Working Backwards
Logical Reasoning
Make a List
Use a Picture of Model
Look for Patterns
100
A teacher bought five flags of different countries, to use in a class activity. She added them to the flags she already had in the classroom. She borrowed four more flags, but two of these weren’t used. In the end ten flags were used in the activity. How many flags were there in the classroom already?
What is 3 flags in the classroom?
100
A zoo keeper was sent a delivery of Kangaroos and Koalas from Australia to look after. There were at least three of each. Kangaroos have 2 legs. Koalas have 4 legs. There were 28 legs altogether. How many Kangaroos were there and how many Koalas?
What is 5 Koalas and 4 Kangaroos?
100
Use the clues to find the number. What is the number? a. The number has 3 digits and they are all different. b. The sum of the digits is 15. c. All the digits are odd and less than 9. d. The smallest digit is in the hundreds place and the largest digit is in the ones place.
What is 357?
100
Stacey and Gregg Doyle are twins. Whenever they have their picture taken, they stand beside each other. Their mum and dad also like to stand beside each other when they pose for pictures. How many different ways can all four Doyles stand in line to have their picture taken? (Hint: A picture of Stacey, Gregg, Mum and Dad is different from one of Gregg, Stacey, Mum and Dad.)
What is 8 different ways?
100
The following sequence of numbers was made by counting by 4s. 1, 5, 9, 13 .. What is the 30th number in the sequence?
What is 117?
200
Daniel has lots of pets. He has four more goldfish than he has turtles. He has one less canary than goldfish. Six of his pets are birds (canaries and parrots). He has two parrots. How many pets does Daniel have?
What is 12 pets?
200
Bam Bam, Pam and Tam are the names of Rose's pet bunny, poodle and turtle. The name of each pet and the kind of pet it is do not begin with the same letter. Bam Bam is not a turtle. What is the name of each animal?
Bam Bam poodle, Tam Bunny and Pam Turtle
200
Michael counted 46 legs on the birds and lions in Animal Country. The number of birds was 2 more than the number of lions. How many birds did Michael see in Animal Country? How many lions did he see? (Hint: Birds have 2 legs. Lions have 4 legs.)
What is 9 birds and 7 lions?
200
You want to hang 5 square pictures on the wall. All the pictures are the same size. You need to be able to see all the pictures. You must put one tack in each corner of every picture. One tack can be in the corner of more than one picture. What is the least number of tacks you can use?
What is 11 tacks?
200
The Newsy Comic Book Company published a new comic book. They sold 200 copies of the book in the first week after it was published. They sold 700 copies in the second week, 1700 copies in the third week, and 3200 copies in the fourth week. At this rate, how many copies will they sell in the eighth week?
What is 14 200 copies?
300
At the party Jade ate less than four jelly beans. Nicole ate twice as many jelly beans as Jade. Kahlee had twice as many as Nicole. Chris had two more than Kahlee. Chris ate ten jelly beans. How many jelly beans were eaten at the party?
What is 24 jelly beans?
300
Arrange the digits 1, 1, 2, 2, 3 and 3 to make a 6 digit number. In you number, the 1s should be separate by one digit, the 2s by two digits and the 3s by three digits.
312 132 or 231 213
300
Kenny has a set of dominoes. Each domino has 2 squares on its face. Each square is marked with 0, 1, 2, 3 or 4 dots. The faces of the dominoes in Kenny’s set are marked in every possible way. No two dominoes in the set look the same. How many dominoes are in Kenny’s set?
What is 15 dominoes?
300
Kate, Pete, Joan, Amos and Paul are the 5 finalists in the Main Street School Spelling Bee. Before the final round of the bee, each student must shake hands with every other student. What is the total number of handshakes?
What is 10 handshakes?
300
Ten friends came home from soccer camp with a lot to tell one another. Each one spoke on the phone with each of his or her friends. How many calls were made?
What is 45 calls?
400
When Ariella climbs aboard there are already some people sitting the bus. At the next bus stop an additional five people get on and two people get off. Two stops later seven people climb on board. All 15 people get off the bus at the ferry. How many were on the bus when Ariella climbed on?
What is 4 people on the bus?
400
Carmen bought five tickets to watch a game of footy with her friends. The tickets were numbered in order. When the numbers are added together, they total 110. What were the ticket numbers?
What is 20, 21, 22, 23, 34?
400
In their basketball final, the Sunnyvale Swifts scored 42 points and won by six points. Sunnyvale scored the same number of three-point goals, two-point goals and one-point goals. How many of each type of goal did Sunnyvale score?
What is 7 of each type of goal?
400
Kelsie has 18 coins. One sixth of the coins are twenty-cent coins, one third of the coins are ten-cent coins and one half of the coins are 5-cent coins. What is the value of Kelsie's coins?
What is $1.65 or 165c?
400
Carlos is starting Spanish Club at his school. He is the only member right now. Starting this month, Carlos plans for every member to find 2 new members each month. How many members will be in the club at the end of 6 months?
What is 729 members?
500
Four children were bouncing balls. Jeff’s ball bounced eight more times than Michael’s. Michael’s ball bounced half as many times as Olivia’s. Olivia’s bounced eight times. How many times did Jeff’s ball bounce?
What is 12 times?
500
Five cars are in a race. Their number plates are: 1733 5824 9762 6465 7525 - The car with the highest number finished last - When the digits in the numberplates of the cars that came first and second were added, they give the same total - The cars that came in second and third both have an odd number as the last digit - The cars that came in third and fifth both bear numbers that are multiples of five. Use these clues to work out how the racing cars placed in the race.
What is 5824, 7572, 6465, 1733, 9762?
500
How many numbers between 10 and 99 have two different digits?
What is 81?
500
Eight people were waiting in line to buy concert tickets. Richard was the first in line and Vikki was not last. The girls' numbers were all even. Gary was in front of Ronny and Naomi was between them. Suzy's number was a multiple of 3. Judy and John were also in line. List the eight people in order in line.
What is Richard, Vikki, Gary, Naomi, Ronny, Suzy, John, Judy?
500
If you start with 2 and count by 4s until you reach the number 202, you will have the following number sequence. 2, 6, 10, 14... 202 If 2 is the first number in the sequence, 6 is the second number and so on, what number in the sequence is 202?
What is the 51st number?
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