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New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
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4th Grade
Number Sense &
Algebraic Concepts
2012-07-17
www.njctl.org
Setting the PowerPoint View
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To use the interactive elements in this presentation, do not select
the Slide Show view. Instead, select Normal view and follow these
steps to set the view as large as possible:
• On the View menu, select Normal.
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minimize the ribbon at the top of the screen.
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• On the View tab, click Fit to Window.
Use Slide Show View to Administer Assessment Items
To administer the numbered assessment items in this
presentation, use the Slide Show view. (See Slide 13 for an
example.)
Table of Contents
Read and Represent Multi-Digit Numbers
Compare numbers
Order Numbers
Round Numbers
Patterns
Click on a topic
to go to that section.
Read & Represent
Multi-Digit Numbers
Click to return to the
table of contents
Read Multi-digit Numbers
Words to Remember
Whole numbers: The numbers 0, 1, 2, 3, 4, 5, 6, 7 . . . . . .
Even :
Even numbers make pairs.
Odd:
Odd numbers have one left over.
Fill in the chart with 8 odd and 8 even numbers
ODD
EVEN
Counting by Ones and Tens
Goal: Count and group objects in ones and tens
Materials: apples, counters, index cards
Step 1
Count to 25 by ones using the apples (see next page)
Step 2
Regroup the apples into piles of 10. Separate the 25
apples into two groups of 10 and one group of 5.
Step 3
Replace each pile of 10 apples with one counter. Draw
the new model showing 2 counters and 5 apples.
Step 4
Replace the new model with a number. Remember that
each counter equals 10. Two counters and five apples
equals 20 + 5, or 25.
Students Groups
Form groups of 4-5 students. Each student should have piles
of macaroni, counters, and 4-5 index cards.
Each student writes a whole number under 25 on each of the
4-5 cards.
Students switch cards, models the numbers with macaroni,
and then with counters, and check each other's work.
Money
Two-digit numbers can be represented with dimes
and pennies
3 dimes
30
+
+
5 pennies
5
equals
35 cents
4 dimes represents
40
40 + 6 = 46 cents
6 pennies represents
6
1
There are 4 groups of ten in the number 54?
Yes
No
2
Which is the correct grouping of the number
37?
A
7 tens and 3 ones
B
3 tens and 7 ones
C
37 tens
3
Which explanation is correct for the number
72?
A
7 tens and 3 ones
B
3 tens and 7 ones
C
7 tens and 2 ones
4
Which explanation is correct for the number 35?
A
5 tens and 3 ones
B
5 ones and 3 tens
C
3 ones and 5 tens
5
Enter the correct number for the illustration below.
tens
ones
6
Is the number even or odd?
A
even
B
odd
tens
ones
7
If you had 62 cupcakes, would have and even
number to share with a friend.
Yes
No
8
If you had 15 pencils, would have and even
number to share with a friend.
Yes
No
Write 46 in words
Step 1
Ask yourself questions about the number.
How many groups of tens are in 46? four
How many ones are in 46? six
Step 2
Write the numbers as groups of tens and ones.
46 equals 4 groups of ten and 6 ones.
ANSWER 46 = 4 tens + 6 ones
Write the following numbers to words in groups
Students Response
Erase to check
98 ________________________
9 tens and 8 ones
52 ________________________
5 tens and 2 ones
64 ________________________
6 tens and 4 ones
29 ________________________
2 tens and 9 ones
125 ________________________
1 hundred, 2 tens and 5 ones
9
The number 84 would have 8 tens and 5 ones.
True
False
10
The number 749 would have 7 hundreds, 9 ones
and 4 tens.
True
False
11
The number 259 has 5 groups of ___
A
ones
B
tens
C
hundreds
12
Enter the correct number for 5 tens and 6 ones
13
Enter the correct number for 4 hundreds and 3
tens
14
Enter the correct number for 7 ones and 5 tens
15
Enter the correct number for 3 ones and 4
hundreds
Place Value of Large Numbers
1
,
7
4
1
,
8
7
9
Read the number. Be careful of the zeros!
1
,
0
7
0
,
4
5
0
Read the following numbers.
43,201
1,000,281
673,503
53,600
7,007
1,800,003
60,492
84,905
16
In the number 4632 six is in the hundreds place.
