Math Kangaroo Contest

Ultimate Math Contest Preparation, Problem Solving Strategies, and Math IQ Puzzles for grades 1 to 7

This set of publications is unique and the world's first because not only can a teacher use this workbook to train students to prepare for the world-class math contests, but they can also supplement the class with fun math puzzles. This is the only English math contest workbook that truly integrates Chinese classic word problems curricula and Western problem-solving curricula and puzzles all in one workbook – this is why each workbook has close to or over 600 pages.

The readers can see how the Classic Chinese word problems are being trained in many after-school learning centres on their methods and the types of their problems. In contrast, we have added so much of our research and new ways of solving word problems in improving the shortcomings of Chinese methods. We also point out how Westerners can learn by using the classical word problem-solving methods in today's high-level international and local math contests.

The trend of getting away from formalizing a method to solve word problems has led me to believe the training of math contest is not just to use data bank to let students work on them, instead of how to get them to do deep thinking is the way to go and truly will benefit students when they grow older. Therefore, we can see a benefit to do elementary math contests using arithmetic instead of algebra for contest purposes. It is much more straightforward for some fraction remaining problems to use arithmetic instead of algebra once the students understand how to work backwards. We have pointed out this in many of our workbooks and given some comparisons on when to use arithmetic and algebra.

Ho Math Chess has published a series of math contest workbooks, entitled Math Contest Preparation, Problem Solving Strategies, and Math IQ Puzzles for grades 1 to 7. For example, the Table of Contents and its preface to Math Contest Preparation, Problem Solving Strategies, and Math IQ Puzzles for Grade 1 and 2 are as follows. Each contest workbook also has its accompanying answer book.

All workbooks' contents are written in English other than some headings for using them in China.These workbooks can be purchased from www.amazon.com.

Sample

The Contents of the Math Contest Preparation, Problem Solving Strategies, Math IQ Puzzles Grades 1 and 2 is listed as follows.

Table of Contents 目錄

Chinese Preface 何数棋谜棋谜式教学法 .................................................................... 9
This workbook is aimed at math contests preparation for grades 1 and 2 專为一二年级凖備的書 .................................................................................................................... 11
English Preface英文前言 ........................................................................................... 12
Why do we like the Math Kangaroo Contest? ............................................................. 15
What does it take to be a good math contestant? ...................................................... 20
A sample of math, chess, and puzzles integrated worksheet ....................................... 21
Introduction of contents and inventions 内容介绍及創新發明 ................................... 22
Why are Chinese classic model word problems included in this workbook? 本書为何有中国笵题? .................................................................................................................. 24
Why is it important to do math puzzles? 本書为何有谜题? ........................................ 25
Prerequisites for students who want to use this workbook 使用本書的先決条件 ...... 26
Computation ability assessment 学生计算能力评估,查缺补漏 ................................. 27
Numerical ability assessment 数的评估 ...................................................................... 34
Grade 1 math ability assessment 一年级数学能力评估 ............................................. 35

Part 1 Intelligent math basics worksheets, smart computation, and speedy computation ....... 38

Part 1 棋谜式智能数学, 巧算, 与速算 ........................................................................ 38
Intelligent math basics worksheets 智能基本運算 ..................................................... 40
Why are integrated worksheets better? 为何棋谜式作業纸比较好? ......................... 42
Chess Pieces and their mathematical values 棋子的点数 ............................................ 43
One worksheet fits all grades 一纸包多年级计算题 ................................................... 46
Knight moves to make 10 跳马凑十 ............................................................................ 47
High performance multi-digit addition 高效率多数字加法 ......................................... 49
Computing additions using math and chess integrated puzzle 棋谜式加法 ................ 50
Addition and subtraction by link 加减的互联 ............................................................. 52
Picking your own number 自选数 ............................................................................... 53
Math, chess, and puzzles integrated problem 棋谜式智趣算题 .................................. 54
Number relations in robotic form机器人数谜........................................................................................... 55
Spatial relation and logic 逻辑及空間感 .................................................................................................... 56
Adding with convergent thinking 向心力加法 ........................................................................................... 57
Chess intersection and set 棋步的交义与集合 .......................................................................................... 58

Chessboard and coordinates 棋盤及坐标 ................................................................................................. 60

