RAVEN’S GUIDE TO
ALBERTA
MATHEMATICS GRADE 4
LINKED DIRECTLY TO NEW CURRICULUM REQUIREMENTS
FROM THE WESTERN PROTOCOLS FOR 2008 AND BEYOND
STUDENT GUIDE AND
RESOURCE BOOK
Key to Student Success
with Grade 4 Mathematics
One of a series of publications by Raven Research Associates
for Secondary and Elementary Mathematics
Alan R. Taylor, Ed. D.
Raven Research Associates, Inc.
 June 2008
Table of Contents
Page
Chapter 1 Number Concepts
1.1 Representing and Describing Whole Numbers
- Whole numbers
- Digits and numerals
- Place value
- Expanded notation
1.2 Comparing and Ordering Numbers
- Less than, equal to and greater than
- Ordering numbers by size (magnitude)
1.3 Representing and Classifying Numbers
- Representing numbers in different ways
- Classifying numbers according to properties
2
2
4
4
5
13
13
15
22
22
22
Chapter 2 Number Operations
2.1 Addition and Subtraction of Numbers
2.2 Properties of 0 and 1 for Multiplication and Division
2.3 Rounding Numbers
2.4 Mental Mathematics
2.5 Multiplication of Numbers
2.6 Multiplication Using a Variety of Methods
2.7 Division of Numbers
29
38
41
46
48
55
60
Chapter 3 Fractions and Decimals
3.1 Fractions
3.2 Decimals and Relations with Fractions
3.3 Addition and Subtraction of Decimals
75
79
86
Chapter 4 Patterns
4.1 What is a Pattern?
4.2 Describing Patterns
4.3 Patterns in Tables, Charts and Graphs
4.4 Using Charts and Tables to Solve Problems
95
99
101
106
Chapter 5 Variables and Equations
5.1 Placeholders, Equations and Word Expressions
5.2 Working with Story Problems
117
123
Chapter 6 Measurement
6.1 Time of Day
6.2 24-Hour Clock
6.3 Calendar Dates
6.4 Review of Length and Perimeter
6.5 Area of Shapes and Rectangles
134
139
143
146
151
Chapter 7 Prisms and Lines of Symmetry
7.1 Prisms and Other 3-D Objects
7.2 Solids and Nets
7.3 Lines of Symmetry
7.4 Symmetrical Shapes and Mirror Symmetry
166
170
175
179
Chapter 8 Data Analysis
8.1 One-to-One and Many-to–One Correspondence
8.2 Pictographs
8.3 Bar Graphs
188
191
196
Hints and Puzzles
207
Appendix – answers to exercises and chapter tests
215
SAMPLE FROM RAVEN GRADE 4 MATH
2.3 Rounding Numbers
When rounding a number to a given place value, go to the digit in that
place-value location and either round it up or leave it the same. Then
replace all digits to the right of it with zeros.
e.g 1. Round 3475 to the nearest 100
- Go to the digit in the hundreds place and either round up or
leave the same
- Is 3475 closer to 3400 or to 3500?
- Since 75 is more than half way between 0 and 100, we round
the 4 up to 5 and replace all digits to the right with zeros to get
3500
2. Round 3480 to the nearest 1000
- Go to the digit in the thousands place and either round up or
leave the same
- Is 3480 closer to 3000 or to 4000?
- Since 480 is less than half the way between 0 and 1000, leave
the 3 the same and replace all digits to the right with zeros to
get 3000
3. Round 549 to the nearest 10
- Go to the digit in the tens place and either round up or leave the
same
- Is 549 closer to 550 or to 540?
- Since 49 is closer to 50 than to 40, we round up and replace the
digit to the right with zero to get 550
Rounding numbers involves place value and the value of digits (equal to
or greater than 5 or else digits less than 5). We round up when the digit to
the right of the one of interest is 5 or greater and leave as is when the digit
to the right is less than 5. In both cases, digits to the right of the one of
interest are replaced with zeros.
Rules for Rounding
To round numbers, use the following procedure.
