Mousematics for children ages 7-8

+ =8
А
Jane Kats
Ш
ЕМАТИ
от
Ж
КА
МЫ
А
Learning Math the Fun Way
Workbook of Logic Problems
For children ages 7-8
ц
ени Ка
2
FOREWORD
Mousematics – Learning Math the Fun Way is a series of workbooks for children four
to eight years of age. You are holding the first workbook in the series for children who
already attend school. It was designed for ages 7-8, and is great for children in first
and second grade in Russia (where children start school at 7), or for second and third
graders in the US.
Mousematics tasks are, first of all, not standard math problems and expand, not repeat,
the school math curriculum by adding fun, playful tasks. Even a wise and experienced
second grader will be surprised to learn many new things from this workbook: that a
problem can have more than one correct solutions; that it’s possible to draw a diagram
to represent a family with many children and arrange different animals into a table;
and also that delicious pizza, a hopping bird, a chess bishop, and even a beautiful
snowflake have something to do with mathematics.
Even though most tasks do not involve numbers over 20, many of them are truly
difficult to solve for lower elementary students, and sometimes even adults find it
hard to discover all the solutions. Why are we not afraid to include difficult tasks in
the workbook? First of all, we hope that an adult will attack them together with a
child. In order to learn to think on their own, children need to see an adult’s train of
thoughts. It’s important for children that adults don’t just give out hints based on their
experience, but really solve the problems together (“I also don’t see any identical bead
structures yet. Let’s try this… And what if we stretch them all out…”) Secondly, we
really want to dismiss the school stereotype that “difficult means boring”, which often
makes schoolchildren lose interest before even starting to solve a problem. This is why
our tasks are interesting, and you do not want to quit doing something interesting halfway. Thirdly, most often the difficulty of our problems is tied to very important skills
that, unfortunately, do not get enough attention in school.
What skills are they?
Understanding word problems (for example, the problem about names). In the
modern society, being able to quickly extract information from text and operate with
it is a vital skill. However, even we often need to re-read a phrase 5 times before we
correctly understand the relationship between all the details. And what if the problem
is read aloud, can we understand it just by hearing it?
Spatial perception. Have you ever seen tourists who have to turn a map around in
their hands in order to figure out where they need to go? This is a good illustration
of lack of special perception. This is why this workbook has many tasks that require
turning a shape around in your head, straightening out a piece of string, building a
cube out of its net, etc.
Interpreting graphic diagrams, tables, graphs. A child will need all this in the future,
but becoming acquainted with it right now, in a fun and playful form, will ensure that
these constructs will not seem complicated or boring later.
Vivid acquaintance with symmetry, coordinates, and topology.
Ability to find more than one solution for a problem.
3
Just like in the other workbooks of this series, we arrive at difficult problems gradually,
as a next step from similar, but simpler ones. If your child cannot solve a problem, try to
go back to a similar simpler one. It’s okay if some manipulations are hard to do mentally
at first. You can “hold” most of our tasks in your hands: you can cut cube nets out of
paper, fold and glue them; you can string bead structures; you can put half a figure
next to a mirror; you can play with chess pieces; you can set cards with names of boys
next to each other in height order; and, of course, you can move around the hands of
a clock or watch. If you play a bit like this to solve a problem, then you can try to solve
the next similar problem in your head.
We hope that children will enjoy solving interesting and difficult problems as they go
through the tasks of this workbook.
G
Tasks with higher difficulty
!
Tasks with multiple solutions
Find houses according to the chart
ROOF HOUSE WINDOW
4
Use the same color for houses built from the
same sets of blocks
The greedy crocodile chooses
the bigger portion
?
?
?
?
?
Write in the
correct sign
5
Follow the grid to continue the patterns
Write the answers to the questions
into the empty table cells
Is it domesticated? Does it eat meat?
