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

Welcome to the Make Math Meaningful Audio-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 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 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 piece of candy is packaged 10 pieces in roll 10 rolls fit into box 10 boxes fit into carton 10 cartons fit into a crate We shipped cartons to a store The first day they sold 10 boxes and rolls of candy How much they have left? A customer bought rolls and pieces of candy Now how much they have now? They ordered another carton and boxes Now how much 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 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 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 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 • 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, 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 • x means + + + + + + or + + + + + 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 – 5) http://teacher.scholastic.com/fieldtrp/math/numbersense_3_5.htm • Number Sense and Sensibility (gr – 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 ... 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... cartons to a store The first day they sold 10 boxes and rolls of candy How much they have left? A customer bought rolls and pieces of candy Now how much they have now? They ordered another carton... 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