Problem Solving
1) Treasure is hidden under one of these numbered stones. Use the map and the clues below to find the correct stone where the treasure is. Colour this stone.
Clue 1 : The number is in this number pattern.
2 , 4 , 6 , 8 , 10 , . . .
Clue 2 : The number is between 15 and 18.
here they have given two clues.
Clue 1 : Number pattern ( increasing , twos )
2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20
Clue 2 : The number is between 15 and 18.
that is 16 , 17
16 is the common number present in both Clue 1 and Clue 2
Hence Treasure is hidden Under 16.
2) Find Rita's and Tom's Number.
Rita : I have a number. It is 2 more than Ari's number and smaller than Mini's number. The number is in this number pattern.
Start with 19. Count back in twos.
Min : My number is 15.
Ari : My number is smaller than Min's number. It is a two digit number.
Tom : I have a number. It is 2 less than Ari's number. It is a single digit number.
its given that Min's number = 15
Ari's number is smaller than Min's number also its a two digit number
smaller than min's number also two digit number = 14 , 13 , 12 , 11 , 10
( 9,8,7,... are all smaller than 15 but they are all single digit (one digit) number)
So Ari's number be any one of these 14 , 13 , 12 , 11 , 10
Tom's number be 2 less than Ari's number. It is a single digit number.
2 less than Ari's number = 12 , 11 , 10 , 9 , 8
2 less than Ari's number & It is a single digit number = 9 , 8
So Tom's number be 9 , 8
Rita's number be in this number pattern. Start with 19. Count back in twos.
that is 19 , 17 , 15 , 13 , 11 , 9 , 7 , 5 , 3 , 1
Also It is 2 more than Ari's number = 16 , 15 , 14 , 13 , 12
also,
smaller than Mini's number = 14 , 13 , 12 , 11 , 10 , 9 , 8 , 7 , 6 , 5 , 4 , 3 , 2 , 1
from the above three clues, 13 is common in all the clues
hence Rita's number be 13
Further practice
1) Circle the group with the greater number of things.
By seeing the picture kids can easily find out the greater number of groups.
lets teach them how to check it out.
first count and write the number of circles in each group
we have 9 circles in one group and 7 circles in another group.
In counting number , 7 comes first then 9 comes.
(counting number always be in increasing order)
Hence a group which has 9 circles is the greater number of circles.
2) Which number is bigger?
a) 11 or 5
Counting number, 5 comes first then 11 comes.
Hence 11 is the bigger number.
b) 19 or 16
Counting number, 16 comes first then 19 comes.
Hence 19 is the bigger number.
3) Look at the box of pencils.
Can 18 children each have a pencil?
Write YES or NO. Explain Why?
1 Child ---- 1 pencil
2 Children ---- 2 pencils
3 Children ---- 3 pencils
18 Children ---- 18 pencils
( if we have 18 children atleast we need 18 pencils )
We have 18 Children, if each children can have 1 pencil we need 18 pencils.
In our Pencil box we have 20 pencils
20 Pencils > 18 children
which means 18 children can have 1 pencil and 2 pencils left.
Yes 18 children each can have a pencil.
Number of pencils is greater than the number of children.
4) look at this number track.
10 11 12 13 14 15 16 17 18 19 20
Write a number that is smaller than 16 but greater than 13
Method 1
first lets mark smaller than 16 (which means counting order-backwards from 16)
10 11 12 13 14 15 16 17 18 19 20
now lets mark greater than 13
10 11 12 13 14 15 16 17 18 19 20
now,
10 11 12 13 14 15 16 17 18 19 20
10 11 12 13 14 15 16 17 18 19 20
14 and 15 are common in both
hence 14 and 15 are the numbers that are smaller than 16 but greater than 13
Method 2
Smaller than 16 : 15 14 13 12 11 10
Greater than 13 : 14 15 16 17 18 19 20
now we have to check the common numbers present in both
Smaller than 16 : 15 14 13 12 11 10
Greater than 13 : 14 15 16 17 18 19 20
hence 14 and 15 are the numbers that are smaller than 16 but greater than 13
Method 3
Smaller than 16 but greater than 13
we have to list the numbers greater than 16 and stops before 13 (because Smaller than 16 but greater than 13)
15,14
hence 14 and 15 are the numbers that are smaller than 16 but greater than 13
5) Count the number of fruit.
