Process Worksheet: Make a Table

1. Mr Green has a small farm near Steinbach, Manitoba. He has chickens and cows on his farm. If there are 32 legs altogether, what is the greatest number of cows possible?

2. List the different combinations of 5-¢ coins and 10-¢ coins that make 55¢.

3. Each time 2 dice are rolled, 2 numbers land flacing up.A) How many different combinations of numbers can there be?Hint: Only count different sets of numbers. Example: 1, 3 and 3, 1 are the same.

B) How many different products can there be?

4. In a box there are twelve pieces of paper, each with a number. The first is numbered 1, the second 2, the third 3, and so on until 12. The box is shaken and the numbers drawn out in pairs. If the sums for each of the six pairs are 4, 6, 13, 14, 20, and 21, what are the numbers that make up the pairs?

5. Sally is having a early. The first time the doorbell rings, one person enters. If on each successive ring a group enters that has two more persons than the group thot entered on the previous wring, how many people enter on the sixth ring?

6. A kennel owner has the following dogs: a blonde collie, a brown terrier, a black poodle, a black collie, a blonde poodle, a while terrier, a brown collie, a black terrier, a while poodle, and a blonde terrier. If he wants to have one of each colour and breed combination, what types of dogs should he get?

solution1. Mr Green has a small farm near Steinbach, Manitoba. He has chickens and cows on his farm. If there are 32 legs altogether, what is the greatest number of cows possible?

Always maintain a constant total of 32 legs in total.If all the legs belong to cows only, then 8 cows (32÷4) are possible.But there must be at least 1 chicken on the farm.Exchange 1 cow for 2 chickens.Chickens Cows Legs

0 8 32

2 7 32

There are at most 7 cows.

 2. List the different combinations of 5-¢ coins and 10-¢ coins that make 55¢.5-¢

coins11 9 7 5 3 1

10-¢ coins

0 1 2 3 4 5

As there must be at least 1 coin of each, only 5 different combinations exist.

3. Each time 2 dice are rolled, 2 numbers land flacing up.A) How many different combinations of numbers can there be?Hint: Only count different sets of numbers. Example: 1, 3 and 3, 1 are the same.

B) How many different products can there be?

DicePair

xDicePair

xDicePair

xDicePair

xDicePair

 Process Worksheet: Make an Organised List

1. Doug has 2 pairs of pants: a black pair and a green pair. He has 4 shirts: a white shirt, a red shirt, a grey shirt and a striped shirt. How many different outfits can he put together?

2. Ryan numbered his miniature race car collection according to the following rules:

    a. It has to be a 3-digit number.

    b. The digit in the hundreds place is less than 3.

    c. The digit in the tens place is greater than 7.

    d. The digit in the ones place is odd.

If Ryan used every possibility and each car had different number, how many cars did Ryan have in his collection?

3. There will be 7 teams playing in the Maple Island Little League tournament. Each team is scheduled to play every other team once. How many games are scheduled for the tournament?

4. Marvin counted the marbles he had collected. He counted more than 40 but less than 70. When he put the marbles in groups of 5, he had 1 left over. When he put them in groups of 4, he had 1 left over. When he put them in groups of 3, he had 1 left over. How many marbles did Marvin collect?

5. The number 475 is a three-digit number that uses only the three digits 4, 5, 7. How many three-digit numbers can be formed using these three digits, if repeated digits are allowed?

6. I am a counting number. All three of my digits are odd but different. The sum of my digits is 13. The product of my digits is greater than 30. The sum of my tens’ and hundreds’ digits is less than my units’ digit. Which two numbers could I be?

solution

1. Doug has 2 pairs of pants: a black pair and a green pair. He has 4 shirts: a white shirt, a red shirt, a grey shirt and a striped shirt. How many different outfits can he put together?Draw a picture Make a table

  WS RS GS SS

BP / / / /

GP / / / /

To check:No. of Pants

No. of Shirts

Total Outfits

2 4 2 x 4 = 8He can put 8 outfits together.

 

2. Ryan numbered his miniature race car collection according to the following rules:

    a. It has to be a 3-digit number.

    b. The digit in the hundreds place is less than 3.

    c. The digit in the tens place is greater than 7.

    d. The digit in the ones place is odd.

