Ultimate Guide to Getting

YOUR Child to LOVE Math (Even If You Don't!)

By Raj Shah, Ph.D.

Founder of Math Plus Academy

1 Don’t Fall Victim to Math Myths

Sadly, most people believe one or more of the following myths about math:

• Math is just a collection of facts, formulas, and procedures to be memorized • Math is about getting the right answer as quickly as possible • Some people have a natural ability to do math and others don’t

Allowing your child believe any of these will destroy their interest and enjoyment of mathematics. (If you believe, any of these, please don’t tell your child!)

A New Way to Look At Math

Most people describe math as addition, subtraction, multiplication, algebra, and so on. Those are all nouns that merely label the content. But there’s so much more to math.

I encourage you to think of mathematics as a VERB! Math is THINKING, REASONING, ANALYZING, ASKING QUESTIONS, DISCOVERING PATTERNS, and SOLVING PROBLEMS.

If you create a culture in your home that allows for your children to explore their own questions, make mistakes without being judged, and solve challenging problems, then you will have created the ideal space for them to develop mathematical thinking skills.

In this guide, I will show you how to build that culture. I truly believe anyone can do math and LOVE math!

Raj Shah, Ph.D. Founder - Math Plus Academy [email protected]

2 Table of Contents

This guide is structured in three sections:

1) Attitude is Everything - Make sure your child has the right perspective about what math is and how to learn it effectively while building their interest in math.

2) Mindset - Developing a growth mindset about mathematics and encourage your child to embrace the struggle of working through difficult challenges — this is when the learning happens

3) Having Fun - Ideas for how to have fun doing mathematics WITH your child.

Is Math About Trial & Error or Right vs. Wrong? ...... 4

Think! Don’t Just Memorize ...... 6

Stop Pushing the Rock Uphill! ...... 8

Why won’t my child let me help them?...... 10

Let Your Child’s Curiosity Be Your Guide ...... 11

Change Your Child’s Mindset ...... 14

Your Child Is More Capable Than You Think!...... 16

You Can Help Your Child Even When You Don’t Know the Math ...... 18

Foster a Love of Math Using Games ...... 20

The Surprising Benefits of Puzzling ...... 23

Problems to PLAY with! ...... 25

More Resources ...... 27

3 Is Math About Trial & Error or Right vs. Wrong?

The answer math is about BOTH! Now take a look at the words mathematicians use to describe Of course, the math we learn in school mathematics: (Images by Tracy Zager) has right answers and producing those right answers is a huge goal of traditional math education.

HOWEVER, when you worship at the “Altar of Right Answers”, you inadvertently remove much of the fun and joy from mathematics. What a difference!

You want your child to see that there is Mathematicians seek answers, but they room in mathematics for trial and error. often choose their own questions and

Take a look at the words most people spend days, weeks, or years in trial and associate with mathematics: error. And they LOVE it!

Let your child know that trial and error is part of mathematics. In fact, these are the times when they will learn the most.

Try This Problem With Your Child Here an illustrative example about the benefits (and joy) of trial and error. You won’t know the answer right away, but

4 anyone can get started on it if they are 2) Try a simpler problem like how many willing to try. ways are there to get the top if the staircase is only 2, 3, 4, or 5 steps? Problem: A rabbit hops up a 12-step staircase. With each hop, he jumps up 3) Have an idea? Try it! Don’t worry if it one or two steps at a time. How many doesn’t lead you to the answer. Often, it different ways can he reach the top step? will lead you to something helpful anyway.

4) Work with your child as a team. Don’t tell them what to do! Let them engage and start asking questions. Feel free to go off on tangents and see what happens!

5) As you play, you might even discover that your child has some other interesting math questions (kids are inherently

One way is for the rabbit to take 12 curious). Set aside some time to explore single-step hops. Another way is to take those questions too! 6 double-step hops. 6) Remember, the goal is to explore, play,

Can you find all the other ways? and have fun! Focus on the journey, not the result. Remember, there really is Hints & Tips more to math than right answers! 1) Sometimes it’s best to just start listing all the possibilities as best you can and then look for patterns along the way.