True
False
17
In the number 5,002 the number five is in what
place value?
A
tens
B
hundreds
C
thousands
18
In the following number, which digit is in the
millions place?
1,450,382
19
In the following number, which digit is in the
thousands place?
1,265,309
20
In the following number, which digit is in the
ten-thousands place?
841,032
21
In the following number, which digit is in the
hundreds place?
43,791
22
In the following number, which digit is in the
hundred-thousands place?
1,034,762
Drag the place value digits to the
right to make a 4 digit number.
+
+
+
+
+
+
Drag each digit to the left to see the expanded form.
+
+
+
+
+
+
Writing a Number in Expanded Form
In order to represent a number in expanded form show the
values as addition.
1236 = 1000 + 200 + 30 + 6
TRY THIS Write the value in expanded form.
3649 =
+
+
+
4216 =
+
+
+
9834 =
+
+
+
6203 =
+
+
+
Right the number for each Expanded Form
3000,000 + 40 + 1
300 + 40 + 1
30,000 + 4,000 + 1
300,000 + 4,000 + 10
30,000 + 400 + 1
3,000 + 400 + 1
3,000 + 40 + 1
23
Which is the correct way to express 9,231 in
expanded form?
A
9 hundreds, 2 thousands, 3 tens, 1 one
B
9 thousands, 2 hundreds, 3 tens, 1 one
C
9 hundreds, 23 tens, 1 one
24
Which is the correct way to express 73,040 in
expanded form?
A
700 + 30 + 4
B
70,000 + 3,000 + 400
C
70,000 + 3,000 + 40
25
Enter this number in standard form.
7000 + 300 + 20 + 7
26
Enter this number in standard form.
50,000 + 3,000 + 200 + 50 + 7
27
Enter this number in standard form.
60,000 + 500 + 20 + 1
28
Enter this number in standard form.
400,000 + 6,000 + 300 + 30 + 1
29
Enter this number in standard form.
9,000 + 300 + 5
Place Value Number Line
National Library of Virtual Manipulatives
Click for web site
Step 1
Step 2
Step 3
Note: The place
value can be
changed at the
bottom of the web
page.
0
A
B
C
D
1,000
Where does 600 go on the number line?
500
30
31
Where does 310 go on the number line?
200
A
BC
D
400
32
Where does 625 go on the number line?
500
A
B
C
D
700
A
BC
D
10,000
0
5,000
Where does 7,300 go on the number line?
33
0
A
BC
D
10,000
Where does 2,100 go on the number line?
5,000
34
0
A BC
D
10,000
Where does 7,800 go on the number line?
5,000
35
What number does the "?" on the number line
represent?
0
?
10,000
36
37
What number does the "?" on the number line
represent?
0
?
250
500
38
What number does the "?" on the number line
represent?
0
?
250
500
More Practice
39
Even numbers can be divided into equal groups
with nothing left over?
True
False
40
If you have 30 balloons you can....
A
put them in 3 groups of ten
B
put them in 4 groups of 5
C
put them in 2 groups 25
41
The number is 11 is even?
True
False
42
If you have 5 hundreds, 4 tens, and zero ones
you have what number?
43
Cindi has 7 dimes and 8 pennies. How much
does Cindi have?
A
87 cents
B
7.80 cents
C
78 cents
44
When writing 978 in expanded form, the
number ____ would be in the ones position.
______hundreds + _____tens + ____ ones
45
4 thousands + 8 hundreds + 5 ones =
___________
46
In the number 6,014 the number zero
is in what place value?
A
thousands
B
hundreds
C
tens
47
What number is represented below?
4000
300
+
10
+
9
+
46
Which numbers are represented in standard
form? (You can pick more than one.)
A
4,031
B
4,000 + 30 + 1
C
60,009
D
60,000 + 9
Compare Numbers
Click to return to the
table of contents
There are two symbols we use to compare numbers.
> (greater than)
< (less than)
One number goes on the left of the symbol and another number
goes on the right of the symbol.
The number on the left of the ">" shows the larger number.
For example: 2 > 1
The number on the left of the "<" shows the smaller number.
For example: 1 < 2
Remember, one number goes on the left of the symbol and
another number goes on the right of the symbol.
The number on the left of the ">" shows the larger number.