Strawberries : 16
Oranges : 20
Pears : 17
Fill in the blanks with strawberries, oranges or pears.
a) The number of __________ is the greatest
lets take the numbers alone
16,20 and 17
here 20 is the biggest number since it comes last in counting numbers
Oranges - 20
hence The number of Oranges (20) is the greatest
b) The number of ___________ is the smallest
lets take the numbers alone
16,20 and 17
here 16 is the smallest number since it comes first in counting numbers
Strawberries - 16
hence The number of Strawberries (16) is the smallest
6) Fill in the missing numbers.
a) 1 less than 9 is 8 (given 1 less than, so we have to go one step backward )
b) 2 more than 11 is 13 ( given 2 more than, so we have to go two steps ahead )
c) 12 is 2 less than 14 ( given 2 less than, so we have to go two steps backward from 14 )
d) 19 is 1 more than 18 ( given 1 more than, so we have to go one step
ahead from 18 )
e) 22 is 10 more than 12 (22 is greater than 12 so its more and from 22 to reach 12 , it takes ten steps)
f) 6 is 10 less than 16 (6 is smaller than 16 so its less and from 6 to reach 16, it takes ten steps)
7) There are 19 cherries in a basket. Rita puts 1 more cherry into the basket. How many cherries are there in the basket now?
19 cherries are there. Rita puts one more candy to that.
ONE MORE which means leave a finger and count ahead
that is 20.
hence there are 20 cherries now
8) a) Write a number between 6 and 12
To find the between numbers,
in counting order, start next to 6 and stops before 12
so, 7 , 8 , 9 , 10 , 11 are the numbers between 6 and 12
7 is one of a number between 6 and 12
b) Write a number between 11 and 19
To find the between numbers,
in counting order, start next to 11 and stops before 19
so, 12 , 13 , 14 , 15 , 16 , 17 , 18 are the numbers between 11 and 19
14 is one of a number between 11 and 19
9) Tom, Rita and Ari play a computer game.
Tom : My score is 17 points
Rita : My Score is 2 less than Ari's
Ari : My score is one more than Tom's
Write the scores in order.
Begin with the largest ______ , _____ , ______
we know Tom's score = 17 points
To find Rita's Score we need to find Ari's score first.
Ari's score is one more than Tom's
that is move ahead one step from 17(Tom's score)
Ari's score = 18
Rita's score is 2 less than Ari's
that is move backward two steps from 18 (Ari's score)
Rita score = 16
17,18,16 are the score of Tom , Ari , Rita
Lets write in order (with biggest)
18 , 17 , 16
10) Look at this pattern.
Draw what comes next and write the number.
first they have given 8 circles.
if we cancel out 2 circles we will get the next pattern 6
similarly if we cancel out 2 circles again we will get the next pattern 4
to get the next pattern we have to cancel out 2 more circles which gives 2
11) Write the missing numbers in these patterns.
a) 15 , 16 , 17 , 18 , 19 , 20 ( 1 more , count ahead )
b) 9 , 11 , 13 , 15 , 17 , 19 ( 2 more , count ahead )
c) 10 , 8 , 6 , 4 , 2 , 0 ( 2 less , count back )
d) 10 , 9 , 8 , 7 , 6 , 5 ( 1 less , count back )
12) Tom has some stickers.
The number of stickers is between 13 and 18.
What is the greatest number of stickers that Tom can have?
First we have to find the numbers between 13 and 18
lets list numbers from 13 to 18
13 14 15 16 17 18
numbers between 13 and 18 = 14 , 15 , 16 , 17
here the greatest number is 17
hence Tom can have 17 number of stickers
13) Put these numbers in order. Begin with the smallest.