5 Think! Don’t Just Memorize

The process is more important than the In a recent study published in answer. the Journal of the Learning Sciences, Manu Kapur and a co- You read that right, the process of author, Katerine Bielaczyc, applied the attempting to solve a problem is more “ principle of productive failure to important to learning than getting the mathematical problem solving in three right answer! schools in Singapore. With one group of Education research clearly shows that students, the teacher provided intensive students who are left to struggle in “scaffolding”—instructional support— problem solving with limited help from and feedback. With the teacher’s help, a teacher or parent, perform better on these pupils were able to find the subsequent tests than students answers to their set of problems. whose’s teachers help them to arrive at Meanwhile, a second group was directed the right answer. to solve the same problems by It may seem counter-intuitive, but it’s collaborating with one another, absent true. I’ve seen it time and again at Math any prompts from their instructor. These Plus Academy over the last 8 years. students weren’t able to complete the problems correctly. But in the course of trying to do so, they generated a lot of Want proof beyond my first hand ideas about the nature of the problems experiences? Here’s an excerpt from and about what potential solutions would “Bigger Gains for Students Who Don’t look like. And when the two groups were Get Help Solving Problems” by Annie tested on what they’d learned, the Murphy Paul.

6 second group “significantly harm it does to students in the long- outperformed” the first. run.

The struggles of the second group have Encourage Thinking what Kapur calls a “hidden efficacy”: Ask your child questions that help you they lead people to understand the deep ascertain their level of understanding. structure of problems, not simply their correct solutions. When these students • Do they know why and how a procedure works? encounter a new problem of the same type on a test, they’re able to transfer the • Can they explain why they followed a particular process? knowledge they’ve gathered more effectively than those who • Ask them to convince you that their were the passive recipients of answer is right. someone else’s expertise. If you spot errors in their thinking, ask more questions to help them identify The Perils of “Answer Getting” ” where they went wrong. By focusing only on procedures and not on understanding the underlying concepts, the U.S. has turned math into a collection of arbitrary processes completely divorced from reality. Phil Daro, a key contributor to the Common Core State Standards for Mathematics, calls the focus on procedures to expedite getting the answer and obscuring the mathematics in the process, “answer- getting“. He warns teachers of the

7 Stop Pushing the Rock Uphill!

We all know that it’s much easier for our kids to learn when they enjoy what they are doing.

Kids love to play, that’s why they enjoy sports. But if sports were all practice and no games, their interested would quickly dissipate.

Parents are encouraged to read story books to young children because they feature engaging illustrations and playful You can only push your kids to do math stories. The goal of a bedtime reading for so long before they lose interest in routine is simply to get kids to enjoy start pushing back. reading. Do you remember your parents forcing

Whether it’s sports or reading, we start you to do an activity or sport you didn’t by making it fun FIRST. Then, once a enjoy? I do! positive connection is established, we My parents wanted me to play an help them build the necessary skills instrument so I would learn to appreciate through lessons and practice. The same music. I chose the violin. After a few should be true for math! months, I lost interest because I didn’t

Sadly, most people never experience enjoy playing classical music. math in a joyful way. Instead, they feel Instead of allowing me pick another forced to do boring, repetitive exercises. instrument, they forced me to take violin

8 lessons for EIGHT more years! (Indian puzzles together, and trying a few math parents can be very “persuasive”.) projects at home.

After they finally let me quit, I NEVER Once you’ve increased their desire to do touched the violin again. math, you can add practice exercises to your routine. They believed that someday I would wish that I could play music and they were right. Unfortunately, they never figured out how how to make it fun for me.

We all know that our kids need to have strong math and problem solving skills. Will you take an approach that builds their engagement along with their skills?

Or will we try to keep pushing the rock uphill and force them to do math even if they don’t like it.

Both can work, but only one will result in your child CHOOSING to do math after you are out of the picture.

