Mystery Triangle Numbers in a Line...3. Break the Cube Missing Signs...4. Backward Numbers...5. Toothpick Triangles X Is to Y...

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2 Numbers in a Line...3 Missing Signs...4 Backward Numbers...5 Number Switch....6 Calculator Riddles...7 At the Bakery...8 A Family Portrait....9 Amazing Sums...10 Mysterious Multiplication...11 Crisscross...12 Dotted Hexagons...13 Paper Patterns...14 Dots and Squares...15 Circle Puzzles...16 Shapes and Numbers...17 Number Cubes...18 Number Riddles...19 Find the Numbers...20 Hidden Numbers...21 Missing Steps...22 Puzzle It Out...24 Hide-and-Seek...25 The Total Mystery Triangle...29 Break the Cube Toothpick Triangles...31 X Is to Y...32 Word Equations A Good Reason...36 Odd Word Out...38 Oxymorons...39 Palindromes and Reflections...41 Word Reflections...42 Change-a-Word...43 Letter Swaps Perplexing Puzzles...45 Fractured Words Breakdown...51 Word Origins...52 Word Squares...53 Root Words Idioms Fantastic Phrases...56 Word Buddies Twisted Words...59 Answer Key Mystery Squares...27

3 Consecutive numbers are numbers that follow one after the other. Write the consecutive numbers that answer the questions below. 1. Which three consecutive numbers add up to 123? 2. Which three consecutive odd numbers add up to 123? 3. Which three consecutive numbers add up to 456? 4. Which three consecutive even numbers add up to 456? 5. Which three consecutive numbers add up to 789? 6. Which three consecutive even numbers add up to 150? 7. Which four consecutive odd numbers add up to 240? 8. Which five consecutive numbers add up to 100? 9. Which five consecutive numbers add up to 150? 10. Which five consecutive numbers add up to 500?

4 Add one operation sign ( +,, x, or ) and one equal sign ( = ) to each row to make an equation that is true. Write the equations on the lines. Example: =

5 A math teacher wrote math problems on the board for her class to copy. The problems are shown below The teacher assigned the problems for homework. Whitney was in a hurry, and she copied all of the problems backward. Whitney's problems are shown in the box at the right. The next day, the students checked their work. The teacher called out the answers for each problem, and Whitney found that she had gotten every problem right! How did Whitney do it? First, write the answers to all of the problems above. Compare the sums in both sets of problems. Explain why you got the results you did. Do you think that all two-digit addition problems will give you the same results?

6 Marvin put number cards together to make math problems. However, for each problem he accidentally put two cards in the wrong places. Switch the numbers around and rewrite the problems to correct them. 1 3 x x x 6 x x 3 x

7 Use a calculator to solve the problems below. Do not use the order of operations. Instead, do the calculations in the order they appear. Then, turn the calculator upside down to find the answer to each riddle. Write the answers on the lines x = Which animal is the best speller? A spelling = What should you say when you meet a giant alien at your door? 3. 2,001 x , = What honks but isn t a car? 4. 96, , x 4 = What things get larger the more you take away? , x = What does a table have that you also have? _ , x 17 4,755 = What comes in different sizes but are always one foot long? , = What does the farmer say when he hears a good joke?

8 A baker prepared several trays of cookies for sale. Then, the baker set out the trays and opened the door to the bakery. Mrs. Lee was the first customer. She was buying cookies for her office luncheon. She looked at the trays and immediately bought ¼ of the cookies. Next, Mr. Lang entered the bakery. He wanted to buy a treat for his students. Mr. Lang bought ½ of the cookies that were left on the trays. Ms. Lopez was the third customer. She wanted to give her neighbor a birthday treat. She bought 1 /3 of the remaining cookies. Mrs. Brenner came next. She wanted to take cookies to her grandchildren. She bought ½ of the cookies that were left. Mr. Murray was the fifth customer. There weren t many cookies left. He didn t want to seem greedy, so he bought only 1 /3 of the cookies that were still on the trays. Ryan walked into the bakery. He was hungry and wanted a quick snack. After he bought ½ of the cookies, only 4 cookies were left. 1. How many cookies did each customer buy? Mrs. Lee cookies Ms. Lopez cookies Mr. Murray cookies Mr. Lang cookies Mrs. Brenner cookies Ryan cookies 2. How many cookies did the baker set out for sale in the morning?

9 Mr. and Mrs. Jackson are having a family portrait taken with their son and daughter. The photographer wants to have two people sit in the front and two people stand in the back. The Jacksons have decided that they want to send a copy of their portrait to each of their relatives. However, they don t want any two portraits to be the same. Mr. Wilson has asked the photographer to place the family in as many different positions as possible. How many different portraits are possible? Work out the solution in the space below. Is there a quick way to find out how many arrangements are possible? For example, how many different arrangements would there be if there were 5 people in the family instead of 4?

