Name ________________________________ Date ___________________________
CORE STANDARD 2 - OPERATIONS AND ALGEBRAIC THINKING
STUDY GUIDE
Key
Vocabulary
When you do not need an exact answer, you can _____________________.
A model with columns and rows is an ________________.
461,902 is _________________________________ 461,922.
Place Value
Standard Form
Expanded Form
Word Form
Estimate
Greater Than
Less Than
Rounding
Array
Fact Family
Product
Quotient
Factor
Multiples
Commutative
Property
Associative
Property
Distributive
Property
You can estimate by _________________________ when you do not need
an exact answer.
The ___________________________________ says that when multiplying,
the order of the factors does not change the product.
The _________________________ of the 7 in 27,495 is in the thousands.
10, 15, 20, and 30 are all ____________________ of the number 5.
85,927 is ________________________________ 82,763.
Writing in ______________________________ means to write a number
using digits.
____________________________ is adding together the value of each digit.
To write out a number using words is to write in ____________________.
The answer to a division problem is the ____________________.
Two or more numbers that are multiplied together to form a product are called
_________________.
The ______________________________ says that the way in which the
factors are grouped does not change the product.
A _____________________ is a set of four related multiplication and division
facts.
7 x 12 written as (7x10) + (7x2) is an example of the ___________________.
The answer to a multiplication problem is the _______________.
!
!
!
!
I can read and write multi-digit whole numbers using base-ten numerals,
number names, and expanded form.
4.NBT.2
Write in Standard Form:
1. 800,000,000+3,000,000+50,000+6,000+300+10+4
____________________
2. twenty-four million, eighty-nine thousand, two hundred six _______________
Write in Word Form:
3. 50,000,000+900,000+10,000+8,000+300+70+2 ________________________
____________________________________________________________
4. 921,830,536 _________________________________________________
____________________________________________________________
Write in Expanded Form:
5. four million, seven hundred thirty-two thousand, eight hundred ten
____________________________________________________________
6. 63,926,081 _________________________________________________
Real-World Problem Solving
7. In 2005, the population of Philadelphia was one million, four hundred sixty-three
thousand, two hundred eighty-one. Write this number in standard form.
_____________________
8. The land area for Florida is 100,000 + 30,000 + 9,000 + 800 + 50 + 2 square
kilometers. Write the area of Florida in word form.
____________________________________________________________
!
!
!
!
I can compare two multi-digit numbers based on meanings of the digits
in each place, using <,>,+ to record comparisons.
4.NBT.2
Compare with >, <, or = :
9. 24,921
24,291!
!
!
10. 320,427
321,427
Compare using words is greater than, is less than, or is equal to:
11. 802,490 ___________________ eighty-two thousand, four hundred ninety.
12. 3 x 8 _____________________ twenty-four
Order from least to greatest:
13. 289,561; 298,410; 829,603; 928,536
____________________________________________________________
Order from greatest to least:
14. 25,901; 205,629; 502,724; 52,703
____________________________________________________________
Real-World Problem Solving
Whale Migrations
Whale
Top Online Languages
Language
Blue Whale
1,600 miles
Gray Whale
12,500 miles
Chinese
105,736,236
Humpback Whale
3,500 miles
English
286,642,757
Orca Whale
800 miles
! Japanese
!
!
! Spanish
!
!
!
Internet Users
Distance
!
!
!
!
!
66,763,838
!
!
!
!
55,887,063
!
!
!
!
!
!
!
16. Which language is used most on
!
the internet? !
15.
Order the whale migration
distances from least to greatest.
!
!
!
!
I can use place value understanding to round multi-digit whole numbers
to any place.
4.NBT.3
Write the value of the underlined digit:
17. 152,593 _____________! !
18. 238,402 ______________
Write the place that the underlined digit is in:
19. 9,621,805 _________________ 20. 418,287 __________________
Round each number to the given place-value position:
21. 493,580; thousand
22. 77,631; hundred
_________________
_________________
24. 9,158; hundred
25. 296,404; ten thousand
_________________
_________________
23. 4,728,366; million
_________________
26. 142,484; thousand
_________________
Real-World Problem Solving
27. The largest house made out of playing cards used 91,800 cards. To the nearest
ten thousand, how many cards were used?
28. Yuma, Arizona gets 4,127 hours of sunlight each year. Round Yuma’s average
hours of sunlight to the nearest hundred.
Linwood’s favorite Ice Cream Flavors!!
!
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!
!
!
!
!
!
Flavor
Number of Students
!
!
!
!
!
!
!
Chocolate
410
!
!
!
!
!
!
!
!
!
