Лузгин Владимир Николаевич : другие произведения.

Math-B (grade 5)

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  • Аннотация:
    Math lessons for Canadian students grade 5.

Vladimir Luzgin

 Math Lessons for Gifted Students

Level B

(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

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 1


1. Round each number to the nearest

whole number
tenth
hundredth
167.18
aaaaaaaaaa
2.781
aaaaaaaaaa
   0.08269   
aaaaaaaaaa
300.07
aaaaaaa
3.1423
aaaaaaa
76.5448
aaaaaaa
49.49
aaaaaaa
   203.962   
aaaaaaa
1.35506
aaaaaaa
159.54
aaaaaaa
62.35
aaaaaaa
4.4551
aaaaaaa
   999.623   
aaaaaaa
80.45
aaaaaaa
19.997
aaaaaaa


2. Complete mentally these flow charts.

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3. Two angles are supplementary. Find the angles if one angle is 4 times the other.

4. Todd had more milk than his younger brother Alan so he poured into Alan's glass as much milk as Alan's glass already contained. Then he poured from Alan's glass into his own, as much as his own glass contained. Finally he poured back into Alan's glass as much milk as Alan presently had. Then, both glasses contained 256 mL of milk. How much did each boy start with?

5. Pat bought 7 pairs of earrings on sale. The normal price is $6.40 a pair, but they are on a sale for $1.00 off. Find the final cost of her purchase in dollars.

6. Using all the digits 1, 6, 8, and 9, the operations +, -, x, : , and brackets, if required, form expressions for all the integers from 1 to 10.

7. Complete the following:

1)   3    =    12 aaaaaaa 2)   5   =       aaaaaa 3)   5   =       aaaaaaa 4)   7   =   28  
aaa 5 aaaaaaaaaaaaaaaaaaa 6       12 aaaaaaaaaa 8       24 aaaaaaaaaa 9

5)   7    =        aaaaaaa 6)   9   =   54 aaaaaa 7)   8   =       aaaaaaa 8)   6   =      
aaa 12        60 aaaaaaaaaa 13 aaaaaaaaaaaaaaa 11       99 aaaaaaaaaa 7       63

8. Solve the following word problems.

a) Margaret handed the cashier a $10 bill for the purchase of 3 tennis balls. After $0.54 tax was added, the clerk gave her $2.71 change. What was the cost of each tennis ball?
b) Cindy saw a house that was 1 807 square feet listed for $96 500. What is the cost per square foot, rounded to the nearest cent?

9. Find the missing digits in the problems below.

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

1) 68.7 : 5 = ________ aaaaaaaaaaaaa 2) 121.641 : 13 = ________

3) 7.84 : 0.7 = ________ aaaaaaaaaaa 4) 42.069 : 3.7 = ________

5) 452.628 : 12.7 = ________ aaaaaaa 6) 28.566 : 2.07 = ________

7) 10.1153 : 2.51 = ________ aaaaaaa 8) 402.9942 : 12.57 = ________



Lesson 2


1. Complete mentally these flow charts.

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2. Complete the chart.

   number   
: 10
+ 0.4
: 0.01
x 0.001
- 0.04
x 100
0.6
aaaaaaaaaaaa
aaaaaaaaaaaa
aaaaaaaaaaaa
aaaaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaaaa
21
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
64
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
432
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa
aaaaaaaaaa


3. Two angles are complementary. What is the sum of their supplements?

4. Judy buys 3 CDs at $19.50 and a book at $25.00 (including tax). She has a $10.00 off cupon and her mother agrees to pay half the cost. Find the total amount Judy pays.

5. Jim has a weekend job wich pays $8.50 per hour and $10.50 per hour overtime. Once week befor Christmass, Jim worked 7 hours on Saturday and 6 hours on Sunday plus 4 hours overtime. In addition, he received a bonus of $25.00. How much did he earn?