If Ryan used every possibility and each car had different number, how many cars did Ryan have in his collection?Conditions

a. H T O

b. H <31, 2

c. T >78, 9

d. O odd1, 3, 5, 7, 9

List systematically:beginswith 18

beginswith 19

beginswith 28

beginswith 29

181 191 281 291

183 193 283 293

185 195 285 295

187 197 287 297

189 199 289 299

 To check:No. of digits in hundreds place

No. of digits in tens place

No. of digits in ones place

Total possibilities

2 2 5 2 x 2 x 5=20

Ryan had 20 possibilities.

 

3. There will be 7 teams playing in the Maple Island Little League tournament. Each team is scheduled to play every other team once. How many games are scheduled for the tournament?

  1 2 3 4 5 6 7 No.

1   / / / / / / 6

2     / / / / / 5

3       / / / / 4

4         / / / 3

5           / / 2

6             / 1

7               0

Total 21To check:(7 x 6) ÷ 2 = 21

4. Marvin counted the marbles he had collected. He counted more than 40 but less than 70. When he put the marbles in groups of 5, he had 1 left over. When he put them in groups of 4, he had 1 left over. When he put them in groups of 3, he had 1 left over. How many marbles did Marvin collect?

To find the common number of marbles which can be put into groups of 3, 4 and 5 less the 1 left over is equivalent to finding the common multiple between 40 and 70.Begin with a multiple greater than 40.3: ... 42 45 48 51 54 57 604: ... 44 48 52 56 605: ... 45 50 55 60

OR simply 3 x 4 x 5 = 60

60 + 1 = 61 marbles

 

5. The number 475 is a three-digit number that uses only the three digits 4, 5, 7. How many three-digit numbers can be formed using these three digits, if repeated digits are allowed?

List systematically:444 555 777

445 554 774

447 557 775

454 544 744

455 545 745

457 547 747

474 574 754

475 575 755

477 577 757

9 x 3 = 27 numbersTo check:No. of digits in hundreds place

No. of digits in tens place

No. of digits in ones place

Total possibilities

3 3 3 3 x 3 x 3=27

 

6. I am a counting number. All three of my digits are odd but different. The sum of my digits is 13. The product of my digits is greater than 30. The sum of my tens’ and hundreds’ digits is less than my units’ digit. Which two numbers could I be?Conditions

a. H T Oodd and different

1, 3, 5, 7, 9 1, 3, 5, 7, 91, 3, 5, 7,

9b. H + T + O = 13

1, 3, 9 or 1, 6,

7c. H x T x O = 30

1, 5, 7

c. H + T < O157 and

517

 Process Worksheet: Look for a Pattern

1. Find the next 3 numbers in the following sequence.

    2, 5, 11, 23, ____, _____, ______.

2. If this pattern was formed to make a cube, what numbers would appear where the question marks are?

3. The number of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points.

4. For the hexagon with 42 dots, how many dots are there on each side?

5. Look for a common element in each of the following.

This is a RUMDA. This is a not RUMDA.

This is a RUMDA. Is this a RUMDA (A)?

This is a RUMDA. Is this a RUMDA (B)?

This is a not RUMDA.

6. If the figure on the left is continued, how many letters will be in the J row?

   Which row will contain 27 letters?

            A          BBB        CCCCC       DDDDDDsolution

1. Find the next 3 numbers in the following sequence.

    2, 5, 11, 23, ____, _____, ______.

Pattern : x 2 + 1

47, 95, 191

 

2. If this pattern was formed to make a cube, what numbers would appear where the question marks are?

?=1 ?=4 ?=2

 

3. The number of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points.

Points 2 3 4 5 ...... 8 9 10 n

Lines 1 3 6 10 ...... 28 36 45 n(n-1)÷2

  +2   +3   +4   +5 ...... +7   +8   +9  

 

4. For the hexagon with 42 dots, how many dots are there on each side?

No. of dots 6 12 18 ...... 42 n

Dots per side 2 3 4 ...... 8 (n÷6)+1

 

5. Look for a common element in each of the following.

This is a RUMDA. This is a not RUMDA.

This is a RUMDA. Is this a RUMDA (A)? Yes

This is a RUMDA. Is this a RUMDA (B)? No

 

6. If the figure on the left is continued, how many letters will be in the J row?

   Which row will contain 27 letters?

            A          BBB        CCCCC       DDDDDDLetter A B C D E ...... J K L M N General

Numeral Order

1 2 3 4 5 ...... 10 11 12 13 14 n

Total No.

1 3 5 7 9 ...... 19 21 23 25 27 2n-1

 

 Process Worksheet: Guess and Check

1. Mary has 6 coins, which have a total value of 67 cents. What combinations of coins could she have? Use denominations of 1¢, 5¢, 10¢ and 25¢.