Vanilla
!
!
Strawberry
!
240
!
99
!
!
!
29. To the nearest hundreds, how many
students like vanilla ice cream best?
___________________________
!
!
!
!
I can illustrate and explain multiplication calculations by using equations,
arrays, and/or area models.
4.NBT.5
30. Write an equation for this numberline.
!
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!
!
!
!
!
________________
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Complete the Fact Families.! !
!
31.! !
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!
32.! !
12 x __ = 72
!
!
__ ÷
!
6
!
= __
!
9 x 7 = __
12 = __
!
33. What are the factors
in this array?
__ x 9 = 63
6 x __ = 72!
72 ÷
!
!
__ ÷ 9 = 7!
!
!
!
!
!
!
63 ÷ __ = 9
!
!
!
!
!
!
!
!
!
!
34. Draw and label an array for the number 24.
!
_____ , _____
Real-World Problem Solving
35. A chameleon eats 6 crickets a day. How many crickets does a chameleon eat in
one week? Draw and label an array to show your answer.
!
!
!
!
!
!
Multiply multi-digit whole numbers using strategies based on place value
and the properties of operations.
4.NBT.5
PROPERTIES OF MULTIPLICATION KEY
Identity Property - When any number is multiplied by 1, the product is that number.
Zero Property - When any number is multiplied by 0, the product is 0.
Associative Property - The way in which factors are grouped does not change the product.
Commutative Property - The order of the factors does not change the product.
Distributive Property - To multiply larger numbers, you can multiply the addends of a number
and then add the products.
Identify the property or rule shown by each number sentence.
36. 127 x 1 = 127
________________
37. 8 x 5 = 5 x 8 ______________
38. 7 x 12 = (7x10) + (7x2)!__________________________
39. (7x2) x 3 = 7 x (2x3)
__________________________
Complete each number sentence and identify the property used.
40. 3 x (___ x 6) = ___ x (3 x 9)
41.
___ x 1 = 32
!__________________________
__________________________
42. 9 x 17 = (___ x 10) + (9 x ___)! __________________________
Real-World Problem Solving
43. Nadia bought 2 oranges for each member of her family. Nadia has 4 family
members. Each orange has 10 sections. How many sections will there will be in all.
Use the Associative Property to show at least two equations for this problem.
!
!
!
!
!
!
I can find all factor pairs for a whole number in the range 1-100,
recognize that a whole number is a multiple of each of its factors, and
determine if it is prime or composite.
4.OA.4
44. List all the factors from least to greatest. Is it a prime or composite number?
23
_________________________
circle one:
prime
OR composite
48
_________________________
circle one:
prime
OR composite
45. Find all the factor pairs.
90
_____________________________________________________
46. Fill in the missing multiples of 6.
!
6!
24
48
54
47. Fill in the missing multiples of 4.
8
24
32
Real-World Problem Solving
48. A fourth grade class is having a class picture taken for the yearbook. There
are 24 students in the class. Explain the different arrangements of rows that
students could stand in for their picture.
!
!
!
!
I can solve multistep word problems with whole numbers and having
whole-number answers using the four operations.
4.OA.3
48. Grace started her own landscaping business. She charges $6 an hour for mowing
lawns and $11 per hour for pulling weeds. In September she mowed lawns for 63
hours and pulled weeds for 9 hours. How much money did she earn in
September? (show your work)
49. Brayden and Gavin were playing touch football against Cole and Freddy.
Touchdowns were worth 7 points. Brayden and Gavin scored 7 touchdowns. !Cole
and Freddy's team scored 9 touchdowns. How many more points did Cole and
Freddy have than Brayden and Gavin? (show your work)
!
!
!
!
I can generate a number or shape pattern that follows a given rule and
explain why the numbers will continue to alternate in this way. 4.OA.5
50. Identify and extend the pattern.
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4, 9, 14, 19, 24, ___, ___, ___
!
41, 38, 35, 32, 29, ___, ___, ___,
!!
51. Describe the relationship between the !
number of movie tickets and the price.
tickets
Cost
1
2
$8
$16
3
4
5
pattern? _________________
! pattern? _________________
52.!
!
!
Input
6
$40
!
!
Output
2
9
4
11
6
13
8
10
12
!
!
!
!
!
!
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!
!
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Real-World Problem Solving! !
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! !
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53. The bus company charges a !
!
flat fee of $50 for each field trip, plus
an additional $10 for every 10 students.
How much would it cost to take 60 kids
on a field trip to the zoo?
!
!
rule: ________
Zoo Field Trip
Students
Cost ($)
10
20
$70
30
40
50
60
$100