155_Welcome to the Make Math Meaningful AudioWeb Conference Jan. 27, 2004

Emphasis of these Content Standards by Grade Levels Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, pg... Numbers and Operations Standard o

Welcome to the Make Math Meaningful Audio-Web Conference

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

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

- 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

- relationship among numbers and

- 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

- efficient and accurate methods for

computing

Divide 728 by 34 in two ways

- efficient and accurate methods for

computing

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.

computational algorithm exists for each arithmetic operation.” Find two ways of computing:

What about memorizing the facts?

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

Internet Sites for Lessons on