Vladimir Luzgin

Math Lessons for Gifted Students

Level A

(grade 5)

Center Impulse

Week-end and evening classes for gifted students grades 5-9
Canada, ON, L4K 1T7, Vaughan (Toronto),
80 Glen Shields Ave., Unit #10,
Phone (416)826-7270
[email protected]

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Content

"Consumor aliis inserviendo"

Click on the lesson!

Lesson 01.

Lesson 02.

Lesson 03.

Lesson 04.

Lesson 05.

Lesson 06.

Lesson 07.

Lesson 08.

Lesson 09.

Lesson 10.

Lesson 01

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1. Add or subtract (do without a calculator and show your work).

1) 359 078 694 + 840 968 527 = _______________

2) 1 351 792 648 + 4 887 964 375 = _______________

3) 825 036 046 - 718 495 378 = _______________

4) 2 164 706 523 - 1 987 656 734 = _______________

2. Calculate mentally and record your answer.

23 + 32 - 14 - 41 + 28 + 82 - 19 - 91 + 43 + 34 - 16 - 61 = _________

3. Find the missing digits in the problems below:



4. If the nails are bought at 35 cents per dozen and sold at 8 for 25 cents, what is the total profit on 10 dozen?

5. Find 3 consecutive integers with a sum of 375.

6. Insert brackets to make each of the following statements true.

1)   15   +   9   :   3   +   5   x   2   =   18

2)   15   +   9   :   3   +   5   x   2   =  6

3)   15   +   9   :   3   +   5   x   2   =  31

7. Write the numbers 1, 2, 3, 4, 5, 6, and 7 in the empty circles, so that the sum of the numbers in each of the two columns and one row is the same and equals 12. How many different ways can you find?

8. Write numbers in the empty circles, so that the sum of the numbers in each of the two rows, two diagonals, and one column is the same.

9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) 85 397 - 408 x (155 - 96) aaaaaa 2) 417 908 + 6 073 x 56 + 627 004

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Lesson 02

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1. Add (do without a calculator and show your work).

1) 4 387 284 364 + 13 542 357 287 + 12 070 358 348 = ______________

2) 368 534 247 962 + 4 869 029 451 + 17 696 632 597 = ______________

2. Calculate mentally and record your answer.

1) 522 + 225 - 324 - 423 = _________

2) 458 + 333 + 42 + 67 = _________

3. Find the missing digits in the problems below:



4. If a block weighs 7 kg plus half a block, what is the mass of a block?

5. A store has bicycles and tricycles for sale. How many of each are for sale if you count 99 wheels and 42 frames in the store.

6. Place signs of addition between some of the digits on the left side of the equals sign to make the statement true.

8    8    8    8    8    8    8    8    =    1000

7. Write the numbers from 1 to 9 in the empty squares so that the addition of the numbers horizontally and diagonally give the same result.

aaa	aaa	aaa
aaa	aaa	aaa
aaa	aaa	aaa

8. Write numbers in the empty circles, so that the sum of the numbers in each of the two rows, two diagonals, and one column is the same.



9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) (1 202 + 914) x 83 + 7 996 - 110 888

2) 705 x (77 719 - 69 713) + 1 121 394

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Lesson 03

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1. Evaluate (do without a calculator and show your work).

1) 159 866 537 + 69 133 684 - 198 357 643 = __________

2) 3 758 933 824 - 1 796 745 785 + 5 039 423 184 = __________

2. Calculate mentally and record your answer.

1) 411 + 419 + 145 + 725 + 87 = _________

2) 635 + 308 + 1 365 + 392 = _________

3. Find the missing digits in the problems below:



4. A pet store sells only birds and puppies. Tom works at the store and counts animals. He counts 30 heads and 94 feet. How many birds are in the store?

5. Rancher Roy's field has 15 horses and chickens in it. He counts 48 legs. How many horses and how many chickens does Rancher Roy have? Remember, horses have 4 legs and chickens have 2 legs.

