Muffles' Truffles

Multiplication and Division with the Array

Author: Antonia Cameron,Catherine Twomey Fosnot

Publisher: Greenwood International

ISBN: 9780325010199

Category: Education

Page: 64

View: 5417

DOWNLOAD NOW »

Muffle's Truffles: Multiplication and Division with the Array is one of five units in the Contexts for Learning Mathematics' Investigating Multiplication and Division (3 - 5) The focus of this unit is the development of the open array as a model for multiplication and division. This unit uses a series of investigations based on the context of Muffles' Truffles shop. The questions posed in the first investigation (how many boxes of ten can be made with a given quantity of truffles; how many leftovers will there be from a given quantity and how can they be combined to make assortment boxes; and what is the cost of a given quantity of truffles if they cost $1 each) give students an opportunity to explore place value - the multiplicative structure of our base-ten system and quotative division. In the second and third investigations, students build two-dimensional blueprints of one-layer boxes and use these arrays to explore some of the big ideas in multiplication (the distributive, associative, and commutative properties). In the fourth and final investigation, students work with open arrays in the context of labeling and pricing wrapped boxes of truffles. To figure out the dimensions of the wrapped boxes (or open arrays) and the cost, students need to apply a number of big ideas previously developed in this unit. There are three different kinds of minilessons for multiplication included in the unit as well: counting around the circle, strings of related problems, and quick images. The count-around is used to support the development of place value as it relates to multiplication. The strings of related problems are explicitly designed to guide learners toward computational fluency with whole number multiplication and to build automaticity with multiplication facts by focusing on relationships. The quick images use 2 x 5 and 1 x 5 arrays as units to build larger arrays. In the last days of the unit, more complex minilessons (double-digit multiplication problems) generate a wider range of student strategies that can be explored (and modeled) with the open array. To learn more visit http://www.contextsforlearning.com
Release

The Teachers' Lounge

Place Value and Division

Author: Catherine Twomey Fosnot,Chris Natale

Publisher: Firsthand

ISBN: 9780325010229

Category: Education

Page: 64

View: 704

DOWNLOAD NOW »

The Teachers' Lounge: Place Value and Division is one of five units in the Contexts for Learning Mathematics' Investigating Multiplication and Division (3 - 5) The focus of this unit is division. It begins with the story of a teacher noticing a service person in the teachers' lounge fill two different vending machines with beverages. In the first machine, there are bottles of water only. The machine holds 156 bottles of water when full and the teacher wonders how many six-packs that might be. The second problem involves the juice machine. It also holds 156 bottles when full, but the bottles are partitioned into six columns because there are six different flavors of juice. The teacher wonders how many there are of each flavor. Although most students do not realize it at the start, the two problems are related. The first problem is a quotative division situation - the amount in each group is known, the number of groups is not. The second problem is a partitive division situation - the number of groups is known, the amount in each group is not. The problems are juxtaposed and given together to encourage students to examine the relationship between the two kinds of division. This story context of the teachers' lounge sets the stage for a series of investigations designed to support the development of a repertoire of strategies for multiplication and division, including the use of: * the ten-times strategy * partial products and partial quotients * the associative property * the distributive property of multiplication over addition - the basis for the long division algorithm Several minilessons for multiplication and division are also included in the unit. These are structured as strings of related problems designed to more explicitly guide learners toward computational fluency. Toward the end of the unit, discussion shifts to how the context of a division problem influences what to do with the remainder. Note: The context for this unit assumes that your students will have had prior experience using arrays for multiplication. If this is not the case, you might find it helpful to use the unit Muffle's Truffles first. To learn more visit http://www.contextsforlearning.com
Release