Preface - Oak Hall School

Preface

This Summer Math Sampler was created by Sarah Schaefer who instructed and

implemented Primary Mathematics on a daily basis. Concepts that students find

challenging at each grade level are incorporated in each session, so mastery at the

next grade level can be achieved. Each question came directly from the content

taught within both the The Primary Mathematics Standards and U.S. Editions. It is

suggested that students complete one session in a sitting, followed by a fact and a

mental math challenge located in the back of the book. Solutions to all sessions

are provided in the back of this book.

Primary Mathematics emphasizes a pictorial approach to problem solving using the

bar model. Each session in the Summer Sampler contains word problems that

require use of a bar model. Solutions for these problems are given in the back of

this book.

The purpose for a summer math review is to practice throughout the summer

rather than completing the book at the very beginning or very end of the

summer. Your child should plan to spend about 1 hour each week on the math

problems. This will help to provide a smoother transition to the next grade level.

You can use the graph paper (attached) to solve the model drawing problems.

Please keep track of your work and include it when you turn your packet in at the

beginning of the 2020-21 school year. Thank you, and I hope that you have a great

summer!

Sincerely,

Michelle Mills

Director of Lower School

Push-Ups 21.00 41>

15.75

10.50

5.25

The graph -shows the number of push-ups done in .. Oht31:r'riin'ute by'Klm antJi.Shannoh'. .. ·' ...

1a) Overall, who.dicl'n1ore push-ups in a minute? ' , ,n > ' -� "

1 b) The most push-ups for Kim occurre� on which day?··

4/11/11 4/12/11 4/13/11 4/14/11 4/15/11j Jc) FQLShannon, giyeJhe fracti9n(i11 $i,nplest form)of push-ups on 4/11 compared to• the total amount of

0 Kim

Kim

.. -;. Shannon

push-ups? ·

2. Complete the following number pattern. Write a rule that follows th,, pati,rn.

a) 5 10 20 {"''

b) 665 645 625

c) 6780 6980

d) 15,835 16,035

3. Arrange the numbers in increasing order.

a) 0.285 2 5

5 20 0.208·

3

16,235

rule

+5,w, • ,;.

'•,

· 21 hantjrsdths

SESSION# 1

4. Estimate each answer by rounding to the appropriate place.

Estimate Actual

a) 807, 152 + 997 = b) 807,152 + 997 =

C) 3207 X 58 = d) 3207 x 58 =

e) 5237 + 9 = f) 5237 + 9 =

5. Find the value of each of the following by using the traditional algorithm as wellas a mental math strategy.

Mental Math Strategy Algorithm

a) 82 X 3 =

b) 700 X 300 =

c) 64,000 + 8 =

d) 48 x 25 =

e) .16+2=

4

SESSION# 1

6. James watched the neighbor's dog for 1 week. He earned $15 a day. With themoney he earned, James bought a bathing suit for $35 and put half of the remainingmoney in his bank account. How much money was put into the bank account? Show amodel drawing to support your answer.

7. Dawn collected sharks teeth and sea glass at the beach. The number of sharksteeth found was 3 times the amount of sea glass. If Dawn found 141 sharks teeth, howmany more sharks teeth than sea glass did she find? Show a model drawing to supportyour answer.

Test taking quantitative reasoning skills: 8.

9.

-20

A

The value of the digit 4

in 28,699.400

A

10.

The sum of the first three

prime numbers

A

0 A is greater than B.

0 B is greater than A.

0 A and B are the same.






5

-40

B

The value of the digit 4

in 28,699.4

B

The number of factors of 14

B

SESSION #2

200,130,150

29,999,997

2. Find the value of the following expressions:

a) 7+6+3-5

b) (3 X 8 + 2) + 2

c) 9-5+3- 2

ct) 6x2+4+5

e) (4 + 7) X (8 - 4)

3. Use the clues to find the mystery number.

1) It is between 34,000 and 35,000.2) The ones digit is double the thousands digit.3) The ten thousands digit is half the hundreds digit.4) The tens digit is a prime number that is odd and a factor of 14.

