Book 12: Puzzles & Games - GSSD...

Math 21 Recreation and Wellness

Book 12: Puzzles & Games

Teacher Version – Assessments and Answers Included

Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Year Overview:

Earning and Spending Money

Home Travel & Transportation Recreation and Wellness

1. Budget 2. Personal Banking 3. Interest 4. Consumer Credit 5. Major Purchases

6. Scale Drawings & Ratios

7. Area & Volume 8. Angles 9. Triangles 10. Slope & Elevation

11. Travel Project 12. Puzzles & Games 13. Understanding

Statistics 14. Budgeting Recreation

Topic Overview Recreational activities such as playing games, solving puzzles, and participating in sporting events as well as activities connected to personal wellness all involve problem solving strategies, reasoning, and budgeting skills. This section of the recreation and wellness unit is designed to give you an opportunity to use math in puzzles and games.

Outcomes

Theme Specific Outcomes

M21.2 Demonstrate understanding of numerical reasoning and problem solving strategies by analyzing puzzles and games.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Contents Topic Overview.................................................................................................................. 2

Outcomes ....................................................................................................................... 2

Theme Specific Outcomes ....................................................................................... 2

Glossary of Terms ........................................................................................................... 5

11.1 The Math of Playing Games and Doing Puzzles .................................................. 6

11.1 Practice Your Skills – Games and Puzzles ....................................................... 6

11.2 Inductive and Deductive Reasoning .................................................................... 8

11.2a Practice Your Skills - Analyze and Strategize ............................................ 10

11.2b Practice Your Skills - Deductive Reasoning .............................................. 14

11.3 Puzzles ....................................................................................................................... 15

A. KAKURO .................................................................................................................... 15

11. 3 Practice Your Skills: ......................................................................................... 17

B. CalcuDoku ............................................................................................................... 19

3.2 Practice Your Skills: ............................................................................................ 20

C. Sudoku ..................................................................................................................... 22

11.3 Practice Your Skills: .......................................................................................... 22

D. Chain Sudoku (Strimko) ......................................................................................... 28

11.4 Practice Your Skills: .......................................................................................... 29

E. Golf the card game................................................................................................ 31

Discuss the Ideas ...................................................................................................... 33

11.5 Practice Your Skills ........................................................................................... 33

Student Evaluation .......................................................................................................... 35

Learning Log .................................................................................................................... 36

11.2 Show What You Know: Inductive and Deductive Reasoning ......................... 37

Show What You Know - Puzzles ..................................................................................... 40

Show What You Know – Quiz ........................................................................................ 44

Answers ............................................................................................................................. 50

11.1 Practice Your Skills – Games and Puzzles ..................................................... 50

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015

11.2 Practice Your Skills: Analyze and Strategize ................................................ 50

11.2 Show What You Know: Inductive and Deductive Reasoning ................. 51

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Glossary of Terms alternative approaches

a problem solving strategy that is made up by a person to solve a non-routine problem

conjecture a guess, or conclusion based on the information you have

deductive reasoning a conclusion that is a fact based on true statements

draw or model a problem solving strategy that has you draw a sketch that represents the

information you are given and being asked for

eliminate possibilities a problem solving strategy that has you try different possibilities in order to

eliminate them, leaving only the right answer

guess & check a problem solving strategy that involves guessing the answer to a problem

and then checking to see if it makes sense inductive reasoning

a probable conclusion that has a lot of evidence to support it look for a pattern

a problem solving strategy where you can find patterns in numbers, items, or events that repeat

make a systematic list a problem solving strategy that has you make a list or fill in a table so that

information is organized in a logical way

solve a simpler problem a problem solving strategy that has you use smaller numbers in order to find

out how to solve the problem work backwards

a problem solving strategy where you start with the end result mentioned in a problem, and work backwards to find the answer

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Math 21 Recreation and Wellness

11.1 The Math of Playing Games and Doing Puzzles When playing games or doing puzzles you are using mathematical reasoning and you may not even know it. If you are focused on the task you will be using a combination of Number Sense, Spatial Sense, and Logical Thinking. Look at the following and make a conjecture for the next part.

Look carefully at the following figures, what do you think the next figure in the pattern will be?

11.1 Practice Your Skills – Games and Puzzles Different strategies can be used to solve a puzzle: guess & check, look for a pattern, make a systematic list, draw or model, eliminate possibilities, solve a simpler problem, work backwards and develop alternative approaches.

