multiplying+and+dividing

Learning "math facts" (use the fluency assessments here)
//"First, you don’t have students memorize the multiplication facts until you have taught the concept. Make sure the kids feel comfortable in what they are learning. Second, notice we have not taught the facts sequentially. We taught them in an order to help students learn so students experience a sense of accomplishment."// Bill Hanlon

[|Developing fluency with multiplication & division facts.doc] This lists the steps to developing fluency in students above 3rd grade. (3rd grade is where they are all suppose to learn the multiplication and division facts up to 10x10 and related division facts, but not all students know them in 4th grade and above.)

[|Facts I need to learn worksheet.doc] A 10x10 blank multiplication chart that allows students to record the facts they still need to learn, and write a strategy for each fact.

[|Types of multiplication & division problems.doc] These "well-structured problems" illustrate the various concepts involved with multiplication and division. Students learn how to multiply and divide in the early grades by working on various types of these problems over time, using counters, pictures, strategies, and eventually coming to know the number combinations.

[|Strategies for whole number combinations.pdf] A list of "thinking strategies" for basic number combinations ("math facts"), from Hanlon Math Also see related resources at Southern Nevada Regional Professional Development Program (rpdp.net )

The Facts that Need to be Learned Most multiplication combinations can be found by using strategies, but some just need to be memorized. This website shows that strategies that are available, and those combinations that we all wind up memorizing.

[| Illuminations lessons on multiplication] from NCTM These lessons are good for introducing multiplication in 2nd and 3rd grade. Includes: Hopping on the number line, Learning the concept of groups; Rows and columns - another concept of multiplication; Balance beam; Product game

[|Concepts of division.doc] Includes alternative algorithms for multi-digit division.

Computer simulations
(To leave this wiki open while you visit any of these links, right-click on the link and choose "Open in New Tab.") Rectangle multiplication with different algorithms A dynamic explanation of how the area model, the distributive property, and multiplication algorithms work together. Product Game other simulations from the NCTM Illuminations website Factor Game simluation Number line simulation for skip counting (multiplication as repeated addition) Rectangle division simulation Word Problems from Math Playground website

Many good on-line manipulatives are available at the [|National Library of Virtual Manipulatives].

Fluency with multi-digit computation
[|Developing Computational Fluency with Whole Numbers.pdf] An in-depth article by a lead author of Investigations in Number, Data and Space

[|Objects-pictures-symbols for multiplication.doc] Start with objects, have students draw pictures, then move to symbolic representations of multiplication

[|Learning About Multi-digit Multiplication.doc] -- [|Problems to illustrate the multiplication learning progression.doc] A learning progression for multi-digit multiplication -- and a set of problems to illustrate steps in the learning progression

[|Analyzing students' multiplication difficulties.doc] Working backwards along the multi-digit multiplication learning progression

[|Multiplication diagnostic assessment.doc] Assess concepts as well as fluency

[|Models for multiplication & division.doc] Illustrations of the partial product method and the area method for multi-digit multiplication, and the partial quotient method for division.

[|DI readiness asmts narration.doc] - read this first, then read it again as you watch the powerpoint. [|DI readiness assessments math.ppt] - this runs automatically when you play the slide show. Each slide is about 20 seconds.
 * Powerpoint on using learning progressions for assessing students' computational understanding:**

[|Multiplication and Division by topic & grade.pdf] The GLCEs by topic and grade