The mystery number is ______ _

4. Arrange the numbers in increasing order.

a) 1/3 , 0.75, 3/5, 7/10

b) 40, -20, -1, 0, 3, -5, 30

c) 1/3, 1, 4/6, 6/12

6

SESSION# 2


Estimate Actual

a) 56,783 - 996 = b) 56,783 - 996 =

C) 28,320 X 5 = d) 28,320 X 5 =

e) 1980 + 3 = f) 1980+3=

6. Find the value of each of the followlna bv uslnQ the tradltlonal algorlthm as wellas a mental math strategy.

- --


a) 532,896,051-100 =

b) 5.01 - .9 =

c) 72 x4 =

d) .03 x 7 =

e) 346 + 598 =

7

SESSION# 2

7. Brenda baked 40 cookies for the class. The students ate }_ of the cookies. How10 many cookies did she have left? Show a model drawing to support your answer. - . .

8. The perimeter of a rectangle is 42 in. If the length is 15 in., find the width.b) What is the area of the rectangle?


0 X 12

A

10.

12x6x48

A

11. forty thousand, ninety-four

A



0 A and Bare the same.


0 Bis greater than A.




0 A and Bare the same.

8

0-:-12

B

6x3x4x12x3

B

ninety-four hundred three

B

60

30

0

Monday

SESSION #3

■ Fish caught

Tuesday Wednesday Thursday

1) The graph shows the number of fish caught by Brian during the week.

a) On which day did Brian catch 35 fish?

b) How many fish did Brian catch in all?

c) On Wednesday, he caught equal amounts of two different types of fish. How manyfish of each type did he catch?

d) On which day did he catch 4 times the amount on Monday?

e) On Thursday he caught half as many as which day?

2) Use mental math and place value concepts to answer a-e.

a) What number is 100 less than 521,039?

b) What number is 1 O more than 32,596?

c) What number is 1000 less than 32,521?

d) What number is 100 more than 59,952?

e) What number is 10 less than 2000?

3) Find the number represented by n to make a true statement.

a) 48 x 5 x 10 = 25 x 2 x 6 x n

b)3x7x4 =12xn

c) 3 x 56 x 25 = 40 x 35 x n

d) 15 = 5 x n

9

SESSION #3


Estimate Actual

a) 3001 - 408 = b) 3001 - 408 =

C) 38 X 2,326 = d) 38 x 2,326 =

e) 4372 + 4 = f) 4372 + 4 =



a) 74 X 6 =

b) 489 - 13 =

C) 6 X 900 =

d) 5500 + 11 =

e) 1.4 + 7 =

10

SESSION #3

6. Jackie wants to buy 2 bathing suits. She has $63.47. One suit cost $45.80 and theother one cost $32.99. How much more money does she need to purchase the suits?Show a model drawing to support your answer.

7. Katie spent 2/3 of her money on running shorts. She had $18 left. How much moneydid the shorts cost? Show a model drawing to support your answer.


9.

700-n = 500The value of n

A

6x8+4

A







11

500-n=200The value of n

B

4+8x6

B

SESSION #4

1. Find the missing digits.

a) b)

3 □ 8 5 8 9 4 □

+ □ 2 7 □ + 1 5 □ 6

7 9 □ 9 □□□ 3 4

2. Use mental math and place value concepts to fill In the blanks.

a) is 10 more than 74,837.

b) is 100 less than 50,000.

c) is 10 more than 993.

d) is 1000 less than 20,589.

e) -100 = 40,895

f) + 10 = 32,000

g) + 1000 = 80,422

h) -5000 = 9754

3. Find the quotient and the remainder. Remainders should be written in fractionform.

a) 6789 + 6 = b)1203 + 5 =

12

8040 c) -=

4

SESSION #4

4. Add or Subtract. All answers should be in simplest form.

1 3 a)-+-=

3 6

2 3 b)-+-=

5 10

2 3 c)---=7 21


Estimate

a) 80,435 - 378 =

C) 494 X 62 =

e) 482+ 5=

b) 80,435 - 378 =

d) 494 x 62=

f)482+5=

Actual

6 5 d)---=

8 12

6. Use the following 3 numbers: 6, 5, and 2 to create a true statement; eachnumber can only be used once In each equation.

a) __ + __ x __ =16

b) __ x __ __ =7

c)(� __ + _ __,)x __ =42

d) ( )+ __ =3

e) __ + __ __ =8

7. Twice as many pitches were thrown on Tuesday as on Saturday. There were 10more pitches were thrown on Wednesday than on Tuesday. If the pitcher throws atotal of 225 pitches on the three days, how many pitches did he throw onWednesday? Show a model drawing to support your answer.