Wolf
Dog
Deer
Tiger
Rooster
—
+
—
+
+
+
+
—
Lion, cat, boa constrictor, rabbit
6
Cross out the cells with the listed addresses
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
A B C D E F GH
A B C D E F G H
В1, С3, D4, E3, F7, G1, H5,
A6, B5, C7, G4, F4, G3, H6,
A5, C6, F1, C2, D3, G7, H4,
C4, C1, B6, C5, E4, F3, G2
A3, B2, C3, D8, E7, F6, G2
G5, H3, D6, E2, F3, D4, E5
B3, C2, D7, E3, D2, F2, G3
D3, E6, F5, D5
Which cell is each truck heading for?
12
21
13
31
18
7
Write the neighboring numbers in the empty
spots
7 8 9
12
9
19
14
22
11
17
21
28
19
14
30
16
24
20
27
23
Pick a graph to represent each word problem
AJO
Alice is older than Julie.
Julie is older than Olivia
JAO
Oak trees are thicker than
aspens and maples.
Maples are thicker than
aspens and poplars.
OJA
MAPO OAMP
OMPA AMOP OAPM OMAP
8
Move one stick to make the number problem
correct
Which side has more pizza?
Write in the correct sign
9
Connect pictures with the same number
of objects to the number
8
9
10
11
12
10
Write in the correct initial
Mike is taller than Donny, but shorter than Keith
Oliver is taller than Arthur. Arthur is taller than Jack
Billy is taller than Pete. Ted is taller than Billy
М
О
P
Dennis and Martin had the same number
of cars. Dennis gave 2 of his cars to Martin.
How many more cars does Martin now have
than Dennis does?
______________________________
Dena and Iris have 16 dolls together.
Dena has 6 dolls more than Iris.
How many doll does Iris have?
______________________________________________________
G
11
Continue the sequence of images
2
6
4
1
3
5
12
10
8
6
12
The same numbers put
on the same masks.
Which number is
wearing which mask?
+2=7
5
–1=8
–2=6
+ =4
+1=5
A snake is hiding under small rugs.
It has a round head and a triangular tail.
Draw in the head and the tail
13
! Divide chocolate bars into 2 parts
that are identical in shape and size
Find a few different
solutions
!
Move the residents into their correct houses
R
ED
ROUND
GRAY
SQUARE
14
Cross out the cells with the listed addresses
ABCDE
5
4
3
2
1
ABCDE
5
4
3
2
1
ABCDE
5
4
3
2
1
ABCDE
5
4
3
2
1
A3, B1, C5 D2, A2, B5 C1, D4, A4 D3
A4, D2, B5 C1, A2, D4 C5, B1, A3 A3, B5, D2
B3, D1, A1 D3, A4, C3 A2, D4, C5
C1, C4, B5 C3, D5, C2 C5
What word do the letters spell?
Finish the pictures and letters in all the mirrors
15
Draw an arrow pointing from the larger number
to the smaller
7+1
4+2
5+4
6+4
8
6
8+1
2+5
3+6
6+1
1+6
5+3
1+8
5+3
8+1
2+6
8+2
7+2
4+2
7+3
Maria’s strip looks like this: А
Circle it in red
Tim’s strip looks like this:
А
Circle it in green
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
16
Write in the initials (first letters) of each name
Ben has two sisters, Joy and Amy
Kate has a brother named Jim
Lizzy has twin brothers, Evan and Seth
Victor has a brother named Alex
George has twin sisters, Sophie and Ally
B J A
Here are the heads, middles, and tails of number
snakes. A snake cannot crawl through the colored
cells. Write in all the numbers in the correct order
1 2 3 4
5 6
7
4
1
1
4
7
7
9
5
9
9
1
5
1
1
5
17
Collect the right plates to put a whole pizza
together
G The girls encoded their names using different
codes. The same letters were replaced
with the same symbols
746
3628
1718
6116
1526
LORA
ALLA
MILA
LILY
IDA
3716
Connect the names with their encoded forms
18
Count and draw the arrows pointing
from the larger number to the smaller
10
13
1+7
3+6
9+2
3+7
4+9
11 5+6
6+6
3+7
5+7
7+7
2+8
4+7
1+9
7+4
9+4
7+9
4+5
9+2
Complete the drawings of snowflakes
19
Continue the sequence
1 3
5
36 9
7
20
Jane cut the ribbon in 6 places. How many pieces
of ribbon does Jane have now?
