Creative Learning ClassMath!

This is an Open Educational Resource for the Developing World compiled and designed through a partnership by:

PEPYPEPY (Promoting Education, emPowering Youth) is a 501(c)3 organization registered in the

United States and based in Cambodia. We began in 2005, with a mission to improve access to quality education in rural Cambodia, and primarily ran projects supporting government

schools in Kralanh District, Siem Reap Province. Over time, our mission and focus has evolved to meet community needs and to leverage on our strengths. As a result, some of our programs are expanding, and several of our programs that no longer align with our

goal, are now drawing to a close. This has coincided with a process of localization, and in 2014 our Cambodian-led team created a new local organization, with their own mission statement, core values, and vision. The overall approach to programs remains the same, with commitments to providing education and youth empowerment initiatives for young

people in Kralanh District. We are very happy to support their new programs!

We are also proud of the programs that PEPY-US has created and implemented in Kralanh over the past eight years. These manuals describe several programs that PEPY-US created

and implemented in Kralanh, Siem Reap. They share the lessons we’ve learned, the successes we have had, the challenges we have faced, and tips and best practices for those

interested in implementing similar programs.

To learn more about where we have been and where we are headed, visit:

www.pepycambodia.org

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opportunities to champions of education in the developing world. We firmly believe, and have consistently demonstrated, that it is possible to provide world-class educational

experiences using the physical resources already available to educators and NGOs working in the most underfunded classrooms on earth.

www.openequalfree.org

Creative Learning ClassMath!

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Contents

Activities and Art — 14A Trapped Ghost — 15

A Strange Builder — 16

The Bridges of Konigsburg — 17

Math Scavenger Hunts — 18

Exponential Explosion — 19

Measurement Estimation — 19

Tangrams — 20

Folding Fractions and Fractals — 22

Tesselations — 23

4 Color Maps — 24

Factor Tree Mobile — 25

Games & Puzzles — 26Trail Makers — 27

Surround and Conquer — 28

Fortune Tellers — 29

Laws of Nature — 30

Math Bingo — 31

4 Bingo Cards — 32

Problem and Answer Sets — 33

Paper Tetris — 35

Hexagon Puzzles — 36

Sudoku Puzzles — 48

Gold Hunt — 56

Make Your Own! — 63

Riddles — 64Riddles in the Classroom — 65

Which Switch Is Which? — 66

Magic Ball — 66

Attacking the Fort — 66

Alien Plants — 67

Three Young Monks — 67

Days of the Month — 67

How Many Monks? — 68

What Time Is It? — 68

The Length of a Life — 69

Connect the Dots — 69

Four Sisters — 69

Cows — 70

Two Caves — 70

Measuring Water — 71

A Worthy Husband — 71

Crossing the River — 72

How Many Children — 72

How Many Fingers — 72

A Fatal Flaw — 73

A Mysterious Death — 73

A Small Miracle — 73

Leap to Freedom — 74

Fuse Time — 74

A Crazy Cook — 74

A Little Bit Off — 75

A Perfect Match — 75

I. Abbreviations CLC - Creative Learning ClassPEPY - Promoting Education emPowering YouthCD - Chanleas DaiJHS - Junior High School

II. General Information about CLC

Project Objective

To enhance knowledge and skills of the students in creative thinking, enable problem solving through technology, and raise the quality of education in Chanleas Dai Junior High School.

CLC Background

Creative Learning Class (CLC) was created in November 2009. CLC is the development and expansion of an XO laptop class which was implemented in grades 4, 5, and 6 in Hun Sen Chan-leas Dai Primary School. After working in the primary school for several years, PEPY found that students in other schools also wanted the opportunity to learn and experience XO computers. PEPY then decided to move XO classes from the Hun Sen Chanleas Dai Primary School to Chan-leas Dai Junior High School in order to engage students from the whole commune. As a result, students throughout the commune were able to get the same educational opportunities.

How We Started Our CLC Program

Creative Learning Class (CLC) is an experiential education class offered at Chanleas Dai Junior High School and incorporates aspects of science, English, math, creative writing, critical thinking, social studies, and art. The program was created in November 2009. Previously, between 2005 and 2009, PEPY delivered a program called ‘XO Class’, a computer and creative thinking class for Grades 4, 5, and 6 in Hun Sen Chanleas Dai Primary School.

It became apparent that students who went on to junior high school from Hun Sen Chanleas Dai Primary School had far superior skills in English and computers and had gained confidence through additional educational experiences through their XO classes. To work towards evening the playing field across all schools, and to create a higher level learning program appropriate for the junior high school level, CLC was developed as an expansion of the successful XO Class offer-ings.

About CLC

The PEPY team conducted a survey and found that many students in Chanleas Dai Junior High School lacked confidence in science and math, especially since they had very little hands on practice with using those subjects experientially. Other students were shy and most felt they had very little creative outlets in school. Additionally, they were not encouraged to think critically in their other classes. To address this issue, the Creative Learning Classes were designed with experi-ments and curriculum inspired from a range of books, science learning kits, and visiting educators from across Cambodia and the world. In the end, the curriculum was divided into three areas – science, social studies, and technology. Each class was designed to foster critical thinking skills through research, group work, and experimentation.

Impact

• 80% of students in the Junior High School registered for the PEPY’s CLC class in 2011/2012• 180 parents attended the opening presentation to support their children• Parents noted children are more confident in their learning ability and asking and answering

questions• Further impacts can be found through our Creative Learning Clubs

Challenges / Lessons Learned

• Critical thinking and problem solving are not familiar concepts in Cambodia and many don’t recognise the benefits of these skills. We strive to make classes relevant to the student’s everyday lives.

• It’s no good having amazing learning tools if teachers don’t know how to use them! Our Educators have spent a lot of time learning about XO Computers and LEGO kits to be able to use these resources to their full capacity.

• Nothing lasts forever! While the XO computers are robust machines – the battery and the mouse pad are the first things to break. PEPY was faced with either reinvesting in more computers or finding another, innovative way of teaching these same skills once the XOs are no longer usable.

III. Running the ProjectCLC is provided to students in grades 7,8 and 9 for four hours per week. These classes run as

supplementary classes to scheduled government classes. CLC takes place between 7-11 in the morning and 1-5 in the afternoon from Monday to Friday, with classes filling empty slots in student schedules.

Yearly Activities Plan Development

Developing a yearly activities plan is a very important step for implementing the project smoothly and effectively. The yearly activities plan helps the team understand clearly where, how,

and what is going to happen during the whole year. In order to develop a good yearly activities plan our CLC team does the following:

• Brainstorming supplemental topics and activities for the whole year in addition to reviewing the curriculum

• Analyzing and prioritizing activities• Reviewing activities, discussing implementation, and troubleshooting likely problems as

much as possible• Document all activities, making note of the following: number of activities, team member

responsible, year, month, and comments• Project manager needs to list all materials needed for the activities in the yearly activities

plan• Project Manager then needs to insert all the materials needed along with the cost into an ap-

propriate budget for submission to management team• Yearly activities plan and budget should be submitted to the management, revised, and ap-

proved• Finally, it’s important to revisit the plan throughout the year. Reality requires changes and

moving of schedules and it’s important that all team members know when this happens

Coordinating With the Government School

Before starting to implement the project we have to get approval from the principal. To that end, we schedule a meeting with him or her and other teachers. This meeting is conducted with the purpose of improving communication and collaboration with the school, informing them about what we are planning to do, and classifying what roles and responsibilities that the school has to ensure the project will run properly.

For example:

Before the meeting day

• The project manager has to prepare and organize a presentation on the project, documents related to the project such as yearly activities plan, curriculum, and the contract before the meeting

• Prepare the invitation letter to send to the principal, teachers, and school support committee

Meeting day

• The project manager presents the project’s purposes and detailed plan• All the participants are encouraged to ask questions or comment about the project• Finally, a contract is signed between the school principal and project manager. The contract

should be made in collaboration between a program representative and the school principal before the meeting day.