Use one of these strategies to solve the puzzle on the following page:


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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.2 Inductive and Deductive Reasoning

There are two different types of reasoning that let us make conclusions about the world around us:

Inductive Reasoning: Inductive reasoning is a conclusion based on several past observations. The conclusion is probably true, but not necessarily true. Inductive reasoning is used when we collect evidence, observe patterns and draw conclusions from these observed patterns. This evidence does not prove conclusions, but suggests the conclusion.

Example: Because the sun has risen every day of our lives, we conclude that the sun will rise tomorrow.

Deductive Reasoning: Deductive reasoning is a conclusion based on accepted statements such as definitions, postulates, theorems, given information and known properties of mathematics. Deductive reasoning uses logic that is based on accepted facts to draw conclusions.

Example: All oranges are fruits. All fruits have seeds. Therefore, all oranges have seeds.

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Learn More At:

Inductive Reasoning: http://www.youtube.com/watch?v=HFqFZXTnMGM

Deductive Reasoning: http://www.youtube.com/watch?v=6d0LVrNPMoU&list=PL1WsG9pe4MZq8OtaQLyizEmJ03_J_Qp8S

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http://www.youtube.com/watch?v=HFqFZXTnMGM

http://www.youtube.com/watch?v=HFqFZXTnMGM

http://www.youtube.com/watch?v=6d0LVrNPMoU&list=PL1WsG9pe4MZq8OtaQLyizEmJ03_J_Qp8S




Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.2a Practice Your Skills - Analyze and Strategize

1. Look carefully at the following figures, what do you think the next figure in the pattern will be?

2. Look at the following patterns, what do you think the next number will be?

a) 3, 6, 12, 24, …

b) 2, 6, 12, 20, 30, 42,…

You just used reasoning to create a conjecture, a conjecture is

• a testable expression • based on available evidence • is not yet proven.

So really, a conjecture is a best guess at an answer based on what you have seen/know about the question. Mathematically this process is known as Inductive reasoning, defined as drawing general conclusions by observing patterns and identifying properties in specific examples. That is exactly what you did in the above examples. Let’s do one more…

A helpful website for information on how to approach puzzles is here: http://www.planetseed.com/relatedarticle/eleven-strategies-solving-math-puzzles

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 3. Do the following number trick two times then make a conjecture about the relationship between the original number and the final number in the following process.

First Second

Pick a number.

Multiply the number by 5

Add 10 to the product

Divide the sum by 5

Subtract 1 from the quotient

4. What is your conjecture about the relationship between the original number and the final number?

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Deductive reasoning is a different type of logic which draws a specific conclusion t by starting with general assumptions that are known to be true. A conclusion reached with deductive reasoning is logically sound, assuming the first statements are true.

Example:

• All birds have wings, • I have caught a bird. • I conclude that the animal I have caught has wings.

You try…..

1. All the planets revolve around the sun in an elliptical orbit.

Mars is a planet

Therefore, Mars .

2. All dogs are mammals

All mammals have kidneys.

Therefore, dogs .

3. All squares are rectangles.

All rectangles have four sides.

Therefore, all squares .

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 4. Now let us go back to the number trick, to solve this deductively use the

variable X to start rather than a number. Does this follow your conjecture?

Pick a number. X

Multiply the number by 5

Add 10 to the product

Divide the sum by 5

Subtract 1 from the quotient

What is the relationship between X and the final number?

5. Three men – Fred, Ed and Ted – are married to Joan, Sally and Vickie, but not necessarily in that order. Joan, who is Ed’s sister, lives in Detroit. Fred dislikes animals. Ed weighs more than the man who is married to Vickie. The man married to Sally breeds Siamese cats as a hobby. Fred commutes over 200 hours a year from his home in Ann Arbor to his job in Detroit. Match up the men with the women they married.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.2b Practice Your Skills - Deductive Reasoning

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.3 Puzzles Over the next few pages you will be introduced to different types of puzzles. Use the information to build and practice your skills.

A. KAKURO Each puzzle consists of a blank grid with sum-clues in various places. The object is to fill all empty squares using numbers 1 to 9 so the sum of each horizontal block equals the clue on its left, and the sum of each vertical block equals the clue on its top. In addition, no number may be used in the same block more than once.

A tutorial on Kakuro:

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/kakuro/tutorial

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Some helpful number combinations for you to use when completing Kakuro puzzles are:

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11. 3 Practice Your Skills:

1.

2.

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3.

