Math for Smart Kids Book 1: Multiplication & Division By Mor Harchol-Balter, Ph.D. Copyright March...

Math for Smart Kids

Book 1: Multiplication & Division

By Mor Harchol-Balter, Ph.D.

Copyright March 2003

Stars in my skyMy sky is filled with stars.

There are 4 rows, each with 10 stars. The total number of stars is therefore 4 x 10.

There are 10 columns, each with 4 stars. The total number of stars is therefore 10 x 4.

How many stars are there? ___________

Flowers in my gardenMy garden is filled with flowers:

There are ______ rows, each with _______ flowers. The total number of flowers is therefore _____ x _____.

There are ______ columns, each with _______ flowers. The total number of flowers is therefore ______ x _____.

How many flowers are there? ___________

If there are 3 kids in my class (including me) they can each have ______ cars,which is the same thing as _______ rows. We write this as: 18 / 3 = 6.

If there are 6 kids in my class (including me) they can each have _____ cars,which is the same thing as _______ columns. We write this as: 18 / 6 = 3.

If there are 2 kids in my class (including me) they can each have _____ cars,which is the same thing as _______ columns. We write this as: ___ / ___ = ___.

If there are 9 kids in my class (including me) they can each have _____ cars.We write this as: ___ / ___ = ___.

Sharing race carsI have 18 toy race cars which I want to share:

Tic-tac-toe for smartysPlay these games: Player 1 uses X’s. Player 2 uses O’s. Players alternate turns. On a turn, a player places his marker in one of the empty boxes. The goal is to get 3 of your markersin a row (row may be horizontal, vertical, or diagonal). In later games the goal is 4 in a row.

3-in-a-row wins

Number squares = ____ x ____ = _____

3-in-a-row wins

Number squares = ____ x ____ = _____

4-in-a-row wins

Number squares = ____ x ____ = _____

4-in-a-row wins

Number squares = ____ x ____ = _____

Flowers in my gardenMy garden is filled with flowers and some bees:

How many flowers do you seein the above garden? ______

How many flowers do you seein the above garden? ______

How many flowers do you see in the garden to the left? ______

Flowers in my gardenWrite the answers as a multiplication followed by a subtraction:

How many flowers do you seein the above garden? ____ x ____ - _____ = ____

How many flowers do you see in the garden to the left?_____ x _____ - _____ = ____

How many flowers do you seein the above garden? ____ x ____ - _____ = ____

24 / 4 = _______

Division = Sharing

24 / 2 = _______

24 / 3 = _______

24 / 6 = _______

24 / 12 = _______

24 / 8 = _______

48 / 3 = _______

Factoring a chocolate barI have 24 squares of chocolate. There are so manypossible chocolate bars ...

Number squares = ___ x ____




How many rectangular chocolate bars can I make with 24 squares, where the number of rows is smaller than the number of columns? _______________Suppose the number of rows doesn’t have to be smaller than the number of columns, now how many rectangular chocolate bars can I make? ___________

Factoring a chocolate bar

Number squares = ___ x ___



I have 20 squares of chocolate. How many rectangular chocolate bars can I make where the number of rows is no larger than the number of columns? _______________

I have 16 squares of chocolate. How many rectangular chocolate bars can I make using 16 squares, where the number of rows is no larger than the number of columns? _______________ Draw these chocolate bars below:

Prime chocolate barsA number is called prime if there is only one way to make a chocolate bar out of that number of squares (assuming numberof rows is no larger than the number of columns).

The number 13 is prime. Here’s the only rectangular chocolate bar with 13 squares:

Circle those numbers below which are prime numbers:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Theorems and FallaciesA theorem is a statement that is always true.A fallacy is a statement which may be true sometimes, but is alsosometimes false. Circle the THEOREMS on this page.

A chocolate bar with2 rows, can always beredrawn as a chocolatebar with 4 rows.


Any number which is divisible by 2 (with no remainder) is also divisible by 4.

Any number which isdivisible by 4 (with noremainder) is also divisible by 2.

