Transcript Document

Welcome to the
Make Math Meaningful
Audio-Web Conference
Jan. 27, 2004
Sheryl Beglinger
Comprehensive Center
Region VI
[email protected]
What procedures help children remember the
mathematics taught to them?
• Teach math content in a meaningful way
• Adjust the learning tasks to the appropriate
achievement level and intellectual level of
the child
– Sara had ___ when she went shopping. She
spent ____. How much money does she have
left? ($20, $13) ( $25, $14.25) ($50, $27.76)
• Review and retest on a regular basis
Riedesel, C. A. & Schwartz, J. E. (1999). Essentials of elementary
mathematics 2nd ed. Boston: Allyn and Bacon.
Emphasis of these Content Standards by
Grade Levels
(Principles and Standards for School Mathematics, National Council of Teachers
of Mathematics, pg. 30)
Session 1
Number and Operation
Numbers and Operations
Standard of the NCTM
Instructional programs from pre-kindergarten
through grade 12 should enable all students to• understand numbers, ways of representing
numbers, relationship among numbers and number
systems
• understand operations and how they relate to one
another
• compute fluently and make reasonable estimates
(Principles and Standards for School Mathematics, National Council of
Teachers of Mathematics, pg. 32)
-understand numbers
• Students need to have a firm foundation of place value
Candy Factory
1 piece of candy is packaged 10 pieces in roll
10 rolls fit into 1 box
10 boxes fit into 1 carton
10 cartons fit into a crate
1. We shipped 2 cartons to a store. The first day they sold 10 boxes and
3 rolls of candy. How much do they have left?
2. A customer bought 3 rolls and 7 pieces of candy. Now how much do
they have now?
3. They ordered another carton and 5 boxes. Now how much do they
have?
-ways of representing numbers
• Numbers have more than one way to be
represented
– Tell me all the ways you can represent 36
Understanding Fractions
• Using manipulatives to understand fractions
– Using Pattern Blocks to Explore Fractions http://ejad.best.vwh.net/java/patterns/patterns_j.
shtml
– The Pizza Fraction Kit
from: Sowder, J. T., & Schappelle, B. P. (Eds.).
(1995). Providing a foundation for teaching
mathematics in the middle grades. Albany, NY:
SUNY Press.
Pizza Fraction Kit
Pizza Fraction Kit
Pizza Fraction Kit
Questions to use with the Pizza Fraction Kit
1.
2.
3.
4.
Pretend you are working in a shop that sells pizza in many
different kinds of slices from a whole pizza. One person ordered
2/3 of a pizza. The waiter could fill this order by bringing two
1/3 slices. But what if the shop was out of thirds? Are there
other ways that would give the customer the right amount of
pizza?
Suppose the shop had 2 ½ pizzas left at the end of the day. A
soccer team with 15 players shows up, and each player wants
1/8 of a pizza. Can this order be filled? How many 1/8 could be
filled from 2 ½ pizzas?
From your kit, find one kind of piece that will cover all of the
pieces in this sum: ½ + 2/3 + 5/8. Write about this sum using
the name of the fraction piece that fits.
Write or show five things that you know to be true about threefourths.
From: Sowder, J. T., & Schappelle, B. P. (Eds.). (1995). Providing a foundation for teaching mathematics in the
middle grades. Albany, NY: SUNY Press.
-relationship among numbers and
number systems
• Comparing fractions
– Using benchmarks such as 1/2 and 1
• Compare 2/5 and 5/8
– 2/5 is less than 1/2 and 5/8 is more than 1/2 so 2/5 is less
than 5/8
• Comparing decimals
– Students need a firm foundation in what a
decimal is, do not teach them rules that loses
the idea of place value.
• Example: Which is larger 2.65 or 2.7?
-understand operations and how they
relate to one another
• Tell me two ways of dividing 254 by 18
-understand operations and how they
relate to one another
• Multiplication of fractions http://matti.usu.edu/nlvm/nav/frames_asid_
194_g_1_t_1.html
Compute Fluently
• Computational fluency –
– having efficient and accurate methods for
computing
– Demonstrate flexibility in the computational
methods they choose, understand and can
explain these methods and produce accurate
answers efficiently
(Principles and Standards for School Mathematics, National Council of
Teachers of Mathematics, pg. 152)
-efficient and accurate methods for
computing
Divide 728 by 34 in two ways.
-efficient and accurate methods for
computing
• As students develop methods to solve multi-digit
computation, they should be given many chances
to share their methods with others. As they listen
to others methods they will learn more efficient
ways to solve the computations.
• “More than one efficient and accurate
computational algorithm exists for each arithmetic
operation.”
Find two ways of computing:
4307 - 2741
(Principles and Standards for School Mathematics, National Council of
Teachers of Mathematics, pg. 153)
What about memorizing the facts?
• Remember: Fluency is having efficient and
accurate methods for computing
– Drill and practice of number facts should come after the
extensive learning in what does that operation really
mean
• 6 x 7 means 6 + 6 + 6 + 6 + 6 + 6 + 6 or
7 + 7 + 7 + 7 + 7 + 7 depending on how you interpret the
problem. Students need to learn to group the numbers to get
the answer more efficiently.
• Games and computer activities than require speedy recall of
facts is then appropriate to use.
Internet sites for practicing facts
• Add It Up http://www.flasharcade.com/game.cgi?additup
• Batter’s Up Baseball http://www.prongo.com/math/multiplication.html
• Fantastic Four http://www.exploratorium.edu/math_explorer/fant
asticFour2.html
Internet Sites for Lessons on
Number Sense
• Developing Number Sense http://illuminations.nctm.org/lessonplans/6-8/number_sense/
• Making Sense of Numbers (gr. 3 – 5)
http://teacher.scholastic.com/fieldtrp/math/numbersense_3_5.htm
• Number Sense and Sensibility (gr. 6 – 8)
http://teacher.scholastic.com/fieldtrp/math/numbersense_6_8.htm
• SCORE Mathematics Number Sense
http://score.kings.k12.ca.us/number.sense.html
Session Wrap Up
• Check out our webpage: Make Math
Meaningful http://www.wcer.wisc.edu/ccvi/mmm/
• Questions/Comments???
• Next Week - Algebra