Coordinating with Government Teachers

• It is important to present the curriculum to the government teachers so that they can under-stand the CLC lessons and give us feedback.

• Finally, once both government teachers and the PEPY team agree, we can sign the contract and get started.

• Note: It is important to update and improve lessons each year based on experience from previous years

Student Selection

CLC was not a government class and was implemented directly by PEPY with students during their free time from school. Students who want to join this project have to sign up at the beginning of school year. The process of selecting students to join the class was:

• Project staff announce to students in the Junior High School at the same time they register for their government class

• Students have to fill out the PEPY application form Students have to submit their application forms to PEPY before the deadline

• PEPY team announces to students who are qualified to attend the class. Students were gen-erally always qualified to study in the class except those whose parents did not provide the approval by signing the application form.

Starting Class

Before starting class we would organize a meeting with students, teachers, the project man-ager, school support committees, and parents. The purpose of this meeting was to share with the participants what PEPY will do for the whole year, and get more collaboration from the parents. Parents’ engagement is important as they have a lot of influence over their children. The agenda of the meeting was: project presentation, question and answer session for parents and students, and a speech from the principal of schools about education.

Home Visits

In rural communities some students lack motivation and some students are forced to stay at home and help with chores. As a result, this often affects school attendance. Going to see their house and meeting members of their family is important to better understand their living condition and why they may not be attending class. It is a good opportunity to provide them with more infor-mation about what their children are doing at school; especially in CLC. This is because families often do not really understand what activities are taking place at school. During these visits our team documents all the information that we receive for later trouble shooting. It is a good idea to also bring government teachers or the principal along with us because they are influential figures in the community and understand the community culture more deeply.

Parent Engagement

In the rural community parents have a strong influence on their children; engaging them with our activities is a very important part of the project. In PEPY, we involve them in our project by organizing a meeting with them at the beginning and end of the year.

Teachers’ Involvement

Along with parents, the government teachers play very important role in ensuring the project runs smoothly. We invited teachers to come see our project once a month. We sought feedback on our teaching style and hoped that they could also learn from us.

Weekly Team Meeting

At PEPY we coordinated via team meeting every week. In this meeting we shared what we have learned from the previous week, any issues faced, ideas to solve problems, and worked to develop the weekly plan. We found the weekly meeting to be very important for keeping every-one working as a team and informed. Our meetings lasted about 1 hour because members were strongly encouraged to be well prepared with their agendas and issues before the meeting.

IV. Introduction to PEPYPEPY (Promoting Education, emPowering Youth) is Cambodia-based Non-Governmental

Organization started in 2005. We started with the belief that education is the best way to improve Cambodia’s future. Our team of about 35 Cambodians and about 6 international staff work on education programs where we partner with government schools and Community Development Programs. We also work with children and families outside of school. These programs focus on the Chanleas Dai Commune in the district of Kralanh.

At PEPY, we believe that all students should have the chance to learn, and their education should teach them to think creatively, to solve problems, and to be leaders. This is because we want all young Cambodians to have the power to make their dreams happen. Our main goal is to help young people get the skills they need. Second, we connect them with systems outside their communities (for example, we guide them when they want to go to college but they don’t under-stand how to get in.) Third, we stay positive and inspire them to work towards their goals, raise standards of living and improve education in their communities.

Originally The PEPY Ride, PEPY was incorporated in the state of New York in the United States in February 2006, and is a tax-exempt organization under section 501(c)(3) of the United States Internal Revenue Code. The roots of PEPY began when cofounders Daniela Papi and Greta Arnquist began planning a cycling adventure across Cambodia to learn about and contribute to development, aid, and sustainable adventure tourism in the region. They were joined by a team of four friends, and together they raised funds to support educational non-governmental organiza-tions (“NGOs”) they had identified. Following their five week ride, they began laying the ground-work for PEPY, an organization inspired by the inadequacies of the funding organizations they had worked with and seen. PEPY Founders were inspired by a commitment to working directly with the community of Chanleas Dai to improve education, specifically health and environmental knowl-

edge in the area. In March 2007, PEPY signed an MOU with the Ministry of Foreign Affairs, as an official INGO in the Country. PEPY also has agreements with the Ministry of Education, Youth and Sports, and the District Office of Education in Kralanh.

At PEPY, we believe that education is the key to sustainable change and recognize the impor-tance of the holistic impact of development programs. Our programs work in concert with one an-other, both in and out of the classroom, to create an atmosphere where education becomes valued and valuable.

Vision

All young Cambodians empowered to achieve their dreams.

Mission

To invest time and resources in young people in Cambodia, working with them to connect them to the skills, systems, and inspiration necessary to achieve their goals, raise standards of living, and improve the quality of education in their communities.

Core values

• Commit to our unending potential for improvement • Think unreasonably. Dream BIG• Focus on impact, not inputs. Invest in people, not things• Be strategic in our choices, and thoughtful in our plans• Collaborate, both within and beyond• Create and sustain a culture of open feedback• Work with, not for• Do more with less. Be responsible in our environmental and economic choices• Be humble in success, transparent in failure and share the lessons we learn• Nurture the creative and quirky PEPY culture• Stay connected with the PEPY family. Wave until you can’t see them anymore• Live the principles we promote. Work with integrity

Activities and Art

Activities and Art A Trapped Ghost• A ghost has been trapped by a monk in an old house. • The monk said, you can only escape if you walk through each door once and only once. • The ghost has tried it many different ways, starting many different places, but still remains

trapped. • Is there any way for it to ever be free?

A Strange Builder• An builder designed the house below in a very strange way. She put her pencil down and did

not pick it up again until the drawing was finished. Even more strange, she didn’t cross any line she had already drawn or retrace over any lines.

• Can you figure out how she did it?

The Bridges of Konigsburg• Once upon a time there was a city called Konigsburg. • Konigsburg was built on two islands in the middle of a large river. • Seven bridges connected the islands with each other and the banks of the river. • People believed there was a way to cross all 7 bridges crossing each one only once but

they’ve never figured out how. • Can you?

Math Scavenger Hunts• A scavenger hunt is an activity where students search for items on a list you give them. They

can either collect the items and bring them back, or take pictures of them, or record informa-tion about them.

• Some math scavenger hunts you can do in include:

Distance Scavenger Hunt• Before class, make a list of things for students to search for and measure the distance of

each thing from the teacher’s desk. • To begin the activity, tell students they must look for everything on the list you give them.

When they find each item, they should not touch it (or tell anyone else where it is!). The only thing they should do is write down how many meters or centimeters away from the teacher’s desk they think it is.

• When everyone has found all the items, have them check their guesses against the actual measurements. The student with the most correct guesses wins!

Geometric Figures Scavenger Hunt• This scavenger hunt is easy to do quickly! Give students a list of geometrical shapes. The

list can be as simple as 2 circles, 3 squares, and 4 triangles. Or can get more complicated, with hexagons and pentagons or shapes near one another (a circle inside a square, etc.).

• Then, have students search out the objects. They can either write where they found each object or take pictures of the objects if cameras are available.

Tessellation Scavenger Hunt• Tell students to search for tessellations in the classroom or around the school. Give them a

time limit and the student or group to find the most wins the scavenger hunt!

Numerical Pattern Scavenger Hunt• For this scavenger hunt students are to find sets of objects in order. • The simplest version would be for them to find 1 of something, then 2 of something, then 3

of something. For example, 1 boy, then 2 cats, then 3 nails, then 4 pencils, etc. • More complicated versions can include finding multiples of 2 or 3, or powers of 2 or 3, or

even fractions!• This is best done with each group using a camera to take pictures of the objects.

Measurement Scavenger Hunt• In this scavenger hunt, students are looking for objects of different measurements. • Students can be asked to find objects of different lengths (1 cm, 2 cm, 3 cm, etc), perim-

eters, surface area, or even volume. • To do this students will need rulers or measuring tape and should write down the object and

the measurement in addition to any formulas (such as for perimeter, surface area, or volume).

