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 world's first because not only teacher can use this workbook to train students to prepare for the world-class math contests, they can also supplement the class with fun math puzzles. This is the only English math contest workbook so far which truly integrates Chinese classic word problems curricula and Western problem-solving curricula and puzzles all in one workbook – this is the reason why each workbook has close to or over 600 pages. The readers can clearly 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 own research and new ways of solving word problems in improving the shortcomings of Chinese methods. We also point out how the Western 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 formulizing 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 to work on them, instead 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 there is a benefit to do elementary math contests using arithmetic instead of using algebra for contest purposes because, for some fraction remaining problems, it is much clearer to use arithmetic instead of using 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 when to use algebra.

Ho MATH CHESS will offer training classes at the Spring Break time as in the past few years. Ho Math Chess has written contest materials and its teachers are very experienced in training. Students normally would have the possibility to gain higher points or gain confidence after the training camp.

For details on Spring Break training camp, please phone 604-263-4321.

Ho Math Chess has published a series of math contest workbooks, entitled, *Ultimate 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 *Ultimate Math Contest Preparation, Problem Solving Strategies, and Math IQ Puzzles for Grade 1 and 2* are as follows. Each contest workbook also has its accompanied 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.

**Communication**

For people using WeChat (微信),you can join the Elementary Math Contest WeChat Group by searching**小学数学竞赛微信群**. Others can email us at fho1928@gmail.com.

**Sample**

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

**Table of Contents ****目錄**

*Preface**前言... 7*

*Introduction of contents and inventions **内容介绍及創新發明... 10*

*Why are Chinese classic model word problems included in this workbook?. 12*

*Why is it important to do math puzzles? **本書为何有谜题?. 13*

*Prerequisites for students who want to use this workbook **使用本書的先決条件... 14*

*Computation ability assessment **学生计算能力评估,**查缺补漏... 15*

*Numerical ability assessment **数的评估... 22*

*Grade 1 math ability assessment **一年级数学能力评估... 23*

*Part 1 Intelligent math basics worksheets, smart computation, and speedy computation. 26*

*Part 1 **棋谜式智能数学, **巧算, **与速算... 26*

**Intelligent math basics worksheets ****智能基本運算... 28**

**Why are integrated worksheets better? 30**

Chess Pieces and their mathematical values 棋子的点数... 31

Chess pieces’ names and moves 棋子名及走法... 32

One worksheet fits all grades 一纸包多年级计算题... 34

Knight moves to make 10 跳马凑十... 35

High-performance multi-digit addition 高效率多数字加法... 37

Computing additions through math and chess integrated puzzle 棋谜式加法... 38

Addition and subtraction by link 加减的互联... 40

Picking your own number 自选数... 41

Math, chess, and puzzles integrated problem 棋谜式智趣算题... 42

Buildings 看高楼 ... 42

Number relations in robotic form机器人数谜... 43

Spatial relation and logic 逻辑及空間感... 44

Adding with convergent thinking 凝聚心(向心力)加法... 45

Chess intersection and set 棋步的交义与集合... 46

Chessboard and coordinates 棋盤及坐标... 48

Doubling and difference of 2 双倍及差2. 49

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... 50

Number relationships 数的關係... 51

Consecutive numbers 连續数... 53

Paired whole numbers 配对正整数... 55

Addition and subtraction by link 和差互连... 57

Reverse addition and subtraction 和差倒算... 59

Frankho Abacus Math™ 算盤数学... 60

Math and chess integrated addition 棋谜融合加法题... 61

Multiplication, addition, and subtraction 加减乘... 63

Memory and computation training 乘法记憶... 64

Learning multiplication and division 乘除... 65

Magic square and chess九宫格(幻方)与囩际象棋数学... 66

Multiplication using partial figure and spatial relation 图案及空間乘法... 67

multiplication (order of operation) 先乘除後加减... 70

Learning division from multiplication (Concept used for % and getting one factor) 由乘学除... 71

