Lesson 1Size of Divisor and Size of Quotient
Learning Goal
Let’s explore quotients of different sizes.
Learning Targets
When dividing, I know how the size of a divisor affects the quotient.
Warm Up: Number Talk: Size of Dividend and Divisor
Problem 1
Find the value of each expression mentally.
Activity 1: All Stacked Up
Problem 1
Here are several types of objects. For each type of object, estimate how many are in a stack that is 5 feet high. Be prepared to explain your reasoning.
Cardboard boxes
Bricks
Notebooks
Coins
Problem 2
A stack of books is 72 inches tall. Each book is 2 inches thick. Which expression tells us how many books are in the stack? Be prepared to explain your reasoning.
Problem 3
Another stack of books is 43 inches tall. Each book is
Print Version
Another stack of books is 43 inches tall. Each book is
Activity 2: All in Order
Problem 1
Your teacher will give your group two sets of division expressions. Without computing, estimate their values and arrange each set of expressions in order, from largest to smallest. Be prepared to explain your reasoning. When finished, pause for a class discussion.
Problem 2
Record the expressions in each set in order from largest to smallest.
Set 1
Set 2
Problem 3
Without computing, estimate each quotient and arrange them in three groups: close to 0, close to 1, and much larger than 1. Be prepared to explain your reasoning.
close to | close to | much larger than |
---|---|---|
Are you ready for more?
Problem 1
Write 10 expressions of the form
Lesson Summary
Here is a division expression:
We don’t always have to make calculations to have a sense of what a quotient will be. We can reason about it by looking at the size of the dividend and the divisor. Let’s look at some examples.
In
and in the dividend is larger than the divisor. is very close to , which is 9. The quotient is close to or 6. In general, when a larger number is divided by a smaller number, the quotient is greater than 1.
In
and in the dividend and divisor are very close to each other. is very close to , which is or 0.99. The quotient is close to , which is 1. In general, when we divide two numbers that are nearly equal to each other, the quotient is close to 1.
In
and in the dividend is smaller than the divisor. is very close to , which is or 0.1. The division is close to , which is or 0.25. In general, when a smaller number is divided by a larger number, the quotient is less than 1.