For example: 2 > 1
This means that "2 is greater than 1"
The number on the left of the "<" shows the smaller number.
For example: 1 < 2
This means that "2 is less than 1"
Symbols and Words to remember
when comparing numbers
SYMBOL
WORDS
>
greater than/largest
<
less than/ smallest
=
equal
SYMBOL
>
<
=
MEANING
Greater than
More than
Bigger than
Larger than
Less than
Fewer than
Smaller than
Equal to
Same as
EXAMPLES IN
SYMBOLS
8>3
3<8
8=8
EXAMPLES IN
WORDS
8 is greater than 3
8 is more than 3
8 is bigger than 3
8 is larger than 3
3 is less than 8
3 has fewer than 8
3 is smaller than 8
8 is equal to 8
8 is the same as 8
Way 1 to compare numbers is by a number line. The
number farthest to the right is the greatest. The
number farthest to the left is the least.
0
1
2
3
4
5
6
7
9
8
Move numbers to their place on the number line
Fill in the blanks using the symbols
_____
>
10
8
2
_____ >
3
______
least number
0
greatest number
500
625
350
____ > _____
1,000
least number
0
greatest number
500
213
401
____ < _____
1,000
least number
6,421
3,509
____ < _____
10,000
5000
0
greatest number
least number
1,059
7,995
____ > _____
10,000
5000
0
greatest number
Use the number line to help determine which
symbol to use.
>
B
<
C
=
0
4,031
2,500
10,000
A
5,000
49
Use the number line to help determine which
symbol to use.
>
B
<
C
=
0
8,300
830
10,000
A
5,000
50
Use the number line to help determine which
symbol to use.
>
B
<
C
=
0
7,250
7,900
10,000
A
5,000
51
Use the number line to help determine which
symbol to use.
>
B
<
C
=
0
3,040
6,030
10,000
A
5,000
52
Use the number line to help determine which
symbol to use.
>
B
<
C
=
0
9,500
9,500
10,000
A
5,000
53
Way 2 Place Value
4, 3 7 2
Take the number
Place each digit in the
proper place value box
4,3 9 8
Start with the greatest place value and move right to where the
numbers are different. The bigger of the two numbers is 4,398
8, 2 9 7
8, 2 8 9
______ > ______
2 5, 3 6 1
2 5, 3 7 1
______ > ______
7 1, 9 0 1
7 1, 8 2 6
______ < ______
54
The number 765 is smaller than 769?
True
False
55
Which number is the largest?
A
325
B
335
C
343
56
Of these four numbers, which is the smallest?
888, 898, 878, 899
57
Compare the numbers using the correct
symbol.
A
>
B
<
C
=
5,429
5,409
58
Compare the numbers using the correct
symbol.
A
>
B
<
C
=
32,461
32,086
59
Compare the numbers using the correct
symbol.
A
>
B
<
C
=
8,730
87,300
60
Compare the numbers using the correct
symbol.
A
>
B
<
C
=
540,389
540,389
61
Compare the numbers using the correct
symbol.
A
>
B
<
C
=
9,049
9,051
62
Kyle has $15.25, Harry has $13.50, and Leon has
$17. Which of the following correctly compares the
amount of money each person has?
A
17 > 15.25 > 13.50
B
15.25 > 13.5 < 17
C
17 < 13.50 < 15.25
63
Sam is 54 inches tall, Tatiana is 52 inches tall and
Ariana is 49 inches tall. Which of the following
correctly compares their heights?
A
54 < 52 > 49
B
49 < 52 < 54
C
49 < 52 > 54
Order Numbers
Click to return to the
table of contents
• To order a group of numbers, you need to compare the digits.
• If the numbers all have the same number of digits, look left to
right to see the which one is greatest or smallest.
Order these numbers least to greatest.
1,791
2,871
1,732
1,489
1,491
Order these numbers least to greatest.
1,791
2,871
1,732
1,489
1,491
Step 1 look at the farthest left digit.
2 is greater than 1, so this is the greatest number.
Order these numbers least to greatest.
1,791
1,732
1,489
1,491
least
2,871
greatest
Step 2 - Look at the next digit (hundreds place) 4 is less than 7,
so 1,489 and 1,491 are less.
Order these numbers least to greatest.
