Newark USD Grade 4
1
Benchmark 1 Study Guide
Ex1: Joseph saved $400. Josephs’ sister has
ten times as much money. How much money
does his sister have? Use numbers and words
to explain how you got your answer.
Chart
10 times as many as 4 = 40
10 times as many as 40 = 400
10 times as many as 400 = 4000
1´
You try: Savannah saved 5 ten dollar bills
and 4 one dollar bills to buy a new computer.
The computer costs 10 times as much as she
has saved. How much does the computer
cost? Use numbers and words to explain how
you got your answer.
Place value Chart
4 hundreds × 10 = ___hundreds = ______
thousands hundreds tens ones I can group 40 hundreds into 4 groups of 10
hundreds. Each group of 10 hundreds can be
bundled into 1 thousand. Josephs sister has 4
thousand dollars.
Ex 2: Represent the addend with number
disks in the place value chart. Show the
compositions of larger units from 10 smaller
units. Write your answer in expanded form
and standard form.
12 thousands + 21 hundreds = ____________
hundred
thousands
ten
thousands
thousands
hundreds
tens
1´´ You try: Represent the addend with number
disks in the place value chart. Show the
compositions of larger units from 10 smaller
units. Write your answer in expanded form
and standard form.
24 ten thousands + 13 thousands = ________
ones
Expanded Form:
10, 000 + 4, 000 + 100
Standard Form: 14,100
4.NBT.1,2
Page 1 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
Benchmark 1 Study Guide
Express 902,376 in word form and expanded
form.
2
Thousands
Period
2´
You Try: Express 715,098 in word form and
expanded form.
3´
You Try: Write 547,745 in expanded form.
Ones
Period
902,376
902 thousand , 376 (ones)
nine hundred two thousand , three hundred seventy six
Thousands
Period
Ones
Period
902,376
9 0 0, 0 0 0
2,000
300
70
6
902,376 = 900,000 + 2,000 + 300 + 70 + 6
4.NBT.2
3
Write 452,627 in expanded form.
400,000 + 50,000 + 2,000 + 600 + 20 + 7
452,627
A B
547,745
How are the underlined digits alike and
different? Both A and B are the same digit, 2. A is
in the thousands place. It has a value of 2,000. B is in
the tens place. It has a value of 20.
AB
How are the underlined digits alike and
different?
Match the expression to the value of A or B.
2 × 1,000
A
B
2 × 10
A
B
20 × 100
A
B
20,000 ÷10
A
B
70 × 100
A
B
200 ÷ 10
A
B
70,000 ÷ 10
A
B
70 × 10
A
B
452,627
A
B
True or False? A ÷ B = 100
This is true because B is 2 places to the right of A.
2,000 ÷ 20 = 100. 20 is 1 hundredth of 2,000.
Match the expression to the value of A or B.
547,745
A B
True or False? A ÷ B = 100 Justify your
answer.
4.NBT.1,2
Page 2 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
4
Benchmark 1 Study Guide
Compare. Justify your answer at least 2
ways.
r answer348,604
at least 2 ways.
309,738
4´
You Try:
Compare. Justify your answer at least 2 ways.
1,258,934
1,259,034
Expanded Form and Place Value
H.Th.
T. Th.
Th.
H
T
O
348,604 = 300,000 + 40,000 + 8,000 + 600 + 0 + 4
349,738 = 300,000 + 0
+ 9,000 + 700 + 30 + 8
Which ways will you choose?
Expanded Form
Place Value
Explain with Words
Number Line
3 4 8 , 6 0 4
3 0 9 , 7 3 8
∴ 348,604
> 309,738
Another Way (Explain with Words):
348,604 and 309,738 both have 3 hundred
thousands, but 348,604 has 4 ten thousands,
and 309,738 has 0 ten thousands, so
348,504 > 309,738.
Possible Number Lines:
Since the difference is in the ten thousands place,
both numbers are between 300,000 and 400,000.