6. Make the statements true by inserting parenthesis and any of the four arithmetic operations.

1)   5   5   5   5   =   3 aaaaaaaaaaaaaaaaa 2)   5   5   5   5   =   4

3)   5   5   5   5   =   5 aaaaaaaaaaaaaaaaa 4)   5   5   5   5   =   6

7. Reduce to simplest form.

1) 2/4 aaaaaaaaaaaa 2) 3/6 aaaaaaaaaaaa 3) 3/12 aaaaaaaaaaaaa 4) 5/20
5) 12/16 aaaaaaaaaa 6) 8/12 aaaaaaaaaaa 7) 9/15 aaaaaaaaaaaaa 8) 14/21
9) 27/54 aaaaaaaaaa 10) 48/72 aaaaaaaaa 11) 125/30 aaaaaaaaa 12) 36/42
13) 120/180 aaaaaaa 14) 75/125 aaaaaaaa 15) 18/300 aaaaaaaaa 16) 100/250

8. Solve the following word problems.

a) Josh and his brother Ben help their grandfather pick apples. In 15 days, they picked 44.5 bushels. How many bushels did they average each day? Round your answer to the nearest hundredth.
b) Marion is paid $24 for 5 hours of work in the school office. Janet works 3 hours and makes $10.95. How much more per hour does Marion make then Janet?

9. Find the missing digits in the problem below.

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10. Divide and round the answer to the nearest hundredth (do without a calculator and show all your work).

1) 171.72 : 17.6 = ________ aaaaaaaaa 2) 16.348 : 0.153 = ________

3) 72.64 : 3.75 = ________ aaaaaaaaaa 4) 893 : 2.9 = ________

5) 643.5 : 0.26 = ________ aaaaaaaaaa 6) 984.351 : 0.962 = ________

7) 61.9 : 0.305 = ________ aaaaaaaaaa 8) 834.731 : 6.52 = ________



Lesson 3


1. Complete mentally these flow charts.

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2. Write as an improper fraction.

1) 31/4 aaaaaaaa 2) 52/3 aaaaaaaa 3) 27/9 aaaaaaaaa 4) 45/6
5) 71/8 aaaaaaaa 6) 35/9 aaaaaaaa 7) 17/10 aaaaaaaa 8) 914/15
9) 513/17 aaaaaa 10) 149/16 aaaaa 11) 2715/37 aaaa 12) 368/103

3. Add mentally and record your answers in lowest terms.

1) 13/23 + 5/23 + 6/23 aaaaaaaaaaaa 2) 1/10 + 3/10 - 2/10
3) 4/15 + (7/15 + 7/15) aaaaaaaaaaaa 4) (10/13 - 8/13) + 5/13
5) 4/15 + 3/15 + 7/15 - 2/15 aaaaaaaa 6) (9/10 - 6/10) + (7/10 - 5/10)

4. Write two different expressions for the perimeter of the rectangle with length 16 cm and width 7 cm, one with brakets and the other without. Show that the answers are same.

5. Stan has made 2 long distance calls. The first call lasted 12 minutes longer than the other. The 2 calls lasted a total of 56 minutes. How long was each call?

6. Make the statements true by inserting parenthesis and any of the four arithmetic operations.

1)   5   5   5   5   =   7 aaaaaaaaaaaaaaaaa 2)   5   5   5   5   =   30

3)   5   5   5   5   =   50 aaaaaaaaaaaaaaaa 4)   5   5   5   5   =   120

7. Reduce to simplest form.

1) 8 x 8 - 56 aaaaaaaaaa 2) 14 x 5 - 28 aaaaaaaa 3) 19 x 8 - 19 x 6
        8 x 5 aaaaaaaaaaaaaaaaaa 28 aaaaaaaaaaaaaaaaaaaa 38
4) 15 x 7 - 30 x 3 aaaaa 5) 12 x 5 + 4 x 27 aaaa 6) 81 x 17 - 15 x 81
    15 x 17 + 30 x 3 aaaaaaaaa 7 x 36 aaaaaaaaaaaa 81 x 17 + 162 x 2

8. Solve the following word problems.

a) The Suez Canal is 80.3 km longer than the Panama Canal. The sum of their lengths is 243.5 km. Find the length of each canal.

b) A gold pen and a pencil set cost $69.98. The pen costs $6.50 more than the pencil set. What is the cost of the pencil set?