Takeaway Kids are naturally curious about mathematical concepts. You can foster their natural curiosity and desire to solve problems by playing games, doing

9 Why won’t my child let me help them?

It’s frustrating when you know you can When you help, try to ask questions that help your child, but they aren’t receptive. point them in the right direction, rather The surprising reason kids resist your than just showing them exactly what to help is they don’t want to disappoint do. Your guidance should be tuned so you! that your child still feels like they did most of the work. Kids are extremely perceptive. They hear every subtle tone in your voice -- your Let Mistakes Be OK exasperation when they don’t get Explain to your child that mistakes are a something obvious, your sarcasm when natural consequence of learning. In they complain it’s too hard but you know basketball, we don’t expect you to make they can do it, or your disappointment every shot, the same is true in math. when they get incorrect answers. Then, teach them that it’s what they does after making a mistake that’s most Toss Out Your Expectations important. High achievers go back and You must remove your expectations from learn from mistakes and practice until the equation. If you can be gentle, they get it right. Encourage your child to accept mistakes, and remove the do the same. pressure, you’ll see profound changes.

Wait Until They’re Ready Often, parents give advice before the child is truly ready to listen which makes the situation worse. Ask them to confirm they really want your help before you start assisting. !

10 Let Your Child’s Curiosity Be Your Guide

“I have no special talents. I am just what your child already knows as well as passionately curious.” — Albert what concepts have yet to learn. Einstein Parking Spaces Did you know that an average 4 year-old My eight year old son asked a LOT of asks 65 questions per day? By age 8 that questions. He’s very observant and highly number drops to 32 and by age 45 we inquisitive. ask just 6 questions per day. On a Saturday afternoon in late autumn, Children are born with insatiable our family went to a popular local curiosity, but during school their curiosity shopping mall. When we arrived it was fades. It doesn’t have to be this way. cold and rainy so I decided to seek

The Best Way to Answer “Why?” shelter in a covered parking garage. The Questions garage had an electronic sign that indicated how many spaces were open. First, realize that it is NOT your responsibility to answer all of your child’s questions. Your role is to facilitate your child’s ability to answers their questions on their own.

I’ve found the best answer to “Why …?” is “Why do you think?”. This allows for you to have a productive conversation where you can learn much more about

11 My son noticed the sign and asked, ME: “How many entrances and exits “Dad, how do they know how many does the garage have?” spots are empty?”. THE BOY: “There’s only one way in and ME: “How do YOU think they know how one way out.” many spots are available?” ME: “Hmmm… interesting… I wonder if THE BOY: (after a brief pause) “They the garage starts out empty early in the must have a camera over every spot, morning.” then they can count the open spots.” At this point, he had his “AHA” moment. ME: “I don’t see cameras over every I know because he literally stopped in his spot, do you? Plus, I would imagine that tracks and looked up at me smiling ear to a camera over every spot would be quite ear. expensive. Can you think of another THE BOY: “I got it! They just count the way?” cars going in and out! When a car goes THE BOY: (another brief pause) “Maybe in, that’s one less space and when one they have a person at the end of every comes out, that’s one more space.” row that counts the empty spaces in that ME: “That makes sense, I bet that’s how row.” they do it!” ME: “I don’t see anyone watching the If I hadn’t been so excited at his spots like that and how would they epiphany, I would have tried to extend communicate when something changed. this even further with “Can you imagine Any other ideas?” other situations where you could know He was stuck, temporarily out of what’s inside by counting what goes in inspiration. So, I waited and then gave and what comes out?” him a gentle hint.