348,604
309,738
300,000
350,000
309,738
300,000
400,000
348,604
350,000
∴ 348,604
400,000
> 309,738
Page 3 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
5
Benchmark 1 Study Guide
5´
Round to the given place: 37,084
nearest ten
nearest ten
37,084
37,080
37,085
nearest hundred
37,000
You Try: Round to the given place : 26,896
37,090
37,084
37,050
nearest hundred
37,100
nearest thousand
nearest thousand
37,084
37,000
37,500
38,000
nearest ten thousand
37,084
30,000
35,000
nearest ten
nearest ten thousand
40,000
37,084 → 37,080
nearest ten
○26,000 ○26,800 ○26,900 ○27,000
nearest hundred
○26,000 ○26,800 ○26,900 ○27,000
○26,000 ○26,800 ○26,900 ○27,000
nearest hundred
37,084 → 37,100
nearest thousand
37,084 → 37,000
nearest thousand
nearest ten thousand
thousand
37,084 → 40,000
nearest ten thousand ○20,000 ○27,000 ○30,000 ○37,000
4.NBT.3
Page 4 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
6
Benchmark 1 Study Guide
6´
Subtract: 8,413-5,646
You Try: Subtract: 27,217-6,834
Open Number Line
Open Number Line:
+4
5,646
+50
+300
5,650
5,700
+413
+2,000
6,000
8,000
8,413
4 + 50 + 300 + 2,000 + 413 = 2,767
∴8,413 − 5,654 = 2,767
Standard
Decomposition
Expanded Form
Algorithm
7
8/ ,13 4/ 10 1/1 3
− 5, 6 4 6
2, 7 6 7
8, 413 = 7,999 + 414
− 5, 646 = −5, 646
2,353 + 414
Standard Algorithm:
= 2, 767
4.NBT.4
7
Solve for L.
3,214 ft.
L
1,719 ft.
829 ft.
One Way:
7´
You try: Solve for N.
12,000 m
1
3,214 ft
L
1,719 ft
829 ft
4, 933 ft
=
L
829 ft
4, 933 ft
=
4,104 ft
5,204m 4,679 m
3,214
N
+ 1,719
4,933
2 13
4,933
−829
4 ,10 4
1
Check:
829 ft
4,104
+ 829
4,933
∴ L = 4,104 ft.
4.MD.2
Page 5 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
8
Benchmark 1 Study Guide
Solve the Problem
8´
Madelyn’s family went on two long road trips.
The first trip was 2,245 miles! The second
trip was 496 miles longer than the first. How
many miles did they travel in all?
What do we need to find out?
How many miles did they travel on both trips
combined?
What do we know?
Trip 1: 2,245 mi
Trip 2: 496 mi more than Trip 1
Models:
You Try: Solve the Problem
There are 2 giraffes and 1 rhinoceros at the
zoo. One giraffe weighs 1,945 pounds. The
other weighs 2,464 pounds. The rhinoceros
weighs 4,575 pounds. How much more does
the rhinoceros weigh than the 2 giraffes
combined?
What do we need to find out?
What do we know?
Total miles
2,245
2,245
496
Trip 1
Trip 1
2,245
Model:
Trip 2
Trip 2
2,245
0
496
total mi.
Decide:
Decide: Add 2,245, 2,245, and 496 together to
get the total number of miles.
Solve:
11
2,245
2,245
+ 496
4,986
Solve:
Check:
2,245
2,245
+ 496
4,000
800
170
+ 16
4,986
Check:
2,000 + 2,000
200 +200+400
40 + 40 + 90
5+5+6
Conclude: Madelyn’s family traveled 4,986
miles total.
Conclude:
Unit 1 Constructed Response will address this std: .4.MD.2
Page 6 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
9
Benchmark 1 Study Guide
9´
How is a multiplication equation also a
comparison?
You Try:
How is a multiplication equation also a
comparison?
Think about the product 15.
Write comparisons that go with the product of
35.
15=3×5
15 is 3 groups of 5.
