Building Powerful Numeracy from Whole Numbers to Ratios, 5-7

1
Building Powerful Numeracy from Whole Numbers to
Ratios, 5-7

• Pamela Weber Harris
• _at_pwharris
• pamelawharris.com
• pharris_at_byu.net
• facebook.com/numeracy

2
Math is figure-out-able!
pharris_at_byu.net
3
0.26 x 24
pharris_at_byu.net
4
(No Transcript)
5
Counting StrategiesAdditive ThinkingMultiplicati
ve ThinkingProportional ReasoningAlgebraic
Reasoning
pharris_at_byu.net
6
(No Transcript)
7
15 - 7
pharris_at_byu.net
8
(No Transcript)
9
Counting RackRekenrek
pamelawharris.com
10
Counting RackRekenrek
11
Problem Strings
12
As Close As It Gets
409 1.19
a) 400
b) 410
c) 419
d) 500
13
As Close As It Gets
13.2 1,989
a) 14
b) 1,900
c) 2,000
d) 2,100
14
As Close As It Gets
a) 0
b) 0.5
c) 0.75
d) 1
15
Relational Thinking
36 97 ______ 100 3,5542,849 3,403
____ True or False? 19.8 2.03 20 0.03
16
(No Transcript)
17
As Close As It Gets
14,009 - 9.19
a) 14,000
b) 5,000
c) 13,000
d) 4,000
18
As Close As It Gets
1,002 - 899
a) 3
b) 100
c) 200
d) 300
19
As Close As It Gets
a) 5
b) 6
c) 4
d) 3
20
Relational Thinking
36 - 19 ______ - 20 3,554 - 2,849 ______ -
3,000 True or False? 6.2 - 3.8 6 - 4 19.8 -
1.98 20 - 2
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
Counting StrategiesAdditive ThinkingMultiplicati
ve ThinkingProportional ReasoningAlgebraic
Reasoning
pharris_at_byu.net
30
11 x 12
pharris_at_byu.net
31
132 ... Um, I knew 10 x 12 120, and um, then I
just add 12 because 1 x 12 12 and um I just add
12 to 120 and I got 132.
32
I didnt ask you if you know it, I asked you what
it is.What do you know...and figure it out from
there!
pharris_at_byu.net
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
TENS
41
5 IS HALF OF 10
TENS
42
5 IS HALF OF 10
TENS
43
5 IS HALF OF 10
TENS
44
Practice with a Game
pharris_at_byu.net
45
TI-Nspire, 84, 83 and APPS
pharris_at_byu.net
46
How to Build Multiplicative Proportional
Reasoning at the Same Time?

• Good, rich contexts - See Cathy Fosnot
• Mini-lesson Problem Strings

pharris_at_byu.net
47
2 x 27 4 x 27 8 x 27 10 x 27 9 x 27 5 x 27 100 x
27 99 x 27 324/27 405/27
Problem Strings
pharris_at_byu.net
48
Consider the Multiplication and Division
Algorithms
pharris_at_byu.net
49
Graph it
pharris_at_byu.net
50
What kind of relation?

• Open
• packs sticks.tns
• Enter the values in lists
• Enter the equation in
• What questions could
• you ask?

pharris_at_byu.net
51
2 x 3.24 x 3.28 x 3.210 x 3.29 x 3.25 x 3.2 15 x
3.2100 x 3.299 x 3.2 44.8/3.2 323.2/3.2 313.6/3.2
480/3.2
Problem Strings
pharris_at_byu.net
52
PB CC
2
4
8
10
9
6
5
3
400
450
456
18
25
Problem Strings
pharris_at_byu.net
53
(No Transcript)
54
pharris_at_byu.net
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
25 x 36 1/4 x 36 0.25 x 36 0.26 x 36 0.24 x
36 0.25 x 24 0.75 x 24 0.76 x 24
Problem Strings
pharris_at_byu.net
59
pharris_at_byu.net
60
Math is Figure-out-able

• Look to most efficient strategies and build
  proportional reasoning at the same time
• Teachers build own numeracy
• Its about relationships
• Among numbers to solve problems
• Between teachers and students to build young
  mathematicians

pharris_at_byu.net
61
Building Powerful Numeracy from Whole Numbers to
Ratios, 5-7

• Pamela Weber Harris
• _at_pwharris
• pamelawharris.com
• pharris_at_byu.net
• facebook.com/numeracy