Transcript FlexibleThinkingPPT

The Magnificent Thing About
Flexible Thinking in Mathematics
http://lead4ward.com/k2-handouts/
password – start-early
Nancy Crouch
[email protected]
Students move
their finger along
the 100s chart
Students record their
actions with arrows
15
Students relate
arrows to a number
sentence
16
Can you think
of another
way?
Use of Mental
Math
Coordinate
manipulation of
base ten blocks
with place value
chart recordings
17
18
Composing/
Decomposing
Numbers
Working Vertically and
Horizontally
Properties of
Operations
Subtraction as a
distance problem
instead of take away
The distance
between 24 and
63 is 39.
19-20
•
•
•
Flexible Thinking in Grade 2
2.4(C) solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of
strategies based on place value, including algorithms
2.4(D) generate and solve problem situations for a given mathematical number sentence involving addition and subtraction
of whole numbers within 1,000
2.4(B) add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on
knowledge of place value and properties of operations
63
-21
?
62
-20
?
61
-19
?
60
-18
?
63
-21
42
62
-20
42
61
-19
42
60
-18
42
600
- 18
?
599
- 17
?
599
- 17
482
63-24
as a takeaway
problem
63-24
as a comparison
problem
21
Coordinate
manipulation of base
ten blocks with place
value chart recordings
22
Teacher…can I put a -1
here because I am short
one to be able to
subtract 4 from 3?
Composing/
Decomposing
Numbers
23
Working Vertically and
Horizontally
Properties of
Operations
Flexible Thinking in Kindergarten
•
•
K.2(I) compose and decompose numbers up to 10 with objects and pictures
K.2(B) read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
Pictorial Model
Number of
Red
Number of
Yellow
Total Number
4
1
5
5
5
5
5
5
Flexible Thinking in Kindergarten
•
•
K.2(I) compose and decompose numbers up to 10 with objects and pictures
K.2(B) read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
Pictorial Model
Number of
Red
Number of
Yellow
Total Number
4
1
5
5
5
5
5
5
5
Flexible Thinking in Kindergarten
•
•
•
K.2(I) compose and decompose numbers up to 10 with objects and pictures
K.2(B) read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
K.3(C) explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete
and pictorial models, and number sentences
Pictorial Model
Number Sentence
5=4+1
2+2+1=5
3
Flexible Thinking in Kindergarten
•
•
K.2(I) compose and decompose numbers up to 10 with objects and pictures
K.2(B) read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
Pictorial Model
Number Sentence
4
Flexible Thinking in Grade 1
•
•
1.2(B) use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many
hundreds, so many tens, and so many ones
1.2(C) use objects, pictures, and expanded and standard forms to represent numbers up to 120
Pictorial Model
Place Value
Number Sentence
Hundreds
Tens
Ones
0
4
2
Hundreds
Tens
Ones
0
3
12
Hundreds
Tens
Ones
4 tens + 2 ones = 42
or
10 + 10 + 10 + 10 + 1 + 1 = 42
or
10 + 10 + 10 + 10 + 2 = 42
or
40 + 2 = 42
42 = 3 tens + 12 ones
or
42 = 10+10+10+1+1+1+1+1+1+1+1+1+1+1+1
or
42 = 10 + 10 + 10 + 12
Or
42 = 30 + 12
5
Flexible Thinking in Grade 1
•
•
1.2(B) use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many
hundreds, so many tens, and so many ones
1.2(C) use objects, pictures, and expanded and standard forms to represent numbers up to 120
Pictorial Model
Place Value
Number Sentence
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
6
Flexible Thinking in Grade 2
•
•
2.2(A) use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum
of so many thousands, hundreds, tens, and ones
2.2(B) use standard, word, and expanded forms to represent numbers up to 1,200
Pictorial Model
Place Value
Number Sentence
Hundreds
Tens
Ones
1
4
2
Hundreds
Tens
Ones
0
14
2
1 hundred + 4 tens + 2 ones = 142
or
100 + 10 + 10 + 10 + 10 + 1 + 1 = 142
or
100 + 10 + 10 + 10 + 10 + 2 = 142
or
100 + 40 + 2 = 142
142 = 14 tens + 2 ones
or
142 = 10+10+10+10+10+10+10+10+10+10+10+10+10+10+1+1
or
142=10+10+10+10+10+10+10+10+10+10+10+10+10+10+2
Hundreds
Tens
Ones
1
7
Flexible Thinking in Grade 2
•
•
2.2(A) use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum
of so many thousands, hundreds, tens, and ones
2.2(B) use standard, word, and expanded forms to represent numbers up to 1,200
Pictorial Model
Place Value
Number Sentence
Hundreds
Tens
Ones
Hundreds
Tens
Ones
Hundreds
Tens
Ones
8
Flexible Thinking in Grade K
•
•
•
K.2(I) compose and decompose numbers up to 10 with objects and pictures
K.2(B) read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
K.3(C) explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number
sentences
Pictorial Model
Number Sentence
2+3=5
4+1=5
2+2+1=5
3+3–1=5
9
Flexible Thinking in Grade K
•
•
•
K.2(I) compose and decompose numbers up to 10 with objects and pictures
K.2(B) read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures
K.3(C) explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words, concrete and pictorial models, and number
sentences
Pictorial Model
Number Sentence
10
Flexible Thinking in Grade 1
•
•
1.2(B) use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many
hundreds, so many tens, and so many ones
1.2(C) use objects, pictures, and expanded and standard forms to represent numbers up to 120
Pictorial Model
Number Sentence
10 + 10 + 10 + 10 + 1 + 1 = 42
10 + 10 + 10 + 10 + 2 = 42
40 + 2 = 42
42 = 10+10+10+1+1+1+1+1+1+1+1+1+1+1+1
42 = 10 + 10 + 10 + 12
42 = 30 + 12
11
Flexible Thinking in Grade 1
•
•
1.2(B) use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many
hundreds, so many tens, and so many ones
1.2(C) use objects, pictures, and expanded and standard forms to represent numbers up to 120
Pictorial Model
Number Sentence
12
•
•
Flexible Thinking in Grade 2
2.2(A) use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum
of so many thousands, hundreds, tens, and ones
2.2(B) use standard, word, and expanded forms to represent numbers up to 1,200
Pictorial Model
Number Sentence
100 + 10 + 10 + 10 + 10 + 1 + 1 = 142
100 + 10 + 10 + 10 + 10 + 2 = 142
100 + 40 + 2 = 142
142= 10+10+10+10+10+10+10+10+10+10+10+10+10+10+1+1
13
142=10+10+10+10+10+10+10+10+10+10+10+10+10+10+2