Exponential Explosion• It is often difficult to imagine how quickly something grows when it grows exponentially. With

this activity, students will count grains of rice to show exponential growth. They will quickly realize what “to the second power” really means!

• Each group starts with 2 grains of rice. Each round they will have 60 seconds to double the number of rice grains.

• At first this will be very easy. 2 will become 4, 4 will become 8, which will become 16, then 32, then 64.

• Within a few minutes, it will be impossible for each group to count out the next set of rice.

Measurement Estimation• Give each group a set of items. They can be anything, toothbrushes, notebooks, pencils,

pens, crayons, etc. • Have each group write down an estimate for how long and how wide they think each item is. • After they have written down each estimate, pass out rulers. • Have students measure the items and compare them to their estimations. • Discuss the results as a class.

Tangrams• For this activity each student (or group) will need their own tangram square that they can cut

into pieces. • Once they have the pieces cut out, they can rearrange them to create new shapes and de-

signs. You can present shapes for them to recreate or they can design their own!• Below are some examples of images you can make using tangrams. You can use these to

get students started, but a fun idea is to have students make designs and work with partners to copy someone else’s design!

Folding Fractions and Fractals• Tell students that today they will be making folded examples of a kind of math art: Fractals.

These fractals can also be used to learn fractions. • Give each student a piece of printer paper and follow the following directions. It will help if

you make it with them and show them each step.

• Repeat these steps one or two more times. If they are measuring correctly when they cut, they should be able to do two easily. If not, one more may be as many as they can fit.

• When it is finished, you should be able to open and close it like a birthday card. When it is open, all of the pieces should “pop up” making smaller and smaller boxes, almost like stairs.

• This is known as a fractal because each smaller piece is a copy of the whole design. • It can also be used to teach fractions. The paper is one whole folded into two halves. The

biggest box is ¼. The next biggest boxes are 1⁄8 and so on.

Fold the paper in half, lengthwise

Make two cuts from the folded edge 1/4 of the way from the side and

1/2 the way up.

Open the paper up. You should have two cut lines next to each other. Pull the center of the cut piece up

and refold the paper.

Again, find the places 1/4 in from the edge and cut

1/2 of the way up.Again, open the paper up. You should have two new cut lines

next to each other. Pull the center of the cut out piece up and re-

fold the paper. The original piece should also be folded up.

Tesselations• For this activity you will need index cards or small squares of paper, scissors, and markers

or crayons. • A Tessellations is a work of art that is made by putting many shapes that fit together into a

pattern.

A simple tesselation More complex tesselations

• You can have students make tessellations using regular geometric shapes like the two above, or you can use this activity to make very complicated and unusual tessellations.

• It is actually very simple. Take an index card or a square of paper and cut a piece out of it, then tape that piece to the opposite side. Trace the shape you’ve made onto a piece of paper, move it over, and trace it again. Move it over, and trace it again, and so on, until the pattern repeats!

Now you’ve got a stencil you can use to trace a new tesselation!

4 Color Maps• There is a mathematical rule that states any map can be colored with only 4 colors so that

no touching shapes or regions that share a side have the same color. • Below are some maps. Challenge students to color them using only 4 colors so that no

touching shapes have the same color! • Two shapes can share a point and have the same color, but not a side!• Have students start trying to color these maps with only four colors. Then, have them try to

make their own maps and challenge each other to color them with only four colors.

Factor Tree Mobile• A prime number is a number that can’t be divided by anything but itself and 1. Examples

include 1, 2, 3, 5, 7, 11, and 13. • Prime factorization is taking a number and dividing it, little by little, until you have all of the

prime factors that make it up.

• So, the prime factorization of 24 is 2 ×2 ×2 ×3 or 2^3 ×3• Students can make mobiles that show the prime factorization of different numbers. They can

make small mobiles individually, or large mobiles in groups. • Students can create physical factorization tree mobiles using index cards or pieces of paper

and string. Each card has a number in the tree on it and they are strung together by string. • Students should be encouraged to color and decorate their mobiles! •

24

12 2

3 4

22

Games & Puzzles

Trail Makers• At the start of the game each player will choose either white circles or black circles. • They each take turns by connecting two of their circles, up and down or left and right. • No player can cross another player’s line. • The goal is to connect the two sides of the board with your trail without crossing the other

player’s trail.

Surround and Conquer• Players take turns connecting 2 dots that are next to each other, either left and right or up

and down. • The goal is to make as many small squares as possible. Whoever makes the 4th side of a

square can color that square (or put their initials in it) and gets 1 point. • Whoever has the most squares at the end wins!

Fortune Tellers• Each team needs 3 students to play.• Two students sit on either side of a deck of cards (the players) while the third sits in the

middle (the caller). • The two players across from each other pull a card from the deck without looking at it! When

the caller “Go” they hold the cards up to their foreheads so that everyone but them can see it (They should never see their own card!)

• The caller says the sum of the two cards. The first of the two players to guess their own card wins!

• You can also play this game using multiplication. The caller tells the two players the products of their cards and they must guess their own card based on the product and the other per-son’s card.

Laws of Nature• For this game you need a simple deck of playing cards (no jokers). • Each team should have 4 or 5 students. One student is the “Lawmaker” and the rest are

players. • To start, the lawmaker deals the cards so that each player has the same number of cards. • Before the game begins, the lawmaker must choose a “law of nature.” This is a rule that

must be followed when laying out the cards. The rule can be anything, some examples:• Red must always follow black or black must always follow red. • Even must always follow odd or odd must always follow even. • Cards must be placed in order (2, 3, 4 etc.) until a court card is placed, then you can start

with any number. • The players then take turns putting cards down. If the card follows the law, it can stay. If not,

they have to pick it back up. • The goal is to get rid of all your cards first. The faster you figure out the law, the easier this

will be. • The caller says the sum of the two cards. The first of the two players to guess their own card

wins! • You can also play this game using multiplication. The caller tells the two players the products

of their cards and they must guess their own card based on the product and the other per-son’s card.

Math Bingo• Math Bingo is a great way for students to practice doing simple math in their heads. • At the beginning of the chapter is a blank set of four bingo cards. Because the goal is to get

numbers in a certain order, it is important that no two cards are identical. • Each game consists of a list of math problems and answers. Before the game begins. • Before you begin, print out the list of problems and cut them out. Put all the cut out pieces

into a box, hat, cup, or something else that you can pull them out of one by one. Have an-other copy of the problems and answers in order to read the answers so students can fill out their bingo cards.

• To begin, give each student a blank bingo card. • Read out the answers (not the questions!) from the list. As you read, instruct students that

they should write the numbers into their boxes randomly. The goal is for everyone to have a different card.

• Once everyone has a bingo card ready, you can begin. Pull out the questions one by one and read them out loud. When students figure out the answers, they should make a small mark on that number’s box. Be sure to keep the answers you have read so you can check and make sure students are correct when they say BINGO!

• The first person to get 5 in a row (up, down, across, or diagonally) wins! They should call out “BINGO!” and you can check their work to make sure they were correct.

• You can keep playing to have a 2nd and 3rd place. • You can also start the game over, this time telling students to make a different kind of mark

so they can remember which boxes were marked off this game.• Of course, you can always make your own! The last set is left blank for you to make your

own. Try to avoid having more than one of the same answer. If you need to, be sure to in-struct students to only mark off one at a time.

