# Decimal Multiplication

Decimal Multiplication is one of a series of Labs to help you understand and learn to use decimals. I think you will find it fun because it uses random numbers and it will help you visualize decimal operations. Take a look at Decimal Addition and Decimal Subtraction and Decimal Division. Remember like all of our spreadsheets you can look at and change the rules to try different things.

# Decimal Division

Decimal Division is one of a series of Labs to help you understand and learn to use decimals. I think you will find it fun because it uses random numbers and it will help you visualize decimal operations. Take a look at Decimal Addition and Decimal Subtraction and Decimal Multiplication. Remember like all of our spreadsheets you can look at and change the rules to try different things.

# Multiplying Integers

We have made a big deal of the times table and of other tables.Now we extend the times table to negative numbers and thus to all 4 quadrants of the real number space. We hope to build student intuition about this space and to gain a spatial sense of graphing as well as of multiplication. So we as usual focus on patternmaking and take students through extending the table first left by rows and then down by columns before we have them build the table as a whole. We moved the axes to the outside so that we do not interfere with the table. There are many things you can do with such a table and we urge you to explore it.

# Pennies to Heaven

Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of the greatest experimental and theoretical physicists of the 20th century, are real-world estimation problems. So we ask, “If we had a stack of pennies as tall as the Empire State Building, how big a room would we need to hold them?” Like most Fermi problems the answer to this one is a delightful surprise and requires us to think out-of-the-box. Always ask, “What do you guess?” “Would you need a whole house or something bigger, just your bedroom, or a closet, or something even smaller?”

# Common Denominators

We can use these proportions to compare two ratios with different denominators by finding a denominator that their proportions have in common. Thus the common denominator of 2/3 and 3/4 is 12. We then can use the common denominator to add/subtract and divide common ratios (fractions). This approach to division is quite different from the traditional approach and does not rely on the mechanical process of inverting the divisor and multiplying which most students find difficult to understand. Using common denominators means that to divide two fractions we simply divide the numerators of their common denominators, because when we divide common denominators they =1 since both have the same value.