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

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 are the advantages of using invented strategies?

What are the disadvantages of using invented strategies?

What depth of knowledge does this activity lead to?

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

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.

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

32

+2911

+50

61

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

32

+2911

+50

61

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

3276

+ 4785

7000

900

150

+ 11

8061

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

- Problem 1: 73 – 26
- Problem 2: 60 – 32

73

-26

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

60

13

7

+ 40

47

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?

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)?

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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?

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