4.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 B. CalcuDoku Each puzzle consists of a grid containing blocks surrounded by bold lines. The object is to fill all empty squares so that the numbers 1 to N (where N is the number of rows or columns in the grid) appear exactly once in each row and column and the numbers in each block produce the result shown in the top-left corner of the block according to the math operation appearing on the top of the grid. In CalcuDoku a number may be used more than once in the same block.

SAMPLE PUZZLE SAMPLE SOLUTION

Check out this tutorial on CalcuDoku

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/calcudoku/tutorial

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 3.2 Practice Your Skills:

1.

2.

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3.

4.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 C. Sudoku 11.3 Practice Your Skills:

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23


24


25


26


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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 D. Chain Sudoku (Strimko)

Chain Sudoku is a number logic puzzle similar to Classic Sudoku except that the numbers are grouped in chains instead of boxes. Each puzzle consists of a group of circles arranged in a square grid and containing given clues in various places. The object is to fill all empty circles so that the numbers 1 to 5 for 5x5 puzzles and 1 to 6 for 6x6 puzzles appear exactly once in each row, column and chain.

In this example, looking at the bottom right chain, we need to add the numbers 1 and 4. Working horizontally I cannot put the number 4 in the bottom right because it is already in that horizontal line, so I know it must be a 1. Now forcing the only open space left in the chain to be a 4. Just looking at the number 4 I know the very top right circle must be a 4 because I need a 4 in the furthest right column and it cannot go in the middle circle because of our newest 4 being the 4 in the middle row. To finish off the 4’s we know second row middle circle must be a 4 so that we now have a 4 in every row and every column.

Check out more information on Chain Sudoku.

http://2.bp.blogspot.com/_qKif7BN6IxI/SoQDeXJ-FgI/AAAAAAAAACM/c_4YSylLYMM/s1600-h/strimko.jpg

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http://www.google.com/url?sa=i&rct=j&q=chain+sudoku&source=images&cd=&cad=rja&uact=8&docid=ocSzQS2EbyRRJM&tbnid=lzNP0hoKJqvlQM:&ved=0CAUQjRw&url=http://onevideogameaday.com/post/13767917909/chain-sudoku&ei=tjZMU75TypjIAandgPAB&bvm=bv.64764171,d.aWc&psig=AFQjCNF8RGHbNXiXv5lh--ZbuP6OtbmHqg&ust=1397589969711200



Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.4 Practice Your Skills:

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 E. Golf the card game Two, three or four players use a standard 52-card pack. The dealer deals six cards to each player, one at a time, arranging them face down in a rectangle in front of each player like this:

The remaining undealt cards are placed face-down in the center of the table to form a drawing pile. The top card of the pile is turned face up and placed beside the stock to start the discard pile. Before play begins, each player looks at any two of the cards in their hand. You only get to look at two cards and you only get to look once. If you forget to bad. The other layout cards may not be looked at until they are discarded or turned up in the course of the play.

Playing

The player to the dealer's left begins, and the turn to play passes clockwise. At your turn you must either draw the top card of the face-down pile, or draw the top discard card. If you draw from the face down pile then you must decide if you are going to keep the drawn card or not. If yes replace one of your face down cards with the drawn card but put it face up, and discard your face down card by turning it face up and placing it in the discard pile. If you do not want to keep your drawn card then discard it face up in the discard pile, and turn over one of your six cards in front of you so it is now face up. If you decide to draw from the discard pile you must keep that card by placing it face up in place of one of your face down cards, discard your face down card by turning it face up and placing it on the discard pile.

Once a card is face up it cannot be changed. Now it is the next player's turn.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 The play ends as soon as the last of a player's six cards is face up. This will happen in six round because at the end of your turn you should have a card turned face up. The hand is then scored.

Scoring - You want a low score.

After all six cards are face up you can score your hand.

• Kings are worth 0 points • Aces are worth 1 point • 2 – 9 are worth face value, so a 6 is 6 points a 7 is 7 points etc. • 10, Jacks, Queens are each worth 10 points • If you are able to pair the same cards then they each count as 0. So if you

have 2 Jacks they are worth 0 points. Here are some example scores: • King, Ace, Ten, Nine, Nine, Four is worth 15 points • 0 for the king, 1 for the ace, 10 for the ten, 0 for the pair of nines and 4 for

the four.

End of the game

Usually golf is done after 9 hands, the player with the lowest score is the winner.

Adaptations

• You can let the dealer decide how many cards to start with rather than 6 anywhere from 4 – 8.