Emma sawed the log in 8 places. How many
pieces of wood does Emma have now?
Children took rides in the elevator.
Mark the children who always went up in red.
Mark the ones who always went down in green.
Mark the children who went up and down in orange.
Tommy 2–4–5–8–11
Liza
10–6–8–9–14
Anna
1–3–5–9–12
Molly
18–14–9–6–4
Ben
14–12–8–6–2
Rob
1–3–5–9–12–15
Jack
16–14–19–5–9–6
Ken
19–14–12–10–7
Jane
20–11–9–5–2
Mark
13–9–6–4–2
21
Color the square where the bird will end up
Connect each house to its diagram
22
Divide the objects equally among three people
The bishop moves only along diagonal lines.
Mark all the squares each bishop (B) can attack
4
3
2
1
B
4
3
2
1
A B C D
4B
3
2
1
A B C D
4
3
2
1
B
A B C D
4
3
2
1
B
A B C D
4
3
2
1
B
A B C D
B
A B C D
4
3
2
1
B
A B C D
4
3
2
1
B
A B C D
23
Find a diagram for
each word problem
BROTHER
SISTER
Emily has 2 sisters and 1 brother.
Bobby has 2 sisters.
Leo has 2 brothers and 1 sister.
Kate has 1 sister and 2 brothers.
Tony has 1 brother and 1 sister.
А
А
Anna has this figure:
Circle it in red
А
Danny has this figure:
Circle it in green
А
А
А
А
А
А
А
А
А
А
А
А
А
24
The boys have lined up in order, according to
their height. It turned out that Will is taller than
Tim, but shorter than Nick. Jake is taller than Al,
but he is not the tallest boy. There are two boys
who are shorter than Al.
Who is the tallest?
Who is the shortest?
Connect the clocks that are showing
the same time
08:00 07:40 16:00 20:00
18:00 05:00 00:00 04:00
G
25
Color the same birds the same way
Connect the plates that have the same amount
of pizza
26
Which of these chocolate bars can be divided
into two equal parts?
Circle the ones that cannot be divided
Divide each set of toys equally for two children
!
27
Jill connected a few beads with pieces of string
and drew a diagram of the structure she ended
up with. Find her bead structures
28
Divide whichever figures you can
into these trimino shapes:
!
9
Write the number of squares in each figure
Grandpa was building a fence.
He was nailing 2 boards between the columns
How many boards
will he need to nail
to 4 columns?
How many boards will
he need for a fence
with 6 columns?
How many boards will he need for a fence
with 11 columns?
G
29
G
Towers built from a set of blocks were
photographed from the front (F), left (L),
and above (A). Where are the photographs
of each of the towers?
A
F
L
A
A
F
F
L
A
F
A
L
A
F
F
L
A
L
F
A
F
L
L
L
30
Find this figure and circle it in green
Find this figure and circle it in red
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
А
Follow the arrows to read the words and mark
everything that flies in red and everything that
is alive in green
TORА PR
T I GL E P
OOT AMT
RH C T I SO
L ARENPA I
GEAE L
31
G
E
Everybody
in the Smith family has their father’s
name as their middle name. Nick’s father’s name
is Peter Matthew Smith. What is Nick’s younger
brother Jack’s full name?
Leo Alex Smith named his daughter after his
father. What is her full name?
Which square is the bishop (B) standing
on if it can attack the marked squares?
4
4
4
4
3
3
3
3
2
2
2
2
B
1
1
1
1
A B C D
A B C D
A B C D
A B C D
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
A B C D
A B C D
A B C D
A B C D
Which of these problems have 2 solutions?