1,791
1,732
1,489
1,491
least
2,871
greatest
Step 3 - 8 is less than 9, so this is the smallest number
Order these numbers least to greatest.
1,791
1,732
1,489
least
1,491
Step 4 - 3 is less than 9, so 1,732 is less than 1,791
2871
greatest
Order these numbers least to greatest.
1,489
least
1,491
1,732
1,791
2,871
greatest
Put these numbers in order from least to greatest.
6,503
6,531
4,921
7,000
7,008
4,871
4,874
4,329
Put these numbers in order from greatest to least.
13,671
13,607
11,461
11,462
13,208
15,298
13,099
15,321
64
Which of the following shows the numbers in
least to greatest order?
A
2516, 2561, 2615, 2651
B
2651, 2615, 2561, 2516
C
2561, 2516, 2651, 2615
65
Which of the following shows the numbers in
greatest to least order?
A
4508, 4502, 3281, 3287
B
3281, 3287, 4502, 4508
C
4508, 4502, 3287, 3281
66
Which number can go in the blank to make the
numbers be ordered least to greatest?
A
6,591
6,474
B 6,509
6,539
?
______
C
6,541
6,597
67
Which number can go in the blank to make the
numbers be ordered least to greatest?
A 3,309
B 3,294
?
3,289 ______ 3,300
C 3,280
3,481
68
Which number can go in the blank to make the
numbers be ordered greatest to least?
A 15,811
15,861
B 15,711
15,809
?
______
C 15,750
15,721
Take these numbers and order them greatest to least
(numbers will move into boxes)
10,315
5 digits
823
819
5643
4329
When looking at multi-digit numbers it is easiest to
group the numbers by the number of digits. Then
move right to where the numbers are different.
4 digits
click is the only number that has five
Since 10,315
digits, it makes sense that it is the largest number.
3 digits
Both 823 and 819 have three digits but when
moving right the digit 2 is bigger than 1, therefore
819 is smaller
click than 823.
Order the numbers least to greatest
499
625
3 digits
1,390
1,399
4 digits
32,961
674
216,712
5 digits
32,768
6 digits
Order the numbers greatest to least
879,043
8,768
6 digits
405
16,300
741
450
8,761
679,043
5 digits
16,099
4 digits
3 digits
Put these numbers in order from least to greatest.
31,729
15,851
7,436
5,871
15,825
29,410
15,829
5,902
Put these numbers in order from greatest to least.
64,329
5,999
7,329
64,842
67,328
7,261
67,305
26
69
Which of the following shows the numbers in
least to greatest order?
A
1653, 16539, 15789, 15809
B
16539, 1653, 15809, 15789
C
15789, 15809, 16539, 1653
70
Which of the following shows the numbers in
greatest to least order?
A
671, 659, 5783, 5780
B
5783, 5780, 671, 659
C
659, 671, 5780, 5783
71
Which of the following shows the numbers in
least to greatest order?
A
33, 3003, 303, 30003
B
30003, 3003, 303, 33
C
33, 303, 3003, 30003
72
Which number can go in the blank to make the
numbers be ordered least to greatest?
B 129
A 1,201
134
140
?
______
1,142
C 1099
1,204
10,503
73
Which number can go in the blank to make the
numbers be ordered greatest to least?
A 8,893
45,381
40,619
B 9,500
9,321
C 794
?
______
7,905
Round Numbers
Click to return to the
table of contents
Rounding makes numbers that are easier to work
with in your head.
• Rounded numbers are only approximate.
• An exact answer generally can not be obtained using
rounded numbers.
• Use rounding to get an answer that is close but that does
not have to be exact.
The number line is useful to help when rounding
numbers.
130
135
Step 1: Find 132 on the number line and label it.
Step 2: Is 132 closer to 130 or 140? _____
Step 3: What is 132 rounded to the nearest ten? _____
140
130
132
135
Step 1: Find 132 on the number line and label it.
Step 2: Is 132 closer to 130 or 140? _____
Step 3: What is 132 rounded to the nearest ten? _____
140
130
132
135
Step 1: Find 132 on the number line and label it.
Step 2: Is 132 closer to 130 or 140? _____
Step 3: What is 132 rounded to the nearest ten? _____
140
3300
3350
3400
Step 1: Find 3365 on the number line and label it.