2-piece outfits

I have 4 shirts in my closet:

I have 3 pairs of shorts in my closet:

How many different outfits can I wear? _________

Suppose I had only 2 shirts in my closet, but still 3 pairs of shorts.How many different outfits can I wear? _________

Suppose I have 8 shirts in my closet, and 3 pairs of shorts.How many different outfits can I wear? _________

3-piece outfits

I have 4 shirts in my closet:

I have 3 pairs of shorts in my closet:

How many different outfits can I wear? _______________

I have 2 hats in my closet:

Secret Function 1I have a secret coding box. When you give it a number on the left, it transforms the number into a new number on the right. Can you figure out what my coding box is doing?Look at the first 3 examples to figure out my secret transforming function.

Secretfunction3 15

Secretfunction5 25

Secretfunction2 10

Secretfunction10 15

Secretfunction

3 20

Secretfunction 303

Fill inthe blanks!

Fill inthe blanks!

Secret Function 2OK, so that was too easy for a smartypants like you. Try this one!

Secretfunction3 14

Secretfunction5 22

Secretfunction2 10

Secretfunction10 15

Secretfunction

3 18

Secretfunction 303

Fill inthe blanks!

Fill inthe blanks!

Secret Function 3This secret function takes 2 inputs and returns one output.

Fill inthe blanks!

Fill inthe blanks!

Secretfunction

124

3

Secretfunction

40 104

Secretfunction

126

2

15Secretfunction

60

3

Secretfunction 4

2

Secretfunction

102

15

15

Secret Function 4This secret function takes 2 inputs and returns one output.

Fill inthe blanks!

Fill inthe blanks!

Secretfunction

125

3

Secretfunction

40 114

Secretfunction

126

3

15Secretfunction

60

3

Secretfunction 4

2

Secretfunction

106

15

15

The poison game -- level 1Rules: You need 2 players. Youngest player chooses who goes first. Players alternate turns. On each turn, a player is allowed to eat 1 cookie. Player who eats the poison loses.

Game1:

Game2:

Game3:

Game4:

The poison game -- level 2Rules: You need 2 players. Youngest player chooses who goes first. Players alternate turns. On each turn, a player is allowed to eat 1 or 2 cookies (player decides how many cookies to eat). Player who eats the poison loses.

Game1:

Game2:

Game3:

Game4:

The poison game -- level 3 Rules: You need 2 players. Youngest player chooses who goes first. Players alternate turns. On each turn, a player is allowed to eat 1 or 2 or 3 cookies (player decides how many cookies to eat). Player who eats the poison loses.

Game1:

Game2:

Game3:

Game4:

Building with blocks

How many blocks are in a tower of height 2? ________

I love to build with blocks. To make a stable tower, you want to makesure that each block is supported by 2 blocks underneath, one on each side.





A tower of height 100 will have how many more blocks thana tower of height 99? __________

My allowance

In 1 week, my allowance will be 2 cents.In 2 weeks, my allowance will be 4 cents.In 3 weeks, my allowance will be _________ cents.In 4 weeks, my allowance will be _________ cents.In 5 weeks, my allowance will be _________ cents.In 6 weeks, my allowance will be _________ cents.In 7 weeks, my allowance will be _________ cents.

I made a deal with my parents. My allowance is only 1 cent this week,but every week my allowance doubles.

In how many weeks will my allowance be over $10? ______________

In how many weeks will my allowance be over $100? _____________

Cool, more than a

buck a week already!

Growing younger?

My mom is growing old. She’s already 35 years old, and I’m only 5. That makes her 7 times my age!

5 years from now, my momwill be 40, and I will be 10. My mom will be how manytimes my age? __________

10 years from now, my mom will behow many times my age? ________

25 years from now, my mom will behow many times my age? ________

Martian countingHere on Earth we have 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 We make all our numbers out of these 10 digits.Mars is so far away that they only got to hear about the first 6 digits: 0, 1, 2, 3, 4, 5. Martians need to make all their numbers out of these 6 digits.

1 flower

2 flowers

3 flowers

4 flowers

5 flowers

10 flowers

11 flowers

12 flowers

13 flowers

Try counting up to 100 in Martian... How long does it take you? (Remember there’s no 6, 7, ...)

Earthlings versus MartiansI see

11 flowersI see

15 flowers

I see12 flowers

I see20 flowers

I see____ flowers

I see30 flowers

I see____ flowers

I see_____flowers

Secret Function 5What’s this secret function doing?