Doubling and difference of 2 双倍及差2 ................................................................................................ 61
The least and the largest, even and odd, sum and average 最小值及最大值, 奇偶值, 總和及平均值 ..... 62
DIY word problems 自己动手文字題, 答案因人而異 ................................................ 63
Number relationships 数的關係 .................................................................................. 64
Doubling and difference of 2 .................................................................................................................... 65
Consecutive numbers 连續数 ................................................................................................................... 66
Paired whole numbers 配对正整数 .......................................................................................................... 68
Addition and subtraction by link 和差互连 ............................................................................................... 70
Reverse addition and subtraction 和差倒算 ............................................................................................. 72
Frankho Abacus Math™ 算盤数学 ............................................................................................................ 73
Math and chess integrated addition 棋谜融合加法题 ............................................................................... 74
Multiplication, addition, and subtraction 加减乘 ...................................................................................... 76
Memory and computation training 加法記憶 ........................................................................................... 77
Learning multiplication and division 乘除 ................................................................................................. 78
Magic square and chess九宫格(幻方)与囩际象棋数学........................................................................... 79
Multiplication using partial figure and spatial relation 图案及空間乘法 .................................................... 80
multiplication (order of operation) 先乘除後加减 .................................................................................... 83
Learning division from multiplication (Concept used for % and getting one factor) 由乘学除 ..................... 84
Division and remainder 有除馀数 ............................................................................................................ 85
Division with minimum quotient and no remainder 最小值商及無馀数 .................................................... 86
dd divided by dd 二位数除以二位数 ........................................................................................................ 87
Commutative law 交換律 ......................................................................................................................... 89
Addition and subtraction facts 加减的恆等式 .......................................................................................... 91
Partitioning a sum 凑和 ........................................................................................................................... 94
Mixed Computation 混合计算 .................................................................................... 98
Adding numbers in expanded form 展開式加法 ...................................................................................... 102
Mixed Computations with parentheses 有括号计算 ................................................................................ 104
Adding numbers ending in 8 or 9 尾数是8或9的加法 ........................................................................... 108
Skilful adding 巧算 .................................................................................................... 111
Speedy math using shortcuts 巧算 .......................................................................................................... 112
Adding 5’s multiples 加5的倍数 ............................................................................................................ 116

Greater than, less than, or equal ............................................................................... 124

A number representing by a letter ............................................................................ 125

Part 2 Chinese classic model word problems and others ........................................... 126

Part 2 中国奧数古範題及其他奧数考题 .................................................................. 126
Telling time 看时間 .................................................................................................. 127
What time is it to the nearest 5 minutes? ................................................................................................ 131
Draw the hands on the clock to show the time. ....................................................................................... 132
Clock math ............................................................................................................................................. 135
Column and row additions 列row与行column的加法 ............................................ 141
Placing numbers in empty spaces 植入数於空白形内 .............................................. 142
Find out the values of A, B, and C. 找A, B, 及C ..................................................... 147
Finding missing numbers – addition 数字谜加法 ...................................................... 148
Finding missing numbers − subtraction数字谜减法 ............................................................................... 152
One drawable graph 一笔画 ..................................................................................... 155
Counting paths by counting on the dots 通路的计算 ................................................ 157
How many shorter paths are there from A to B? ...................................................................................... 162
Matchsticks math 火柴棒数学 ................................................................................. 163
Matchsticks figures 图形火柴棒 .............................................................................................................. 171
Matchsticks number math 数字火柴棒 ................................................................................................... 172
Age problem 年龄問题 ............................................................................................. 175
Logic problems 逻辑思唯推理問題........................................................................... 179
Square grid math 2 by 2二階正方格数谜 ............................................................................................... 183
Lineup problems 排隊 ............................................................................................... 188
Even and odd numbers 偶奇数 ................................................................................. 190
Geometry几何 ......................................................................................................... 195
Missing part of a figure or dividing a figure 分割或填充图形 ................................................................... 198
Name of lines 线的分類 .......................................................................................................................... 203
Perimeter 周長 ....................................................................................................................................... 206
Rectangle, square, and their prisms 立体 ................................................................................................ 207
Solids 立体 ............................................................................................................................................. 209
Dividing shapes 图形分割 ....................................................................................................................... 211
Symmetry ............................................................................................................................................... 215
Rotation ................................................................................................................... 216

Virtual toy cube math 虛擬玩具方塊数学 ............................................................................................... 220

