Welcome to the Make Math MeaningfulAudio-Web Conference

Jan. 27, 2004

Sheryl Beglinger

Comprehensive Center Region VI

smbeglinger@wisc.edu

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 basisRiedesel, 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 1Number 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 box10 boxes fit into 1 carton10 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. 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?

2. 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?

3. 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.

4. Write or show five things that you know to be true about three-fourths.

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/fantasticFour2.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