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Addition and SubtractionPowerPoint Presentation

Addition and Subtraction

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Addition and Subtraction Scaffolding Instruction Big Picture of Session TEKS Focus : Addition and Subtraction Instructional Focus : Scaffolding Scaffolding Focus : Effective use of graphic organizers and representational tools to develop, bridge, and build conceptual understanding

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### Scaffolding

### What is Scaffolding in Mathematics Instruction?

### Scaffolding Instruction Through Questioning

Big Picture of Session

- TEKS Focus: Addition and Subtraction
- Instructional Focus: Scaffolding
- Scaffolding Focus: Effective use of graphic organizers and representational tools to develop, bridge, and build conceptual understanding

Instructional Focus: Scaffolding

According to Lev Vygotsky . . .

“The zone of proximal development is the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.”

L.S. Vygotsky, (1978)

Scaffolding

Unknown

“Through scaffolding, the teacher was able to build bridges from the unknown and not understood to the known and understood.”

Henderson, Many, Wellborn, and Ward. (2002, Summer). Reading Research and Instruction, 41(4), p. 310.

Known

Video Reflection

- How does the instructor scaffold Tomika’s learning?
[Tomika Video]

First Turn/Last Turn

- Read individually. Highlight 2-3 items.
- In turn, share one of your items but do not comment on it.
- Group members comment in round-robin fashion* – about the item (without cross-talk).
- The initial person who named the item then shares his or her thinking about the item and takes the last turn, making the final comments.
- Repeat the pattern around the table.

*Round-robin is a highly structured participation strategy.

Group members speak in turns, moving around the table in one direction.

What Is Scaffolding in Mathematics Instruction?

Scaffolding Focus

Bridging conceptual understanding using:

- Graphic organizers
- Representational Tools

Video Reflection

What are some examples of videos shown yesterday that use a graphic organizer to enhance understanding?

“Teachers can use questions as a kind of scaffolding to help students reach higher levels of thinking and learning. . . In the asking of questions, teachers are thinking actively and helping students be active thinkers” (Walsh and Sattes, 2005, p 23).

Video Reflection

How do the teacher’s questions help Shania become successful with the problem 15 minus 1?

[Shania Video]

1st Series of Lessons: Modeling Addition & Subtraction

Linking Cubes to Represent Characters

1 gorilla – 1 blue cube

2 elephants – 2 white cubes

3 tigers – 3 orange cubes

4 parrots – 4 red cubes

5 monkeys – 5 brown cubes

One gorilla is out of his cage,

Oh my, what a rage!

Two elephants followed in line,

Parading, strutting, looking fine!

As they join the fun galore.

What a crazy looking group.

Which manipulative is easier to use and to understand the concepts for this activity?

Part-Part-Whole Mat for Addition

Explore

Quickly fly back to feed.

As they swiftly spring to their feet.

They must eat not to be rude!

What do you think he should do?

How did we use visuals to move the students from the concrete to the abstract level of learning?

1st Series of Lessons: Modeling Addition & Subtraction

Linking Cubes on a String

Engage Optional Tool

- Which representational tools have we used so far?
- How have we used them?
- Fill the Reflection Sheet

