This activity explains what is happening in the traditional multiplication algorithm. It should be done many times BEFORE the algorithm is introduced in order to aid in full comprehension. This can be done with very young children if they are familiar enough with the rods. You don't have to wait until 3rd-4th grade - just wait until then to introduce the algorithm!
Formulas and algorithms should always be introduced last, after much play with manipulatives and discussion about what is happening with the numbers. Unfortunately, most schools and teachers skip right to the symbols after a very short period of explanation with manipulatives and many times with no explanation at all!
This is an important concept to understand for place value, the distributive property, and long multiplication and division. Start small, and, over time, work your way up to the type of problem we did at the end. Let children figure out the pattern for themselves by using the Cuisenaire Rods to actually SEE how you are just jumping up to the next decimal place.
This video shows how to easily represent multiplication of numbers in the teens visually. Most children (and adults!) have no understanding of what they are actually doing when they perform the multiplication algorithm. After watching this video and trying it a few times on your own, you should begin to understand what it's really all about and may even begin to multiply big numbers in your head!
Cuisenaire Rods are an effective tool in developing a conceptual understanding of mathematical topics in children and adults. Our minds remember pictures and color much better than symbols. This is the perfect way to introduce long multiplication.
This video shows my 6 and 8 year old daughters figuring out the squares of numbers 10 through 20. We use a variety of strategies. This activity is helpful in building thinking skills and further developing number sense. They are beginning to see numbers as a picture in their minds that they will carry with them forever.
Square numbers are used frequently in higher math. If they come into contact with them enough now while they are young, they will have no trouble applying this knowledge later on in middle and high school.
This video shows you how to introduce the traditional multiplication algorithm (or formula), but in a conceptual way using Cuisenaire rods as manipulatives. The multiplication algorithm is usually not understood, even by teachers. This video will make it clear what it's all about.
This method will work for everyone, but it works especially well for visual and kinesthetic learners as well as those with dyscalculia/dyslexia, global thinkers, right-brained learners, and others for whom the traditional school approach does not work well.
Before teaching the algorithm, make sure your students have had plenty of practice doing these types of problems with just the rods and figuring them out in their heads! It will be a greater benefit to their future to build number sense that way first and then introduce the formal short-cut method.