6. Place signs of addition between some of the digits on the left side of the equals sign to make the statement true.

1)   1    2    3    4    5    6    7    8    9    =    99

2)   9    8    7    6    5    4    3    2    1    =    99

7. The number in an unshaded box is obtained by adding the numbers connected to it from the row above. Place numbers in the empty boxes.

8. Add.

1) 2.3524 + 181.928 + 15.7196 = ____________

2) 12.3751 + 0.192 + 357.4329 = ____________

3) 0. 003958 + 0.07543 + 0.020612 = ____________

4) 0.64705 + 0.259 + 0.0921 + 0.00184 = ____________

9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) 51 003 - (4 968 + 709 x 52) + 203

2) (59 531 - 58 926) x 6 004 - 1 221 485

3) 1 255 041 : 47 + 1 605 741 : 53

4) 49 x 23 + 3 914 : 38

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Lesson 04

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1. Multiply (do without a calculator and show all your work).

1) a 5 309 247 x 3 089 = aaaaaaaaaaaa 2) a 796 053 x 4 928 =

3) a 258 306 x 9 703 = aaaaaaaaaaaaaa 4) a 307 908 x 760 054 =

2. Calculate mentally and record your answer.

1) 11 + 12 + 13 + 17 + 18 + 19 = _________

2) 54 271 + 39 999 + 10 001 = _________

3. Find the missing digits in the problems below:



4. Mary buys gumballs at 4 for 15 cents and sells them at 6 for 25 cents. Find the number of gumballs Mary must sell to make a profit of $1.00.

5. An organization sent out a monthly newsletter to each of its 4 000 members. When the cost of postage was increased from 32 cents a letter to 34 cents a letter, the organization decided to issue only 10 newsletters each year. Find the yearly savings in postage that results from this decision.

6. Place signs of addition between some of the digits on the left side of the equals sign to make the statement true.

1)   1    2    3    4    5    6    7    8    9   =   45

2)   9    8    7    6    5    4    3    2    1   =   90

7. Place numbers in the empty boxes, so that the number in each box equals to the sum of the two numbers in the boxes above it.



8. Subtract.

1) 465.9853 - 97.0462 = _______________

2) 1.00453 - 0.97583 = _____________

3) 1.020304 - 0.9182736 = ______________

9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) 545 454 : 27 - 91 x 62

2) (523 - 318) x 84 : 41

3) (281 878 + 69 543 - 286 413) : 68

4) (5 893 + 9018) : 37 x (424 - 396)

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Lesson 05

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1. Divide (do without a calculator and show all your work).

1) 3 213 : 9 aaaaaa 2) 46 053 : 7 aaaaaa 3) 384 288 : 3 aaaaaa 4) 210 504 : 6

5) 37 072 : 4 aaaaa 6) 381 945 : 5 aaaaa 7) 296 295 : 3 aaaaaa 8) 315 063 : 9

2. Calculate mentally and record your answer.

1) 18 356 + 1 644 + 2 135 = _________

2) 937 - (137 + 798) = ________

3. Through what angle does the hour hand of a clock turn between noon and 05 : 00 p.m.?

4. What is the number of hours and minutes from 6:14 a.m. sunrise until 8:02 p.m. sunset?

5. Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point. If Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?

6. Place signs of multiplication between some of the digits on the left side of the equals sign to make the statements true.

1)   1   2   3   4   5   =   120

2)   1   2   3   4   5   =   270

3)   1   2   3   4   5   =   340

7. Write the numbers from 1 to 13 in the circles, so that the sum of the numbers in each line is 37.

8. Find the missing digits in the problems below.

9. Find the missing digits in the problems below.

1) * 5²   =   4 * * * aaaaaaa 2) * 5²   =   * 6 * *

10. Find the value of the following (do without a calculator and show all your work).

1) 350 x 26 + 68 200 : 31

2) 230 441 - (229 682 - 228 904 : 52)

3) 510 081 - (90 334 + 66 144 : 53)

4) 36 366 - 17 366 : (200 - 162)

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Lesson 06

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1. Divide (do without a calculator and show all your work).

