What Is Number Sense and Why Don ’ t My Students Have It?
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Transcript of What Is Number Sense and Why Don ’ t My Students Have It?
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Slight modification of the presentation at the NCTM Annual Conference
by
Dr. Eric MilouRowan University
Department of [email protected]
856-256-4500 x3876
What Is Number Sense and Why Don’t My Students Have It?
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Content Overview
National Math PanelNumber Sense & Computation
ProficiencyAlgebraic Symbolic Manipulation vs
Algebraic ThinkingThe role of Technology
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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.
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NMP
A major goal for K–8 mathematics education should be proficiency with
fractions (including decimals, percents, and negative fractions).
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Response by Peppermint Patty
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Your Test!
4 x 9 x 25
How many ounces are in a gallon?
50 ÷ 1/2
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Conceptual Understanding
24 ÷ 4 = 624 ÷ 3 = 824 ÷ 2 =1224 ÷ 1 = 2424 ÷ 1/2 = ??
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Fractions - Conceptually
More than 1 or Less than 1
Explain your reasoning
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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
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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
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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
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Flags
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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?
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Chocolate Bar
LAURAP A U L
16 pieces
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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
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Computation
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Active Computation
Virtual Manipulatives
http://illuminations.nctm.org nlvm.usu.edu/en/nav/vlibrary.html
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Conceptual & Contextual
8 + 7 = ?How do we teach this?
xx xx x x
xx
xx
xx
xx
x
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8 + 7 = ?
8 + 7 = ?
2 5
10 + 5 = 15
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Number Line Addition 5 + 4 =
nlvm.usu.edu/en/nav/vlibrary.html
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1000 - 279 = ?
279 +1 = 280 + 20 = 300 +700 = 1000
1000 - 279 = 721
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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
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Conceptual approach leads to ?
x 7 x
3
x2
3x
7x
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Algebra: (x + 3) (x + 7) =
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Example: Drug Steady State
10 mg Zrytec daily50% of Zrytec is eliminated dailyWhat % is in the body
after 7 days10 daysn days?
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10mg Daily of Zrytec
Day Mg. of Zyrtec
1
234
56
10
1517.518.75
19.37519.6875