Step 2: Is 3365 closer to 3200 or 3300? _____
Step 3: What is 3365 rounded to the nearest hundred? _____
3300
3350
3365
3400
Step 1: Find 3365 on the number line and label it.
Step 2: Is 3365 closer to 3200 or 3300? _____
Step 3: What is 3365 rounded to the nearest hundred? _____
3300
3350
3365
3400
Step 1: Find 3365 on the number line and label it.
Step 2: Is 3365 closer to 3200 or 3300? _____
Step 3: What is 3365 rounded to the nearest hundred? _____
74
30
What is 38 rounded to the nearest ten?
35
40
75
What is 874 rounded to the nearest ten?
870
875
880
76
500
What is 527 rounded to the nearest hundred?
550
600
77
What is 3,721 rounded to the nearest hundred?
3700
3750
3800
78
What is 5,835 rounded to the nearest hundred?
5800
5850
5900
Round Numbers
Rounding numbers means identifying a designated place value and the
number (digit) in that place.
Rule One. Determine what your rounding digit is and look to the right
side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit.
All digits that are to the right hand side of the requested rounding digit
become 0.
Rule Two. Determine what your rounding digit is and look to the right
side of it. If the digit is 5, 6, 7, 8, or 9 your rounding digit rounds up by
one number. All digits that are to the right side of the requested
rounding digit become 0.
Round 641 to the nearest ten.
1. Put your pencil point under the digit in the tens place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the tens place?
Those digits always remain the same.
5. Write the answer ____________
Round each number to the nearest ten.
42
1,284
754
3,527
45
5,521
1,289
758
Practice - Round to Tens
273 =
544 =
912 =
1232 =
4542 =
7334 =
Round 8,702 to the nearest hundred.
1. Put your pencil point under the digit in the hundreds place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the hundreds
place?
Those digits always remain the same.
5. Write the answer ____________
Round each number to the nearest hundred.
5,750
749
115,709
15,799
780
115,760
5,738
15,729
Practice - Round to Hundreds
939 =
509 =
627 =
3921 =
4644 =
6233 =
79
In the number 5,439 the number 4 is in
the______ place value.
A
tens
B
hundreds
C
thousands
80
What digit is in the tens place?
9632
81
Sam has 491 sea shells. He wants to round his
collection to the nearest hundred. He says he
would then have 400 sea shells. Is he correct?
True
False
82
If you round 863 to the nearest hundred you
would get?
A
800
B
963
C
900
83
Round 739 to the nearest ten.
84
Round 5,685 to the nearest ten.
85
Round 5,685 to the nearest hundred.
86
Round 65,380 to the nearest hundred.
87
Round 839 to the nearest ten.
88
Round 541 to the nearest ten.
89
Round 585 to the nearest hundred.
90
Round 3,471 to the nearest hundred.
91
Round 227 to the nearest ten.
92
Round 227 to the nearest hundred.
Round 15,821 to the nearest thousand.
1. Put your pencil point under the digit in the thousands place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the thousands place?
Those digits always remain the same.
5. Write the answer ____________
Round each number to the nearest thousand.
7,459
5,555
7,058
4,801
5,924
6,468
6,910
6,703
5,189
4,524
5,803
7,239
5,458
5,067
6,078
6,589
Round 74,891 to the nearest ten-thousand.
1. Put your pencil point under the digit in the ten-thousands place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the ten thousands place?
Those digits always remain the same.
5. Write the answer ____________
Round each number to the nearest ten thousand.
41,587
55,430
44,321
57,876
58,410
35,721
49,000
60,899
59,303
51,768
45,341
38,568
40,571
48,201
53,008
61,487
93
In the number 54,718 the number 5 is in
the______ place value.
A
hundreds
B
thousands
C
ten thousands
94
Which digit is in the thousands place?
83,517
95
Round 3,471 to the nearest thousand.
96
Round 25,512 to the nearest thousand.
97
Round 7,831 to the nearest thousand.
98
Round 27,813 to the nearest ten-thousand.
99
Round 643,712 to the nearest ten-thousand.
100 Round 94,785 to the nearest thousand.
101 Round 743,876 to the nearest ten-thousand.
102 Round 543,802 to the nearest thousand.
Rounding Special Cases
Round 1955 to the nearest hundred.
