The fifth chapter of the fifth grade math book focuses on division. The standards for chapter 5 are:

Chapter 5

Number Sense: Students compute with positive integers

Number Sense: Estimate, round and manipulate very large (eg., millions) and very small (eg., thousandths) numbers

Number Sense: Demonstrate proficiency with division, including long division with multidigit divisors.

Algebra and Functions: Use a letter to represent an unknown number.

Algebra and Functions: Write and solve one-step linear equations in one variable.

Mathematical reasoning: Use a variety of methods, such as words, symbols, tables, diagrams, and models, to explain mathematical reasoning.

Mathematical reasoning: Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

Statistics, Data Analysis, and Probability: Know the concepts of mean, median, and mode; compute and compare simple examples to sow that they may differ.

This chapter connects with previous and future learning in this way:

Looking Back	Right Now   Dividing Whole Numbers	Looking Ahead
In chapter 4, students learned how to multiply numbers.	In this chapter, students will learn to divide whole numbers.	In chapters 6 and 8, students will learn how to divide decimals and fractions.

The chapter has three sections of problem solving where the students are introduced to new strategies or are asked to apply previously learned concepts in new problems. The strategies for the fourth chapter are:

Interpreting Remainders pages 176-177

Logical Reasoning pages 188-189

Analyzing Data pages 192-193

In addition to the practice opportunities on this webpage, there are many links to math websites beyond this page to help you practice many math topics!

Now, try these problems!

Sue and Tom like to challenge each other with number puzzles. One of them gives clues that can be used to find two numbers less than 100. The other tries to use the clues to find the numbers. Try your luck at playing along with them!

Day 1: Two numbers have a product of 100. Their quotient is 4. What are the

numbers?

 

Day 2: The two numbers have a sum of 64. Their quotient is 7. What are the two

numbers?

 

Day 3: One number is divisible by 5 and the other by 2 and 3. Their sum is 51. What

are the two numbers? (Two pairs of numbers will answer this one!)

 

Day 4: Sue has two numbers with a sum of 75. Both are divisible by 3 and 5. What are

the numbers? (Two pairs of numbers will answer this one!)

 

Day 5: Tom has two numbers with a sum of 100. Both numbers and their quotients

are divisible by 4 but not by 5. What are the numbers?

 

Day 6: Sue's clues are that one number is twice the other and that both are divisible

by 4, 6, and 9. What are the numbers?

 

Day 7: Tom's clues are that the two numbers have a sum of 30 and that their product

is the same as the quotient of 416 divided by 4. What are the numbers?

 

Day 8: Sue's clues for the two numbers are that one is 8 more than the other and that

their average is 39. What are the numbers?

 

Day 9: Tom's clues for the two numbers are that twice their difference is 72 and that

their average is 35 less than 100. What are the numbers?

 

Day 10: Sue's clues for the two numbers are that their sum added to 4 is 30 and that

their difference subtracted from 10 is 2. What are the numbers?

 

 

Wasn't that fun!

 

Let's practice some skills now!

Name the smallest number divisible by the following:

2 and 3	2, 3 and 5
2 and 5	2, 3, and 10
2 and 10	2, 5, and 10
3 and 5	3, 5, and 10
3 and 10	2, 3, 5, and 10

Complete the divisibility table by answering yes or no:

Divisible by:	18	36	60	90
2
3
5
9
10

Find the missing number in each set :

Numbers:	Average:
27, 36, and	26
110, 117, 130, and	124
64, 73, 59, and	68
23, 87, 54, and	62

Work backwards to solve these problems:

If you double my age and then add 3, the result is 33 years old. How old am I?

If you double my age and then add 3, the result is 19 years old. How old am I?

If you double my age and then add 3, the result is 43 years old. How old am I?

If you double my age and then add 3, the result is 11 years old. How old am I?

How many of each smaller bill would equal the value of the bill in the first column?

Bill	$100	$10	$1
$100
$1000
$10,000
$100,000

Write the digit that would make the given estimate a reasonable one.

Dividend	Divisor	Is About
438	___0	7
216	___0	5
1,976	___0	60
3,682	___0	40
2,258	___0	30
4,215	___0	80
7,164	___0	700
1,754	___0	20
3,165	___0	70

Find an estimate of each quotient below by using a calculator to multiply the divisor by 1, 2, 3, 4, and so on until the product is greater than the dividend.

