1

Slight modification of the presentation at the NCTM Annual Conference

by

Dr. Eric MilouRowan University

Department of Mathematicsmilou@rowan.edu

856-256-4500 x3876

What Is Number Sense and Why Don’t My Students Have It?

2

Content Overview

National Math PanelNumber Sense & Computation

ProficiencyAlgebraic Symbolic Manipulation vs

Algebraic ThinkingThe role of Technology

3

National Math Panel (NMP)

A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.

4

NMP

A major goal for K–8 mathematics education should be proficiency with

fractions (including decimals, percents, and negative fractions).

5

Response by Peppermint Patty

6

Your Test!

4 x 9 x 25

How many ounces are in a gallon?

50 ÷ 1/2

7

Conceptual Understanding

24 ÷ 4 = 624 ÷ 3 = 824 ÷ 2 =1224 ÷ 1 = 2424 ÷ 1/2 = ??

8

Fractions - Conceptually

More than 1 or Less than 1

Explain your reasoning

9

Which is larger?

(2/3 + 3/4 + 4/5 + 5/6) or 4

12.5 x 45 or 4.5 x 125

(1/3 + 2/4 + 2/4 + 5/11) or 2

10

Where’s the Point?

2.43 x 5.1 = 12393 4.85 x 4.954 = 240269 21.25 x 1.08 = 2295 1.25 x 64 = 80 4.688 x 1.355 = 635224 46.88 x 1.355 = 635224 4.688 x 135.5 = 635224 46.88 x 13.55 = 635224

11

Conceptual Fraction task

Kim’s teacher asked her class to design a flag using four colors, dividing a square into parts, and to color the parts as follows:1/2 is colored red1/4 is colored blue1/8 is colored greenAny other part is to be left white

12

Flags

13

Harder Task

A chocolate bar is separated into several equal pieces.If Laura eats 1/4 of the pieces; andPaul eats 1/2 of the remaining pieces;There are six pieces left overInto how many pieces was the original bar

divided?

14

Chocolate Bar

LAURAP A U L

16 pieces

15

Decimals

1000 ÷ 1.49= 671.1409396

= Torture!Big Macs Sell for $1.49, how many Big Macs can

I buy for $10.00?1 is $1.502 are $34 are $66 are $9

Number Sense

is a vital skill

1.49 1000

16

Computation

17

Active Computation

Virtual Manipulatives

http://illuminations.nctm.org nlvm.usu.edu/en/nav/vlibrary.html

18

Conceptual & Contextual

8 + 7 = ?How do we teach this?

xx xx x x

xx

xx

xx

xx

x

19

8 + 7 = ?

8 + 7 = ?

2 5

10 + 5 = 15

20

Number Line Addition 5 + 4 =

nlvm.usu.edu/en/nav/vlibrary.html

21

1000 - 279 = ?

279 +1 = 280 + 20 = 300 +700 = 1000

1000 - 279 = 721

22

Multiplication

13 x 17 = ?

1 3

x 1 7

1

2

9031

2 2 1

-------

-------

10 7 10

3

1 0 0

3 0

7 0

2 1

221

23

Conceptual approach leads to ?

x 7 x

3

x2

3x

7x

21

Algebra: (x + 3) (x + 7) =

24

Example: Drug Steady State

10 mg Zrytec daily50% of Zrytec is eliminated dailyWhat % is in the body

after 7 days10 daysn days?

25

10mg Daily of Zrytec

Day Mg. of Zyrtec

1

234

56

10

1517.518.75

19.37519.6875