2. Navigate your spaceship to the "Black Hole". The product of the numbers along your path must be 2592.Start

6

2 103 4

9 27 1

8 2

4 5Black Hole

  

3. The sums of numbers on each side of the magic triangle are all the same. Find two solutions for the magic triangle using a different number in each box. 

10/ \

24  / \

16 ------   ------  

  

4. a) How many shots at this target are needed to make a score of 300?

    b) Find four different combinations where the value of the shots on the target totals 300.

5. If r is less than 10, what value of r makes r3749r0 divisible by 60? (there are two possibilities.)

6. Find a set of 3 consecutive even numbers whose sum is 294.solution

1. Mary has 6 coins, which have a total value of 67 cents. What combinations of coins could she have? Use denominations of 1¢, 5¢, 10¢ and 25¢.

Penny 1¢ Nickel 5¢ Dime 10¢ Quarter 25¢ Total

2 1 1 2 6

 

2. Navigate your spaceship to the "Black Hole". The product of the numbers along your path must be 2592.Start

62 10

3 49 2

7 18 2

4 5Black Hole

2 x 3 x 6 x 4 x 9 x 2 = 2592  

 

3. The sums of numbers on each side of the magic triangle are all the same. Find two solutions for the magic triangle using a different number in each box. 

10 Sum = 10 + 24 + 16 = 50/ \ A + B = 40 & B + C = 32

24 A Fix a number for B and the  will / \ difference from the above sums

16 ------ C ------ B yield A and C

  

4. a) How many shots at this target are needed to make a score of 300?

    b) Find four different combinations where the value of the shots on the target totals 300.

Numbers 45 48 51 54 57 Total

No. of shots 0 3 2 1 0 300

No. of shots 2 1 1 1 1 300

No. of shots 2 2 0 0 2 300

No. of shots 2 1 0 3 0 300

 

5. If r is less than 10, what value of r makes r3749r0 divisible by 60? (there are two possibilities.)

r3749r0 ÷ 60 ====> r3749r ÷ 6A number divisible by 6 is even and divisible by 3.So r must be even and r3749r is its divisibility by 3.

3 + 7 + 4 + 9 = 23

23 + r + r  is divisible by 3 and r < 10 and even

===> r = 2 and 8

 

6. Find a set of 3 consecutive even numbers whose sum is 294.

294 ÷ 3 = 9898 - 2 98 98 + 2

96 98 100

Process Worksheet: Draw a Picture

1. John gets on an elevator at the first floor. He goes up to the ninth floor then comes down 3 floors. He then goes up 1 floor and down 4 floors. What floor is John on?

2. John always sits in the same pew at the church. The pew is second from the front and eighth form the back. There is a centre aisle. Each pew seats 6 persons. What is the seating capacity in John’s church?

3. Wesley fenced a square piece of land. There are 9 posts on each side. How many posts did he use altogether?

4. If Marie had three different skirts and four different sweaters, how many different outfits could she wear?

5. A rubber ball is dropped from a height of 10m on the asphalt. The ball bounces 8m on the first bounce, 6.4m on the second bounce. Each bounce is eight-tenth as high as the previous bounce. Make a table and bar graph to show the height of each bounce for the first 8 bounces. Round your answer off to the nearest tenth. What is the number of the first bounce which has a height less than 3m?

6. Five kissin’ cousins meet at the family reunion. Each cousin kisses each of the other cousins just once. How many kisses were given in all?

7. Steve, Michael, Sandra, Lesley are standing in line to buy tickets for a movie. In how many ways can they stand in line to buy their tickets?

solution

1. John gets on an elevator at the first floor. He goes up to the ninth floor then comes down 3 floors. He then goes up 1 floor and down 4 floors. What floor is John on?

9 - 3 + 1 - 4 = 3rd floor

 

2. John always sits in the same pew at the church. The pew is second from the front and eighth form the back. There is a centre aisle. Each pew seats 6 persons. What is the seating capacity in John’s church?

FRONT6

 

6

2nd from front/8th from back

6

6 6

6 6

6 6

6 6

6 6

6 6

6 6BACK

Total seating capacity = 6 x 18 = 108

 

3. Wesley fenced a square piece of land. There are 9 posts on each side. How many posts did he use altogether?

x x x x x x x x x

x x

x x

x x

x x

x x

x x

x x

x x x x x x x x x

9 x 4 = 3636 - 4 = 32

 

4. If Marie had three different skirts and four different sweaters, how many different outfits could she wear?

3 x 4 = 12

 

5. A rubber ball is dropped from a height of 10m on the asphalt. The ball bounces 8m on the first bounce, 6.4m on the second bounce. Each bounce is eight-tenth as high as the previous bounce. Make a table and bar graph to show the height of each bounce for the first 8 bounces. Round your answer off to the nearest tenth. What is the number of the first bounce which has a height less than 3m?