Division and remainder 有除馀数... 72

Division with minimum quotient and no remainder 最小值商及無馀数... 73

dd divided by dd 二位数除以二位数... 74

**Commutative law ****交換律... 76**

**Addition and subtraction facts ****加减的恆等式... 78**

**Partitioning a sum ****凑和... 81**

**Mixed Computation ****混合计算... 85**

**Adding numbers in expanded form ****展開式加法... 89**

**Mixed Computations with parentheses ****有括号计算... 91**

Mixed Computations 混合式计算... 94

Adding numbers ending in 8 or 9 尾数是8或9的加法... 95

Skillful adding 巧算... 98

Speedy math using shortcuts 巧算... 99

Speedy math using shortcuts (addition and subtraction) 加减巧算... 100

Adding 5’s multiples 加5的倍数... 103

*Part 2 Chinese classic model word problems and others. 111*

*Part 2 **中国奧数古範題及其他奧数考题... 111*

**Telling time ****看时間... 112**

**Calendar problems ****日曆... 121**

**Column and row additions ****列与行的加法... 122**

**Placing numbers in empty spaces ****植入数於空白形内... 124**

**Find out the values of A, B, and C. ****找A, B, ****及C. 129**

**Finding missing numbers – addition 数字谜加法... 130**

**Finding missing numbers **__ subtraction____数字谜减法__**... 134**

**One drawable graph ****一笔画... 137**

**Counting paths by counting on the dots ****通路的计算... 139**

**Matchsticks math 火柴棒数学... 145**

Moving Match sticks math 移动火柴棒遊戲数学... 145

Matchsticks figures 图形火柴棒... 153

Matchsticks number math 数字火柴棒... 154

**Age problem ****年龄問题... 157**

**Lineup problems ****排隊... 163**

**Even and odd numbers ****偶奇数... 165**

**Geometry****几何... 170**

shapes形狀... 170

What kind of lines does each picture have? 直线, 曲线, 平行线... 171

Missing part of a figure or dividing a figure 分割或填充图形... 173

Name of lines 线的分類... 175

Angles and its classification 角及角的分类... 176

Rectangle, square, and their prisms 立体... 178

Dividing shapes 图形分割... 182

**Line Segment Diagram ****线段图... 186**

**Give and Take problem ****取捨問题... 197**

Given amount = half of difference 给数=差数的一半... 199

**Amount given = half of the difference ****给数=****差数的一半... 199**

**Relationships of two quantities ****二个数量的關係... 201**

Give and Take 取捨問题... 205

Sum and difference 和差問题... 206

Addition and subtraction 和差問题... 210

Sum and Difference variations 和差问题变题为異题同解... 216

Adding numbers in table 表格内数的加法... 217

Counting figures and angles 数图形及角... 218

**Sequence ****数列... 219**

**Arrangement ****排列... 221**

**Equation ****等式... 225**

**Finding Pattern ****找规律... 226**

Number pattern 数字规律... 226

Pattern and relation (Tabulation) T-表格式規律... 232

Shape pattern 形狀规律... 243

Figure pattern 图形規律... 244

Connected pattern shapes 连續形狀規律... 246

Puzzle pattern 谜题規律... 248

Chess pattern 国際象棋棋子規律... 249

Pythagoras triangle 楊輝三角形... 250

Fibonacci number 斐波那契数... 252

**Inequality ****不等式... 254**

*Part 3 Problem solving strategies. 258*

*Part 3**解题策略... 258*

**Wording can make problems complicated ****文字困擾学生... 259**

Scale Problem.. 260

**Using diagrams or tables ****用图形或表格解题... 261**

Line Segment Diagram 线段图... 261

T-table T-表... 262

Give and Take 取捨问题... 263

Chickens and Rabbits problem 鸡兔同笼... 265

Tree diagram 树狀图... 266

**Forward and Backwards (Reverse) calculation ****前算及倒算法... 269**

Reverse subtraction 倒算减法... 286

Reverse multiplication 倒算乘法... 287

Reverse Division 倒算除法... 289

**Substitution method ****代換法... 295**

Scale problems - making each weight scale balanced 天平称重平衡... 296

**Marking or writing answers while reading ****边唸边写答案... 304**

Coding 数字化... 308

**Using a sample or small number to solve gap or tree planting problems****小様本解間隔或植树题... 312**

*Part 4 Fun Math IQ Puzzles including Frankho ChessDoku and Frankho Maze. 315*

*Part 4 **趣味数学IQ**及棋谜式智趣迷题... 315*

**Matrix reasoning ****以矩阵拚图... 316**

**Cognitive math IQ test preparing ****数学認知(****理智辯識)****及智商测试準備... 336**

**Frankho ChessDoku ****何数棋谜算独... 345**

**Frankho ChessMaze ****何数棋谜迷宫... 352**

**Square grid math and puzzles ****正方格数谜... 356**

3 by 3 Sudoku 三階数独... 356

4 by 4 Sudoku 四階数独... 358

Finding intersections 找交义点... 359

Finding reflections 找反射... 360

Frankho unequal ChessDoku 何数棋谜不等算独... 361

Matching the number of cherries 物与其数的配对... 362

Matching math operators配对数学運算符号... 363

Square grid math 2 by 2二階正方格数谜... 364

Sudoku math 算独... 366

Fencing 盖围墙... 367

Amandaho moving dots动点迷... 368

Connecting rooks 走车... 369

**Integrated math, chess, and puzzles ****数学智趣混合题... 370**

IQ math puzzles 智商数谜... 371

Future math star 明日之星... 403

Rising star 旭曰之星... 406

Four coloured map 四色地图... 417

Virtual cell phone operating math 虛擬手机操作数学... 419

Virtual toy cube math 虛擬玩具方塊数学... 424

Cube math transformation 方塊翻转数学... 429

**Math IQ fitness puzzles ****数学IQ****健腦... 437**

*Part 5 English word problems. 457*

*Part 5 **英语文字問题... 457*

**Basic word problems ****初级文字問题... 458**

Addition word problems. 458

Addition word problems. 461

Subtraction word problems. 462

Subtraction word problems. 463

Addition or subtraction word problems. 466

Addition or Subtraction Word Problems. 467

Multiplication word problems. 469

Division word problems. 472

Mixed word problems of four operations 四則運算文字題... 476

**Intermediate word problems ****中级文字应用题... 484**

Two-step word problems 二步算文字题... 484

**Advanced word problems ****高级文字应用题... 490**

*What unique is Chinese math? **中国小学数学有何特色?. 510*

**Times Table ****九九乘法表... 510**

**Smart phrases of positive and negative integer operations****正負整数運算口诀... 512**

**Classic model word problems ****中囯四则运算古算题... 513**

**Math Terminology ****数学名词... 515**

**Line Segment Diagram ****线段图... 515**

**Chinese character itself teaches math ****中文方塊字本身可教数学... 516**

*Ho Math Chess Franchise information **何数棋谜连锁消息... 519*

**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 table at 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 the math contests in China where direct computation problems could include skilful 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 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 creativities. The above subjects are now included in this workbook.

Frank Ho

November 2016

**Preface ****前言**

I have been teaching math to kindergarten to grade 12 students for the past 21 years every night, 7 days a week at the Ho Math Chess Learning Centre based in Vancouver, Canada. I have encountered many problems 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 comes to have 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 diversified background?
- Children not only need to learn math, some of them 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 4 workbooks to teach one child. In 2015, I started to pay attention to Chinese after-school learning centre’steaching 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 own 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 themselves 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. In addition, 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