9. Find the missing digits in the problem below.

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

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Lesson 4


1. Fill in the sign of one of the four arithmetic operations and the missing number in these flow charts. Do not use a calculator!

[]

2. Write as a mixed number.

1) 7/3 aaaaaaaaa 2) 35/4 aaaaaaaa 3) 29/2 aaaaaaa 4) 8/5
5) 11/8 aaaaaaaa 6) 32/7 aaaaaaaa 7) 28/9 aaaaaaa 8) 49/6
9) 53/6 aaaaaaaa 10) 27/10 aaaaaa 11) 136/3 aaaaa 12) 135/4

3. Add mentally and record your answers in lowest terms.

1) (3/100 + 23/100) - (8/100 + 4/100) aaaaaaaaa 2) 18/25 - 33/100 + 49/100
3) 12/3 + 42/3 aaaaaaaaaaaaaaaaaaaaaaaaaaaaa 4) 51/5 + 41/5 - 92/5
5) 47/12 - 15/12 + 211/12 aaaaaaaaaaaaaaaaaaa 6) 614/15 - 32/15 - 17/15

4. Jane buys 2 pairs of jeans. She pays $17.00 more for one pair than the other. She pays with a $100 bill and gets $15.00 change. What is the price of the more expensive pair?

5. The sum of 2 consecutive numbers is 897. What are the two numbers?

6. Make the statements true by inserting parenthesis and any of the four arithmetic operations.

1)   4   5   6   7   =   2

2)   4   5   6   7   =   32

3)   5   6   7   8   =   25

4)   5   6   7   8   =   49

7. Add. Write answers in simplest form.

1) 1/2 + 1/4 aaaaaaaaaa 2) 2/5 + 1/4 aaaaaaaaaaa 3) 1/3 + 1/4
4) 5/6 + 1/3 aaaaaaaaaa 5) 2/5 + 1/10 aaaaaaaaaa 6) 2/3 + 3/10
7) 1/3 + 5/8 aaaaaaaaaa 8) 2/3 + 3/5 aaaaaaaaaaa 9) 1/6 + 3/4

8. Solve the following word problems.

a) If 12 candies cost $1.70, how many of these candies can be bought for $ 10.20?

b) Vlad buys coca cola cans at $2.88 per dozen and sells them for 30 cents each. What will be his profit on a day when he sells 27 dozen cans?

9. Find the missing digits in the problem below.

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

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Lesson 5


1. Fill in the sign of one of the four arithmetic operations and the missing number in these flow charts. Do not use a calculator!

[]

2. Express these fractions as decimal numbers.

1) 1/2 aaaaaaaaaaaa 2) 1/4 aaaaaaaaaaaa 3) 3/4
4) 1/5 aaaaaaaaaaaa 5) 3/5 aaaaaaaaaaaa 6) 4/5
7) 1/8 aaaaaaaaaaaa 8) 3/8 aaaaaaaaaaaa 9) 7/8
10) 3/10 aaaaaaaaaa 11) 11/20 aaaaaaaaa 12) 13/25

3. Write as a fraction in simplest form.

1) 0.8 aaaaaaaaaaa 2) 0.25 aaaaaaaaaaa 3) 0.12 aaaaaaaaaaa 4) 0.55
5) 0.75 aaaaaaaaaa 6) 0.24 aaaaaaaaaaa 7) 0.65 aaaaaaaaaaa 8) 0.36
9) 0.125 aaaaaaaa 10) 0.124 aaaaaaaaa 11) 0.275 aaaaaaaa 12) 0.436