Secretfunction6 10

Secretfunction24 40

Secretfunction25 41

Secretfunction30 15

Secretfunction

3 30Fill in

the blanks!

Fill inthe blanks!

Secretfunction36 15

What is a square?A square is a type of rectangle whose sides have the same length.Sounds easy, huh? Cut out these 4 shapes and fit them together to make a square.

What is a square number?A number N is called a perfect square if one can arrange N chocolate squaresinto a square shape.

For example, the number 16 is a perfect square, because16 chocolate pieces can bearranged in a square.

The number 20 is not a perfect square,because 20 chocolate pieces can not bearranged into a square. This is as close as you get:

The numbers: 1, 4, 9, 16, 25 are all perfect squares. What are the next couple perfect squares? ______, _____

Instant LawnMy dad spends a lot of time talking about our neighbor’s lawn. Our neighbor’s lawn grew out of a truck. The truck driver brought in 70 squares of grass. Each squareof grass measured one yard on each side (that’s called a square yard).

The driver arranged all the squares into a huge 7 x 10 rectangle. The areais the space the lawn takes up -- that’s 70 square yards. My dad says theperimeter of the lawn is the number of yards of fence our neighbor needsto buy to surround his beautiful lawn.

The perimeter of our neighbor’s lawn is __________ yards. The area our neighbor’s lawn is __________ square yards.

1 yard long

1 y

ard

wid

e

1 square yard

Instant LawnThe perimeter of thislawn is __________ yards. The area this lawn is _______ square yards.

The perimeter of thislawn is __________ yards. The area this lawn is _______ square yards.

Hint: Think aboutmultiple rectangles

Notice how the perimeter number seems to always be less than the area number?Is this always true, or are there some lawns for which the perimeter numberis greater than the area number? ____________________________________

Multiplying in the big leagues

What’s 7 x 13?

7 x 10 = 70 7 x 3 = 21

TOTAL = 91

7 x 13 =

Multiplying in the big leagues

What’s 6 x 14?

___ x ___ = ___

TOTAL = _____

6 x 14 =

___ x ___ = ___

ANSWERS

Stars in my skyMy sky is filled with stars.

There are 4 rows, each with 10 stars. The total number of stars is thus 4 x 10.

There are 10 columns, each with 4 stars. The total number of stars is thus 10 x 4.

How many stars are there? 40

I f there are 3 kids, each gets 6 cars, which equals 1 row.

I f there are 6 kids, each gets 3 cars, which equals 1column.

I f there are 2 kids, each gets 9 cars, which equals 3columns. 18 / 2 = 9.

I f there are 9 kids, each gets 2 cars. 18 / 9 = 2.

Sharing race carsI have 18 toy race cars which I want to share:

Flowers in my gardenMy garden is filled with flowers and some bees:

How many fl owers? 17 How many fl owers? 14

How many fl owers? 37

Tic-tac-toe f or smartys3-in-a-row wins

4-in-a- row wins4-in-a- row wins

3-in-a-row wins

XO

O

X

XO

# Squares =3 x 3 = 9 # Squares =4 x 4 =16

# Squares =5 x 5 =25 # Squares =6 x 6 =36

Flowers in my gardenWrite the answers as a multiplication followed by a subtraction:

4 x 5 - 3 = 17 4 x 4 - 2 = 14

4 x 10 - 3 = 37

Flowers in my gardenMy garden is filled with flowers:

There are 4 rows, each with 7 fl owers.

The total number of flowers is thus 4 x 7.There are 7 columns, each with 4 flowers.

The total number of fl owers is thus 7 x 4.

How many fl owers are there? 28

24 / 4 = 6

Division = Sharing

24 / 2 = 12

24 / 3 = 8

24 / 6 = 4

24 / 12 = 2

24 / 8 = 3

48 / 3 = 16

Factoring a chocolate bar# squares = 1 x 24

# rectangular chocolate bars with 24 squares, where the

number of rows is smaller than the number of columns? 4I f number rows doesn’t have to be smaller than number of

columns, then can make 8 chocolate bars.