• You can have the five cards count as -5 • You can add Jokers that count as hazards and if you discard or flip a joker

you get an extra counting card from the top of the deck. Face up Jokers count as 11.

• You can play more or less total hands.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Discuss the Ideas

1. What did you learn while playing Golf?

2. What strategies can you use while playing Golf?

11.5 Practice Your Skills 1. Multiply three odd numbers and examine the answer. Do this a

few times, what conjecture could you make about the product of three odd integers?

2. Perry works at a bakery shop in Regina. He goes to the farmer’s market and buys enough fruit to bake 20 Saskatoon berry pies and 10 rhubarb pies. Which conjecture has Perry most likely made?

3. All camels are mammals. All mammals have lungs to breathe air. Humphrey is a camel. What can be deduced about Humphrey?

4. Try the following number trick with different numbers. Make a conjecture about the trick.

• Choose a number. • Multiply by 3. • Add 5. • Multiply by 2. • Subtract 10. • Divide by 6.

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5. Determine the unknown term in this pattern.

1, 4, 16, 64, ___, 1024, 4096


4, 7, 5, 8, ____, 9, 7, 10, 8

7. Draw the next figure in this sequence.

Figure 1 Figure 2 Figure 3

8. What number should appear in the centre of Figure 4?

Figure 1 Figure 2 Figure 3 Figure 4

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Student Evaluation

M21.2 Demonstrate understanding of numerical reasoning and problem solving strategies by analyzing puzzles and games. [FM20.2 and WA20.2]

a. I can make conjectures by observing patterns and identifying properties, and justify the reasoning.

b. I can observe and analyze errors in solutions to puzzles or in strategies for winning games to identify and correct errors, if necessary, and explain the reasoning.

c. I can solve questions that involve numerical reasoning.

Insufficient Evidence (IE)

Developing (D) Growing (G) Proficient (P) Exceptional (E)

Student has not demonstrated the criteria below.

Student has rarely demonstrated the criteria below.

Student has inconsistently demonstrated the criteria below.

Student has consistently demonstrated the criteria below.

Student has consistently demonstrated the criteria below. In addition they have shown their understanding in novel situations or at a higher level of thinking than what is expected by the criteria.

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Learning Log Date Starting Point Ending Point

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.2 Show What You Know: Inductive and Deductive Reasoning

1. Multiply any two even numbers and one odd integer together. Do this a few times and examine the answers, what conjecture could you make about the answer of two even integers and one odd integer?

2. Chantel works part-time at a clothing store in Calgary. The manager has ordered 20 red shirts and 20 blue shirts. Which conjecture has the manager most likely made?

3. All birds have feathers. Robins are birds. Spencer is a Robin. What can be deduced about Spencer?

4. Try the following calculator trick with different numbers. Make a conjecture about the trick.

• Start with your age.

• Multiply it by 3.




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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 5. Determine the unknown term in this pattern.

4, 8, 16, 32, ____, 128, 256


12, 7, 14, ____, 16, 11, 18

7. Draw the next figure in this sequence.


8. What number should appear in the center of Figure 4?


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9. Bob and Anne are playing darts. Bob has a score of 36.

To win, Bob must • reduce his score to

zero • have his last

counting dart be a double.

Give a strategy that Bob might use to win.

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Show What You Know - Puzzles

1. In a Kakuro puzzle, you fill in the empty squares with the numbers from 1 to 9.

• Each row of squares must add up to the circled number to the left of it. • Each column of squares must add up the circled number above it. • A number cannot appear more than once in the same sum.

a) Complete this Kakuro puzzle by filling in the grey squares.

b) Complete the following Kakuro puzzle by filling in the grey squares.

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2. Place the numbers 10 to 14 in a V-shape, as shown, so the two arms of the V have the same total.

3. Place the numbers 2 to 8 in a V-shape, as shown, so the two arms of the V have the same total.

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4.

From: http://cf.ltkcdn.net/kids/files/1956-Lets-Get-Moving-Logic-Puzzle.pdf

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http://cf.ltkcdn.net/kids/files/1956-Lets-Get-Moving-Logic-Puzzle.pdf


5.

From: http://cf.ltkcdn.net/kids/files/1955-Its-Time-for-Pie-Logic-Puzzle.pdf

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http://cf.ltkcdn.net/kids/files/1955-Its-Time-for-Pie-Logic-Puzzle.pdf

Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Show What You Know – Quiz 1. Gary works at a bicycle store in Vancouver. For the start of spring, the

manager of the store has ordered 50 mountain bikes and 10 racing bikes.