4. The sum of two consecutive odd numbers is 744. What are the two numbers?

5. The sum of two consecutive even numbers is 962. What are the two numbers?

6. Make the statements true by inserting parenthesis and any of the four arithmetic operations.

1)   3   4   5   1   =   3

2)   3   4   6   7   =   4

3)   8   8   8   8   =   4

4)   8   8   8   5   =   12

7. Subtract. Write answers in simplest form.

1) 5/8 - 1/4 aaaaaaaaaaa 2) 4/5 - 1/2 aaaaaaaaaaaa 3) 3/4 - 1/3
4) 2/5 - 3/10 aaaaaaaaaa 5) 9/10 - 2/5 aaaaaaaaaaa 6) 3/5 - 1/4
7) 5/6 - 1/4 aaaaaaaaaaa 8) 7/8 - 5/12 aaaaaaaaaaa 9) 1/2 - 3/8

8. Solve the following word problems.

a) Company A rents cars for $17.00 per day plus 8 cents per km. Company B rents cars for $21.00 day plus 7 cents per km. What is the difference in total rental charges on a trip of 1 789 km, if the trip takes 3 days?

b) A worker is paid $8.60/h for 40 h week and time and a half for overtime. How many hours are worked to earn $414.95 in one week?

9. Find the missing digits in the problem below.

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

[]




Lesson 6


1. Fill in the sign of one of the four arithmetic operations and the missing number in these flow charts. Do not use a calculator!

[]

2. Copy and complete.

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3. Write > or < for each square to make a true statement.

[]

4. The difference between the squares of 2 consecutive numbers is 17. Find the numbers.

5. Find all 2-digit numbers wich have a remainder os 3 when divided by 4, and a remainder 6 when divided by 7.

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

1)   4   x   12   +   18   :   6   +   3   =   14

2)   4   x   12   +   18   :   6   +   3   =   23

3)   4   x   12   +   18   :   6   +   3   =   50

4)   4   x   12   +   18   :   6   +   3   =   63

7. Subtract. Write answers in simplest form.

1) 7/9 - 1/6 aaaaaaaaa 2) 7/10 - 1/6 aaaaaaaaaa 3) 2/3 - 3/5
4) 5/6 - 7/10 aaaaaaaa 5) 4/5 - 1/10 aaaaaaaaaa 6) 3/4 - 1/3
7) 1/4 - 1/6 aaaaaaaaa 8) 5/12 - 1/6 aaaaaaaaaa 9) 1/5 - 1/15

8. Solve the following word problems.

a) A sign painter is to center two 7-letter and 9-letter words on a 18-foot signboard. Each letter is to be 0.75 of a foot wide and there is to be 0.8 of a foot between words. Find the number of feet will be left at each end of the board.

b) Marilyn works in a car assembly plant. She is paid $14.50 per hour for working the day shift. She receives an additional $7.25 per hour for working the night shift. In one month, Marilyn works two 40 h day shifts and two 40 h night shifts. Find her gross wages for the month.

9. Draw two straight lines in the circle such that the sum of the numbers in each of the three areas is equal.

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

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Lesson 7


1. Complete mentally these flow charts.

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2. The mass of 1 L of water is 1 kg. The mass of gasoline is 0.68 times the mass of water. What is the mass of the gasoline in a full tank that holds 75 L?

3. Write as a fraction of an hour in simplest form.

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4. Find all 2-digit numbers wich have a remainder os 2 when divided by 3, and a remainder 3 when divided by 5.

5. Write the digits from 1 to 6 to get: a) the smallest positive answer; b) the largest answer.

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

1)   72   :   12   +   6   x   4   =  2

2)   72   :   12   +   6   x   4   =  16

3)   72   :   12   +   6   x   4   =  30

4)   72   :   12   +   6   x   4   =  48

7. Add. Write answers in simplest form.

1) 2/5 + 1/3 aaaaaaaaaaa 2) 1/3 + 4/9 aaaaaaaaaaaa 3) 1/2 + 4/5
4) 7/10 + 1/4 aaaaaaaaaa 5) 5/6 + 1/20 aaaaaaaaaaa 6) 3/10 + 1/3
7) 22/3 + 32/3 aaaaaaaaa 8) 35/8 + 27/8 aaaaaaaaaa 9) 23/4 + 33/8