32
Color the houses so that all the rules are followed
GREEN
WINDOW
BLUE
HOUSE
RED
ROOF
Each number put on its own mask. The same
numbers are wearing the same masks
+ = 12
+ + = 12
+ + + = 12
+ + 2 = 16
+ + 2 = 20
33
Continue the sequence
3
6
4
9
9
30
26
22
34
A snake hid under the rugs. Draw how it could
have been crawling, where its head and its tail are
Some letters were replaced with numbers, and
the code was used to write the words. Decode
the words, and color all the edible things red
7 5 8 1 8 5
P O T A T O
4 9 8 8 0 29
2 5 4 7 0 8 9 6
Key
8 53 185
4 9 8 8 9 6
1 2 3 4 5 6 7 8 9 0
A C M L O R P T E U
2 1 3 9 6 1
35
Pieces made out of 4 cells are called tetramino.
There are 5 types of tetramino pieces made
out of square cells:
Divide the figures into 2 identical tetramino
shapes in different ways
36
Ancient Greek numerals slightly resembled
Roman numerals. Try to figure out their system
for writing down numbers and find the answers
3
7
13
21
63
3
3
6
Cut a cake with flowers for two people so thatt
each one gets a piece of same size and shape,
and with the same number of flowers (you can
only cut along the borders of squares)
G
37
Mark the squares that the
chess knight (K) can attack
4
4
4
К
3 К
3
3
2
2
2
1
1
1
К
A B C D
A B C D
A B C D
4
3
2
1
4
3
2
1
К
A B C D
4К
3
2
К 1
A B C D
A B C D
4
3
2
1
К
A B C D
4
3
2
1
К
A B C D
Each number put on its own mask. The same
numbers are wearing the same masks
+
+
+
+ 1 = 15
=9
+
+ 2 = 14
8+
= 13
+ +
+2=8
+
+ 3 = 11
+
– 1 = 17
+
–
= 12
=2
38
Write down the addresses of the marked
squares
6
5
4
3
2
1
6
5
4
3
2
1
A B C D E F
A B C D E F
А6
Which has more? Write in the signs
39
The shooting gallery: who got the most points?
MIKE
0 1 5 10
15
JANE
0 1 5 10
15
JOHN
0 1 5 10
15
0+1+5+15 = 21
PETE
0 1 5 10
15
LIZA
0 1 5 10
15
Mary connected balls
with pieces of string:
Find identical bead structures
and circle them
TONY
0 1 5 10
15
40
Which square is the chess knight (K) standing
on if it can attack the marked squares?
What other squares can it attack?
К
Read the names by visiting the addresses
(entryway, floor)
3rd floor
2nd floor
1st floor
MA
TO
RI
TO
NA
TE
LY
AB
BY
DO
LE
KA
GA
DA
KY
1st entryway 2nd entryway 3rd entryway 4th entryway 5th entryway
TO-BY
(2,3) (3,1)
(1,3) (1,1) (2,2)
(3,3) (4,2)
(5,3) (4,2)
(4,1) (1,1) (2,2)
(3,2) (3,1)
(1,3) (2,1)
(1,2) (2,1)
(5,2) (4,2)
(5,1) (4,2)
41
Games in the 100 table
1
2
3
4
11 12
5
6
9
15 16 17 18
10
20
21 22 23 24
31
33 34 35 36
42
45
51 52 53 54
63
71
91
47
56
65
74
82 83
38
50
58
67
60
69
77
85 86
94
80
88 89
97
Fill in the empty cells of the table.
Fill the cells holding numbers that are made up of two
identical digits with red.
Use blue to fill the cells holding numbers whose digits
sum up to 3, 6, 9, 12, 15, or 18 (for example, the digits
of 18 add up to 9: 1+ 8 = 9).
Circle the numbers that have both digits that are even.
42
Snakes and turtles hatched from 8 eggs.