4 Bingo CardsCut them out and give one to each student.

Problem and Answer Sets

2+ 2

4 7 + 5

12 20 + 1

21 8 + 6

14 12 + 17

29

3 + 2

5 6 + 7

13 18 +11

29 14 + 4

18 17 + 17

34

7 + 2

9 27 +13

40 7 + 3

10 2 + 17

19 38 + 14

52

1 + 1

2 14 + 3

17 7 +4

11 12 + 15

27 7 + 7

14

12 + 7

19 2 + 6

8 3 + 0

3 29 + 14

43 12 + 11

23

48 - 23

25 82 - 43

39 30 - 18

12 13 - 12

1 68 - 30

38

92 - 25

67 25 - 10

15 47 - 28

19 19 - 1

18 57 - 28

29

43- 5

38 28 - 12

16 12-8

4 20 - 17

3 39 - 24

15

28 - 19

9 7- 5

2 18 - 9

9 21 - 4

17 72 - 34

38

36 - 2

34 34 - 17

17 27 - 9

18 87 - 46

41 69 -21

48

3 x 3

9 9 x 3

27 9 x 7

63 12 x 12

144 3 x 7

21

2 x 5

10 4 x 8

32 3 x 8

24 3 x 4

12 5 x 9

45

8 x 8

64 4 x 1

4 2 x 6

12 11 x 5

55 8 x 9

72

7 x 5

35 0 x 11

0 8 x 2

16 10 x 7

70 2 x 3

6

2 x 1

2 3 x 8

24 9 x 10

90 2 x 12

24 12 x 3

36

12 ÷ 3

4 22 ÷ 2

11 9 ÷ 9

1 100 ÷ 2

50 48 ÷ 3

16

14 ÷ 7

2 12 ÷ 4

3 60 ÷ 6

10 97 ÷ 1

97 54 ÷ 2

27

18 ÷ 3

6 16 ÷ 2

8 39 ÷ 3

13 210 ÷ 3

70 1000 ÷ 10

100

35 ÷ 7

5 45 ÷ 5

9 56 ÷ 4

14 420 ÷ 7

60 720 ÷ 9

80

36 ÷ 3

12 21 ÷ 3

7 75 ÷ 3

25 90 ÷ 6

15 450 ÷ 25

18

0.12 12% 0.3 30% 0.23 23% 0.011 1.1% 1.1 110%0.1 10% 0.03 3% 0.04 4% 0.92 92% 0.82 82%

0.78 78% 0.201 20.1% 0.4 40% 0.13 13% 2 200%1.2 120% 0.09 9% 0.89 89% 0.5 50% 0.4 40%

0.34 34% 1 100% 0.27 27% 0.56 56% 0.99 99%

Make Your Own!

Paper TetrisPrint and cut the shapes below. Students can try to arrange them to make a 6x10 unit rectan-

gle, a 5x12 rectangle, a 4x15 rectangle, or a 3x20 rectangle.

Hexagon Puzzles

Using Hexagon Puzzles In The Classroom• Print out enough puzzles for each student or for each group of students.• Cut the hexagons apart and shuffle them so that they are in a random• order.• Make sure that each puzzle stays in a set on its own! If the sets get mixed• up they won’t work!• Pass out the hexagon pieces. Instruct students that their goal is to find the• sides that match to make a single “flower” shape out of all the hexagons.• One hexagon should be in the middle with all of the other hexagons• around it.• Let them know that each side may have more than one match, they need• to find a way to match up all the sides so that they make a single shape.• At the end of the chapter is a page with two blank puzzles on it. You can• print them out and fill them in any way you like. This way, if you would• like a different version of one of the puzzles, or a brand new puzzle, you• can make your own! Puzzles could even test things other than math.• Students could match Khmer words to English words, or shapes to their• definitions, or anything you can think of!

3 + 3

19 - 2

12 + 11 4 - 4

13 + 12

10 - 7 1 + 8

12 - 5

2 + 2

4 - 1

12 + 5

2 + 1

3 + 4

2 + 7

3 + 3

19 - 2

12 + 11 4 - 4

13 + 12

10 - 7 1 + 8

12 - 5

2 + 2

4 - 1

12 + 5

2 + 1

3 + 4

2 + 7

283 +39

73 + 388

14 + 278 145 + 237

212 + 34

231 - 36 101 + 44

138 - 80

115 +201

17 - 7

34 + 77

512 - 317

14 + 44

23 + 122

283 +39 73 + 388

14 + 278 145 + 237

212 + 34

231 - 36 101 + 44

138 - 80

115 +201

17 - 7

34 + 77

512 - 317

14 + 44

23 + 122

13 + (-2)

-3 - 2

-7 + 7 9 – (-1)

-3 + 7

8 - 13 5 + (-2)

-7 - 4

-15 + 9

3 + (-3)

-7 + 2

5 + (-10)

-13 + 2

-4 + 7

13 + (-2)

-3 - 2

-7 + 7 9 – (-1)

-3 + 7

8 - 13 5 + (-2)

-7 - 4

-15 + 9

3 + (-3)

-7 + 2

5 + (-10)

-13 + 2

-4 + 7

0.8 + 0.3

2.7 + 3

3.1 + 1.2 4.2 – 1.9

2.8 – 0.1

0.7 + 1.2 0.8 – 0.1

4.3 + 1.2

3.8 – 2.2

1.2 – 0.9

7.2 – 1.5

1.9 - 0

3.2 + 2.3

0.3 + 0.5

0.8 + 0.3

2.7 + 3

3.1 + 1.2 4.2 – 1.9

2.8 – 0.1

0.7 + 1.2 0.8 – 0.1

4.3 + 1.2

3.8 – 2.2

1.2 – 0.9

7.2 – 1.5

1.9 - 0

3.2 + 2.3

0.3 + 0.5

23 − 12

26+ 3

5

22− 1

2

56− 1

6

27+ 1

8

45− 1

3

38+ 1

4

110+ 3

5

15 + 24

16 + 49

45 − 13

28 − 14

18 + 12

15 + 8

30

23 − 12

26+ 3

5

22− 1

2

56− 1

6

27+ 1

8

45− 1

3

38+ 1

4

110+ 3

5

15 + 24

16 + 49

45 − 13

28 − 14

18 + 12

15 + 8

30

1 x 4

8 x 2

2 x 7 3 x 5

5 x 5

8 x 2 3 x 7

14 x 2

3 x 7

5 x 6

4 x 4

4 x 4

4 x 7

7 x 3

1 x 4

8 x 2

2 x 7 3 x 5

5 x 5

8 x 2 3 x 7

14 x 2

3 x 7

5 x 6

4 x 4

4 x 4

4 x 7

7 x 3

0.12 x 2.1

2.1 x 1.4

3.1 x 1.8 3.2 x 1.3

3.4 x 0.9

4.6 x 0.8 0.2 x 1.8

16.1 x 0.2

3.2 x 0.9

2.7 x 0.4

4.2 x 0.7

2.3 x 1.6

2.3 x 1.4

0.6 x 0.6

0.12 x 2.1

2.1 x 1.4

3.1 x 1.8 3.2 x 1.3

3.4 x 0.9

4.6 x 0.8 0.2 x 1.8

16.1 x 0.2

3.2 x 0.9

2.7 x 0.4

4.2 x 0.7

2.3 x 1.6

2.3 x 1.4

0.6 x 0.6

0.432

38%

102% 300%

38%

1200% 13%

120%

0.7

0.9

0.38

12

1.2

0.13

0.432

38%

102% 300%

38%

1200% 13%

120%

0.7

0.9

0.38

12

1.2

0.13

18 ⃝ 12

15 ⃝ 7

2 ⃝ 1 -2 ⃝ -3

14 ⃝ 28

= 3 ⃝ |-3|

-2 ⃝ -1

8 ⃝ -1

>

<

8 ⃝ 8

>

=

18 ⃝ 12

15 ⃝ 7

2 ⃝ 1 -2 ⃝ -3

14 ⃝ 28

= 3 ⃝ |-3|

-2 ⃝ -1

8 ⃝ -1

>

<

8 ⃝ 8

>

=

23

26

22

46

27

45

38

210

15

49

45

14

614

810

23

26

22

46

27

45

38

210

15

49

45

14

614

810

Sudoku Puzzles

Using Sudoku Puzzles In The Classroom• Print out enough puzzles for each student or for each group of students. The goal of a Su-

doku puzzle is for each row and column to have all the• number 1 – 9 only once.• It seems simple at first, but when each row also effects the numbers of each• column, it can get complicated very quickly!• Next to each puzzle are the answers. Students can be given entire pages• with the answers folded under, or they can be given a single puzzle while• the teacher keeps the answers to check completed puzzles.