15 is 3 times as many as 5.
15=5×3
15 is 5 groups of 3.
15 is 5 times as many as 3.
3×5=5×3
3 groups of 5 is the same as 5 groups of 3.
3 times as many as 5 is equal to 5 times as
many as 3.
Draw a line from the expression on the left with an
answer choice on the right.
5 times as many as 4
A) 96
9 times as many as 6
B) 54
5 groups of 4
C) 20
8 × 12
4.OA.1
10´ You Try:
Multiply 42×31
10
Area Model:
Multiply 23×25 using an Area Model.
Decompose the factors into base ten components.
Find the partial products. Add the partial products.
Multiply 42×31
10
10
10
10
100
100
100
100
10
100
100
100
100
10 10
10
100
100
100
100
10 10
1
10
10
10
10
1 1
10
1 1
10 10
1, 200
60
40
+ 2
1,302
End of Study Guide
4.NBT5
Page 7 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
1´
Benchmark 1 Study Guide
You Try Solutions:
You try: Savannah saved 5 ten dollar bills
and 4 one dollar bills to buy a new computer.
The computer costs 10 times as much as she
has saved. How much does the computer
cost? Use numbers and words to explain how
you got your answer.
1´´
hundred
Chart
Money saved
5 × $10 = $50
4 × $1 = $ 4
You try: Represent the addend with number
disks in the place value chart. Show the
compositions of larger units from 10 smaller
units. Write your answer in expanded form
and standard form.
24 ten thousands + 13 thousands = ________
thousands
Money needed
ten
thousands
thousands
hundreds
tens
ones
10 × as much as she saved
10 × $54 = $ 540
$50 + $4 = $54
Expanded Form:
Place Value Chart
200,000 + 50,000 + 3,000
$50 ×10 = _____
Standard Form: 253,000
$4 ×10 = _____
thousands
hundreds
tens
ones
2´
You Try: Express 715,098 in word form and
expanded form.
Word Form: seven hundred fifteen thousand,
ninety-eight
I grouped 50 tens into 5 groups of tens. Each group
of 10 tens can be bundled into 1 hundreds. Then I
grouped the 40 ones into 4 groups of ten and each
group can be bundled into 1 ten.
The computer costs: $500 + $40 = $540
Page 8 of 12
Expanded Form: 700,000 + 10,000 + 5,000
+ 90 + 8
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
3´
Benchmark 1 Study Guide
4´
You Try: Write 547,745 in expanded form.
You Try:
Compare. Justify your answer at least 2 ways.
1,254,934
1,259,034
Expanded Form and Place Value
500,000 + 40,000 + 7,000 + 700 + 40 + 5
547,745
AB
How are the underlined digits alike and
different? Both A and B are the same digit, 7.
A is in the thousands place, so it has a value
of 7,000. B is in the hundreds place, so it has
a value of 700.
M
H.Th
T. Th.
Th.
H
T O
1,254,934= 1,000,000 + 200,000 +50,000 + 4,000 + 900 + 30 + 4
1,259,034= 1,000,000 + 200,000 +50,000 + 9,000 + 0 + 30 + 4
1,2 5 4 , 9 3 4
1,2 5 9 , 0 3 4
Match the expression to the value of A or B.
70 × 100
A
B
70,000 ÷ 10
A
B
70 × 10
A
B
∴ 1,254,934
< 1,259,034
Another Way (Explain):
True or False? A ÷ B = 100 Justify your
answer.
It is false. 7,000 ÷ 700 = 10. Also, 700 is
only one place to the right of 7,000, so 700 is
1 tenth of 7,000.
1,254,934 and 1,259,034 both have 1 million, 2
hundred thousands, and 5 ten thousands. The
important difference is that 1,259,034 has 9
thousands instead of just 4 thousands. Therefore,
1,254,934 < 1,259,034.
