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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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Presentation Transcript
slide1

Addition

and Subtraction

Scaffolding

Instruction

big picture of session
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
according to lev vygotsky
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)

scaffolding7
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
Video Reflection
  • How does the instructor scaffold Tomika’s learning?

[Tomika Video]

first turn last turn
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.

scaffolding focus
Scaffolding Focus

Bridging conceptual understanding using:

  • Graphic organizers
  • Representational Tools
video reflection13
Video Reflection

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

scaffolding instruction through questioning

Scaffolding Instruction Through Questioning

“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 reflection15
Video Reflection

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

[Shania Video]

slide16

Modeling Addition

and Subtraction

Pre Kindergarten and Kindergarten Lesson

linking cubes to represent characters
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

slide24
Two elephants followed in line,

Parading, strutting, looking fine!

slide26
Three tigers let out a roar,

As they join the fun galore.

slide28
Four parrots flew the coop,

What a crazy looking group.

slide30

Time to Reflect

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

slide33

IIII

IIII

Part-Part-Whole Mat

10

slide34
Five monkeys

scream and shout.

It doesn’t take long for them to get out!

slide36

Five monkeys scream and shout.

It doesn’t take long for them to get out!

5

10

+

=

15

slide37
Cling! Clang! It’s dinner time!

Five monkeys swing home in

rhyme.

slide40
Four parrots hungry for seed

Quickly fly back to feed.

slide42
Three tigers smell red meat,

As they swiftly spring to their feet.

slide44
Two elephants run for food.

They must eat not to be rude!

slide46
One gorilla, sad and blue,

What do you think he should do?

slide48

Time to Reflect

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

slide51

Modeling Addition

and Subtraction

First Grade Lesson

linking cubes on a string
Linking Cubes on a String

Engage Optional Tool

slide57

Time to Reflect

  • Which representational tools have we used so far?
  • How have we used them?
  • Fill the Reflection Sheet
slide58

Modeling Addition

and Subtraction

Second Grade Lesson

slide61

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

Units

Tens

linking cube organizer
Linking Cube Organizer

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 23
15 + 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 2364
15 + 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 23 describe the results in words and numbers
15 + 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 36
24 + 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 3667
24 + 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 36 describe results in words and numbers
24 + 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 38
24 + 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 38 describe results in words and numbers
24 + 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
Base Ten Blocks
  • Proportional Relationship between the pieces
    • Unit
    • Rod
    • Flat
    • Cube
  • Represent whole numbers
base ten blocks organizer
Base Ten Blocks Organizer

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 organizer73
Base Ten Blocks Organizer

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 organizer74
Base Ten Blocks Organizer

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
Describe the Results in Words and Numbers

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 carry borrow regroup rename
Which term do we use: Carry? 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)

video reflection77
Video Reflection

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

[Allen Video]

reflection on the first series of lessons

Reflection on the Second Grade Lesson

Reflection on the First Series of Lessons

How 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?

slide79

Basic Addition and

Subtraction Facts

First and Second Grade Lesson

addition and subtraction strategies
Addition and Subtraction Strategies
  • Counting On
  • Counting Back
  • Doubles
  • Near Doubles
  • Make Ten
  • Splitting
  • Related Facts
  • Compensation
doubles
Doubles

5 + 5 =

6 + 6 =

7 + 7 =

10

12

14

video reflection85
Video Reflection

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 doubles86
Doubles and Near Doubles:

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 reflection87
Video Reflection

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 reflection88
Video Reflection

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

[Mrs. MacDonald Video]

video reflection93
Video Reflection

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

[Harrison Video]

splitting strategy
Splitting Strategy

“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

splitting strategy from young mathematicians at work96
Splitting Strategyfrom Young Mathematicians at Work

28 + 44

20 + 8 + 40 + 4

60 + 12

60 + 10 + 2

70 + 2 = 72

slide97

Reflect:

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

slide98

Selecting Addition or

Subtraction to Solve Problems

Second and Third Grade Lesson

slide100

Reflect:

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

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