H 10m            

E   8m          

I     6.4m        

G       5.1m      

H         4.1m    

T           3.3m  

S             2.6

BOUNCE ORDER

1 2 3 4 5 6  

6th bounce

 

6. Five kissin’ cousins meet at the family reunion. Each cousin kisses each of the other cousins just once. How many kisses were given in all?

15 kisses

 

7. Steve, Michael, Sandra, Lesley are standing in line to buy tickets for a movie. In how many ways can they stand in line to buy their tickets?

4 x 3 x 2 x 1 = 24 ways

 Process Worksheet: Work Backwards

1. Rabbits multiply at an amazing rate. In year 1 there are X rabbits. The rabbit population doubles each year. The forest is crowded in year 7 when there are 3200 rabbits. How many rabbits were there in year one if the population doubles each year?

2. I bought a bag of apples. I kept half of them for myself. I gave the rest to 3 friends. Each friend got 2 apples. How many apples did I buy?

3. What is the starting number??

|v

Add 12

---->

Subtract 6

|v

Multiply by 2

---->

20

 4. ?

|v

Divide by 7|v

Multiply by 2|v

Add 2|v

20solution

1.Make a table and work backward from year 7 when there are 3200 rabbits. Since population doubles each year, working backward means halving it.

Year No. of Rabbots

7 3200

6 1600

5 800

4 400

3 200

2 100

1 50

There were 50 rabbits in year one.

 

2. Work backward from each of 3 friend having 2 apples.Forward Step Backward Step

Each of 3 friends has 2 apples Total : 3 x 2 = 6 apples

I kept half of them for myself Total : 6 x 2 = 12 apples

I bought 12 apples.

 

3. Start with the end result 20.Forward Step Backward Step Working

Final Result 20 20

Multiplt by 2 Divide by 2 20 / 2 = 10

Subtract 6 Add 6 10 + 6 = 16

Add 12 Subtract 12 16 - 12 = 4

The starting number is 4.

  

4. Reverse the stepsForward Step Backward Step Working

? ? 63|v

^|

^|

Divide by 7 Multiply by 7 9 x 7 = 63|v

^|

^|

Multiply by 2 Divide by 2 18 / 2 = 9|v

^|

^|

Add 2 Subtract 2 20 - 2 = 18|v

^|

^|

20 20 20

Process Worksheet: Solve a Simpler Problem

1. How many squares are in this figure?     

     

     

2. How many triangles are there in this figure?

3. A total of 28 handshakes were exchanged at a party. Each person shook hands exactly once with each of the others. How many people were present at the party?

4. Find the thickness of one page in your mathematics text book.

5. Mike is paid for writing numbers on pages of a book. Since different pages require different numbers of digits, Mike is paid for writing each digit. In his last book, he wrote 642 digits. How many pages were in the book?

1.Make a table and work backward from year 7 when there are 3200 rabbits. Since population doubles each year, working backward means halving it.Possible size of Square No. of each size  9

   

   4

     

     

     

1

Total = 14

 

2. Divide the large triangle into its smaller components:Component 1 Component 2 Component 3 Component 4 Component 5

   

5 2 2 2 1

Total of 12 triangles can be found within the given triangle

 

3. Make a table and start with the least possible number of people and find a pattern.No. of people 1 2 3 4 5 6 7 8

No. of handshakes 0 1 3 6 10 15 21 28

Pattern 0 +1 +2 +3 +4 +5 +6 +7

8 people were present at the party.

  

4. Method: Measure the thickness of say, 100 pages of the text book. Then divide the result by 100 to obtain the thickness of one page.

 

5. Divide the pages of the book into groups of 1-, 2- and 3-digit pages and count them separately in batches.

Page Number

No. of digits per page

No. of pages No. of digits

1 to 9 1 9 1x9=9

10 to 99 2 99 - 9 = 90 2x90=180

    Total = 99 Total = 189

No. of digits left excluding the 1- and 2-digit pages = 642 - 189 = 453

No. of pages with 3-digit numbers = 453 / 3 = 151

Total no. of 1-, 2- and 3-digit pages totalling 642 digits = 99 + 151 = 250

There were 250 pages in the book.