12 Benefits of Having Kids Answer Their Own Questions Bonus Tip: Use Your Child’s Interests to Your Advantage. The biggest benefit of this strategy is it • If your child enjoys reading, find gets a child to accept the “discomfort” mysteries and other books that of not knowing the answer and teaches include math or puzzles. them to persevere in the face of “not knowing” with the confidence that if they • If your child likes art or animation, keep trying, they will find a solution. Too look for books or videos that can many students lack the ability to manage connect art to architecture or this “discomfort” and tend to beg for an computer animation to geometry. answer or just give up. • If your child likes to play Minecraft Over time, this strategy will also teach or LEGOs, encourage them to your child how to investigate questions build a scale model of your home on their own and it will enhance their or any other building of interest. creativity. Most of the great discoveries in • If your child enjoys cooking, history are the result of passionately recipes are ripe for conversations curious people asking a new question about measurement, unit and seeking out the answer. conversions, and proportions. Next time your child asks one of those The amazing thing about math is “How does it work” type questions, try that you can pursue it’s study just answering with “How / Why do you for fun or you can focus on it’s think?” and see what happens. practical application in almost every facet of human existence.

13 Change Your Child’s Mindset

Stanford psychologist Dr. Carol Dweck identified two learning mindsets which she calls the fixed mindset and the growth mindset. Her research on this topic is summarized in her excellent book, Mindset.

Fixed Mindset

She claims that a person with a fixed mindset believes that traits like A student with a fixed mindset who gets intelligence or musical talent are innate a D on a math test thinks to himself, “I’m and cannot be changed. just not good at math.” and doesn’t go

People with a fixed mindset would say back to learn from mistakes or develop that Tiger Woods had a “gift” for golf or better study habits. that Michael Jordan had an innate talent Fixed mindsets are not just reserved for for basketball or that Einstein was born a people who struggle with math. Dr. genius. Many of us tend to believe this at Dweck found that “gifted” students can least a little. also suffer from a fixed mindset which

Unfortunately, there is an insidious side prevents them from attempting difficult to having a fixed mindset. If you believe problems. talents are fixed, you don’t work as Growth Mindset hard to increase your own talent. A person with a growth mindset believes that abilities and talents can be

14 developed with hard work. They see talented”, we are strengthening the idea failures, not as a judgement on their that talent is innate. talent or self-worth, but as an The good news is that anyone can opportunity to grow and improve. change their mindset. While they feel the sting of a failure, they Research shows that just knowing these can move on to figure out how to two mindsets exist can help a person perform better the next time. move toward the growth mindset A student with a growth mindset who framework. This is true even for children gets a D on a math test, goes back to the — it’s never too early to develop a teacher to find out what they growth mindset! misunderstood. They develop better Praise Effort over Outcomes study habits and seeks extra help until they achieve mastery. When your child comes home with an A on a math test, try saying, “I can see how Changing Your Child’s Mindset your studying paid off. Great work.” These days, it seems that most parents, rather than “Wow! You’re so smart!”. educators and coaches often deliver If your child didn’t put in much effort, but praise and rewards even for average still got a good grade, try saying “Looks results. Studies show the notion that like that test was too easy for you. Maybe everyone deserves a trophy or that we we can work on more challenging should continually praise our children to problems together.” ensure they have self-worth are questionable at best. This will teach them to value the process of learning as much as or even more than It turns out that if we praise children for grades and that it’s OK to struggle with being “smart” or “gifted” or “naturally challenging ideas and problems.

15 Your Child Is More Capable Than You Think!

When your child struggles with math (because that’s how I roll!). At the end, I problems, it’s normal to want to rescue really felt I understood the concepts them. Too often, well-meaning parents much better. will take the pencil away from the child Then I tried a few problems and quickly and so the work for them. While that may got stuck. I had forgotten exactly what I seem like the right thing to do, it’s not! was supposed to do even though I had People learn by DOING, not by just finished the videos which seemed to WATCHING. You wouldn’t try to teach make everything so clear and obvious. your child to ride a bike by watching I’m sure you’ve had this experience too! others. Obviously, that won’t work, you’ve got to get them on a bike and go Be Patient, Your Child Will from there. Surprise You

When your child seems stuck, give them After your child watches you solve a the space to think and encourage them problem, they may say they “get it”. If to press on. you are lucky, they might even remember all the steps, but odds are they will too If you need to help, be sure to ask more forget. questions than you answer. By doing so, you’ll be building your child’s The Person Who Does the Work Does the Learning tolerance to persevere even when they think they are lost. This is such a powerful I recently watched some math videos skill for them to develop. about permutations and computations

16 The greatest part of struggling with Math and Video Games something challenging is the feeling of Videos games do a great job of accomplishment you get when you finally presenting challenges that kids feel like break through. Don’t rob your child of they can solve, which is an enormous this feeling! part of what makes them addictive. What

Every child can persevere (even in math). video games DON’T do is give hints and I know because I see them do it every answers! day while playing video games. Your child can persevere in math too if they feel like there is hope of success. Your job is to encourage that feeling.