13

SESSION #4

8. Max collected lacrosse balls that were used in the Fourth of July tournament. He andhis 3 friends shared the balls equally. Each boy received 5 lacrosse balls and therewere 2 remaining. How many lacrosse balls did Max find? Show a model drawing tosupport your answer.


10.

17

100

A

The perimeter of square

A







0.017

B

The area of square

B

0 There is not enough information to tell. 11.

508,000

A




14

580,000

B

SESSION #5

1. Find a rule for the input and output below.

Input Output

23 33

53 63

8 a)

173 b)

c) 198

d) 400

What's my rule? e)

2. Fill in the blank with a whole or decimal number.

a.__ b.__ c.__ d. __

+ ! ! ! ◄ 111111111111111111111111111111111111111111111111111 ►

-2 -1 0 1 2

Compare the followlng expressions with, <, >, or =·

3 5/8 0 0.65

4 0.601 0 3/5

5 0.44 0 0.404

6 0.08 0 4/25

7 -3 0 -4

15

SESSION# 5

8. Use the clues to find the mystery number.

1) I am a multiple of 10.2) I am between 7,000 and 9,000.3) The hundreds digit is 6 less than the thousands digit.4) The hundreds digit is a prime number that is even.5) The sum of the digits is 15.

The mystery number is ______ _


Estimate Actual

a) 52 + 5 = b) 52 + 5 =

c) 708 + 6 = d) 708 + 6 =

e) 70 - 0.03 = f) 70 - 0.03 =

1 o. Find the value of each of the following by using the traditional algorithm as well as a mental math strategy.

a) 0.6 X 4 = b) 1.8 + 2 =

C) 1.2 X 5 = d) 0.64 + 8=

e) .09 X 8 = f) 4.9 + 7 =

16

SESSION #5

11. Amy mixed 3.2 quarts of pink lemonade with 12.4 quarts of ice tea. She poured themixture equally into 4 pitchers. One of the pitchers knocked over and emptied out.How many quarts of the mixture were remaining? Show a model drawing to supportyour answer.

Test taking quantitative reasoning skills:

12.

1/4 of 16

A

13.

I15 ¢

A

14.

I1.7x4

A










17

1/4 of $5

B

1 /5 of a dollar

B

17 tenths x 4

B

SESSION #6

1. Fill in the missing number by looking for a pattern.

a) 32 x 75 = __ x 25 How did you know? ______ _

b) 3 x208 = 624, then 24 x 208 =--- How did you know?______ _

c) 16 x 22 = 352, then 16 x 66 = How did you know? _______ _

d) 25 x 8 x 14 = 2 x 5 x 7 x How did you know? ______ _

2. What fraction is 2 months out of 2 years?

3. What fraction is 230 g out of a kilogram?

4. What fraction is 15 minutes out of an hour?

5. What fraction is 8 inches out of 3 feet?

6. Add or subtract. Give each answer in simplest form.

a) 1 -4/5 = __ b) 7/8 + 2/4 =-

e) 6/8 -6/10= __

c)3-6ll= __

d) 8/3 + 2/12 =--


Estimate Actual

a) 4160 + 4 = b) 4160 + 4 =

C) 332 X 3 = d) 332 X 3 =

e) 50,000 -92 = f) 50,000 -92 =

18

SESSION# 6


a)4016+4 = b) 51 + 3 =

C) 2.3 X 2 = d) 700 - 280 =

e) 23 + 14 + 77 + 26 = f) 140,267 - 1000 =

9. The sum of two numbers is 228. If one number is one-third the other number, find thetwo numbers. Show a model drawing to support your answer.


1/2 of a 1/2

A

11.

36 + 12 X 2

A







19

1/2 of 2

B

2 X 12 + 36

B

SESSION #6

12. A square tile is made up of 9 identical squares. The tile has a side length of 2 ft.The smaller white square in each black square make up 1 /16 of each black square.What is the area of the black region?

