Math Strategies: Better Ways to Multiply and Divide

Partial Products Multiplication

I picked up on my own some better ways multiplication and division. Hope this helps you in your teaching.

Do your kids struggle with multiplication? Do you pull your hair out when you have to teach it? Maybe this method can help.

When I was in junior high, I discovered a different way to do multi-digit multiplication. I honestly can't remember what book I read, or where I learned it, other than I know it wasn't what was taught by my math teachers.

But as soon as I taught myself the method, I was hooked. I switched completely to using that new method and never looked back.

The partial products methods (although at the time I learned it, I had no idea that's what it was called) improves on the traditional method of multi-digit multiplication in two main ways.

  1. All multiplication is done first, then addition at the end. The current method requires the student to switch back and forth between multiplication and addition. Keeping each operation together prevents errors in calculation.
  2. Rechecking work is quick and easy since the products of each pair of digits is visible in the process of working out the problem. This simply isn't possible with the current method.

My own children use the partial product method when they multiply, and they like that they can recheck their own work without having to totally rework their problems. I like it as well because when they make an error in their work, I can see quickly where in the process they went wrong.

Personally, I think it would be fantastic if this method were taught in the mainstream of math education as a primary method rather than an alternate (if it's even taught at all). I think the partial product method is far superior to the traditional method of multiplication that is taught now and that children would suffer much less over their math homework if they learned this method.

Short Division

You'll notice that the short division method really isn't substantially different from the long division method most of us learned in school. However, the written procedure is different, and in my opinion, much simplified, making the process less daunting. And like the partial products method, short division allows you to check your work and uncover errors more quickly than the traditional long division method.

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  1. Stacey says

    As a math teacher I have also used lattice mulitplication for children who struggle with style that is main stream for teaching multiplying. Partial products is great also. You can also use a partial product method for division.


  2. Marilyn Williams says

    Wow-love the new multiplication method-we need so badly to change over to help Algebra students get the distributive property. Spent 3 years in elementary school in English schools and we did ALL math on graph paper with large squares, only allowed to place one digit or symbol in each square. I'm going to use this method with the grid paper – and I prefer an "x" for the place holder-also I'm now wondering if counting the digits behind to know number of place holders could transfer into helping students understand how many digits are behind the decimal in multiplying decimals??


  3. Jamie Thomson says

    I just want to say thank you for the great maths tips. I'm 34 and have 3 children, 14, 11 & 6. I have long lost touch with my maths, so I've been using your site and tips as much, if not more than my kids!! I've found them really helpful, as has my 11 year old especially. I'm going to recommend your site to my friends, as even I, an older "student" in maths can follow your method!!
    Thank you, Jamie.


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