1. go to the digit with the place value you want to round to
2. next, go to the column immediately to the right of the digit you are
asked to round to
3. round the digit you are asked to up if the digit to the right of it is 5 or
greater (5 to 9) or leave it as is if it is less than 5 (0 to 4)
4. replace all digits to the right of the one you are rounding to with zeros
e.g. Round 4648 to
a. the nearest 10
b. the nearest 100
Go to the tens column
Answer
Next, go to the ones column
It’s 8,so round the tens digit up to 5
Replace all digits to the right of the
tens with zeros
4650
Go to the hundreds column
Next, go to the tens column
It is 4, so leave the hundreds digit
as is
Replace all digits to the right of the
hundreds column with zeros
4600
c. the nearest 1000
Go to the thousands column
Next, go to the hundreds column, it
is 6, so round the thousands
column up to 5
Replace all digits to the rights with 5000
zeros
Examples
1. Round the following number to the
nearest 10.
57
1.
2.
3.
4.
Solution
go to the tens column
next, go to the ones column
7 lies between 5 and 9 so we will
round the tens digit up and replace
digits to the right of it with zeros
the number, rounded to the nearest 10,
is 60 (57 is closer to 60 than to 50)
2.
Round the following number to the
nearest 100.
328
3. Round the following number to the
nearest 1000.
7605
1. Go to the hundreds column
2. Next, go to the tens column
3. 2 lies between 0 and 4, so we will
leave the hundreds digit the same and
replace digits to the right with zeros
4. the number, rounded to the nearest
100, is 300 (328 is closer to 300 than
to 400)
1. go to the thousands column
2. next, go to the hundreds column
3. 6 lies between 5 and 9, so we will
round the thousands digit up and
replace digits to the right with zeros
4. the number, rounded to the nearest
1000, is 8000 (7605 is closer to 8000
than to 7000)
Exercises 2.3 – Rounding Numbers
1. Round each of the following numbers to the nearest 10.
a. 18
b. 45
Answer: _______
c. 133
Answer: _______
d. 2617
Answer: _______
e. 3124
Answer: _______
f. 9008
Answer: _______
Answer: _______
2. Round each of the following numbers to the nearest 100
a. 351
b. 239
Answer: _______
Answer: _______
c. 6271
d. 4539
Answer: _______
e. 4209
Answer: _______
f. 4290
Answer: _______
Answer: _______
3. Round each of the following numbers to the nearest 1000.
a. 2932
b. 3489
Answer: _______
c. 7499
Answer: _______
d. 6543
Answer: _______
e. 38 099
Answer: _______
f. 27 604
Answer: _______
Answer: _______
4. Round each number to the nearest 10, 100, and 1000
Numbers
a. 3934
b. 6176
c. 4021
d. 5687
e. 816
f. 793
Nearest 10
Nearest 100
Nearest 1000
5. The driving distance from
Vancouver to Edmonton is 1215 km.
Find the distance to the nearest
a. hundred kilometres.
b. ten kilometres.
6. The driving distance from Winnipeg
to Ottawa is 2175 km. Find the
driving distance to the nearest
a. hundred kilometres.
b. thousand kilometres.
Extra for Experts
7. Write the numbers from the list that meet each requirement.
a. when rounded to the nearest 10,
they equal 60
52, 57, 61, 69, 66, 55, 65
b. when rounded to the nearest
1000, they equal 3000
2499, 3499, 3200, 2650, 3600,
2475, 299
c. when rounded to the nearest 100,
they equal 100
48, 59, 75, 64, 140, 155, 128
d. when rounded to the nearest 10,
they equal 530
431, 520, 527, 542, 549, 539, 533
a. _________
b. _________
a. _________
b. _________
Answer _______
Answer _______
Answer _______
Answer _______
8. Find all possible numbers which meet the following conditions:
a. These numbers, when rounded to
the nearest 10, are equal to 70
Answer _______
b. These numbers, between 245 and
255, when rounded to the nearest
100 are equal to 300.
Answer _______