8 9 3 2 8 4 6 9 3 7 1 5 29 4 3 1 9 6 2 5 8 4 7

7 2 1 9 6 7 5 2 1 8 4 9 6 32 9 2 8 5 7 1 3 6 9 4

6 7 4 6 3 8 5 9 2 7 17 6 5 9 7 1 2 4 6 3 8 52 7 8 4 6 1 2 7 5 9 8 4 3 63 5 6 3 8 4 7 1 5 2 9

5 6 2 8 5 9 4 3 6 2 7 1 8

3 4 5 8 3 6 7 4 9 1 22 5 7 2 1 4 3 9 5 8 7 67 8 2 4 7 9 6 8 2 1 4 3 54 3 6 4 2 9 5 3 7 6 8 1

7 1 6 9 3 7 5 1 8 6 2 9 91 4 3 8 6 1 9 4 2 7 5 37 1 8 9 6 3 7 4 1 8 5 2 9

4 7 8 9 4 2 7 5 3 1 6 82 3 1 5 8 2 6 9 3 4 7

6 4 9 6 2 4 8 7 3 1 5 93 5 8 7 1 9 2 3 6 4

1 9 5 4 8 2 1 3 9 6 5 4 8 7 28 1 7 3 9 6 4 2 8 5 1 7

8 5 2 3 8 1 5 9 6 7 2 4 37 4 3 7 4 2 3 1 5 6 9 82 8 7 4 9 1 2 5 8 7 4 6 9 3 1

1 4 6 1 2 3 9 7 8 59 4 6 9 7 3 5 8 1 4 2 6

8 3 2 9 8 3 6 5 2 9 1 7 49 7 6 2 9 1 7 4 3 8 6 5

4 1 2 4 7 5 8 1 6 2 9 34 8 2 1 9 5 4 8 6 3 2 7 1 9

9 4 3 6 9 1 7 5 4 8 21 2 9 3 5 1 2 7 9 8 4 3 5 6

4 6 7 9 1 4 2 6 8 5 3 75 1 2 7 5 3 4 9 1 6 2 8

3 5 4 1 6 8 2 3 5 7 9 4 1

3 7 6 3 4 9 7 8 5 1 6 22 6 9 1 2 7 4 6 3 5 8 9

5 9 4 7 8 6 5 2 1 9 3 4 74 8 7 5 4 6 3 2 9 1 8

3 9 4 1 7 6 3 8 9 4 1 2 7 59 6 9 1 2 5 7 8 6 3 42 8 3 7 2 8 6 3 5 4 7 9 14 2 5 4 9 3 1 2 7 8 5 6