The total number of their legs is 12.
How many snakes were there?
Ducks and turtles hatched from 9 eggs.
The total number of their legs is 24.
How many of them are ducks?
Platypuses and ostriches hatched from 7 eggs.
The total number of their legs is 20.
How many of them are platypuses?
How can you cut a cake with flowers for two
people so that each one gets a piece of same
size and shape, and with the same number
of flowers?
G
43
Connect each balloon with the number ray
9 6 21 12 17 14 41 32 45 23 54
0
5
10
15
20
25
30
35
40
45
50
55
60
Find the numbers of buses and trucks
on the number ray
55
31
50
53
45
40
35
43
35
15
30
25
34
51
19
20
15
29
8
10
5
0
17
13
44
Color the number problems that are right
Correct the wrong ones by moving one stick
Connect the little monsters to their descriptions
s
LEGS
HEADS
ARMS
6
2
5
5
3
5
3
3
6
3
2
6
!
45
Continue the patterns on the scarves
Draw the same pattern
on scarves that are the same color
46
G
Write in the numbers so that
the arrows point from larger
numbers to smaller ones
15
17
21
62
28
21
10
25
28
12
45
25
41
33
25
13
18
21
Connect pictures with diagrams
9>6
6>5
9>8
9>7
8>7
7>5
7<8
5<7
5<6
6<7
6<9
8<9
47
In ancient Babylon, the number of objects was
recorded by pressing wedge-shaped marks into
clay tablets. This form of writing is called cuneiform
2
3
4
7
5
6
Tens were written by turning the wedge sideways
Write the following numbers down in cuneiform:
10
12
20
Fill in all the blanks
11
26
13
34
15
41
48
G
Find the nets for this cube
КМN Т
И
I
АМ
N
А
N Т
К
N А ТМ
I
А
I N Т К
М
А
NТ
М
I КN Т
А
К
Т
А
I
МК
The same numbers were replaced with the same
letters. Solve the following puzzles:
АА + АА = ZZ
ZZ + ZZ = BB
BB + BB = CC
B+А=Z+D
C + C = АS
D+D+D=V
DD + ZZ = ММ
М+Z+A=C
S + S = AZ
Z+A=D
Write what the following are equal to:
AZ + AZ =
DA + DA =
SS + DD =
ММ – AA =
49
The shooting gallery: who got the most points?
MARY
0 5 10 15
20
SETH
0 5 10 15
20
ALEX
0 5 10 15
20
10 + 5 + 20 = 35
BILL
0 5 10 15
20
JILL
0 5 10 15
20
ANNE
0 5 10 15
20
Circle the monsters that have more than 1 head, not
more than 6 arms, and less than 7 legs in blue
Circle the monsters that have more than 4 arms,
less than 3 heads, and more than 5 legs in red
50
Jane had the following shapes:
She thought that any figure that is
made up of 9 or 12 squares can be divided
into these shapes
Check – is that true?
Write the number of squares into each figure.
Color only the rectangles
8
G
51
Rick connected balls with pieces of string.
Color the ball in the right photographs
52
There are cookies and cake slices arranged on the
counter in 9 rows, with 10 items per row. There is a
total of 70 cookies. There are only 10 slices of ginger
cake. There is a total of 60 honey cookies and cakes.
HONEY
GINGER
TOTAL
COOKIES
CAKE SLICES
TOTAL
How many honey cookies are on the counter?
