This week students will learn to multiply numbers in many ways. This learning will help students to know numbers well. To know numbers well is one objective of math teaching and learning. I'll introduce the lesson this way:
We work better with others when we know them well and when we understand who they are and how they behave. Knowledge of one another helps us to be a good friend or colleague.
The same is true for numbers. When we know how numbers behave, we can easily work with and manipulate those numbers in useful ways.
For example, when we understand numbers, we can take an expression like this and understand it in many ways.
4,583 divided by 2
- We know 4,583 is an odd number and it won't split into two whole numbers. Our quotient will include a decimal number.
- I know that I can estimate 4,583 to 5,000 and recognize that my quotient will be close to 5,000/2 = 2,500. I know the ballpark where my number will fall.
- I know that I can distribute the problem in this way (4,000/2) + (500/2) + (80/2) + (3/2). This simplifies my quotient to 2000 + 250 + 40 + 1.5 = 2,291.5 which is in the ballpark of 2,500.
- I can easily check my answer with multiplication using the distributive property too like this: (2 X 2,000) + (2 X 250) + (2 X 40) + (2 X 1.5) = 4,000 + 500 + 80 + 3 = 4,583.
By understanding numbers easily, I could easily solve this problem with precision.
So essentially math study, in part, is the study of numbers--getting to understand how numbers behave. This week we'll work a lot with understanding how numbers behave by looking at specific rules, properties, and truths about numbers and multiplication. This will help you to know numbers well and then be able to work with those numbers just like you would work with good friends.