Cube math transformation 方塊翻转数学 ............................................................................................... 224
Line Segment Diagram 线段图 .................................................................................. 233
Draw lines. ................................................................................................................ 235
Drawing Line Segment Diagram ............................................................................................................... 237
Subtraction ............................................................................................................................................. 239
Addition ................................................................................................................................................. 240
Sum ........................................................................................................................................................ 242
Using the Line Segment Diagram to solve Sum and Difference, Sum and Multiplier problems ................... 244
Relationships of two quantities 二个数量的關係 ...................................................... 245
Given amount = half of difference 给数=差数的一半 ............................................................................... 249
The amount given = half of the difference 给数=差数的一半 ................................................................... 249
Give and Take 取捨問题 ......................................................................................................................... 252
Sum and Difference 和差問题 ................................................................................................................. 255
Method 1 - Use the Line Segment Diagram. ............................................................................................. 255
Method 2 – Use a story to act out. ........................................................................................................... 256
Consecutive numbers连續数 .................................................................................................................. 257
Addition and subtraction 和差問题 ......................................................................................................... 259
Sum and Difference expressed in Systems of Equations ........................................................................... 264
Sum and Difference variations 和差问题变题为異题同解 ....................................................................... 265
Sum and Multiplier 和倍问题 .................................................................................................................. 266
Adding numbers in table 表格内数的加法 ................................................................ 267
Counting figures and angles 数图形及角 .................................................................. 268
Sequence 数列 .......................................................................................................... 270
Arrangement and combination 排列組合 ................................................................. 272
Equation 等式 ........................................................................................................... 279
Pattern 找规律 .......................................................................................................... 280
Number pattern 数字规律 ...................................................................................................................... 280
Pattern and relation (Tabulation) T-表格式規律 ..................................................................................... 286
Pattern and relation 表格式規律 ............................................................................................................ 287
Shape pattern 形狀规律 ......................................................................................................................... 297
Figure pattern 图形規律 ......................................................................................................................... 298
Connected pattern shapes 连續形狀規律 ................................................................................................ 301

Word problem patterns involving computations ...................................................................................... 302

Puzzle pattern 谜题規律 ......................................................................................................................... 304
Chess pattern 国際象棋棋子規律 ......................................................................................................... 305
Pythagoras triangle 楊輝三角形 ............................................................................................................. 306
Fibonacci number 斐波那契数 ................................................................................................................ 308
Pattern and clock data ............................................................................................................................ 308
The pattern in words 文字规律 ............................................................................................................... 309
Inequality 不等式 ..................................................................................................... 310

Part 3 Problem solving strategies ............................................................................. 314

Part 3解题策略 ........................................................................................................ 314
Wording can make problems complicated 文字困擾学生 ......................................... 315
Balance Scale Problem ............................................................................................................................ 316
Using diagrams or tables 用图形或表格解题 ........................................................... 317
Line Segment Diagram 线段图 ................................................................................................................ 317
T-table T-表 ........................................................................................................................................... 318
Venn Diagram ......................................................................................................................................... 318
Weight problem...................................................................................................................................... 319
Give and Take 取捨问题 ......................................................................................................................... 319
The amount given = half of the difference ............................................................................................... 320
Chickens and Rabbits problem 鸡兔同笼 ................................................................................................. 321
Tree diagram 树狀图 .............................................................................................................................. 322
Forward and Backwards (Reverse) calculation 前算及倒算法 .................................. 324
Fill in each box with one different digit from 1 to 9 to get different answers............................................. 328
Reverse subtraction 倒算减法 ................................................................................................................ 341
Reverse multiplication 倒算乘法 ............................................................................................................. 342
Reverse calculation using multiplication .................................................................................................. 343
Reverse Division 倒算除法 ...................................................................................................................... 344
Work backwards using symbols ................................................................................ 345
Substitution method 代換法 ..................................................................................... 350
Scale problems - making each weight scale balanced 天平称重平衡 ........................................................ 352
Marking or writing answers while reading 边唸边写答案 ........................................ 361
Coding 数字化 .......................................................................................................... 365
Building up and writing shorthand answers .............................................................. 369

Using a sample or small number to solve gap or Planting Trees problems

小様本解間隔或植树题 ............................................................................................................... 371

Part 4 Fun Math IQ Puzzles including Frankho ChessDoku and Frankho Maze ........... 374

Part 4 趣味数学IQ及棋谜式智趣迷题 .................................................................... 374