7 6 3 5 7 1 8 9 6 4 2 3

2 6 1 9 5 2 7 8 6 4 1 3 97 3 8 1 7 9 5 4 2 6

6 9 3 5 6 4 9 2 3 1 7 8 57 9 6 8 7 5 4 2 9 3 6 1

6 1 3 8 4 9 6 1 7 3 8 5 23 5 7 1 3 2 5 8 6 9 7 4

9 4 5 7 9 6 8 3 4 2 5 1 78 7 5 4 6 1 8 2 9 3

2 3 5 4 2 1 3 9 5 7 6 4 8

4 8 3 1 4 6 7 2 8 3 5 92 3 8 2 5 7 9 1 3 4 6 8

9 4 5 1 3 9 8 4 5 6 1 2 76 1 5 4 8 3 2 6 9 7 1 5

5 3 7 6 5 1 2 3 4 7 8 9 66 7 8 6 7 9 1 8 5 2 3 4

1 9 4 8 7 2 1 6 9 4 5 8 38 5 2 8 6 4 5 3 1 9 7 2

5 8 4 9 3 5 8 7 2 6 4 1

8 2 7 5 8 2 1 3 4 7 6 99 2 6 4 1 9 7 2 5 6 3 4 8

3 8 5 3 4 6 7 8 9 1 2 53 6 2 1 3 4 7 8 5 9 6

5 8 1 2 3 4 5 8 6 9 1 2 3 77 3 8 7 6 9 5 2 3 8 1 46 4 2 6 7 1 3 4 5 9 8 2

2 9 7 5 8 2 4 9 1 7 6 5 35 4 7 9 3 5 8 6 2 4 7 1

9 7 3 1 5 8 6 4 9 2 7 34 6 2 4 7 3 5 8 9 1

9 1 2 8 9 7 3 1 2 8 6 4 51 7 6 2 5 1 7 4 8 3 9 6 2

3 5 8 3 9 6 2 5 7 4 1 84 8 5 3 4 8 2 9 1 6 5 3 7

8 6 1 4 2 3 9 8 6 1 7 5 41 7 4 5 3 9 2 1 8 6

8 6 5 8 6 1 5 7 4 3 2 9

8 5 9 2 6 1 8 4 3 5 7 96 9 1 2 7 3 4 6 9 5 1 2 8

9 3 9 8 5 7 2 1 6 4 37 4 3 9 7 2 8 6 4 1 5

4 6 3 2 7 4 1 6 5 3 9 2 8 72 1 9 8 5 2 1 7 4 9 3 6

6 2 6 4 9 3 1 8 7 5 22 8 6 7 5 2 8 4 6 7 3 9 1

1 3 2 1 7 3 9 5 2 8 6 4

7 5 9 1 4 7 2 5 8 3 6 98 9 3 1 5 8 2 6 9 3 7 1 4

6 1 4 8 6 9 3 1 4 7 8 2 58 9 1 2 5 8 3 6 9 4 7 1

1 8 3 7 1 4 5 8 2 9 3 69 7 2 9 3 6 7 1 4 2 5 8

9 7 1 2 3 6 9 4 7 1 5 8 22 8 3 9 4 2 1 8 3 5 6 9 7

8 2 1 8 7 5 9 2 6 1 4 3

1 9 8 1 4 6 5 3 9 7 8 27 1 3 5 8 9 2 6 7 1 4 3

5 7 2 3 4 1 8 5 9 63 4 5 9 3 1 4 7 5 6 8 2 9

5 8 1 6 9 5 2 8 4 1 3 6 76 2 4 1 6 7 8 9 2 3 4 5 1

7 8 6 7 1 9 4 2 3 54 5 6 4 3 5 6 7 2 9 1 8

9 3 4 2 9 1 3 8 5 6 7 4

6 3 1 5 6 3 9 2 7 4 84 2 6 4 2 3 8 7 5 6 9 1

7 6 4 1 3 8 7 9 6 4 1 3 2 53 7 9 1 4 8 6 5 3 2

3 1 5 7 2 3 8 1 5 9 4 7 66 2 7 5 6 4 2 3 7 1 8 9

5 7 1 8 6 9 4 5 7 1 8 2 6 32 1 7 3 8 2 5 6 4 9 1 7

3 8 6 1 7 9 2 3 8 5 4

6 4 7 5 1 8 6 3 9 25 7 4 8 6 9 3 5 2 7 4 1 8

1 8 3 5 2 1 8 9 3 4 6 5 72 5 3 1 2 6 8 7 9 5 3 4

3 4 1 7 9 3 8 4 2 1 5 7 6 95 9 8 7 5 9 4 6 3 2 8 14 9 1 7 5 4 2 6 9 8 1 7 3

9 7 3 1 9 6 7 3 4 1 8 2 57 8 3 1 7 5 2 9 4 6

7 8 4 7 9 6 8 2 1 4 3 55 6 2 8 5 1 3 6 4 7 2 9

3 9 1 2 4 3 5 7 9 6 8 15 1 9 5 7 8 2 1 6 9 4 3

2 9 5 6 1 2 4 9 3 5 8 6 79 4 2 6 3 9 7 4 8 5 1 2

9 6 3 9 1 5 6 8 2 3 7 48 5 9 3 8 2 4 5 7 1 9 6

7 3 8 4 6 7 1 9 3 2 5 8

6 1 8 6 5 4 1 3 8 2 9 73 6 8 2 1 3 9 6 7 8 4 5

7 4 6 7 8 9 5 4 2 6 1 39 1 4 6 8 2 5 9 7 3 1

9 7 6 2 9 3 1 8 7 6 4 5 25 4 5 2 7 4 1 3 9 8 6

6 8 9 1 7 6 3 8 4 5 2 94 2 9 1 7 3 4 2 6 9 5 1 7 8

7 1 4 8 9 5 7 2 1 3 6 4

9 1 6 8 7 5 2 4 9 36 1 5 3 2 6 4 9 8 7 11 8 3 6 2 5 7 9 4 1 8 3 6 2 5

5 4 6 3 2 5 9 1 8 7 4 69 5 7 3 6 4 9 5 2 7 3 1 8

8 1 9 8 1 7 4 3 6 9 5 22 5 3 8 9 4 2 5 3 8 9 4 1 6 79 5 9 7 1 3 6 5 2 8 4

8 4 8 6 2 7 1 5 3 9

4 6 4 6 2 1 8 5 3 9 78 4 2 8 5 3 9 7 4 1 6 2

2 3 4 5 7 1 9 6 2 3 4 8 58 6 5 1 2 8 3 6 7 9 5 4

7 3 6 7 5 2 4 9 8 3 19 1 7 3 9 4 5 1 8 7 2 6

5 1 7 9 5 8 1 7 9 2 6 4 39 4 8 9 3 6 4 5 1 2 7 8

1 9 2 4 7 8 3 6 5 1 9

5 7 4 9 3 5 1 8 6 7 22 3 4 8 5 2 6 7 3 4 1 9 8

1 2 4 5 7 8 1 9 2 6 4 3 57 3 2 7 8 1 6 3 5 4 9

6 9 3 1 6 4 9 2 7 5 3 8 18 2 3 1 5 8 4 9 7 2 6

9 4 5 8 9 6 4 3 5 2 8 1 78 6 9 5 8 3 7 6 9 1 2 5 4

5 7 1 5 2 4 8 7 9 6 3

8 3 7 2 6 8 4 5 3 7 1 99 5 7 9 4 5 7 1 8 6 3 2

3 9 7 3 1 2 6 9 5 8 42 3 4 8 7 5 2 3 1 9 4 8 7 6

2 8 1 4 6 7 2 9 5 37 9 3 8 2 4 6 7 9 3 8 5 2 4 1

9 2 4 5 7 9 3 6 1 2 87 3 5 1 9 2 8 4 7 3 6 5

6 5 4 3 8 6 5 2 1 4 9 7

2 1 7 6 9 2 4 3 5 87 3 6 4 2 8 7 5 3 1 9 6

4 7 2 5 9 3 8 6 1 4 7 22 7 9 6 3 5 2 4 7 9 8 6 1

7 1 5 8 9 4 7 6 1 5 3 8 9 2 48 6 1 5 9 8 4 6 1 2 5 3 7

8 4 5 8 4 5 2 9 7 6 1 32 3 6 2 1 9 3 8 6 7 4 5

4 6 3 7 1 4 5 2 8 9

Gold Hunt

Using Gold Hunt In The Classroom• Someone has hidden gold underneath the floor tiles of a large room. The tiles that don’t

have gold, however, had traps that are very dangerous.• You must figure out which tiles have gold underneath them and which do• not.• Someone came before you and started to figure it out, mysteriously disappeared. They have

written numbers on some of the tiles. Each• number represents the number of gold coins in the tiles around the tile• with the number.• Can you use the numbers to figure out which tiles have gold?

0 3 1 1 0 3 1 1l l l l

1 1 l

1 2 1 22 l 2 l l

2 2 l l

1 2 1 l 1 2 1

2 l 2 l

3 1 3 l 1 l

1 l l 11 2 1 2

l l

2 2 1 l 2 2 11 1 1 1 l l

2 1 l 2 1 l

2 1 l 2 l 12 1 2 1

0 0 l l

2 20 l 0 l

2 2 l 2 2 l

0 0 2 0 0 2 l

l

2 0 1 2 l 0 1l

l

0 0 3 4 4 2 0 0 3 4 4 20 1 0 1 l l l l

1 0 1 l 1 0 1 l

1 13 2 l 3 l 2

1 1 3 1 1 l 3 l l

2 2 l 2 22 1 2 1 l

1 0 l 1 0

2 1 l 2 1 l l

2 2 l l 2 22 1 1 2 1 1

0 l 0 l

2 2 1 2 2 11 l l l 1

2 2 2 2 l

1 1 1 1 l

1 1 l

3 3 0 l 3 l 3 02 2 l

1 1 l 1 l 1

2 2 l 2 l l 2 l

1 l l l 20 1 2 3 4 4 0 1 2 3 4 5

l l l

1 1 2 2 l 1 1 2 22 2 2 l 2

1 l 1 l

1 1

1 1 3 1 1 3 l l

3 l l l 33 3 3 3 l 3 3

l l l l

l

2 0 1 2 l 0 1l

2 1 l 2 11 l 1 l

1 1 l l

3 l 31 1 2 1 1 1 2 1 l

3 l 3 l

3 l 3 l

3 1 3 l 11 l l l 1 l

2 3 2 21 l l 1

2 1 2 01 l l 1 l

1 1 1 1

2 l 2 l

1 2 1 l 21 3 1 l 3

1 1 l l

l l

3 2 2 3 l 2 2l l

2 l 23 2 l 3 2 l l

l l

1 1 1 12 2

2 l l l 21 2 1 2 l

l l l l

3 0 3 3 0 3l l

1 1 1 1 1 1l

1 1 1 1 1 1l l

0 1 0 0 1 0l

2 2 2 l l 20 l 0 l

l l

1 1 1 l 11 1

l 31 l 2 l l

2

l l 2 l

2 2l 0 l l

l 1 l

1 3l l

l 3 2 12 l l

l 2l 1 0

0 l 1 02

l 1 02 1 l

l 1 l

10 l 0

2 l 2 l

0 1 l 0 1

1 0 1 l l 02 l 2

2 2 l 2 22 l 2 l l l

1 2 1 1 2 1 l

l l

2 0 l l 2 02 l 2

l l

2 3 l 2 3 l

0 0 l

Make the answer first. Put in the gold, then add the numbers. Make sure there is enough overlap so that someone can figure

it out!

2 l 2 l

0 1 l 0 1

1 0 1 l l 02 l 2

2 2 l 2 22 l 2 l l l

1 2 1 1 2 1 l

l l

2 0 l l 2 02 l 2

l l

2 3 l 2 3 l

0 0 l

Make the answer first. Put in the gold, then add the numbers. Make sure there is enough overlap so that someone can figure

it out! Make Your Own!

Riddles

Riddles in the Classroom• Puzzle of the week: Put it up on Monday, offering a clue every day and discuss guesses and

answers on Friday. • Puzzle workshop: Allow students to work on the riddle in groups as a class activity. Have

them share ideas with their groups, and possibly occasionally as a whole class. As the end of class approaches, the teacher can begin giving small hints.

• Puzzle competition: Have a puzzle up in the classroom until it is solved. Whichever student or group comes up with the solution gets a small prize.

• Yes or No?: Present the puzzle to the whole class. Students can ask yes or no questions about the puzzle as the class works together to solve it.

• Puzzle cards: Alternately, these cards can be cut out and provided as a resource for stu-dents to use in the classroom during free time.