8. Solve the following word problems.

a) If shipping charges to a certain point are 62 cents for the first five ounces and 8 cents for each additional ounce, what is the weight of a package, in pounds, for which the charges are $1.66? (1 pound = 16 ounces)

b) Milk is sold in 4 L bags and 2 L and 1 L cartons. The milk is priced at $3.49, $2.31, and $1.20, respectively. By how much would the cost of each carton have to be reduced so that its unit price was equal to that of the 4 L bags?

9. Place positive numbers in the empty boxes, so that the number in each box equals to the product of the two numbers in the boxes above it. Do not use a calculator and show your work.

[]

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

[]




Lesson 8


1. Complete mentally these flow charts.

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2. Find the following.

1) 1/3 of 60 aaaaaaaaaaa 2) 2/5 of 45 aaaaaaaaaaaa 3) 3/4 of 12
4) 5/6 of 24 aaaaaaaaaaa 5) 7/8 of 64 aaaaaaaaaaaa 6) 3/10 of 130
7) 5/8 of 4/5 aaaaaaaaaaa 8) 7/12 of 18/25 aaaaaaaaa 9) 2/3 of 2.4

3. Express the following in minutes.

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4. Express each of the following fractions as a sum of two unit fractions.

1) 5/6 aaaaaaaaa 2) 8/15 aaaaaaaaaaa 3) 9/14
4) 4/9 aaaaaaaaa 5) 13/40 aaaaaaaaaa 6) 7/12

5. Write the digits from 1 to 6 to get: a) the smallest answer; b) the largest answer.

[]

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

1)   120   -   40   :   5   x   2   =   32

2)   120   -   40   :   5   x   2   =   104

3)   120   -   40   :   5   x   2   =   116

4)   120   -   40   :   5   x   2   =   224

7. Subtract. Write answers in simplest form.

1) 3/8 - 1/6 aaaaaaaaa 2) 1/3 - 1/4 aaaaaaaaaaa 3) 1/5 - 1/7
4) 3/5 - 1/4 aaaaaaaaa 5) 4/5 - 2/3 aaaaaaaaaaa 6) 7/8 - 1/6
7) 11/36 - 13/60 aaaaa 8) 7/52 - 3/260 aaaaaaaa 9) 13/120 - 1/45

8. 900 people attended a dance. The cost of admission was $2.00 per person or $3.50 per couple. Twice as many $2.00 tickets as $3.50 tickets were sold. Find the amount of money obtained from ticket sales.

9. Place positive numbers in the empty boxes, so that the number in each box equals to the product of the two numbers in the boxes above it. Do not use a calculator and show your work.

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

1) 37 x 462 x 132 : 231 : 264;
2) 43 x 682 x 143 : 341 : 286;
3) 7 x 132 x 62 x 93 : 312 : 26 : 39.



Lesson 9


1. Complete mentally these flow charts.

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2. Write > or < for each square to make a true statement.

[]

3. Evaluate.

1) 2/3 of $ 420; aaaaaaaaa 2) 3/4 of $ 348; aaaaaaaaa 3) 3/5 of $ 370.

4. Write as a fraction in simplest form.

1) 0.6 aaaaaaaaaaa 2) 0.35 aaaaaaaaaaaa 3) 0.408
4) 6.75 aaaaaaaaaa 5) 0.035 aaaaaaaaaaa 6) 0.625

5. Subtract. Write answers in simplest form.

1) 37/75 - 13/45 aaaaaaaaaa 2) 2 - 5/6 aaaaaaaaaaaaa 3) 7 - 17/8
4) 11 - 72/3 aaaaaaaaaaaaa 5) 10 - 82/3 aaaaaaaaaaa 6) 87 - 4613/17
7) 71/2 - 51/3 aaaaaaaaaaaa 8) 121/2 - 71/6 aaaaaaaa 9) 83/8 - 23/4