10 Solve the addition problems below to find an interesting number pattern , , ,999 Continue the problems at least three more times. What pattern do you see? 10

11 Multiply each of the following three-digit numbers by 11. Then, multiply each product by x 11 x 11 x 11 x 11 x ,130 4,543 4,543 x 91 x 91 x 91 x 91 x 91 Now, write three other three-digit numbers and multiply them in the same way. Did you get the same results as above? Why do you think you got the answers that you did? 11

12 The first three figures in each row were created from the same pattern. Study the pattern and fill in the missing number for the third figure. For the last figure in each row, use the pattern to make your own set of numbers Describe the pattern Describe the pattern Describe the pattern. 1

13 nlskdjflsk dfjsdklfjsl P. 3 Numbers in a Line 1. 40, 41, 42; 2. 39, 41, 43; , 152, 153; , 152, 154; , 263, 264; 6. 48, 50, 52; 7. 57, 59, 61, 63; 8.18, 19, 20, 21, 22; 9. 28, 29, 30, 31, 32; , 99, 100, 101, 102 P. 4 Missing Signs = 60; x 5 = 275; x 10 = 100; = 21; = 107; = 628; = 333; x 60 = 2,100; = 474; x 52 = 4,524 P. 5 Backward Numbers The sums in both sets of problems match: 88, 132, 143, 99, 121, 110. Only two-digit problems in which the sum of the ones digits equals the sum of the tens digits will give the same sum when written backward. P. 6 Number Switch = = = = x 8 = x 3 = = = 45 P. 7 Calculator Riddles , bee; 2. 14, hi; 3. 35,006, goose; 4. 53,704, holes; 5. 5,637, legs; 6. 53,045, shoes; ,304, hoe, hoe P. 8 At the Bakery 1. Mrs. Lee, 24; Mr. Lang, 36; Ms. Lopez, 12; Mrs. Brenner, 12 Mr. Murray, 4; Ryan, 4; P. 9 A Family Portrait 1. There are 24 possible arrangements. 2. Multiply the number of elements: 4 x 3 x 2 x 1 = 24. To find out how many different arrangements there are with 5 people, you can multiply 5 x 4 x 3 x 2 x 1 to get 120. P. 10 Amazing Sums = 1,109 1, ,999 = 11,108 11, ,999 = 111, , ,999 = 1,111,106 1,111, ,999,999 = 11,111,105 11,111, ,999,999 = 111,111, ,111, ,999,999 = 1,111,111,103 Patterns: The number of times that 1 appears in the answer increases with each new sum. The ones digit decreases by 1 each time. The number of digits in one addend equals the number of digits in the other addend each time. P. 11 Mysterious Multiplication ,413; ,736; 3. 80,080; ,653; 5.999,999 Each time a three-digit number is multiplied by 11 and 91, or 1,001. If XYZ stands for a three-digit number, then multiplying produces 1,001 groups of XYZ altogether 1,000 groups of XYZ and 1 group of XYZ. This results in the number XYZ,000 + XYZ or XYZ,XYZ. P. 12 Crisscross 1. The missing number in the third figure is 2. Pattern: Take the sum of the top and bottom numbers and divide it by the sum of the left and right numbers; write the answer in the center circle; 2. The missing number in the third figure is 3. Pattern: Take the product of the top and bottom numbers and divide it by the product of the left and right numbers; write the answer in the center circle; 3. Pattern: Take the product of the top and bottom numbers and divide it by the sum of the left and right numbers. The missing number in the third figure is 3. P. 13 Dotted Hexagons dots were used (4 dots per side); 2. 18, 24, 30; 3. Subtract 1 from the number of dots used per side. Then, multiply the result by 6. For a hexagon with 20 dots per side, there would be (20 1) x 6 dots, or 114. P. 14 Paper Patterns 1. 31; 2. The formula is 3(n 1) + 1, in which n stands for the number of the figure. Take the number of the figure and subtract 1. Then, multiply by 3 and add 1. For example, to find the number of squares needed for the 10th figure, subtract 1 from 10 to get 9. Then, multiply by 3 to get 27. Add 1 to get 28, the number of squares needed; 3. 19; 4. The formula is 2(n 1) + 1. Take the number of the figure and subtract 1. Then, multiply by 2 and add 1. For example, to find the number of squares needed for the 10th figure, subtract 1 from 10 to get 9. Then, multiply by 2 to get 18. Finally, add 1 to get 19, the number of squares needed. P. 15 Dots and Squares For the 3 x 3 grid, there are 6 possible squares. For the 4 x 4 grid, there are 22 possible squares. P. 16 Circle Puzzles First circle Second circle 1