From a brain chemistry perspective, what makes video games addicting is that your brain gets a dopamine hit every time you succeed. Dopamine is the brain chemical causes you to feel reward and pleasure. Once you get a dopamine hit, you crave more.

Imagine how you will feel when your child is addicted to math!

It’s possible, I’ve seen it time and again. But only when kids are given the freedom to find their own way. Children are much more capable than you think!

17 You Can Help Your Child Even When You Don’t Know the Math

It’s true that math education has changed If you’re still confounded by Common considerably in the last 25 years. Parents Core or the “new math”, you can try are often frustrated because the reading “Old Dogs, New Math: techniques and terminology have Homework Help for Puzzled Parents”. It’s changed. Many parents fear that if they co-authored by a professor of math teach their child math the “old way”, education. It’s an easy read, filled with their child will be confused. For most examples and explanations to help you children, this just isn’t true! better help your child.

The fundamental change in math education the focus on understanding AND procedures and memorization. You can help your child, not just by helping them memorize facts and procedures but also by making sure they understand WHY they are doing each step.

In addition, we need to remind students that there is almost always more than one way to solve a problem. This allows for flexibility and creativity, it’s part of what makes studying mathematics so much fun!

18 How to Help Even When You Questions You Can Ask Don’t Know the Math Your job is not to explain the HOW to do I know you may not have time to learn all the math. You can still be helpful even the “new math” before your child when you don’t know all the math! experiences it at school and that is OK! Here are some questions you can use: Your job is not to explain the HOW to do • “What is the problem asking?” the math. You can still be helpful even • “What do you notice?” when you don’t know all the math! You • “What questions do you have?” should focus on: • “How do you know?” • “What if you could simplify the • Foster a SAFE environment for problem?” mathematical thinking

You can not learn without make When Your Child Gets Stuck mistakes. • Help them list all the things they • Build your child’s NUMBER SENSE notice about the scenario (don’t focus Practice doing mental math and on the question at first) making estimates. Provide hints as • Simplify the problem and try to solve needed. that first, then add back the • Developing their understanding over complexity simply executing algorithms to get • Draw pictures and diagrams the answer as quickly as possible. • Swap our complicated numbers • Have FUN! Kids tend to enjoy what (fractions, decimals, negatives) for 1 their parents enjoy, so do some math and 10. This will help build an WITH them. (If you have to, fake it intuition for the mathematics first. until you make it) • Take a break and come back fresh

19 Foster a Love of Math Using Games

As parents, we have been educated on Games are to Math as Books are the importance of reading to our young to Reading children every single day. Research shows The first thing you should do as a pro- that these experiences help children active parent is to play games with your develop early literacy skills. The best part children as often as possible. This is as of a nightly reading time is that it is true for pre-schoolers as it is for middle relaxing and fun for parents and kids. schoolers.

Unfortunately, no one tells parents to do Playing games will help your child the same for math because getting a develop mathematical skills naturally head start on numeracy skills has also without turning math into a chore. been shown to pay long-term dividends. Games Provide Many Benefits Instead of finding ways to immerse kids • They are fun for the whole family in hands-on mathematical experiences, • They are interactive and collaborative parents often get workbooks or • They take the pressure out of math and flashcards and use them to make kids put it into meaningful context. memorize “math facts”. This would be • They involve problem solving, critical like trading in nightly “reading time”, for thinking, and estimation, and arithmetic studying the dictionary. Your child would skills hate that! And yet, that’s exactly what we Which Games are the Best? do to math — reduce it to repetitive Almost any game you can think of drills. The good news is there is an requires strategy, spatial reasoning, and/ analog to “reading time”, it’s “game or pattern recognition — all skills that are time”. vital to excellence in mathematics.

