Math for Smart Kids Book 1: Multiplication & Division By Mor Harchol-Balter, Ph.D. Copyright March 2003

Stars in my sky My 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 garden My 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 cars I have 18 toy race cars which I want to share:

Tic-tac-toe for smartys Play 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 markers in 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 garden My garden is filled with flowers and some bees: How many flowers do you see in the above garden? ______ How many flowers do you see in the above garden? ______ How many flowers do you see in the garden to the left? ______

Flowers in my garden Write the answers as a multiplication followed by a subtraction: How many flowers do you see in the above garden? ____ x ____ - _____ = ____ How many flowers do you see in the garden to the left? _____ x _____ - _____ = ____ How many flowers do you see in the above garden? ____ x ____ - _____ = ____

24 / 4 = _______ Division = Sharing 24 / 2 = _______ 24 / 3 = _______ 24 / 6 = _______ 24 / 12 = _______ 24 / 8 = _______ 48 / 3 = _______

Factoring a chocolate bar I have 24 squares of chocolate. There are so many possible 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 ___ 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 bars A number is called prime if there is only one way to make a chocolate bar out of that number of squares (assuming number of 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:

Theorems and Fallacies A theorem is a statement that is always true. A fallacy is a statement which may be true sometimes, but is also sometimes false. Circle the THEOREMS on this page. A chocolate bar with 2 rows, can always be redrawn as a chocolate bar with 4 rows. A chocolate bar with 4 rows, can always be redrawn as a chocolate bar with 2 rows. Any number which is divisible by 2 (with no remainder) is also divisible by 4. Any number which is divisible by 4 (with no remainder) 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 1 I 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. Secret function 3 15 Secret function 5 25 Secret function 2 10 Secret function Secret function 3 20 Secret function 30 3 Fill in the blanks! Fill in the blanks!

Secret Function 2 OK, so that was too easy for a smartypants like you. Try this one! Secret function 3 14 Secret function 5 22 Secret function 2 10 Secret function Secret function 3 18 Secret function 30 3 Fill in the blanks! Fill in the blanks!

Secret Function 3 This secret function takes 2 inputs and returns one output. Fill in the blanks! Fill in the blanks! Secret function Secret function Secret function Secret function 60 3 Secret function 4 2 Secret function

Secret Function 4 This secret function takes 2 inputs and returns one output. Fill in the blanks! Fill in the blanks! Secret function Secret function Secret function Secret function 60 3 Secret function 4 2 Secret function

The poison game -- level 1 Rules: 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 2 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 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 make sure that each block is supported by 2 blocks underneath, one on each side. How many blocks are in a tower of height 3? ________ How many blocks are in a tower of height 4? ________ How many blocks are in a tower of height 5? ________ How many blocks are in a tower of height 6? ________ A tower of height 100 will have how many more blocks than a 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 mom will be 40, and I will be 10. My mom will be how many times my age? __________ 10 years from now, my mom will be how many times my age? ________ 25 years from now, my mom will be how many times my age? ________

Martian counting Here 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 Martians I see 11 flowers I see 15 flowers I see 12 flowers I see 20 flowers I see ____ flowers I see 30 flowers I see ____ flowers I see _____flowers

Secret Function 5 What’s this secret function doing? Secret function 6 10 Secret function Secret function Secret function Secret function 3 30 Fill in the blanks! Fill in the blanks! Secret function 36 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 squares into a square shape. For example, the number 16 is a perfect square, because 16 chocolate pieces can be arranged in a square. The number 20 is not a perfect square, because 20 chocolate pieces can not be arranged 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 Lawn My 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 square of 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 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 of fence our neighbor needs to 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 yard wide 1 square yard

Instant Lawn The perimeter of this lawn is __________ yards. The area this lawn is _______ square yards. The perimeter of this lawn is __________ yards. The area this lawn is _______ square yards. Hint: Think about multiple 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 number is greater than the area number? ____________________________________

Multiplying in the big leagues What’s 7 x 13? 7 x 10 = 707 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