57 divided by 23

48 divided by 37

97 divided by 15

80 divided by 26

75 divided by 18

62 divided by 12

84 divided by 21

95 divided by 13

About how many items costing $26 each can you buy with $246?

Use the compatible numbers in this chart to make estimates. Use a calculator to identify each as an overestimate or and underestimate.

Compatible Numbers	Estimate	Over or Under?
$200 divided by $20
$210 divided by $30
$250 divided by $25
$240 divided by $30

Use a calculator to find each dividend:

	divided by 84	= 75 r 25
	divided by 32	= 109
	divided by 96	= 27 r 42
	divided by 79	= 131 r 71
	divided by 67	= 309 r 2
	divided by 48	= 450 r 47

Time to be challenged!

Which item does not belong in each set and why doesn't it? 18, 27, 42, 32, 39   1,110; 1,010; 1,101; 1,000; 110   clock, temperature, ruler, scale	The difference between two numbers is 6. Their product is 2,016 . What are the two numbers?
Mr. Watson makes 3-legged and 4-legged stools. Yesterday he used 24 legs. How many of each type of stool did he make?	The Newsbrook Nets scored an average of 80 points in their first four basketball games of the year. The scored 75, 85, and 70 points in their first three games. How many points did they score in the fourth game?

Mr. Watson makes 3-legged and 4-legged stools. Yesterday he used 24 legs. How many of each type of stool did he make?	Students from 5 classes visit an art museum. The largest class has 30 students. If the students divide into viewing tours of 11, there are 4 students left over. If they divide into tours of 15, there are 5 students left over. How many students visited the museum?
The quotient of a 3-digit number divided by 12 is 12 more than the quotient of the same number divided by 18. What is the 3-digit number?	Find the missing factors in this multiplication table: X         1     2,220     74   945          1,302     3,224        750  1,300

to Online Division Practice

DIVISIBILITY PRACTICE~

Practice Divisibility

Divisibility by 2

Divisibility by 3

Divisibility by 4

Divisibility by 5

Divisibility by 6

Divisibility by 7 and 8

Divisibility by 9 and 10

PRACTICE YOUR DIVISION ~

Division by divisors between 1-9

Division by divisors between 1-12

Division with no remainders

Division with remainders

Online Long Division-Interactive

Play Mathjourney-Set the game for Division!

to Standard 2-Relationships

How division relates to subtraction

How multiplication relates to division

How division relates to multiplication

to Division Games and Puzzles

Play Matho

Word Search

Division Basketball

Practice word problems with basketball!

Division Matching Game

Division Concentration Game

Practice the rules of divisibility

Math puzzles to print and solve

Make your own practice worksheets

Division Flashcards-How fast can you get?

Time to Exercise the Brain~

Escape from Knab	Climb Math Mountain	Puzzler Archive
Puzzler	The Train Race	Online Mankala
Who Wants to Win $1,000,000.00?	Grade Five Problems	Family Math Challenges
What's the Best Way to get Paid?	Mystery Math	Coin Flipping

to Multiplication Sites!

Multiplying Tens Practice	Multiplying with Renaming	Multiplication Properties
Multiplying Hundreds Practice	Multiplying Larger Numbers	Multiplication Properties Interactive
Multiplying a 2-Digit Number	Multiplying Three Numbers	Multiplication Facts Review 3 Games to choose from!
Multiplying a 3-Digit Number	Basket Math-Multiplication	Interactive Multiplication Table
Multiplication and Division Relationship	Multiplication Mystery	Division and Multiplication Relationship

to Helpful Math Sites in General

Great Help for Most of Chapter 1	Need help? Ask Dr. Math
Practice rounding with online flashcards	Math Dictionary for Kids
Online Flashcards-all operations	Tons of chances for practice-worksheets
Totally Tessellated	A+ Math Games
Runaway Math Puzzles	Late Delivery-Great Algebra Practice
Mystery Math-How do they do that?	Order of Operations
Puzzler	Math Baseball
Multiplication tips by kids	Exponent Basketball
The Fruit Game	Math Playground

Let's go home!