13. Find the area of a rectangle with a side length 22cm and a perimeter of 158cm.

14. Kelly works for 6 hours 20 minutes at a summer camp 5 days a week. She is paid$6 an hour. How much money does she earn in a week? Show a model drawing tosupport your answer. · · · --- - ---

20

SESSION #7

1. Fill in the ___ using mental math and place value concepts.

a) What number is 0.5 less than 4.01 ? ____

b) What number is 0.02 more than 3.88? ____

c) What is the quotient of 3.6 + 4 ?___ _

d) What is the product of 0.7 and 8? ____

2. Fill in the blanks.

a) There are ___ thirds in 12/3.

b) There are fifths in 5 2110.

c)There are quarters in 8 112.

d)There are eighths in 2 3/4.

Compare the following expressions with, <, >, or =·

3 7.35 0 73/5

4 -100 0 1/2

5 6/10 0 3/5

6 4.30 0 43/10

7 1.9 0 0.195

8. Find the value of the following expressions:

a) 400 - (30 + 2) __ _ b) 43+23+ 14= ____

C) 24 + 4 X 3 = ___ _ d) 25 x ( 30- 20) =---

21

SESSION# 7


Estimate Actual

a) 321 .;- 8 = b) 321 -:- 8 =

c) 603 .;- 6 = d) 603-:- 6 =

e) 65.98 - 0.85 = f) 65.98 - 0.85 =

1 o. Find the missing digits.

a) b)

□ 3 □ 8 6 □ 2 3

1 □ 4 □ 8 □ □

3 1 2 3 □ 8 8 2

11. Molly finished 3/5 of her project in 45 minutes. If she continues at this rate, howmuch longer will she have to work to complete the project? Show a model drawingto support your answer. ,

22

SESSION #7


12.

3m 70 cm

A

13.

5263.84

Digit in hundreds place

14.

A

5263.84

Value of digit in

hundreds place

A










23

265cm

B

5263.84

Digit in hundredths place

B

5263.84

Value of digit in

hundredths place

B

SESSION# 8

1. Find a rule for the input and output below.

Input Output

8 5

9 6

12 9

15 a)

b) 27

c) 36

What's my rule? d)

2. List the common factors of 24 and 36.

3. Write down the first two common multiples of 3 and 5.

4. List the prime numbers between O and 25.

Write<, >, or= in the Q

5 21/7 0 26/14

6 3 9/10 0 12/5

7 6ll 0 9/8

8 1 1/3 0 11/12

9 7 4/5 0 7.45

10. Use the following 3 numbers: 7, 0, and 3. Create a true statement; eachnumber can only be used once in each equation.

a) __ x __ + __ =3

� __ + __ x __ =7

24

SESSION #8 c) (\-__ +_�) x __ = 0

d} __ + __ =10

e) __ X (\-__ + __ )= 21

11 . In the figure, all lines meet to form right angles.

4cm

10cm

13 cm

a) Find the area of the figure. ___ _

b) Find the perimeter . ___ _

6cm

12. Find the value of each of the followlng by using the traditional algorithm aswell as a mental math strategy. .Q!!!.

a) 500,000 - 925 = b) 360 + 6 =

C) 200 X 50 = d) 81tens + 9=

e) 6 hundredths x 8 = f) 32 tenths + 4 =

25

SESSION #8

13. Jack baked three dozen cookies and two and a quarter dozen brownies for the bakesale. He sold each of them in bags of 3 for $1. How much money did he receive?Show a model drawing to support your answer.


14.

The number of factors in 24

A

15.

15 X 28

A

16.