1900
1950
Step 1: Find 1955 on the number line and label it.
Step 2: Is 1955 closer to 1900 or 2000? _____
Step 3: What is 1955 rounded to the nearest hundred?
_____
2000
Round 1955 to the nearest hundred.
1955
1900
1950
Step 1: Find 1955 on the number line and label it.
Step 2: Is 1955 closer to 1900 or 2000? _____
Step 3: What is 1955 rounded to the nearest hundred? _____
2000
Round 1955 to the nearest hundred.
1955
1900
1950
Step 1: Find 1955 on the number line and label it.
Step 2: Is 1955 closer to 1900 or 2000? _____
Step 3: What is 1955 rounded to the nearest hundred?
_____
2000
Round 1955 to the nearest hundred.
1. Put your pencil point under the digit in the hundreds place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
What happens when the 9 needs
to increase by 1?
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the hundreds
place?
Those digits always remain the same.
5. Write the answer ____________
Round 5,995 to the nearest ten.
5900
5950
Step 1: Find 5995 on the number line and label it.
Step 2: Is 5995 closer to 5900 or 6000? _____
Step 3: What is 5995 rounded to the nearest ten?
_____
6000
Round 5,995 to the nearest ten.
5995
5900
5950
Step 1: Find 5995 on the number line and label it.
Step 2: Is 5995 closer to 5900 or 6000? _____
Step 3: What is 5995 rounded to the nearest ten?
_____
6000
Round 5,995 to the nearest ten.
5995
5900
5950
Step 1: Find 5995 on the number line and label it.
Step 2: Is 5995 closer to 5900 or 6000? _____
Step 3: What is 5995 rounded to the nearest ten?
_____
6000
Round 5995 to the nearest ten.
1. Put your pencil point under the digit in the hundreds place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
What happens when the 9 needs
to increase by 1?
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the tens place?
Those digits always remain the same.
5. Write the answer ____________
Round each.
1961 rounded to the nearest 100 ________
197 rounded to the nearest ten ________
194 rounded to the nearest ten ________
963 rounded to the nearest hundred ________
95 rounded to the nearest ten ________
145 rounded to the nearest ten ________
103
Round 79,621 to the nearest thousand.
104
Round 3,992 to the nearest hundred.
105
Round 97 to the nearest ten.
106
Round 1,499,000 to the nearest ten-thousand.
107
Round 19,997 to the nearest hundred.
108
Round 469,971 to the nearest hundred.
109 The middle school has 1,498 students this year.
The principal wants to buy student planners for
next year. The principal will order by rounding to
the nearest ten. How many will be ordered?
110
A large jar has 1,539 marbles in it. What is this
number rounded to the nearest thousand?
111
New Jersey is 166 miles in length from the northern
most point to the southern most point. What is this
number rounded to the nearest hundred?
Patterns
Click to return to the
table of contents
Patterns
A pattern or sequence is either shapes or umbers that
continue to repeat in a specific order (pattern).
You can describe a pattern by
using a rule to get to the next
shape or number.
What would be the rule for the
pattern in the quilt?
Patterns are almost everywhere you look. Look around the
classroom and name some of the patterns.
What is the pattern in this example?
What is the rule?
Move the
shapes to
complete
pattern
Create your own geometric pattern
using these two shapes.
Describe your geometric pattern (write the rule).
Patterns can also be represented by rotating a shape.
Draw the next shape
112
What would be the tenth shape if this pattern
were continued?
A
B
C
113
Which would be the next shape in this pattern?
A
B
C
114
What would be the eleventh shape in this pattern?
A
B
C
Now we will look at number patterns.
Move the
numbers
to complete
pattern
Finding a Missing Number in a Pattern or Sequence
Step 1: Determine if the order of numbers is getting larger or
smaller.
Step 2: Find the difference between numbers that are next to
each other.
Step 3: Use the difference between numbers to find the missing
number.
Find the missing number: 15, 13, ___, 9, ___
1. The order is going down (getting smaller).
2. The difference between numbers 15 - 13 = 2
3. Since the order is going down subtract 2 from 13. The missing
number is 11.
4. Now that you know the pattern is subtract 2, take the last digit
and subtract 2 and you will get 7.