Which conjecture is Gary most likely to make from this evidence?

a. Either type of bike will sell equally well. b. Racing bikes will likely sell better than mountain bikes. c. It will rain all summer and no one will ride bicycles. d. Mountain bikes will likely sell better than racing bikes.

2. Emma works part-time at a bakery shop in Saskatoon. Today, the baker made 20 apple pies, 20 cherry pies, and 20 bumbleberry pies.

Which conjecture is Emma most likely to make from this evidence?

a. People are more likely to buy bumbleberry pie than any other pie. b. People are more likely to buy apple pie than any other pie. c. Each type of pie will sell equally as well as the others. d. People are more likely to buy cherry pie than any other pie.

3. Guilia created the following table to show a pattern.

Multiples of 9 18 27 36 45 54

Sum of the Digits 9 9 9 9 9

Which conjecture could Guilia make, based solely on this evidence? Choose the best answer.

a. The sum of the digits of a multiple of 9 is divisible by 9. b. The sum of the digits of a multiple of 9 is an odd integer. c. The sum of the digits of a multiple of 9 is equal to 9. d. Guilia could make any of the above conjectures, based on this

evidence..

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 4. All alligators are reptiles. All reptiles are covered with scales. Tashi is a cat.

What can be deduced about Tashi?

1. Tashi has scales. 2. Tashi is a reptile.

a. Choice 1 and Choice 2 b. Choice 1 only c. Choice 2 only d. Neither Choice nor Choice 2

5. Make a conjecture as to which line segment is longer, A or B.

a. I conjecture that B is longer than A. b. I conjecture that A and B are the same length. c. I conjecture that A is longer than B.

6. All cats are mammals. All mammals are warm-blooded. Tashi is a cat. What can be deduced about Tashi?

1. Tashi is warm-blooded. 2. Tashi is a mammal.

a. Choice 1 and Choice 2 b. Neither Choice nor Choice 2 c. Choice 1 only d. Choice 2 only

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 7. All birds have backbones. Birds are the only animals that have

feathers. Rosie is not a bird. What can be deduced about Rosie?

1. Rosie has a backbone. 2. Rosie does not have feathers.

a. Neither Choice 1 nor Choice 2 b. Choice 1 only c. Choice 1 and Choice 2 d. Choice 2 only


1, 2, 4, ___, 16, 32, 64

a. 6 b. 12 c. 8 d. 10

9. Which type of reasoning does the following statement demonstrate?

All birds have feathers. Robins are birds. Therefore, robins have feathers.

a. inductive reasoning b. neither inductive nor deductive reasoning c. deductive reasoning


2, 6, 18, 54, ____, 486, 1458

a. 108 b. 162 c. 216

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d. 196 11. Determine the unknown term in this pattern. 101, 1001, 10001, _____, 1000001, 10000001, 100000001 a. 100000 b. 100001 c. 110011 d. 111111

12. Which number should appear in the centre of Figure 4?


a. 41 b. 24 c. 36 d. 11



a. 41 b. 24 c. 36 d. 11

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 14. Choose the next figure in this sequence.


a.

b.

c.

d.



a. 15 b. 240 c. 120 d. 6

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 16. In a Kakuro puzzle, you fill in the empty squares with the numbers from 1 to 9.

• Each row of squares must add up to the circled number to the left of it. • Each column of squares must add up the circled number above it. • A number cannot appear more than once in the same sum.

Complete this Kakuro puzzle by filling in the grey squares.

a. 1, 2, 3, 4, 5 b. 5, 3, 1, 4, 2 c. 5, 4, 3, 2, 1 d. 1, 1, 3, 3, 7

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 Answers

11.1 Practice Your Skills – Games and Puzzles (insert table)

11.2 Practice Your Skills: Analyze and Strategize 1.

2. a) 48

b) 56

3.

4. Answers may vary

You try…

1. Therefore, Mars revolves around the sun in an elliptical orbit. 2. Therefore, all dogs have kidneys. 3. Therefore, all squares have four sides 4. Answers will vary

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Book 12: Math 21 Recreation and Wellness- Puzzles and Games Edited April 2015 11.2 Show What You Know: Inductive and Deductive Reasoning

1. Answers will vary

2. They will sell equal amount of both shirts.

3. Spencer has feathers.

4. Answers will vary.

5. 64

6. 9

7.

8. 18

9. Answers vary

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