17 , 0 , 8 , 2 , 11 , 9
Counting number order which goes like 1,2,3,4,5...
here we have 0. 0 which means nothing.
with 0 if we add 1 more we will get 1.
So 0 comes before 1 that is,
0,1,2,3,4,5...
now lets write with the smallest
0 , 2 , 8 , 9 , 11 , 17
Question 1
Look at the patterns shown below. Then fill in the blanks.
This number pattern starts with _________
To find the next number in this pattern, we count on in ___________
In the above picture the pattern starts with 2
- first we have to check whether the patterns gets increases or decreases.
- Next we have to find the common interval.
here, the patterns gets INCREASES
And the patterns gets increases by 1. that is to get the next pattern we have to add one more circle.
2,3,4,5 with 5 if we add one more circle we will get 6
with 6 if we add one more circle we will get 7 and goes on
so the patterns goes by 2,3,4,5,6,7...
Hence to find the next number in this pattern, we count on in ones
This number patterns starts with __________
To find the next number in this pattern, we count _________ in _________
In the above picture, the pattern starts with 8
here, the patterns gets decreasing.
to get the next pattern we have to cross out two circles
from 8 circles if we cross out 2 circles, we will get 6
from 6 circles if we cross out 2 circles we will get 4
similarly to get the next pattern we have to cross out 2 circles from 4
so we will get 2
hence the patterns be 8,6,4,2...
To find the next number in this pattern, we count back in twos
Question 2
Look at these patterns
Draw what comes next and write the number.
In the above pic, the pattern gets increasing
in each row, the pattern gets increases by 2. that is we have to add 2 more 'x' to get the next pattern
the pattern starts with 2.
with this if we add 2 more 'x' we will get 4
add 2 more with 4 to get next pattern which is 6
add 2 more with 6 to get next pattern which is 8
add 2 more with 8 to get the next pattern which is 10
In the above pic, the pattern gets decreasing
in each row, the pattern gets decreases by 1. that is we have to cancel out 1 circle to get the next pattern
the pattern starts with 8.
with this if we cancel out 1 circle, we will get 7
cancel out 1 circle to get the next pattern, we will get 6
with this cancel out 1 circle to get the next pattern, we will get 5
with this cancel out 1 circle to get the next pattern, we will get 4
Question 3
Look at the number patterns. Then fill in the blanks.
a) 1 , 11 , _____ , 31 , 41 , 51
This number patterns starts with __________
To find the next number in this pattern, we count _________ in _________
here, the numbers gets increasing
first given number is 1, to reach the next number 11 we have to count on in 10's.
so from 11 if we count on in 10's we will get 21.
hence the pattern goes like 1 , 11 , 21 , 31 , 41 , 51
This number patterns starts with 1
To find the next number in this pattern, we count ON in 10's
b) 50 , 40 , ____ , 20 , _____ , _____
This number patterns starts with __________
To find the next number in this pattern, we count _________ in _________
here, the numbers gets decreasing
first given number is 50, to reach the next number 40 we have to count back in 10's.
so from 40 if we count back in 10's we will get 30.
from 30, if we count back in 10's we will get 20(given)
from 20, if we count back in 10's we will get 10
from 10, if we count back in 10's we will get 0
hence the pattern goes like 50 , 40 , 30 , 20 , 10 , 0
This number patterns starts with 50
To find the next number in this pattern, we count back in 10's
c) 23 , ____ , 43 , _____ , 63 , 73
This number patterns starts with __________
To find the next number in this pattern, we count _________ in _________
here, the numbers gets increasing
given, first number = 23
we have to find the next number.
also given third number = 43
5th and 6th number = 63 and 73 respectively.
with the last 2 numbers, to reach 73 from 63 we count on in 10's.
so from 23 if we count on in 10's we will get 33
from 33 if we count on in 10's we will get 43(given)
from 43 if we count on in 10's we will get 53
hence the pattern goes like 23 , 33 , 43 , 53 , 63 , 73
This number patterns starts with 23
To find the next number in this pattern, we count ON in 10's
Question 4
Ari describes his number pattern.
"I Start with 14
Then I count on in twos"
Write the first four numbers in this number pattern.