Some puzzles are harder than others. Teachers can use different puzzles depending on the type of activity or the length of time the students will have. Clues should be given out quickly enough so that students do not become very frustrated, but slowly enough that it’s still a challenge.

For a weekly puzzle, this may mean one hint per day. For a puzzle workshop, this may mean one hint every 15 minutes. For a puzzle competition it may mean one hint a week or less.

The idea is to keep them interested. If it’s too hard for too long, they may give up. If it’s too easy too fast, they might not care.

Which Switch Is Which?There are three light bulbs upstairs that are controlled by three switches downstairs. How can

you figure out which switches control which bulbs with only 1 trip upstairs?

Hints & Helpers• How would you do it if you could make 2 trips?• Is there some way to check if a light bulb that is off has been on recently?• What happens to a light bulb after it’s been on a long time?Answer: Switch on one bulb for a few minutes. It will get hot. Turn it off and turn on another

one. When you go upstairs, the hot one is controlled by the first switch, the on one is controlled by the second, and the one that has been off the whole time is controlled by the third.

Magic BallA young athlete is holding a ball. She throws it as hard and fast as she can and a few seconds

later it comes right back to her. It didn’t bounce off of anything and no one else touched the ball. How is this possible?

Hints & Helpers• What forces make things move without being touched?• The direction she threw the ball matters.Answer: She threw the ball straight up into the air.

Attacking the FortA square fort is surrounded by a square moat 10 meters wide. You are part of a group of bar-

barians that wants to attack the fort. You brought planks of wood to help you get across the moat, but their only 9.5 meters long. How can you use them to get across the moat without rope, nails, or glue?

Hints & Helpers• You will use two bridges to make one bridge. You can only do it at four different places

around the castle. You will make a triangle.Answer: Use one bridge to make a triangle at one of the corners of the moat. Use another

bridge to connect the triangle and the other side. This will make a T shape that you can use to get across!

Alien PlantsOne day you find a strange plant with delicious fruit growing on your farm. The plants are like

nothing you’ve ever seen and they grow very fast. In one day, the number of plants doubles to two. In another day they double again to four. They keep doubling every day, and on the 10th day they fill half of your farm. On what day will your farm be totally full of the new plants?

Hints & Helpers• What do you multiply the number of plants by every day?• How many plants did it take to fill up half your farm?• How many plants will it take to fill up your whole farm?Answer: The 11th day. Doubling half is one whole

Three Young MonksThree young monks were arguing over who was the wisest. Finally, they went to the master

monk to settle their argument. He blindfolded them and told them he was painting either a red dot or a blue dot on each of their foreheads. Actually, he painted red dots on all three. He took off the blindfolds and told them to raise their hands if they saw at least one red dot. They all raised their hands. He declared that the first one to tell him the color of his own dot was the wisest. Finally, the youngest monk raised his hand and declared “my dot is red.” How did he know?

Hints & Helpers• Could there have only been one red dot if all three had their hands up?• Could the wisest monk have had a blue or a red dot based on what he knew?• What did the other monks not knowing the answer right away tell him?Answer: Let’s call the monks A, B, C. The wisest was A. A knew that he could have either a red

or a blue dot because he saw that B and C had red dots. B could have seen A’s or C’s red dot and raised his hand, and C could have seen A’s or B’s red dot and raised his hand. A then realized, if he had a blue dot, the other monks would have realized their own dot color because the only way for all three hands to be up is if there are 2 or more dots

Days of the Month

There are two cubes. They sit next to each other and are used to show the days of the month. What numbers would have to be written on the faces of each cube to be able to show every date in a month from 01 to 31.

Hints & Helpers• You will need a zero on each cube.• You will need a one on each cube. You will need a 2 on each cube.Answer: Cube 1: 0, 1, 2, 3, 4, 5; Cube 2: 0, 1, 2, 6, 7, 8

How Many Monks?There is a large monastery where all monks shave their head on the same day. After one week,

the following is true:1. No two monks have the same number of hairs on their head.2. No monk has exactly 397 hairs on his head.3. There are more monks in the monastery than hairs on any one monks head.What is the largest number of monks that can live in the monastery if all of this is true?

Hints & Helpers• One monk has 0 hairs. Imagine lining them all up in order based on the number of hairs that

they have.• Since there is a monk with 0 hairs, the monk with 5 hairs is the 6th monk, the monk with 10

hairs is the 11th monk. This pattern is true up until another rule takes effect.Answer: 397. If we line them all up in order based on the number of hairs we would have 0 –

396. There can be no monk with 397 hairs. If we add another monk he will be the 398th monk with 398 (or more) hairs. Since the number of monks has to be larger than the number of hairs on any monk’s head, this can’t be. However many more monks we add, he will always have the same number of hairs (or more) as his place in line.

What Time Is It?If it were two hours later, it would be half as long to midnight as if it were one hour later. What

time is it now?

Hints & Helpers• It is night time.

• Try thinking of it as distance instead of time. Make a drawing to help you. Two brings you twice as close to everything as one, but there is only one number that it brings you half as far away from.

Answer: 9 PM

The Length of a LifeA very old man died in a small village yesterday. At his funeral, a monk said of his life: His

youth lasted 1/6 of his life, he had his first beard in the next 1/12 of his life, after another 1/7 of his life he got married. 5 years from his marriage, his son was born. His son lived exactly ½ of his life. He died 4 years after his son’s death. How old was he when he died?

Hints & Helpers• Try writing it as an algebraic equation.• X is his total life. So his youth was 1/6x. His youth plus when he got his beard would be 1/6x

+ 1/12x. Answer: 84 years.1/6x + 1/12x + 1/7x + 5 + 1/2x + 4 = xX = 84

Connect the DotsConnect all the dots with four straight lines without picking up your pen or pencil.

You can go outside of the lines.One of the four lines only goes through two dots. All of the rest go through three.

Four SistersFour sisters are working together to fill bags of rice using different sized cups. The first sister

can fill a bag alone in one hour, the second in two hours, the third in two hours as well, and the fourth can fill it in 30 minutes.

How long can all four sisters fill one bag if they work together?

Hints & Helpers• Think of how much each sister can fill the bag in one minute. The first sister can fill up 1/60

of a bag in one minute• The second sister can fill up 1/120 of a bag in one minute. (So can the third)Answer: ¼ of an hour or 15 minutesThe first sister can fill the bag 1/60 full in one minute, the second 1/120, the third 1/120, and

the fourth 1/30. If we convert these to like denominators and add them together we get: 6/360 + 3/360 + 3/360 + 12/360 = 24/360. We can reduce this to 1/15, which tells us that the bag is 1/15 full if they all work together for 1 minute, so it will be totally full in 15 minutes (1/15 done 15 times is one whole!

CowsA rich man has 100 cows and he loves to decorate them. 70 cows have painted horns, 75 have

bells, 85 have garlands, and 80 have gold rings in their noses. What is the minimum number of cows that could have all 4 decorations?

Hints & Helpers• Try adding up all the decorations. • What is 100 x 3?• 100 x 4?Answer: 10. Add up all the decorations to get 310. That means that 310 decorations occur out

of 400 possible. All 100 cows have at least 3 decorations (3 x 100) with 10 decorations extra, so 10 cows have a 4th decoration.

Alternately, you could line them up and calculate the overlap, but this is slower.

Two CavesA young prince stood at the entrance to two caves. In one cave was a beautiful princess who

would make him happy for the rest of his life. In the other cave was a trap that would kill him in-stantly. A monk had told him that the caves were guarded by two ghosts. One always told the truth and the other always told a lie. There was no way to know which was which, but anyone who asked them more than one question would go mad from their answers. What one question can he ask to find his true love without going mad or dying?

Hints & Helpers• The one that tells the truth could be guarding either cave.