Matrix reasoning 以矩阵拚图 ................................................................................... 375
Figure pattern 图形規律 ........................................................................................... 383
Cognitive math IQ test preparing 数学認知(理智辯識)及智商测试準備 ................. 395
If-then reasoning逻辑问题 ..................................................................................................................... 401
Completing the sequence 排序 ................................................................................................................ 402
Frankho ChessDoku 何算独棋 ................................................................................... 404
Frankho ChessMaze 何数棋谜迷宫 ........................................................................... 412
Frankho ChessMaze 何数棋谜迷宫 ........................................................................... 413
Square grid math and puzzles 正方格数谜 ................................................................ 417
3 by 3 Sudoku 三階数独 .......................................................................................................................... 417
4 by 4 Sudoku 四階数独 .......................................................................................................................... 419
Finding intersections 找交义点 ............................................................................................................... 420
Finding reflections 找反射 ...................................................................................................................... 421
Frankho unequal ChessDoku 何数棋谜不等算独 ..................................................................................... 422
Matching the number of cherries 物与其数的配对 .................................................................................. 423
Matching math operators配对数学運算符号 ......................................................................................... 424
Square grid math 2 by 2二階正方格数谜 ................................................................................................ 425
Sudoku math 算独 .................................................................................................................................. 427
Building fence 盖围墙 ............................................................................................................................. 428
Amandaho moving dots动点迷 .............................................................................................................. 429
Connecting rooks 走车 ............................................................................................................................ 430
Integrated math, chess, and puzzles 数学智趣混合题 .............................................. 431
IQ math puzzles 智商数谜 ....................................................................................................................... 432
Future math star 明日之星 ..................................................................................................................... 464
Rising star 旭曰之星 ............................................................................................................................... 467
Four-colour map 四色地图 ...................................................................................................................... 478
Virtual cell phone operating math 虛擬手机操作数学 ............................................................................. 480
Math IQ fitness puzzles 数学IQ健腦 ........................................................................ 485

Part 5 School Math English word problems ............................................................... 505

Part 5 学校数学英语文字問题 ................................................................................. 505

Basic word problems 初级文字問题 ......................................................................... 506
Intermediate word problems 中级文字应用题 ......................................................... 532
Mixed word problems at contest level ...................................................................... 536
Advanced word problems at contest level高级文字競赛应用题 .............................. 538

What unique is Chinese math? 中国小学数学有何特色? ......................................... 558
Times Table 九九乘法表 ......................................................................................................................... 558
Smart phrases of positive and negative integer operations正負整数運算口诀 ........................................ 560
Classic model word problems 中囯四则运算古算题 ................................................................................ 561
Math Terminology 数学名词 ................................................................................................................... 563
Chinese character itself teaches math 中文方塊字本身可教数学 ............................................................ 564
Appendix A Chickens and Rabbits classic model word problem 鸡兔同笼 ................. 565
介紹何数棋谜 .......................................................................................................... 567
Introducing Ho Math Chess™ ..................................................................................... 568
Other Ho Math Chess Publications ............................................................................ 569

This workbook is aimed at math contests preparation for grades 1 and 2

There are not many math contests for grades 1 and 2. The main reason, I think, is the limited math computation ability of lower grades students. Many North American students will not learn multiplication until grade 3, but many Asian countries and areas learn times tables in grade 2, so there is one year of the difference of learning ahead in China. This workbook has brought its standard to meet the highest possible math curriculum in the world, so four operations of computation appear in this workbook. The earlier the students could master the skills of four basic operations, the more the students could explore many possibilities of word problem computation problems. With this in mind, how does the very popular Math Kangaroo Contest test the grade 1 and grade 2 students? How is it different from other math contests?

The Math Kangaroo grades 1 and 2 Contest almost does not include the direct math computation problems which are very different from some math contests in China, where direct computation problems could include skillful computation problems. I analyzed the most recent years of Canadian Math Kangaroo Contest grade 1 and 2 problems, and they start to emerge some characteristics and categories, so I include here to help students prepare for it. The lower grade math contest tends to skew to the more visual operation type of problems. The problems could be classified as follows:

Arrangement and sorting numbers
Patterns of figures and numbers
Counting figures or shapes or paths
Cubes or cards math Including rotation or folding
Identifying parts of a figure or finding what part of a figure is missing
Number puzzles including filling numbers into empty spaces
Logic and reasoning problems
Word problems including some Chinese model problems
All other problems which do not belong to the above.