1) 630 756 : 84 aaaaaaaaa 2) 31 925 301 : 57 aaaaaa 3) 8 440 308 : 93

4) 7 062 958 : 743 aaaaaa 5) 12 444 288 : 384 aaaaa 6) 25 199 888 : 497

7) 31 939 506 : 7 863 aaa 8) 36 329 634 : 6 438 aaaa 9) 10 850 336 : 45 976

2. Calculate mentally and record your answer.

1) (654 + 289) - 254 = _________

2) 95 837 - (95 137 + 198) = ________

3. Determine the number of degrees the minute hand of a clock rotates in the time interval from 9 : 15 a.m. to 9 : 35 a.m.

4. Joe has some spheres, each of which weighs the same. He also has some cubes, each of which weighs the same. He discovered that 17 spheres and 13 cubes weigh 262 g and that 13 spheres and 17 cubes weigh 278 g. Find the combined weight, in grams, of one sphere and one cube.

5. If the cost of three erases and one pencil is 21 cents, and the cost of four erasers and six pencils is 70 cents, then what is the cost, in cents, of one pencil and one eraser?

6. Place signs of multiplication between some of the digits on the left side of the equals sign to make the statements true.

1)   1   2   3   4   5   =   720

2)   1   2   3   4   5   =   1620

3)   1   2   3   4   5   =   1035

7. Each of the integers 1 to 10 is to be placed in one of the boxes in the diagram. Each integer below two adjacent integers equals their positive difference. Given 4 and 6 in the boxes shown, finish placing the remaining integers in the other boxes.

8. Write > or < for each square.

9. Find the missing digits in the problem below.

10. Find the value of the following (do without a calculator and show all your work).

1) (5 545 + 48 x 35) : 85

2) 439 060 + 432 288 : 72

3) (543 283 - 298 354 - 178 653) : 84

4) 59 400 : 27 + 15 x 240

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Lesson 07

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1. Find the answers by dividing. Then check your answers by finding the total of the remainders in each row and each column.

aaa	aaa				Total
	753 : 3	926 : 5	1 074 : 7	6 785 : 8	5
	3 492 : 6	8 357 : 9	9 731 : 11	6 013 : 12	13
	75 643 : 89	12 080 : 63	26 458 : 37	7 924 : 38	152
	63 521 : 17	43 507 : 26	90 706 : 36	14 668 : 41	71
Total	91	62	35	53	aaa

2. Calculate mentally and record your answer.

1) (227 + 358) - (127 + 258) = _________

2) 4 298 - (4 083 + 198) = ________

3. Determine the number of degrees the minute hand of a clock passes through between 9 : 45 a.m. and 10 : 13 a.m.

4. Four cats and three kittens weigh 44 kg. Three cats and two kittens weigh 32 kg. If all cats have equal weights and all kittens have the equal weights, find the weight, in kilograms, of two cats and one kitten.

5. How many brothers and sisters are there in a family in which each boy has as many sisters as brothers but each girl has twice as many brothers as sisters?

6. Place signs of multiplication or division between some of the digits on the left side of the equals sign to make the statements true.

1)   1   2   8   4   4   8   =   1

2)   1   2   8   4   4   8   =   2

3)   1   2   8   4   4   8   =   8

7. Write numbers in the empty squares so that the sum of each row, column, and diagonal is the same.

5	aaa	6
aaa	aaa	aaa
aaa	3	aaa

7	8	aaa
aaa	10	aaa
aaa	aaa	aaa

8. Estimate these sums and write > or < for each square.

9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) 2 355 264 : 58 + 1 526 112 : 56

2) 1 032 : (5 472 : 19 : 12)

3) 15 732 : 57 : (156 : 13)

4) (37 296 : 37 - 17 780 : 35) : 250

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Lesson 08

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1. Find the answers by dividing. Then check your answers by finding the total of the remainders in each row and each column.

aaa	aaa				Total
	67 954 : 29	69 370 : 48	29 375 : 94	55 249 : 78	89
	65 306 : 121	168 627 : 547	30 394 : 307	58 606 : 197	336
	87 600 : 457	39 861 : 672	35 903 : 276	96 348 : 137	586
	937 463 : 260	730 642 : 418	907 346 : 607	137 000 : 284	1 159
Total	570	770	559	271	aaa

2. Calculate mentally and record your answer.

1) 327 x 19 - 317 x 19 = _________

2) 13 x 24 + 36 x 13 + 60 x 27 = ________

3. Find the angle between the hands of a clock at each time.

a) 01 : 00 aaaaaaaaaa b) 02 : 20 aaaaaaaaaa c) 03 : 30 aaaaaaaaaa d) 04 : 45

4. A clock loses ten minutes each hour. If the clock is set correctly at 12 o'clock noon, what is the correct time when the clock reads 3:00 p.m.?

