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

What Is Number Sense and Why Don’t My Students Have It? Slight modification of the presentation at the NCTM Annual Conference by Dr. Eric Milou Rowan University Department of Mathematics milou@rowan.edu 856-256-4500 x3876

Content Overview • National Math Panel • Number Sense & Computation Proficiency • Algebraic Symbolic Manipulation vs Algebraic Thinking • The role of Technology

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.

NMP • A major goal for K–8 mathematics education should be proficiency with fractions (including decimals, percents, and negative fractions).

Response by Peppermint Patty

Your Test! 4 x 9 x 25 How many ounces are in a gallon? 50 ÷ 1/2

Conceptual Understanding • 24 ÷ 4 = 6 • 24 ÷ 3 = 8 • 24 ÷ 2 =12 • 24 ÷ 1 = 24 • 24 ÷ 1/2 = ??

Fractions - Conceptually More than 1 or Less than 1 Explain your reasoning

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

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

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 red • 1/4 is colored blue • 1/8 is colored green • Any other part is to be left white

Flags

Harder Task • A chocolate bar is separated into several equal pieces. • If Laura eats 1/4 of the pieces; and • Paul eats 1/2 of the remaining pieces; • There are six pieces left over • Into how many pieces was the original bar divided?

Chocolate Bar P A U L LAURA 16 pieces

1.49 1000 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 $1.50 • 2 are $3 • 4 are $6 • 6 are $9 Number Sense is a vital skill

Computation

Active Computation • Virtual Manipulatives • http://illuminations.nctm.org • nlvm.usu.edu/en/nav/vlibrary.html

Conceptual & Contextual • 8 + 7 = ? • How do we teach this? x x x x x x x x x x x x x x x

8 + 7 = ? 8 + 7 = ? 5 2 10 + 5 = 15

Number Line Addition 5 + 4 = nlvm.usu.edu/en/nav/vlibrary.html

1000 - 279 = ? 279 +1 = 280 + 20 = 300 +700 = 1000 1000 - 279 = 721

Multiplication • 13 x 17 = ? 10 7 2 10 3 1 3 x 1 7 1 0 0 7 0 ------- 3 0 2 1 9 1 1 3 0 ------- 2 2 1 221

Conceptual approach leads to ? • Algebra: (x + 3) (x + 7) = x 7 x 3 x2 7x 3x 21

Example: Drug Steady State • 10 mg Zrytec daily • 50% of Zrytec is eliminated daily • What % is in the body • after 7 days • 10 days • n days?

10mg Daily of Zrytec 10 1 15 2 17.5 3 18.75 4 5 19.375 6 19.6875

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