(30 X 3) +(6 X 3)

A










26

The number of multiples of 3

B

12x35

B

(40 X 3) - (2 X 3)

B

1a)

1 b)

1c)

2a)

2b)

2c)

2d)

3)

4a)

4b)

4c)

4d)

Mathodology Summer Sampler Grade 4-solutions

SESSION #1

Shannon 4e} 600 (5400 + 9) answers may vary

4/13 and 4/15 4f) 581 8/9

9/47 5a) 246 (240 + 6)

15, 25 5b) 210,000

605, 585 -20 5c) 8,000

6880, 7080, 7180 + 100 5d} 1200 ( 12 X 100)

15,935, 16,135 +100 5e) . 08( 16 hundredths + 2 = 8 hundredths)

.208, .21, 5/20, .285, 2/5 6) $35 (see video)

808,152 (807,152 + 1000) 7) 94 (see video)answers may vary

808,149 8) A>B

180,000 (3000 X 60) 9) A=B

answers may vary

186,006 10) A>B

27

Mathodology 1Summer Sampler Grade 4-solutions

; 'SESSION #2

i ·. --:···�.·,'t1t::'•:;, --!"=· '··" - .. ,_,,, ;,�;,"• ."1-Wm l "*"""'"""R"- r" r, l* i ft-"'..;- ; ,;; 'Jlwitr<i 1\ � '-"' ;[0 i@f';t(iiiz :,C J"" ;;; ._;,_'- 'x � - _., ~ � /2 '-"' ;; "" � * "" "~ �

1a) 8,000,000 7,900,000 7,870,000

" ' , � "

7,865,000 7,865,300 7,865,320

1b) 200,000,000 200,100,000 200,130,150 200,130,000 200,130,200 200,130,150

1c) 30;000,000 30,000,000 30,000,000 30,000,000 l 30,000,000 30,000,000 " '"'

2a) 4

2b) 13

2c) 5 '

2d) 8

2e) 44

3) 34,678

4a) 1/3, 3/5, 7/10, .75

, 4b) -20, -5, -1, 0, 3, 30, 40

4c) 1/3, 6/12, 4/6, 1

Sa) 55,783 (56,783 - 100) answers may vary

Sb) 55,787

Sc) 150,000(30,000 X 5) answers may vary

5d)

Se)

I

Sf)

6a)

6b)

' 6c)

6d)

6e)

7)

Sa)

Sb)

9)

10)

11)

28

141,600

600(1800+3) answers may vary

660

'

, '� , ..

532;895,951 ' · .. ·

4.11

288(280 +8)

0.21

944(344 + 600)

12 cookies(see video)

6 in

a) 90 sq in

A=B

A> B (Look for patterns)

A>B

,·,·'-"

" � ",.,

'

1b) 140

1c) 30

1d) Wednesday

1e) Wednesday

2a) 520,939

2b) 32,606

2c) 31,521

2d) 60,052

2e) 1990

Sa) 8 (Look for factors)

3b) 7 (Look for factors)

3c) 3 (Look for factors)

3d) 3

4a) 2600(3000-400)

answers may vary

Mathodology Survimer Sampler Grade 4�sQlutioos

SESSION #3

4c)

.. . �).

5d)

29

80,000(40 ... answE1rs.

i. .

. 88,:388 ...

500

r··--·· 0

l �"'t =tt�,:J,c¾R

I*' � t d\.,>till'ttri/ .;.if§.� - a,,�""

1a) 3685 + 4274=7959

Mathodol�•Summer Sampler . ·Grade 4�solutions

SESSION #4

-

• • 0

-

0 '""""o/0"#40MWJFS

-, I/& T" ,,, " ,;0-1'· "" , • ,. •'i0ltiJW. �, 1

: ; tttrnfd�oJriJ;JI �;::, ½

1

~;J!½f!Jia

Sa) 8o;oss(so;43s � 400) answers may vary

16) .

8948+ 1586= 10,534 " ' '

5b) 80,057

· 2af

2b)

2c)

2d}

.. �et

2f)

2g)

2h)

3a)

3�)

... 3c).

4a)

4b)

4c)

4d)

74,847°

49,900

1003

,,!9,589

.�.�9�

.31.!990 ..

79,422

14,754

1131 1/2

240 3/5 ....

2010 . , ...... " ' ,,,.,, , ,_

5/6

7/10

1/7

1/3

'

..

..

�-

·~%»»•••»

.. .

' ,, . . . . .. ..

, , ,, .,.,,,, ,,."

..

' ..

''·"

. .

Sc)

5d)

Se)

Sf)

6a)

6b) ,, e

6c)

6d)

6e)

7)

8)

9)

10)

11)

30

30,000(500 x60) answers may vary

30,628 "''

fOO (ob0+5) . . .answers may vary

'" . .. . , ' ' " ' ' .'