5. Farmer Phil sent his farm hand to town to get five sacks of grain. The store manager loaded the grain in his truck and said, "Tell Farmer Phil that sack 1 and sack 2 together weigh 48 pounds, sack 2 and sack 3 together weigh 54 pounds; sack 3 and sack 4 together weigh 46 pounds, sack 4 and sack 5 together weigh 32 pounds; and sack 1, sack 3, and sack 5 together weigh 64 pounds." How much total grain did the farm hand bring back to Farmer Phil, and what did each sack weigh?

6. Place signs of multiplication or division between some of the digits on the left side of the equals sign to make the statements true.

1)   1   2   8   4   4   8   =   14

2)   1   2   8   4   4   8   =   16

3)   1   2   8   4   4   8   =   21

7. Write numbers in the empty squares so that the sum of each row, column, and diagonal is the same.

4	aaa	6
aaa	aaa	aaa
8	aaa	aaa

6	8	aaa
aaa	aaa	aaa
aaa	10	aaa

8. Calculate mentally and record your answer.

1) 68.7 - (44.7 + 0.375) = ____________

2) (90.4 + 65.4) - 90.8 = ____________

3) 73.12 - (5.34 + 13.12) = ____________

4) 101.3 + (84.7 + 1.11) = ____________

5) (46.83 + 15.77) - 16.83 = ____________

6) (54 - 47.9) + (58.9 - 49) = ____________

9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) (267 484 + 116 555) : 71 - 2 660 + 30 376

2) (504 x 370 - 158 092) : 47 + 1 612

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Lesson 09

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1. Calculate mentally and record your answer.

1) (13.72 - 5.43) - (4.57 + 3.22) = _____________

2) (47.28 - 34.98) + (34.02 + 55.98) = _____________

3) 7.654 + (37 - 2.999) + 0.345 = ____________

4) 13.4 - 7.7 + 4.2 - 8.9 + 3.5 = ____________

5) - 5.9 + 8.6 + 4.7 + 3.9 - 3.7 = ____________

2. Calculate mentally and record your answer.

1) 263 x 36 - 249 x 36 + 14 x 64 = _________

2) 39 x 27 + 26 x 27 - 23 x 17 - 42 x 17 = ________

3. Find the value of x in the diagram below.

4. A rancher buys 100 live animals for $100. Chickens cost 50 cents each, goats cost $3.50 each, and cows cost $10 each. How many of each did the rancher buy? Is more than one combination possible?

5. Every student at Crestview High must take either Physics 1 or Physics 2. Fifty-two more students take Physics 1 than Physics 2, and there are 24 more girls than boys taking each class. If there are 300 students in the school, how many more boys take Physics 1 than Physics 2?

6. Place signs of multiplication or division between some of the digits on the left side of the equals sign to make the statements true.

1)   1   2   4   8   4   8   =   18

2)   1   2   8   4   4   8   =   336

3)   1   2   8   4   4   8   =   1024

7. Write numbers in the empty squares so that the sum of each row, column, and diagonal is the same.

5	9	10
aaa	aaa	aaa
aaa	aaa	aaa

aaa	9	aaa
3	aaa	11
aaa	aaa	aaa

8. Laura cashed a cheque for $28.65 and put the cash in her purse. Then she purchased 2 magazines for $1.95 each, a book for $6.95, and a record for $5.89. She had $21.60 left in her purse. How much money did she have before cashing her cheque?