15, 13, 11, 9, 7
click
Finding a Missing Number in a Pattern or Sequence
1. Determine if the order of numbers is getting larger or
smaller in value, which mathematical function is being used
(+, -, x, ÷) and how many numbers are involved in the
repeating pattern.
2. Find the difference between the numbers that are next to
each other.
Find the missing number
5, 10, 8, 16, 14, 28, ___, ___, ___
x2
-2
x2
-2
115
In the pattern 25, 50, 100, 200, the rule would be
to keep adding 25.
True
False
116
What is the missing number in this pattern?
16, 20, 24, ___, 32, 36
117
Charles was riding his bicycle down the
sidewalk. He was looking at the addresses on
each house as he went by. The first four
addresses he saw were 2455, 2485, 2515, 2545.
What address will Charles see next?
118
Mrs. Hall wrote the following number pattern on
the board.
4; 16; 64; 376
What was the pattern?
A
Add 12
B
Multiply by 4
C
Multiply by 3
119
The water in Sam's full bathtub is 50 gallons
deep. He is draining the bathtub and measuring
the water depth each minute. The first four
measurements were 50 gal., 44 gals., 38 gals.,
32 gals. What depth will Sam see next?
120
What are the next two numbers in the pattern?
3, 12, 10, 19, 17, 26, . . . .
A
33, 24
B
24, 33
C
35, 33
Mr. Block made a function machine that uses a rule to change a
number into a different number. He put three numbers through the
machine. What rule did Mr. Block use to make his machine?
6
4
2
36
24
12
Look at each machine. What happens to the input number inside
the machine to turn it into the output number?
6 x 6 = 36
4 x 6 = 24
The rule for Mr. Block's function machine is
multiply by 6.
2 x 6 = 12
click
Use Mr. Block's function machine from the example to
answer Numbers 1 through 3
1. Maria chose 12 as her input number. What was output
number? 72
click
2. Jose chose 8 as his input number. What was output
number? click
48
3. Caleb put a number through the machine, and his output
number was 120. What number did Caleb put through the
machine? 20
click
Use the following information to answer
Numbers 4 through 6
Ms. Collins made a machine like Mr. Blocks', but she wanted it
to work in reverse. When she put in the number 27, the output
number was 3. She put in 81, and the output number was 9.
She put in 54 and the output number was 6.
4. What is the rule for Ms. Collins machine when it is in reverse?
divide by 9
click
5. Kareem chose 108 as his input number. What was his output
number?
12
click
6. Carmen chose her output number as 15. What was her input
number?
135
click
121 What is the rule for this function machine?
3
A
multiply by 3
B
multiply by 8
C
divide by 3
24
122
The rule for this function machine is multiply by
5, what is the output?
9
?
123 The rule for this function machine is multiply by
7, what is the input?
?
42
Patterns in Tables
Sometimes you can find number patterns in tables. A
function table is a table of ordered pairs that follow a
rule. The rule can be found by going from one column to
the other column. Numbers from a function machine can
also be put into a table.
Example
What is the rule for the function table going from
column x to column y?
x
3
4
5
6
7
y
9
12
15
18
21
Each number in column y is 3 times the
number in column x. The rule going from
column x to column y is multiply by 3.
Multiply 5 by 3 to find the missing value in the
function
table.
You can also use number patterns in tables to solve
real-world math problems.
Example
Sidney ran the same number of laps around the track every
day for 6 days. He made the table below to show the total
number of laps he had run after each of the six days. What is
the total number of laps Sidney had run after six days?
DAY
1
2
3
4
5
6
Number
of Laps
6
12
18
24
30
36
The rule for going from the first row (Day) to the second row
(Number of Laps) is multiply by 6. This means that Sidney ran
6 laps every day. To find out how many total laps he had
run after 6 days, multiply 6 by 6.
124
The rule for the table below of attempted
passes and completed passes is multiply by 7.
Attempted
Completed
Passes
True
False
21
35
42
9
3
5
6
7
125
What is the correct rule for this function table
going from column x to y?
A
add 27
x
y
3
32
7
36
10
39
17
46
B
multiply by 3
C
add 29
126
What is the missing value in the function table?
x
y
225
175
255
205
125
?
97
47