96 2/5

6 + 5 x 2 = 16 or 6 + 2 x 5 =16

2x6- 5= 7 or 6x2-5=7

(2 + 5) � 6 = 42 or (5 + 2)x 6 = 42

(6-5')'+2 = 3. ,. ......... , . .

5+6+'2;;,8' , '"' ' .,, '.,s,

96 pitches(see video)

22 balls(see video)

A>B

. ,,. ,., ,.,

...

There is not eriough information to tell

B>A

1b) 183

1c) 188

1d) 390

1e) +10

2a) -1.9

2b) -0.5

2c) 0.6

2d) 1.9

3) 0.625<0.65

4) 0.601 >0.6

5) 0.44>0.404

6) 0.08< 0.16

7) -3>-4

8) 8250

9a) 10 (50 + 5) answers may vary

Mathodology Summers.ampler Grade 4�solutions

SESSION#5

9c) 120 (720+6) answers may vary

118 .• ,

..... ''9ff 69.97

·1oar

. .

10bJ 0.9

1ocr 6'.. ''10d) 0:08 .

.

) l 10eJ 0.72

. ' 10fJ.

"'11'J

{} ,..., ,_ ,. ····t2)

13)

14)

31

1a)

1b)

1c)

1d)

2)

3)

4)

5)

6a)

6b)

6c)

6d)

6e)

7a)

7b)

7c)


SESSION #6

96 (3 x 32) (Look for factors) 7d) 996

4992 (624 X 8) 7e) 49,900 (50,000 · 100) answers may vary

1056 (352 X 3) 7f) 49,908

40 (5 x 8) (Look for factors) 8a) 1004

1/12 8b) 17

23/100 8c) 4.6

1/4 8d) 420

2/9 8e) 140

1/5 8f) 139,267

1 3/8 9) 57 and 171(see video)

2 1f1 10) B>A

25/6 11) A=B

3/20 12) 240 sq in .(60 x 4)

1000 (4000-;. 4) 13) 1254 sq cmanswers may vary

1040 14) $190 (see video)

900 (300 X 3) answers may vary

32

1a) 3.51

1b) 3.9

1c) 0.9

1d) 5.6

2a) 5

2b) 26

2c) 34

2d) 22

3) <

4) <

5) =

6) =

7) >

8a) 368

8b) 80

Mathodolog{Summer Sampler Grade 4-solutions

SESSION#7

8c) 18

8d) 250

9a) 40 (320 + 8) answers may vary

9b) 40 1/8

9c) 100 (600 + 6) answers may vary

9d) 100 1/2

9e) 65 (66 • 1) answers may vary

9f) 65.13

10a) 4368 • 1245 = 3123

10b) 6723 • 841 = 5882

11) 30 min or 1/2 hour (see video)

12) A>B

13) B>A

14) A>B

33

1a)

1b)

1c)

1d)

2)

3)

4)

5)

6)

7)

8)

9)

10a)

10b)

10c)


SESSION#S

12 10d) 3 - 0 + 7 = 10 or 7 - 0 + 3 =10

30 10e) 7 x (0 + 3):::: 21 or 7 x (3 + 0) = 21 or 3 x (7 + 0 ) = 21 or 3 x (0 + 7) = 21

39 11a) 78 sq cm

-3 11b) 50 cm

1, 2, 3, 4,6, 12 12a) 499,075

15,30 12b) 60

2,3, 5, 7, 11, 13, 17, 19,23 12c) 10,000

> 12d) 90

> 12e) 0.48

< 12f) 0.8

> 13) $21 (see video)

> 14) B>A

7 x 0 + 3 = 3 or 0 x 7 + 3 = 3 15) A=B

7 + 0 x 3 = 7 or 7 + 3 x 0 = 7 16) B>A

(7 + 3) x 0 = 0 or (3 + 7) x o = 0

34

34x6=

45 x3 =

72x8=

22x4=

18 X 5 =

64x7=

51 X 9 =

54x3 =

95x8=

81 x6=

33 x4=

Mental Math-Distributive Property

34 X 8 = (30 X _) + ( 4 X _)

56 x 3 = (_x 3) + (_x 3)

