1510 - Multiplication

Standard long multiplication algorithm? Partial products? Lattice? Fingers? Calculators? Any way they come up with on their own? I never knew there were so many ways to multiply! Thank you to 360 for the summary listed below.

Procedures:

• Repeated Addition
• On the fly shortcuts to Addition
• Doubling and Halving (Egyptian, Ethiopian?, Russian?)
• Doubling and Adding or Duplation (Egyptian)
• Shift and Add
• Grid or Lattice Multiplication (Arabic, Indian?)
• A variation on Grid Multiplication (medieval Italian or earlier)
• “Traditional” or Long Multiplication (medieval Italian or earlier)
• Crocetta, or Vertically and Crosswise Multiplication (Indian)
• Digit-reverse and shift, by Pappus (Greek)
• The Method of the Cups (Spain or the Americas?)
• per Repiego, or multiplying by factors (medieval Italy or earlier)
• Drawing lines like on that YouTube video

Formulas and Tables:

• Babylonian(?) (First Formula)
• Babylonian(?) (Second Formula)
• A third difference of squares (Greek) [
• Prosthaphaeresis or Trig Tables (Europe)
• Logarithm Tables (Europe)
• Physical Objects:
• Napier’s Rods (Scotland)
• Genaille-Lucas Rulers (France)
• Gunter Scale [here]
• Slide Rule
• Abacus (Chinese)
• “Prosthaphaeretic” Slide Rule (based on similar triangles)

Other Methods:

• Similar Triangles (Greek)
• Finger Multiplication by 9
• Finger Multiplication between {5, 6, 7, 8, 9, or 10} (medieval Europe
• Finger Multiplication between {10, 11, 12, 13, 14, or 15} (medieval Europe?)

So, which approach is the right way? The way that teaches your student so she to truly understands. It will be my job to help each student find what method works best for them and to keep it relevant.

I like this approach to introductory multiplication (very early elementary). You start off teaching the idea of "groups of", (you have 2 groups of 3 grapes) even before you introduce any tables or problems. Then, when the student is ready, you will just let them know that multiplication is just a shortcut for "groups of". This website lists a variety of introductory multiplication lessons, and has very clear and basic guidelines. Mathcats

The following Minnesota state standard encompasses part of the 2nd and the 3rd grade:
3.1.2.3 Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.
The 2010 Common Core State Standards and the 2007 Minnesota standards state that in the second grade we should introduce multiplication sentences, multiplication tables up to 10, and divisors and quotients up to 10.  (See these standards outlined at IXL) My son will be in 4th grade this coming September,and they just finished this past year with multiplying to 10, not even addressing division. I know they are well behind these standards, and I wonder when they will have the big push to catch up.