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

1)   20   x   9   -   6   :   3   =   20

2)   20   x   9   -   6   :   3   =   58

3)   20   x   9   -   6   :   3   =   140

4)   19   x   3   -   2   x   4   =   220

7. Multiply. Express your answers in lowest terms.

1) 15 x 2/5 aaaaaaaaaaaa 2) 6 x 3/4 aaaaaaaaaaaaa 3) 18 x 4/27
4) 30 x 2/35 aaaaaaaaaaa 5) 14 x 3/49 aaaaaaaaaaa 6) 42 x 5/126
7) 3/8 x 40 aaaaaaaaaaaa 8) 4/15 x 25 aaaaaaaaaaa 9) 7/16 x 56

8. Divide. Express your answers in lowest terms.

1) 4/3 : 2 aaaaaaaaaaaa 2) 6/11 : 3 aaaaaaaaaaaaa 3) 14/15 : 7
4) 18/19 : 6 aaaaaaaaaa 5) 45/53 : 15 aaaaaaaaaaa 6) 1/2 : 3
7) 3/5 : 4 aaaaaaaaaaaa 8) 6/7 : 5 aaaaaaaaaaaaaaa 9) 10/17 : 6

9. Place positive numbers in the empty boxes, so that the number in each box equals to the product of the two numbers in the boxes above it. Do not use a calculator and show your work.

[]

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

[]




Lesson 10


1. Complete mentally these flow charts.

[]

2. Write > or < for each square to make a true statement.

[]

3. Write as a fraction in simplest form.

1) 0.008 aaaaaaaaaaa 2) 0.015 aaaaaaaaaaa 3) 0.1125
4) 2.625 aaaaaaaaaaa 5) 2.6125 aaaaaaaaaa 6) 1.5725

4. Add. Write answers in simplest form.

1) 52/3 + 35/6 aaaaaaaaaaa 2) 131/5 + 91/2 aaaaaaaaaaaa 3) 243/5 + 171/2
4) 52/3 + 43/5 aaaaaaaaaaa 5) 213/4 + 375/6 aaaaaaaaaaa 6) 263/8 + 421/4
7) 291/6 + 725/9 aaaaaaaaa 8) 231/8 + 121/6 aaaaaaaaaaa 9) 111/9 + 233/5

5. Make the statements true by inserting parenthesis and any of the four operations.

1)   4   4   4   4   =   0.1 aaaaaaaaaaaaa 2)   6   6   6   6   =   1.2
3)   8   8   7   3   =   0.25 aaaaaaaaaaaa 4)   3   8   1   8   =   0.25

6. Write the digits from 1 to 6 to get: a) the smallest positive answer; b) the largest answer.

[]

7. Multiply. Express your answers in lowest terms.

1) 6 x 2 1/4 aaaaaaaaaaaa 2) 15 x 3 1/10 aaaaaaaaa 3) 2 x 5 1/2
4) 3 2/5 x 10 aaaaaaaaaaa 5) 3 4/9 x 18 aaaaaaaaaa 6) 3 5/8 x 12
7) 1/3 x 1/4 aaaaaaaaaaaaa 8) 3/4 x 4/5 aaaaaaaaaaa 9) 3/5 x 4/7

8. Divide. Express your answers in lowest terms.

1) 5/6 : 7 aaaaaaaaaaaa 2) 3/4 : 6 aaaaaaaaaaaaaa 3) 6/13 : 4
4) 8/9 : 10 aaaaaaaaaaa 5) 24/25 : 42 aaaaaaaaaaa 6) 36/125 : 48
7) 6 3/4 : 9 aaaaaaaaaa 8) 2 1/4 : 6 aaaaaaaaaaaaa 9) 3 1/2 : 14

9. Place positive numbers in the empty boxes, so that the number in each box equals to the product of the two numbers in the boxes above it. Do not use a calculator and show your work.

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

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