• He can ask one guard a question about the other one.• Asking one which is the liar won’t help because you won’t know if it’s true or not. Answer:

Ask one guard which cave the other guard would say has the princess. The true answer is always the opposite. If we say the caves are A and B and A is the good cave: the honest ghost will honestly say that the dishonest ghost will say cave B. The dishonest ghost will lie and say the honest ghost will say cave B. Either way, Cave A is the right cave.

Measuring WaterIf you had a 5 liter bowl and a 3 liter bowl, how could you measure exactly 4 liters if you had

unlimited access to water?

Hints & Helpers• You can fill up the 5 liter bowl as often as you need. Never fill the 3 liter bowl from the well,

only fill it with the 5 liter bowl. Instead of adding up to 4 liters, try to think of a way to subtract exactly 1 liter from the 5 liter bowl. Is there a way to make only 1 liter of space in the 3 liter bowl?

Answer: 1) Fill the 5 liter bowl. 2) Pour 3 liters from the 5 liter bowl into the 3 liter bowl. 3) Empty the 3 liter bowl on the ground and 4) refill it with the 2 liters left in the 5 liter bowl. Now, you have just 1 liter worth of space in the 3 liter bowl. 5) Refill the 5 liter bowl. 6) Pour water out of the 5 liter bowl until the 3 liter bowl is full. This should subtract 1 liter from the 5 liters, leaving you with exactly 4 liters.

A Worthy HusbandA young woman wanted to make sure that her future husband would be clever so she put a

gold ring in one of three boxes. Each box had a different clue written on it. She told him he must guess which box the ring is in on the first try. She gave only 1 hint: At least one clue was true and at least one was false. The three boxes had the following clues:

Gold box: The ring is not in the silver boxSilver box: The ring is not in this boxLead box: The ring is in this box

Hints & Helpers• Pretend the ring is in each box and check to see which statements are true or false when the

ring is in that box. They can’t all be true and they can’t all be false. Answer: The ring must be in the golden box otherwise all inscriptions would be either true or

false.

Crossing the RiverA family came to a wide river one day on their travels. The family had a mother, a father, a son,

and a daughter. There was no bridge but there was a small raft tide to the side of the river. The raft was just big enough for one adult or two children. How can they all get across?

Hints & Helpers• It will take 7 trips. • The children go across first. • One child comes back so a parent can cross. Answer: 1) First the children cross. 2) The daughter comes back. 3) The father crosses 4) the

son brings the boat back. 5) Both children cross again. 6) The daughter comes back. 7) The moth-er crosses.

How Many ChildrenTwo men are talking about their families. One asks the other how old his three children are. He

smiles and says “Guess. If you multiply their ages together, it is 36.” The other man says “that’s not enough!” He says “If you add their ages together it is 13.” The other man says “that’s still not enough!” Fine, he says “The oldest is at school today, the others are not.” How old were they?

Hints & Helpers• Figure out what 3 numbers can multiply to make 36. (There are two sets)• Which must be the right answer if only one is in school?Answer: 2, 2, and 9. (not 1, 6, and 6)

How Many FingersLet’s say there are 6,000,000,000 people in the world. If we multiplied the number of fingers

on every person’s left hand, what would you expect the product to be? We will count thumbs as fingers.

Hints & Helpers• Does every single person in the world have 5 fingers on their left hand?• Is there one number that will automatically change any number it is multiplied with to the

same product?

Answer: Zero. One person with no fingers on their left hand brings the product to zero.

A Fatal Flaw In 1942 a famous nightclub in America called the Coconut Grove burned down. One design

flaw in the building made it so that 400 people died. Because of this, regulations were changed so that all American buildings no longer had this flaw. What flaw killed so many people?

Hints & Helpers• When there is a fire, where does everyone go?• What would be hard to do if you were pressed up against something?Answer: The doors opened inward. So many people were rushing for the doors that people

were crushed up against them, trapping the rest inside.

A Mysterious DeathA man is dead in a large concrete room. Other than the man, there is nothing in the room but a

rope and a puddle of water. A police officer comes in, looks at the scene, and declares it a suicide. How did he know? How did the man commit suicide?

Hints & Helpers• The man is hanging from the rope.• The puddle of water is directly underneath the man. The room is quite warm. Answer: The man hung himself by climbing up on a block of ice and waiting for it to melt.

A Small MiracleA man was driving down a dirt road in the rain. As he crossed a bridge, it collapsed and his

car fell into a river. As his car began to sink, he realized that his arm was broken and he could not undo his seat belt. The police found him 2 hours later, alive. How?

Hints & Helpers• He was still in the car.• The car was not airtight.• His head was not wet.

Answer: The river only cane up to the man’s chest.

Leap to FreedomA frog is trapped at the bottom of a 30 meter hole. Each hour he builds enough strength to

jump 3 meters. While he is resting, he slips back 2 meters. How many hours will it take him to jump out of the hole?

Hints & Helpers• On the first jump he jumped exactly 3 meters and still had to wait an hour.• Each hour he effectively gets 1 meter higher.• His last jump is different than all the rest. Answer: 28 hours. Each hour he makes it up one meter, and then after the 27th hour he can

jump the last three meters to the top.

Fuse TimeYou have several strings. They are all thick in some places and thin in others. Although each

one burns differently in different parts, you know that each string takes exactly 1 hour to burn. How can you measure 45 minutes?

Hints & Helpers• You will need to use more than one string.• You will need two strings.• If you light both ends of one string, it will take 30 minutes to burn.Answer: Light both ends of the first string and one end of the second string. When the first

string has burned up completely, 30 minutes will have passed. Now, light the other end of the sec-ond string. Since it has 30 minutes left to burn, lighting the other end as well will make it burn twice as fast, meaning it will be burnt up in 15 minutes. 30 + 15 = 45 minutes.

A Crazy CookA crazy cook has a big pot of beans. The pot has 75 white beans and 150 black beans. Next

to the pot he has a big pile of black beans. He starts taking beans out of the pot two at a time. If at least one is black, he adds it to the pile next to the pot and drops the other bean (white or black) back into the pot. If both beans are white, he throws both away and adds a black bean from the pile to the pot. At the end of the day there is exactly one bean in the pot. What color is it?

Hints & HelpersOnly the last step matters. White beans are only removed two at a time. There are an odd

number of white beans. Answer: White. White beans are only removed two at a time and there are an odd number of

white beans. No matter how long it takes to remove all the other beans, there will always be a white bean left at the end.

A Little Bit OffA rich man puts 100 gold coins on the table divided into 10 sets of 10. He tells you that all of

the coins weigh 1 gram except for one of the piles. In that pile, each coin ways 99 centigrams. You can use a perfectly accurate digital scale only once. If you can guess which pile has the lighter coins, you can keep them all.

Hints & Helpers• The whole pile of 10 coins weighs 10 centigrams less than any other whole pile. • 5 coins weigh 5 centigrams less than any other 5 coins. • If you had two from the lighter pile and one from the normal pile, how much would all 3

weight? Answer: Put 1 from the first pile, 2 from the second pile, 3 from the third pile, and so on. How-

ever many centigrams lighter the total is than a whole gram, that is which pile is lighter. So, if it were the fourth pile it would be 4 centigrams too light, if it were the 6th pile, it would be 6 centi-grams too light.

A Perfect MatchThere are twenty coins at a table. All the coins have a picture of a face on one side and a

building on the other side. 10 are sitting face up and 10 are sitting building up. You are sitting at the table with a blindfold and gloves on. You have to make to separate groups of 10 coins with the same number of “building up” coins and “face up” coins. How do you do it?

Hints & Helpers• You can’t see or feel the coins. You can flip them over after you’ve separated them into two

piles. Answer: Make two groups and then flip over all the coins in one of the groups. This way, both

groups will have the same number of face up and building up coins.

Creative Commons LoveContributing Authors, Organizations, and Photographers

All text and images were created originally by PEPY and their staff, volunteers, and partners.

This book was written by: Michael A. JONES, RITH Sarakk, and LOEM Lida.

The guide was compiled, edited, and finalized by Open Equal Free.