20 Even a “word game” like Scrabble 3. Carcassonne (Ages 8+) involves mathematical thinking! For Carcassonne is a tile based game for 2 to example, the placement of words to 5 players. Players build a landscape by optimize your score is at least as adding tiles to the board as the game important as your vocabulary. goes on. After strategically placing a tile, Five Games to Get You Started players have several options for placing their “followers” on the board. This 1. SET (Ages 7+) allows the game to be played with a This game takes a few minutes to learn diverse set of competing strategies, and enhances visual / spatial reasoning which makes the game a lot of fun. skills. Each player surveys the field of 12 cards looking for groups of 3 cards that are all the same or all different with respect to shape, color, number, and pattern. You can play a single-player online version to learn how the game works. Full rules can be found here.

2. Qwirkle (Ages 6+)

Qwirkle is like Scrabble, but with shapes and colors instead of letters. Players can 4. Settlers of Catan (Ages 8+) build on each others lines with new tiles Settlers of Catan is the winner of several and the creative player can find clever gaming awards and was called “the ways to maximize their score. Qwirkle board game of our time” by The can be played with school age students. Washington Post. Players try to build As you play more, you and your child will colonies as they acquire and trade discover new winning strategies.

21 resources. This is another game that • Zeus on the Loose (Ages 5-9) by allows for multiple competing strategies. Gamewright

A typical games lasts 60 to 90 minutes. • Duck Duck Bruce (Ages 4-7) by Gamewright 5. Forbidden Desert (Ages 8+) These games provide kids with great Forbidden Desert is a cooperative game opportunities to develop their thinking where each player takes the role of an and communication skills. Games present adventurer with a unique skill that will aid a wonderful and natural learning the team. Players work together, using opportunity. each other’s unique skills to survive on an ever-shifting game board. The teamwork Play these games with your kids, I needed to play this game makes it a nice promise you’ll love them! change from most competitive games.

Bonus Tip: Start a Family Game Night

Family traditions are the glue that holds families together. Choose one night a week to play games. Turn off the TV, the phone and all other distractions and just have fun! Many games build number sense and mental math skills. Other Games We Recommend • Chocolate Fix (Ages 7+) by Think Fun • Solitaire Chess (Ages 7+) by Think Fun • Hive (Ages 7+) by Gen42 Games

• Blokus by Mattel

22 The Surprising Benefits of Puzzling

Why Do People Enjoy Puzzles? Puzzles Build Perseverance Many novice puzzlers give up. They will Neuroscientist Daniel Bor, a research say to themselves “I have tried fellow at the University of Sussex in everything I can think of, this puzzle is England, believes it’s because we take impossible.” However, with puzzles, you great pleasure in pattern-finding. In his have the opportunity to conquer the book, "The Ravenous Brain", he asserts impossible. What impossible really that human brains are “ravenous” for means in the puzzle context is that you new innovative solutions to problems. simply haven’t figured out how to get to Puzzles are compelling because they the solution *yet*. This is a great lesson offer a complete problem-solving that children can learn by playing with experience, from defining the goal to puzzles. determining the characteristics of the Puzzles are Fun and Rewarding given information, and finally the Many people find puzzles relaxing. solution. Puzzles provide you with a sense of The Benefits of Puzzling accomplishment which releases

Puzzles Enhance Creativity dopamine in the brain, furthering your Good puzzles require the solver to look sense of happiness. The "Aha!" that at the problem in multiple ways and from happens when a person goes through a different perspectives. As a natural major shift in perception to achieve a consequence, the puzzle solver asks solution to a problem (puzzle) becomes more questions and taps into their just as satisfying as an ice cream cone. imagination to find novel pathways.