Progression of Knowledge and Skill Statements

Linking Cube Organizer 50 40 30 20 10

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

15 50 40 30 20 10 + 23

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

15 50 40 30 20 10 + 23

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

3 8

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

15 50 40 30 20 10 + 23 Describe the Results in Words and Numbers

= 38

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

3 tens and 8 ones

30 + 8

38

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

24 50 40 30 20 10 + 36

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

24 50 40 30 20 10 + 36

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

1

0

6

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

24 50 40 30 20 10 + 36Describe Results in Words and Numbers

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

6 tens and 0 ones

60 + 0

60

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

24 50 40 30 20 10 + 38

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

1

2

6

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

24 50 40 30 20 10 + 38Describe Results in Words and Numbers

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

6 tens and 2 ones

60 + 2

62

10 9 8 7 6 5 4 3 2 1

Ones

Tens

Elaborate

Base Ten Blocks 50 40 30 20 10

- Proportional Relationship between the pieces
- Unit
- Rod
- Flat
- Cube

- Represent whole numbers

Base Ten Blocks Organizer 50 40 30 20 10

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

Tens

67 + 45

Explain

Base Ten Blocks Organizer 50 40 30 20 10

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

Tens

67 + 45

Explain

Base Ten Blocks Organizer 50 40 30 20 10

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

Tens

67 + 45

Explain

Describe the Results in Words and Numbers 50 40 30 20 10

100 90 80 70 60 50 40 30 20 10

9

8

7

6

5

4

3

2

1

10 9 8 7 6 5 4 3 2 1

Ones

1 hundred 1 ten 2 ones

Tens

100 + 10 + 2

67 + 45 = 112

Which term do we use: 50 40 30 20 10Carry? Borrow? Regroup? Rename?

- “Carry” and “borrow” are misleading mathematically - They may promote mechanical manipulation of symbols.
- The term “regroup” is appropriate when manipulatives for a quantity are grouped differently.
- The term “rename” is mathematically correct; the quantity is actually given a different name.
- For example, when computing 273-186, 2 hundreds + 7 tens + 3 ones is renamed as 2 hundreds + 6 tens + 13 ones” .
(Ashlock, 2002, p. 63)

- For example, when computing 273-186, 2 hundreds + 7 tens + 3 ones is renamed as 2 hundreds + 6 tens + 13 ones” .

Video Reflection 50 40 30 20 10

How does the teacher in the video demonstrate how to find the sum of four fives?

[Allen Video]

Reflection on the Second Grade Lesson 50 40 30 20 10

Reflection on the First Series of LessonsHow do you scaffold lessons for students to be able to model addition and subtraction?

What tools could help students to better understand addition and subtraction?

How did we scaffold the lessons in the second

and third grade lesson by bridging

from the concrete to the pictorial to the abstract?

TEKS Focus 50 40 30 20 10

Addition and Subtraction Strategies 50 40 30 20 10

- Counting On
- Counting Back
- Doubles
- Near Doubles
- Make Ten
- Splitting
- Related Facts
- Compensation

Doubles and Near Doubles 50 40 30 20 10

Video Reflection 50 40 30 20 10

How is the organizer used to teach the students doubles from the pictorial to the concrete level?

[Zachary Video]

Fill this section on the Reflection sheet.

Doubles and Near Doubles: 50 40 30 20 10

Explore thinking strategies like these or realizing that 7 + 8 is the same as 7+7+1 will help students see the meaning of the operations. Such explorations also help teachers learn what students are thinking. NCTM

5 + 5 =

5 + 6 =

6 + 6 =

6 + 7 =

7 + 7 =

10

11

12

13

14

Video Reflection 50 40 30 20 10

How is organizer used to teach the students near doubles from the concrete level to the abstract level?

[Avery Video]

Fill this section on the Reflection sheet.

Video Reflection 50 40 30 20 10

How does the teacher scaffold the students’ learning of the concept for adding various numbers?

[Mrs. MacDonald Video]

How can the students use the Make Ten Strategy to solve this problem?

6 + 8 =

6 + 8 = problem?

6 + 8 = problem?

6 + 8 = problem?

Video Reflection problem?

How does Harrison use his mental figuration of make ten to describe how to solve 8 + 5?

[Harrison Video]

Splitting Strategy problem?

“Splitting strategy is a strategy that children develop almost on their own, as soon as they begin to understand place value. They split the numbers up into friendly pieces, usually into hundreds, tens, and ones.”

Young Mathematicians at Work, pp. 134-135

60 problem?

12

Splitting Strategy from Young Mathematicians at Work28 + 44

40

+

4

20

+

8

+

10

+

2

= 72

70

+

2

Splitting Strategy problem?from Young Mathematicians at Work

28 + 44

20 + 8 + 40 + 4

60 + 12

60 + 10 + 2

70 + 2 = 72

Reflect: problem?

What modes of learning were used to help students learn their basic facts? Fill the reflection sheet.

Reflect: problem?

Look at your scaffolding handout and highlight a scaffolding technique you would like to start using immediately.

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