**Do you happen to know the capital of Madagascar? W**

**ith no access to resources, c**

**ould you figure it out through mental problem solving if given enough time? (It's Antananarivo, by the way.) How many students approach learning their multiplication facts the same way? Each one is a discrete piece of information they must commit to memory. "Figuring it out" is not an option. Well, we spent some time in class this week exploring a few very simple (yet very powerful) rules and patterns that make a potentially overwhelming task seem much more doable.**

You see, mastery of basic multiplication facts is foundational to so much of our 5th grade Core Content. Whether the students' goal is multiplying multi-digit numbers, multiplying decimals, performing long division, finding equivalent fractions, multiplying or dividing fractions, or calculating area and volume, those basic multiplication facts are always right there, front and center.

But what do you already know about multiplying any number by zero? What do you already know about multiplying any number by one? What do you know about patterns that emerge when multiplying by 10 or 11? How can you use the answer to 4 X 8 to help you solve 8 X 4? The fact is, just knowing what happens when you multiply by zero will help you solve an

By applying a few simple rules, look what happens very quickly to the number chart below:

You see, mastery of basic multiplication facts is foundational to so much of our 5th grade Core Content. Whether the students' goal is multiplying multi-digit numbers, multiplying decimals, performing long division, finding equivalent fractions, multiplying or dividing fractions, or calculating area and volume, those basic multiplication facts are always right there, front and center.

But what do you already know about multiplying any number by zero? What do you already know about multiplying any number by one? What do you know about patterns that emerge when multiplying by 10 or 11? How can you use the answer to 4 X 8 to help you solve 8 X 4? The fact is, just knowing what happens when you multiply by zero will help you solve an

__infinite__number of multiplication problems. It works for large numbers, small numbers, negative numbers, fractions, decimals. That is incredibly powerful!By applying a few simple rules, look what happens very quickly to the number chart below:

**When we think about patterns involving zeroes, ones, tens and elevens, and toss in the commutative property, w**

**hat started out as 144 discrete facts is quickly whittled down to a list of 36 facts inside the red triangle--plus that 121 hanging out down in the corner. (And for the student who insists, "Yeah but the 2s and 5s are easy!" the number of remaining facts is merely 22.) Here's my point: We can all learn 37 things. And for the other 107 facts, it's not that you don't need to KNOW them--you just don't have to LEARN them. Because the information is already in your head.**

I am convinced that these kids know things they don't even know they know. They just have to relax, breathe deeply, and retrieve the information.

I am convinced that these kids know things they don't even know they know. They just have to relax, breathe deeply, and retrieve the information.