23 Puzzles Develop Critical Thinking • krazydad.com The steps it takes to complete a puzzle • puzzles.com incorporate elements of sequencing, • New York Times Numberplay blog planning, logic, strategy and problem solving. These skills require the work of Looking for More Problem your prefrontal cortex located in the Solving Opportunities? frontal lobe. At Math Plus Academy, we are constantly seeking out the best puzzles for kids. The best puzzles are addictive just like a Unique puzzles that will help students well-designed video game. As soon as build mathematical thinking skills and you finish one, you want to reach for offer just the right level of challenge. another.

Added Benefits of Our Problem Based Try this puzzle for fun (It's a challenging one!) Programs

The members of a math team • We help encourage students to contributed a total of $2.89 for persevere. refreshments for their weekly practice. • We ask questions that spark their Each member contributed the same creativity. amount and paid for his or her share with • We teach kids how to organize their exactly four coins. How many pennies thinking so that can be more were contributed by all of the members productive and efficient problem combined? solvers.

• Students work together to develop Ready to do some puzzles with your solutions and build teamwork skills child? • We review every solution to make sure Here are three great sources for a variety children retain the key insights. of interesting puzzles.

24 Problems to PLAY with!

Problem 1 How many handshakes will there be?

All the members of a math team Hint: What happens with 3, 4, or 5 contributed the same amount for people? Can you draw a diagram for this refreshments. The total contributed was scenario? $2.89. Each member paid for his or her share with exactly four coins. Problem 5 A decadent box of chocolates adorned How many pennies were contributed in the kitchen counter. When Jake saw it, he all? ate 1/6 of the box. The along came Joe Problem 2 and he ate 1/5 of what Jake left. Next, Jill ate 1/4 of the chocolates that Can you place 8 queens on a chess remained. Later that day, Jeff ate 1/3 of board such that no queen attacks the remaining chocolates. By the time I another? If so, how? Is there more than got there, I managed to eat 1/2 of what one solution? remained. When my sister Sandy came Problem 3 along, only 4 chocolates remained in the

How many squares on an 8 x 8 box. chessboard? How many cookies did Jake eat?

64? … 65? … more? Problem 6

Problem 4 Last night there was a party. The doorbell

You are in a roomful of 35 people. rang 20 times. The first time the doorbell Everyone is asked to shake hands exactly rang, one guest arrived. Each time the once with everyone else. doorbell rang after that, two more guests

25 arrived than had arrived on the previous to open a link and $3 to close a link. How ring. How many guests in all attended can you have the four pieces joined to the party? form a continuous-chain bracelet for only $15? Problem 7

The perimeter of a rectangle is 36 feet. The lengths of the sides are whole numbers. Find the greatest area that the rectangle can have.

Problem 8

You have four pieces of chain with three links a piece. A jeweler will charge you $2

26 More Resources

Books for Kids Thinking Mathematically - J. Mason Creative Problem Solving - George Grapes of Math - Gregory Tang Lenchner Math Appeal - Gregory Tang My Best Mathematical and Logic Puzzles Math Curse by Jon Scieszka - Martin Gardner How Much is a Million - David M Puzzle Websites Schwartz Spaghetti and Meatballs for All - Marilyn puzzles.com - variety of logic puzzles Burns nrich.maths.org - games, lessons, ... mathpickle.com - math explorations The Greedy Triangle - Marilyn Burns krazydad.com - Japanese logic puzzles Sir Cumference and the First Round Games Table - Cindy Neuschwander Visual / Spatial: SET, Swish, Shape by Chasing Vermeer - Blue Baillett Shape, Blokus

Books for Parents Strategy: Carcassonne, Settler’s of Mindset - Dr. Carol Dweck Catan, Qwirkle, Hive

The Mathematician’s Lament - Paul Logic: Chocolate Fix, Rush Hour, Solitaire Lockhart Chess

So Good They Can’t Ignore You - Cal Arithmetic / Memory: Zeus on the Newport Loose, Duck, Duck, Bruce, Rat-a-tat-cat

Problem Solving & Puzzle Books

Becoming a Problem Solving Genius - Ed Zaccaro

27