Many of the above problems are not typical problems that appeared in the books where you can buy from a bookstore because the problems in the math contests are much more complicated and involve a lot of creativity. The above subjects are now included in this workbook.

Frank Ho

November 2016

Preface 前言

I have encountered many problems while I was teaching, including some of the followings:

The traditional computation worksheet format is boring. Many research papers have been published to show us how to teach math, but when it comes to having some practice sheets, the choices are few and far between. None of them could have any earth-shattering styles.
I teach in an environment which is very different from regular day schools because I could have students ranging from grade 1 to grade 6 all in one class, although I tried hard to have a similar background of students gathered together, sometimes it is not possible because students have other lessons to go to. Most of my students have after-school classes almost every day.
Some students can only do very basic calculation sheets, yet some of them need to be challenged on advanced word problems including math contest problems. How can I teach students with such a diversified background?
Children not only need to learn math, but some of them also need to do puzzles to activate their brains and increase their IQ.

With the above in mind, I created many separate workbooks including basic calculation, word problems, puzzles, and I even incorporated chess moves into my math worksheets. With all these efforts, ironically, I created an additional problem for myself. That is I have to use four workbooks to teach one child. In 2015, I started to pay attention to Chinese after-school learning centres’ teaching materials and started to compare their teaching materials with our North American materials. At the same time, I researched the materials from Singapore, Taiwan, and puzzles from Japan and Britain. These analytical researches have led me to have an idea to combine all my published workbooks into one large workbook which includes math contest problems, IQ fitness, word problems, and chess and math integrated worksheets.

This workbook is unique and one-of-a-kind. It also represents my idea of showcasing why math is fun to children and my ideas of using inquiry and conceptual teaching (探索及覌念教学法) and then reinforced by procedural practices (步骤及題庫). I have used many of these worksheets on my students in my classes and witnessed their feedback. Most children do not want to do just computation problems for 2 hours; very few students like to work on math contest problems for 2 hours continuously, so puzzles and chess problems are fun for them for a change.

The Ultimate Math Contest Preparation, Problem Solving Strategies, and Math IQ Puzzles series of workbooks are created not for “teaching to test”. It is created with the idea of fostering students’ creativity. For this; it can be seen, in these workbooks, we have demonstrated many different methods of solving the same problem (一题多解), and how to transfer the knowledge of solving a model word problem to expansion problems (举一反三). Some examples have provided the same method to solve the different problems with different data types (異题同解).

This workbook is not created for those students who are having problems with their day school math, but for the students who have shown above the average math ability and are willing to take on the additional challenging by learning something they do not normally learn at their day school’s math classes. Our workbook also shows the variety of math problems a student could learn other than the school math.

This workbook is not only written with a traditional western math teacher’s view but also incorporated some popular classic Chinese word problems to give insights on how Chinese train their elementary math contestants. The advantage of using these classic model problems is to get students to use arithmetic skills to solve complicated word problems, which they naturally possess some beautiful math models. For example, the Tree Planting problem naturally has three equation models, and the Chickens and Rabbits problem is a type of Systems of Equations problem, yet the elementary students need to solve them using arithmetic, instead of using algebra. The traditional style of writing math topics by strategies or math subjects are also included in our workbook.

Besides, we also included some of our puzzle inventions. So overall, this math contest workbook takes on an “all-round and all resources” training approach (飽合训練) which includes the training materials coming from model problems, strategies, word problems, and puzzles.

The purpose of these books is to promote mathematical thinking and to stimulate student's interest in math. The good math contest contestants not only care about getting the correct answer, they also enjoy the process of thinking on how to solve problems.

Our math contest books are suitable for preparing the following math contests or competitions.

Worldwide Math Kangaroo Contests
USA Mathcounts
USA Math Olympiad
Math League Math Contest
Canada BC Math Contest
Canadian Math Challengers Competition
Canadian Gauss & Pascal Mathematics Contests
Mathematica Pythagoras, Euler, Lagrange, Newton contests
Worldwide Caribou Mathematics Online Contest (USA Brock University)
Chinese math contests 中国各類杯賽
Many countries' math competitions

Teachers are encouraged to select materials which are suitable for a student's background.

Frank Ho

December 2014 first edition

November 2016 revised edition