Fill out the table
Here are the heads, middles, and tails of number
snakes. A snake cannot crawl through the
colored cells. Write in all the numbers
1 11 10
9
2
8
3
4 5 6 7
11
6
1
6
11
1
13
13
1
13
7
1
7
7
1
53
Here are some Chinese numbers and number
problems. Try to figure out what each number
character means (all numbers are under 10)
6
54
Fill in the blanks so that the set of words on the
left is the same as on the right
MOTOR
MODEL
O
O
D E
RETRO
RADIO
M E
M
R
RODEO
R O
METRO
T O
ROBOT
R
O
METER
T O
POTATO
A
O
TOMATO
Towers built from a set of blocks
were photographed from the front,
left, and above
A
A
L
A
G
L
F
A
L
F
A
L
F
A
L
F
L
F
A
L
F
A
L
F
A
L
F
F
Connect the block towers with their photographs
55
Pythagorean table
1
2
3
2
4
6
6
9 12
4
4
7
10 12
8
5
6
9
16
11
20
24
18
20
15
35
12
7
28
77
8
80
9 18
45
60
22
12
In the first row, each number is 1 more than the previous
one. In the second row, it is 2 more. In the third one –
3 more. And so on.
Fill in all the blanks in the table.
Color all the 12s red.
Color all the 24s blue.
Color all the 36s green.
Circle the numbers with the sum of digits equal to 9 and 18.
56
Divide the chocolate bars for twins
Rugs were sewn from rectangular scraps of fabric.
Each of them has a number (which stands for the
number of squares in the scrap). Color the scraps
4
5
2
3
4
5
3
2
6
9
3
2
6
3
6
6
10
2
6
8
8
3
3
6
2
4
1
8
57
Jim connected a few beads with pieces of string
G and drew a diagram of the structure he ended
up with. Find the bead in the correct diagram
and color it red
Find identical bead structures and color them
the same
58
Jim is 3 years older than Mike.
Mike is 4 years younger than Ben.
Who is older, Ben or Jim? How much older?
Julie is 2 years younger than Olivia.
Anna is 5 years older than Julie.
How old is Olivia if Anna is 8?
This is Jim’s watch.
It is 5 minutes
behind
13:50
02:10
11:05 02:00 01:05 23:15
14:00 14:15 13:45 03:10
Find and circle Samantha’s watch,
which is 15 minutes ahead
G
G
59
Vera has enciphered different words using
two different codes. Find each word
METER
62379
METRO
94874
COMET
17379
CATER
14349
MOTOR
17394
RODEO
64173
Encipher the following words
ARMOR
CRATER
89721
60
Color the teapots so that all the rules are followed
BLUE
TEAPOT
RED
SPOUT
GREEN
LID
Find the nets for this cube
А
А
ЕТ
А
I Е Т К
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61
Each branch has leaves of the same color
3
5
Color 11 leaves yellow.
Color 18 leaves red.
Color 16 leaves orange.
Mugs and plates are set out on the counter
in 10 rows of 5 items per row. There are only
5 white plates. There are 10 green mugs.
There is a total of 30 plates of all kinds.
WHITE
GREEN
TOTAL
PLATES
MUGS
TOTAL
How many green pieces of dinnerware are
on the counter? Fill out the table
62
It costs 1 dollar to cross any bridge. A traveler
spent a total of 11 dollars on bridges. Where
did he end up, in the city or in the field?
TOWN
FIELD
Divide chocolate bars into rectangular pieces.
The number stands for the number
of squares in each piece
4
4
4
6
6
4
3
8
2
8
8
4
8
10
4
5
6
4
5
4
3
8
6
6
12
6
9
4
6
8
63
Connect each ball to a spot on the number line
2
19
7
17
48
11
0
5
10
15
20
25
30
35
41
33
59
52
56
40
45
50
55
60
On your way to the center of the labyrinth,
collect the exact sum that is drawn in the center
4
3
3
5
4
7
13
5
3
12
2
1
4
2
2
6
3
4
1
7
3
14
1
3
3
4
5
4
5
10
5
3
2
6
11 4
2
1
2
5
2
Jane Kats
MOUSEMATICS - Learning Math the Fun Way. Workbook of Logic Problems for children
ages 7-8
2nd edition
Jane Kats
MOUSEMATICS
Workbook of logic problems for children ages 7-8
Art by Jane Kats and Olga Lehtonen, cover by Olga Lehtonen