48 x 6 = (40 x_) + (_x 6)

27 x 5 = (_x 5) + (7 x_)

61 x 7 =(_x_) +(l x 7)

59x4 =(60x4)-(_x4)

47 X 9 = (_ X 9) -(_ X 9)

76 X 5 = (_ X 5) -(_x 5)

38 x 6 = (40 x_)- (_x 6)

32 X 8 = (_ X 8) + (_x 8)

73 x 3 = (_x 3) + (_x 3)

35

Mental Math-Place Value

8345 - = 8335 3287 - =3286

1468 + = 1568 432+ = 1432

3020- =2920 2841 + = 3041

5760+ = 5780 3900- =3890

8643 + = 8943 20,000 - = 19,000

7251 - =7201 2100- = 1900

8000- =7900 6423 + =6424

3210+ = 3250 9876- =9870

4300- =2300 732+ =2732

2099+ =2109 5020- =4820

2247- =2207 6943 + =7143

36

Mental Math-Decimals

2.50 + 0.08 = 10.50 - 0.60 =

42.0 + 7.5 = 10.0 - 0.75 =

72.5 + 0.04 = 6.50 - 0.30 =

2.09 + 0.8 = 34.05 - 0.4 =

63.5 + 0.5 = 2.72 - 0.99 =

0.48 + 0.02 = 9.98 - 0.98 =

3.25 + 0.75 = 50.09 - 0.10 =

4.40 + 0.05 = 10.50 - 0.25 =

2.50 + 0.80 = 42.80 - 0.03 =

7.5 + 6.0 = 3.8 - 0.4 =

0.02 + 0.20 = 100.0 - 0.01 =

37

Mental Math-Measurement Time

1 h-20 min = mm 3 years = months

3 hr 12 min =

.

48 months =mm years

105 min = h.

10 years = months min

124 sec =

.

days = 3 weeks mm sec

1 hr-8 min =

.

49 days = weeks min

73 sec =

.

8 years = months mm sec

1 h-22 min =

.

26 months =mm yr mo

185 min = hr .

