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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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Slide1 l.jpg

Addition

and Subtraction

Scaffolding

Instruction


Big picture of session l.jpg
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 l.jpg
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)


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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


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Video Reflection

  • How does the instructor scaffold Tomika’s learning?

    [Tomika Video]



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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 l.jpg

What Is Scaffolding in Mathematics Instruction?

What is Scaffolding in Mathematics Instruction?


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Scaffolding Focus

Bridging conceptual understanding using:

  • Graphic organizers

  • Representational Tools


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Video Reflection

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


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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).


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Video Reflection

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

[Shania Video]


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Modeling Addition

and Subtraction

Pre Kindergarten and Kindergarten Lesson


1 st series of lessons modeling addition subtraction l.jpg
1st Series of Lessons: Modeling Addition & Subtraction



Linking cubes to represent characters l.jpg
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


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One gorilla is out of his cage,

Oh my, what a rage!


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Two elephants followed in line,

Parading, strutting, looking fine!


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Three tigers let out a roar,

As they join the fun galore.


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Four parrots flew the coop,

What a crazy looking group.


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Time to Reflect

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



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IIII

IIII

Part-Part-Whole Mat

10


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Five monkeys

scream and shout.

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


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Five monkeys scream and shout.

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

5

10

+

=

15


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Cling! Clang! It’s dinner time!

Five monkeys swing home in

rhyme.


Cling clang it s dinner time five monkeys swing home in rhyme l.jpg
Cling! Clang! It’s dinner time!Five monkeys swing home in rhyme.

15

-

= 10

5


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Four parrots hungry for seed

Quickly fly back to feed.


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Three tigers smell red meat,

As they swiftly spring to their feet.


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Two elephants run for food.

They must eat not to be rude!


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One gorilla, sad and blue,

What do you think he should do?



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Time to Reflect

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


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Modeling Addition

and Subtraction

First Grade Lesson


1st series of lessons modeling addition subtraction l.jpg
1st Series of Lessons: Modeling Addition & Subtraction


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Linking Cubes on a String

Engage Optional Tool


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6 + 4 = 10

Recording Sheet for Linking Cubes on a String Up to 15

Optional Recording Sheet


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Recording Sheet for Linking Cubes on a String Up to 20

6 + 4 = 10

Optional Recording Sheet


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Time to Reflect

  • Which representational tools have we used so far?

  • How have we used them?

  • Fill the Reflection Sheet


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Modeling Addition

and Subtraction

Second Grade Lesson


Progression of knowledge and skill statements l.jpg
Progression of Knowledge and Skill Statements


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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 l.jpg
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 23 l.jpg
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 2364 l.jpg
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 23 describe the results in words and numbers l.jpg
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 36 l.jpg
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 3667 l.jpg
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 36 describe results in words and numbers l.jpg
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 38 l.jpg
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 38 describe results in words and numbers l.jpg
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 l.jpg
Base Ten Blocks 50 40 30 20 10

  • Proportional Relationship between the pieces

    • Unit

    • Rod

    • Flat

    • Cube

  • Represent whole numbers


Base ten blocks organizer l.jpg
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


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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 organizer74 l.jpg
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 l.jpg
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


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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)


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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]


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Reflection on the Second Grade Lesson 50 40 30 20 10

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 l.jpg

Basic Addition and 50 40 30 20 10

Subtraction Facts

First and Second Grade Lesson


Slide80 l.jpg

TEKS Focus 50 40 30 20 10


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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 l.jpg
Doubles and Near Doubles 50 40 30 20 10


Doubles l.jpg
Doubles 50 40 30 20 10

5 + 5 =

6 + 6 =

7 + 7 =

10

12

14


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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 doubles86 l.jpg
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 reflection87 l.jpg
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.


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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]



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6 + 8 = problem?


Slide91 l.jpg

6 + 8 = problem?


Slide92 l.jpg

6 + 8 = problem?


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Video Reflection problem?

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

[Harrison Video]


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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


Splitting strategy from young mathematicians at work l.jpg

60 problem?

12

Splitting Strategy from Young Mathematicians at Work

28 + 44

40

+

4

20

+

8

+

10

+

2

= 72

70

+

2


Splitting strategy from young mathematicians at work96 l.jpg
Splitting Strategy problem?from Young Mathematicians at Work

28 + 44

20 + 8 + 40 + 4

60 + 12

60 + 10 + 2

70 + 2 = 72


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Reflect: problem?

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


Slide98 l.jpg

Selecting Addition or problem?

Subtraction to Solve Problems

Second and Third Grade Lesson


Slide100 l.jpg

Reflect: problem?

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


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