# squares = 2 x 12

# squares = 3 x 8

# squares = 4 x 6

Factoring a chocolate barFor 20 squares of chocolate. How many chocolate bars can I

make where the # rows is no more than # columns? 3

# squares = 1 x 20

# squares = 2 x 10

# squares = 4 x 5

3 chocolate bars16 squares

Prime chocolate barsCircle those numbers below which are prime numbers:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Theorems and FallaciesA theorem is a statement that is always true.Circle the THEOREMS on this page.



Any number which is divisible by 2 (with no remainder) is also divisible by 4.

Any number which isdivisible by 4 (with noremainder) is also divisible by 2.

2-piece outfi ts

How many diff erent outfits? 3 x 4 = 12

I f only 2 shirts, how many outfits? 3 x 2 = 6

I f only 8 shirts, how many outfits? 3 x 8 = 24

3-piece outfi ts

How many outfits? 4 x 3 x 2

Secret Function 1Secretfunction3 15

Secretfunction5 25

Secretfunction2 10

Secretfunction10 50

Secretfunction 20

Secretfunction 30

4

6

Secretf unction 1multipliesits inputs

by 5.


Secretfunction5 22

Secretfunction2 10

Secretfunction10Secretfunction 18Secretfunction 30

Secretf unction 2multipliesits inputs

by 4and thenadds 2.42

44

7

Building with blocks

# blocks in tower of height 2? 3




# blocks in tower of height 6? 21# blocks in tower of height 100 minus # blocks in tower

of height 99? 100

Secret Function 3Secretfunction

124

3

Secretfunction

40 104

Secretfunction

126 2

Secretfunction

603

Secretfunction 4

2

Secretfunction

10 2

20

5

8

Secretf unction 3

dividestop input

by bottominput.

Secret Function 4Secretfunction

125

3

Secretfunction

40 114

Secretfunction

126 3

Secretfunction

603

Secretfunction 4

2

Secretfunction

10 6

21

2

6

Secretf unction 4

dividestop input

by bottom

input, thenadds 1.

My allowanceI n 1 week, my allowance will be 2 cents.

I n 2 weeks, my allowance will be 4 cents.






I n how many weeks will my allowance be over $10? 10I n how many weeks will my allowance be over $100? 14

Over abuck a week

already!

Growing younger?

5 years f rom now, my mom will be how

many t imes my age? 4





Martian counting1 flower

2 flowers

3 flowers

4 flowers

5 flowers

10 flowers

11 flowers

12 flowers

13 flowers

Counting to 100 in Martian:

1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 100.

Earthlings versus MartiansI see

11 flowersI see

15 flowers

I see12 flowers

I see20 flowers

I see

18 flowers

I see

30 flowers

I see

29 flowers

I see

45 flowers


Secretfunction24 40

Secretfunction25 41

Secretfunction30

Secretfunction 30

Secretfunction36

50

18

100

Secretf unction 5transf ormsEarthlingnumbers to the

equivalentMartian numbers.

What is a square?

What is a square number?A number N is called a perfect square if one can arrange N chocolate squares into a square shape.

The numbers: 1, 4, 9, 16, 25 are all perfect squares.What are the next couple perfect squares?

36, 49.

I nstant LawnThe driver arranged all the squares into a huge 7 x 10 rectangle.The area is the space the lawn takes up - - that’s 70 square yards.My dad says the perimeter of the lawn is the number of yards offence our neighbor needs to buy to surround his beautiful lawn.

Perimeter of ourneighbor’s lawn is

7 + 10 + 7 + 10 = 34yards.Area of ourneighbor’s lawn is

7 x 10 = 70square yards.

I nstant Lawn

Perimeter is 42 yards.

Area is 68 sq. yards.

Area= (8 x 17) - (4 x 9)

Perimeter can be larger than area:Example:

Perimeter is 58 yards.

Area is 100 sq. yards.

Multiplying in the big leaguesWhat’s 6 x 14?

6 x 4 = 24

TOTAL = 84

6 x 14 =

6 x 10 = 60

Math for Smart Kids Book 1: Multiplication & Division By Mor Harchol-Balter, Ph.D. Copyright March...

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Transcript of Math for Smart Kids Book 1: Multiplication & Division By Mor Harchol-Balter, Ph.D. Copyright March...