Since Ari described that his pattern starts with 14
The first number be 14
Also Ari said that he count ON in TWOS
which means the numbers gets increasing that is we have to move ahead two steps
Hence the pattern be 14 , 16 , 18 , 20
Question 5
Rita describes her number pattern.
"I Start with 11
Then I count back in ones"
Write the first four numbers in this number pattern.
Since Rita described that her pattern starts with 11
The first number be 11
Also Rita said that she count back in ONES
which means the numbers gets decreasing that is we have to move one step back.
Hence the pattern be 11 , 10 , 9 , 8
Question 6
a) 7 , 8 , 9 , 10 , 11 (increases,Ones)
b) 10 ,12 , 14 , 16 , 18 (increases,twos)
c) 19 , 18 , 17 , 16 , 15 (decreases,ones)
d) 9 , 7 , 5 , 3 , 1 (decreases,twos)
e) 11 , 12 , 13 , 14 , 15 , 16 (increases,Ones)
f) 40 , 30 , 20 , 10 , 0 (decreases,tens)
Question 1
Susie has 12 hair clips.
Jane has 15 hair clips.
Mary has 9 hair clips.
a) Who has the greatest number of hair clips?
first lets take numbers alone 12,15,9
Numbers 1,2,3,4... which means the number gets increasing(bigger).
that is any number which comes first is smaller.
here among 12,15,9
9 comes first in order then 12 then 15.
15 comes last , so 15 is the greatest number.
Hence Jane has greatest number of hair clips = 15
b) Who has the smallest number of hair clips?
from a) we know that 9 is the smallest number.
Hence Mary has the smallest number of hair clips = 9
Another Method
9 is the smallest number and 15 is the greatest number.
Question 2
Put these numbers in order. Begin with the smallest.
a) 20,18,8
since they are asking to begin with smallest, we have to write the number which comes first.
among 20,18,8
8 comes first
remaining 20,18
18 comes first
now remaining 20
20 comes last
hence 8,18,20 be the order
b) 10,17,12
since they are asking to begin with smallest, we have to write the number which comes first.
among 10,17,12
10 comes first
remaining 17,12
12 comes first
now remaining 17
17 comes last
hence 10,12,17 be the order
Question 3
Put these numbers in order. Begin with the largest.
a) 6 , 10 , 16
First let we write the given numbers in counting order.
6 comes first then 10 then 16.
6 , 10 , 16
the counting order be always smaller to bigger
the last number be the biggest number 16
now 6,10 remains
here the last number be 10 which is the next biggest
and 6 remains which comes at the last
hence the order be 16 , 10 , 6
b) 15 , 13 , 19
First let we write the given numbers in counting order.
13 comes first then 15 then 19.
13 , 15 , 19
the counting order be always smaller to bigger
the last number be the biggest number 19
now 13,15 remains
here the last number be 15 which is the next biggest
and 13 remains which comes at the last
hence the order be 19 , 15 , 13
Question 4
Write a number between
a) 9 and 15
Method 1
using number line we can easily find out the between numbers.
10,11,12,13,14 are the numbers between 9 and 15
Method 2
to write the numbers between 9 and 15
just write the counting numbers from 9 to 15
9 , 10 , 11 , 12 , 13 ,14 , 15
here between 9 and 15 we are having numbers 10 , 11 , 12 , 13 , 14
b) 16 and 20
just write the counting numbers from 16 to 20
16 , 17 , 18 , 19 , 20
here between 16 and 20 we are having numbers 17 , 18 , 19
Question 5
Look at the table shown below
a) Who has the greatest number of books?
let we consider the numbers 12,1,20,19
write these numbers in counting order
1 , 12 ,19 , 20
20 comes last. So 20 is the greatest number
now let we check who is having 20 books
Hence MIN has the greatest number of books = 20
b) Who has the Smallest number of books?
counting order be
1 , 12 , 19 , 20
1 comes in first. so 1 is the smallest number
now let we check who is having 1 book
Hence SMARTY has the Smallest number of books = 1