Possible Number Lines:
1,254,934
1,250,000
1,255,000
1,254,934
1,250,000
1,255,000
∴ 1,254,934
Page 9 of 12
1,259,034
1,260,000
1,259,034
1,260,000
< 1,259,034
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
5´
Benchmark 1 Study Guide
7´
You Try:
You Try: solve for N.
Round to the given place.
12,000 m
26,896
nearest ten
5,204m 4,679 m
26,896
26,890
26,895
nearest hundred
26,896
26,800
26,850
12,000
− 9,883
5,204
26,900
nearest thousand
Then subtract that
amount from the
total, 12,000 m.
One Way: Add
5,204 m and 4,679 m.
26,900
+ 4,679
26,896
N
26,500
nearest ten thousand
20,000
27,000
26,896
25,000
Check:
30,000
1 12
12,000 m
nearest ten
26,000
26,800
5,204m 4,679 m
˜26,900
27,000
nearest hundred
− 9,883
2,116 + 1
= 2,117
9,883
26,000
11,999 + 1
26,000
26,800
26,000
26,800
∴ N = 2,117 m
˜26,900
N= 2,117 m
5,204
4,679
+ 2,117
12,000
27,000
nearest thousand
26,900
˜27,000
nearest 6´
ten thousand
You Try: Subtract:
27,217-6,834
20,000
27,000 ˜30,000
Open Number Line:
37,000
+6
6,834
+60
6,840
+100
6,900
+20,000
7,000
+217
27,000
27,217
6 + 60 + 100 + 20,000 + 217 = 20,166
∴ 27,217 − 6,834 = 20,383
Standard Algorithm:
2 6 7/ ,11 2/ 1 1 7
− 6, 8 3 4
2 0, 3 8 3
Expanded Form:
27, 217 = 26,999 + 218
− 6,834 = − 6,834
20,165 + 218
= 20,383
Page 10 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
Benchmark 1 Study Guide
8´ You Try: Solve the Problem
There are 2 giraffes and 1 rhinoceros at the
zoo. One giraffe weighs 1,945 pounds. The
other weighs 2,464 pounds. The rhinoceros
weighs 4,575 pounds. How much more does
the rhinoceros weigh than the 2 giraffes
combined?
What do we need to find out? How much
more does the rhinoceros weigh than both the
giraffes?
9´
You try: How is a multiplication equation also a
comparison?
Think about the product 35.
• 35=7×5
• 35 is 7 groups of 5.
• 35 is 7 times as many as 5.
• 35=5×7
• 35 is 5 groups of 7.
• 35 is 5 times as many as 7.
• 7×5=5×7
• 7 groups of 5 is the same as 5 groups of 7.
• 7 times as many as 5 is equal to 5 times as
many as 7.
What do we know?
giraffes: 1,945 lbs. and 2,464 lbs.
rhinoceros: 4,275 lbs
Model:
rhinoceros
4,575
1,945
2,464
giraffe 1
giraffe 2
difference
Draw a line from the expression on the left with an answer
choice on the right.
Decide: Add the weight of both giraffes.
Subtract that amount from the weight of the
rhinoceros. That’s the difference.
Solve:
Check:
1 1 1
1 1
6 15
4,575
+ 2,464
− 4,409
2,464
+ 166
4,409
16 6
4,575
A) 96
9 times as many as 6
B) 54
5 groups of 4
C) 20
8 × 12
1,945
1,945
5 times as many as 4
Conclude: The rhinoceros is 166 pounds
more than the giraffes.
Page 11 of 12
MCC@WCCUSD (NUSD) 10/05/14
Newark USD Grade 4
10´
Benchmark 1 Study Guide
You try: Multiply 23×25 using an Area Model.
10
10
1
1
1
1
1
10 10 10 10 10
10
100
100
10
100
100
1
10
10
1
1
1
1
1
1
10
10
1
1
1
1
1
1
10
10
1
1
1
1
1
10 10 10 10 10
400
100
60
+ 15
575
Page 12 of 12
MCC@WCCUSD (NUSD) 10/05/14