9. Find the missing digits in the problems below.

10. Find the value of the following (do without a calculator and show all your work).

1) 59 993 - 616 236 : (21 852 - 21 763)

2) 68 080 - (33 333 - 1 609) : 77

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Lesson 10

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1. Multiply or divide mentally and record your answer.

1) 267.078 : 100 = _________ aaaaaaaaa 2) 0.00564 x 1000 = _________

3) 3 081.947 : 0.01 = ___________ aaaaa 4) 3.689 x 0.001 = ___________

5) 7 984.54 : 0.001 = ___________ aaaaa 6) 76.52 x 0.0001 = ___________

7) 646.02054 : 100 = __________ aaaaaa 8) 0.048901 x 0.01 = __________

9) 56.03649 : 0.0001 = __________ aaaa 10) 5 678.32 x 1000 = __________

2. Complete mentally these flow charts.


3. Two angles are complementary and one angle is 48^o greater than the other. What is the size of the smaller angle?

4. Ahmed's plane is to arrive in St. John's at 11:00 Newfoundland time. The flight time is 2 h and 55 min. What time should Ahmed leave his house if it takes about 1 h to drive to Lester B. Pearson airport in Toronto and he wants to arrive 45 min before departure? (Newfoundland is 1.5 h ahead of Toronto.)

5. Mr. Barter didn't have enough money to purchase a book he wanted. He said to the clerk, "If you will give me as much money as I have in my hand, I will spend $6.00." The clerk agreed and after Mr. Barter spent the $6.00 he repeated the offer. The clerk matched the amount Mr. Barter had left, and he spent another $6.00. After MR. Barter repeated the offer a third time, spending another $6.00, he had no more money. How much money did he start with?

6. Place one of the arithmetic operations +, -, x, and : between each pair of successive numbers in the list 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that the result is 100. Find at least three different solutions.

7. Write numbers in the empty squares so that the sum of each row, column, and diagonal is the same.

aaa	3	aaa
9	5	aaa
aaa	aaa	aaa

6	7	aaa
1	aaa	aaa
aaa	aaa	aaa

8. Solve the following word problems.

a) The rental cost of a videocassette recorder is $25 plus a fixed daily amount. Mr. Singh was charged $64 for a 4-day rental period. What is the fixed rental fee?

b) Sung Choi saved his allowance for eight weeks. When he added to this $15.50 he received for his birthday, he had a total $61.50. How much allowance does he receive each week?

9. Find the missing digits in the problems below.

10. Multiply (do without a calculator and show all your work).

1) 37.73 x 46 = __________ aaaaaaa 2) 2.64 x 4.5 = __________

3) 2.03 x 7.006 = __________ aaaaaa 4) 0.015 x 6.34 = __________

5) 25.65 x 0.56 = __________ aaaaaa 6) 45.07 x 30.96 = __________

7) 0.00455 x 765.024 = _________ aa 8) 41.0096 x 0.07504 = _________

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Answers

1.

aa 1) 2.670 78 aaaa 2) 5.64 aaaaaaaaaa 3) 308 194.7 aaaaa 4) 0.003 689 aa 5) 7 984 540

aa 6) 0.007 652 aaa 7) 6.460 205 4 aaa 8) 0.000 489 01 aa 9) 560 364.9 aa 10) 5 678 320

2. aa 1) 350; aaa 2) 1 200.

3. aa 21^o.

4. aaa 4:50.

5. aaa $5.25.

6. aaa 1) 1 + 2 x 3 + 4 x 5 - 6 + 7 + 8 x 9 = 100,
aaaaa 2) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 x 9 = 100,
aaaaa 3) 1 x 2 x 3 x 4 + 5 + 6 + 7 x 8 + 9 = 100,

7.

a4a	a3a	a8a
9	5	1
2	7	6

a6a	a7a	a2 a
1	5	9
8	3	4

8.
aaaaa 1) $9.75; aaaaa 2)$5.75.

9.

10. aa 1) 1 735.58; aa 2) 11.88; aa 3) 14.222 18; aa 4) 0.095 1; aa 5) 14.634; aa 6) 1 395.3 672; aa 7) 3.480 085 92. aa 8) 3.077 360 384.

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