3 yr 5 mo =mm mo

8min = sec 3 wk3 days = days

5 hr = min 5 weeks = days

9min = sec days = 1 year

38

Mental Math Simplifying Fractions

3 5 -

--

9 10

2 8 -

-=

4 16

5 3 -

- -=

25 27

4 10 - -=

16 12

2 9 -

- -=

8 9

3 2 -

--

-

12 20

11 9 -= -=

55 36

15 4 -= -

-

27 40

8 14 -= -

-

24 21

10 9 -

- -

100 18

4 2 -

--

12 4

39

Mental Math-Adding Fractions

2 1 1 4 -+-= -+-=

3 6 5 15

3 3 3 3 -+-= -+-=

8 16 5 10

1 3 5 1 -+-= -+-=

2 4 7 14

7 3 1 1 -+-= -+-=

10 20 4 8

1 7 5 5 -+-= -+-=

3 12 18 6

3 5 1 1 -+-= -+-=

5 15 3 6

2 2 3 7 -+-= -+-=

5 10 4 8

2 1 1 5 -+-= -+-=

10 20 3 9

1 5 3 6 -+-= -+-=

4 12 5 20

6 1 2 1 -+-= -+-=

7 14 5 10

5 7 2 5 -+-= -+-=

9 18 8 16

40

Mental Math - Subtracting Fractions

4 1 ---

-

1 1 9 3 ---

-

5 10

5 1 3 1 ---

----

-

16 4 4 2

1 5 7 2 ---

----

-

2 14 7 7

7 1 4 1 ---= ---

-

10 5 9 3

4 1 5 1 ---

----

-

6 3 10 2

3 5 2 3 ---

----

-

2 4 4 8

5 1 13 2 ---

----

-

8 4 15 5

2 1 1 1 ---= ---

-

10 20 4 8

5 6 3 1 ---

----

-

5 15 2 4

1 2 2 1 ---

- ---=

2 6 5 10

5 1 2 2 ---

----

-

9 3 3 6

41

Mental Math- Fractions of a Set

1

2 -x16=-x15= 4

3

3 -x12=

3 -xl0=

4 5

1 -x14=

1 -x70=

2 7

1 -x50=

2 -x16=

10 8

2 -x14=

1 -xl00=

7 2

1 -x25=

1 -x30=

5 3

1 -x24=

5 -x12=

8 6

1 -x30=

1 -x18=

6 9

2 -x90=

3 -x15=

9 5

2 -X8=

1 -x30=

4 10

1 -x21=

1 -x30=

3 6

42

Mental Math - Decimal Form

3 15 -

- --

100 10

27 32tenths =-

10

5tenths = 57 -

-

100

4 10 -

-

--

10 10

83 hundredths = 9 -

-

100

16 19 hundredths =-

-

10

11 11 -

- --

100 10

13tenths = 41 -

-

100

8 ?tenths= -

-

10

2 hundredths = 5 -

-

100

17 hundredths = 112 -

-

100

43

Mental Math- Decimal Multiplication

0.9 X 3 = 1.5 X 2 =

0.4 X 6 = 0.3 X 9 =

1.2 X 5 = 0.07 X 4 =

0.05 X 3 = 1.1 x6=

0.6 X 5 = 0.08 X 7 =

1.4 X 2 = 0.5 X 8 =

0.3 X 3 = 0.20 X 4 =

2.2 X 2 = 0.7 X 9 =

0.25 X 4 = 0.8 X 5 =

0.06 X 7 = 1.3 X 3 =

0.20 X 5 = 1.8 X 2 = 44

204

135

576

88

90

448

459

162

760

486

132

2.58

49.5

72.54

2.89

64

0.5

4

4.45

3.30

13.5

0.22

Mathodology Summer Sampler Mental Math Grade 4 -solutions

Place Value 4.1 Place Value 4.2

(30 X 8) + (4 X 8) 10

(50 X 3 ) + (6 X 3) 100

answers may vary

(40 X 6 ) + (8 X 6) 100

(20 X 5) + (7 X 5) 20

(60 X 7) + (1 X 7) 300

(60 X 4) - (1 X 4) 50

(50 X 9) - (3 X 9) 100

answers may vary

(80 X 5) - (4 X 5) 40

answers may vary

(40 X 6) - (2 X 6) 2000

(30 X 8) + (2 X 8) 10

(70 X 3) + (3 X 3) 40

Declmals 4.3 Tlme4.4

9.9 40

9.25 192

6.2 1hr45m

33.65 2m4 s

1.73 52

9 1m 13S

49.99 38min

10.25 3h5m

42.77 480

3.4 300

99.99 540

45

1

1000

200

10

1000

200

1

6

2000

200

200

36

4

120

21

7

96

2 y2m

41

24

35

365


Slmpllfylng Fractions 4.5 Adding Fractions 4.6

1/3 1/2 5/6 7/15

1/2 1/2 9/16 9/10

1/5 119 5/4 = 11/4 11/14

1/4 5/6 17/20 3/8

1/4 1 11/12 1 119

1/4 1/10 14/15 1/2

1/5 1/4 6/10 = 3/5 13/8 = 1 5/8

519 1/10 5/20 = 1/4 8/9

1/3 2/3 2f.3 9/10

1/10 1/2 13/14 1/2

1/3 1/2 17/18 9/16

Subtracting Fractions 4. 7 Fractions of a Set 4.8

119 1/10 10 4

1/16 1/4 9 6

2114 = 1n 5n 7 10

5/10 = 1/2 119 5 4

2/6 = 1/3 0 4 50

1/4 1/8 5 10

3/8 7/15 3 10

3/20 1/8 5 2

9/15 = 3/5 5/4 = 1 1/4 20 9

1/6 3/10 4 3

219 2/6 = 1/3 7 5

46


Decimal Form 4.9 Decimal Multlpllcatlon 4.10

0.03 1.5 2.7 3.0

2.7 3.2 2.4 2.7

0.5 0.57 6 0.28

0.4 1 0.15 6.6

0.83 0.09 3.0 0.56

1.6 0.19 2.8 4.0

0.11 1.1 0.9 0.8

1.3 0.41 4.4 6.3

0.8 0.7 1 4

0.02 0.05 0.42 3.9

0.17 1.12 1.0 3.6

47

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