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Additional Investigations

  1. Unit fractions: Terminating, repeating, or never-ending?: Investigate the patterns that emerge when unit fractions are converted into decimal form.

  2. Hot Stuff: If you are in Georgia, it should be easy to find the fraction and decimal that says, "I am hot."

  3. Adding Tenths: Think about tenths with a calculator.

  4. Decimal products: Are the products of repeating decimals always repeating?

  5. What happens when...?: Look for patterns when you multiply numbers by a number less than one.

  6. Ordering fractions: A student has found an "easy" way to find a fraction between two given fractions. Does his method always work?

  7. Those fractions in between: Find three different fractions between 3/5 and 2/3.

  8. Fractional parts: What fractional part of a given figure is shaded?

  9. Let's operate on fractions!: Using an area model, determine what operation is being performed on these fractions.

  10. Musical Chairs: Compare various fractions.

  11. Making unit fractions: Find two fractions that add up to a unit fraction.

  12. Where is that fraction?: Look for patterns when multiplying fractions.

  13. Can you tell?: Multiplying, dividing, and then comparing fractions.

  14. Mysterious numbers: Discover some strange properties about a mysterious number.

  15. Digital fractions: Use the digits 0 - 9 to make the fraction 1/3.

  16. Johnny's Rule: A student has "discovered" a rule for subtracting fractions. Does his method always work?

  17. Remainders of Three: Find the remainder when a large number is divided by 3.

  18. Missing Hundreds: Determine the sum of all the digits that could replace the digit d in a given number.

  19. Growing Tree: After four years, how many feet high was a tree that Mrs. Johnson's class planted?

  20. Approximate Digit Use: Use the digits 1, 2, 3, 4, 5, 6, 7, and 8 exactly once to make two decimal numbers whose product equals a particular number.

  21. Folders for Sale: Determine how much the manager of a store reduced the price of a folder.

  22. Pricing Notebooks: How much did John and his twin brothers pay for one notebook?

  23. Shopping for Plants: Help Mr. Alvarez determine which shop has the better buy on marigolds.

  24. Adding Fractions: Describe a set of natural numbers that fits a certain description.

  25. Spending it All: Help a shopper spend $62.

  26. Collecting Dimes: How many dimes did the driver receive in his tip?

  27. Bouncing Ball: Determine how many times a ball hits the ground.

  28. The Secret Pocket: How many of each kind of coin does Keith have in his secret pocket?

  29. Canceling Jumps: Find the value in simplest terms.

  30. Difficult Change: Can you guess what coins I have if I tell you what I can't give change for?

  31. Using up Digits: Find a multiplication sentence using the digits 1, 2, 3, 4, 5, and 6 so that the product is closest to a certain number.

  32. Fractional Triangle: Fill in the circle using fractions so that each side of the triangle will have a particular sum.

  33. Mailbox Letters: Find five words that are worth $1.00.

  34. Library Fines: Help Minerva understand her charges from the school library.

  35. Log Cutting: How long does it take to cut a wooden log into a certain number of parts?
  36. Portions of 1000: Which numbers have the digit 7 as at least one of the digits?

  37. Counting Zeros: How many zeros are at the end of a factorial?

  38. Dimes and Quarters: Determine the combination of quarters and dimes in a given amount of money.

  39. Paper Folding: Determine the thickness of the folded paper.

  40. Pandigital Fraction: Examine situations with fractions that have the property of all digits from 1 to 9.

  41. Unit Fractions and Fibonacci: Represent unit fractions as the sum of other fractions.

  42. Fraction figures: Using basic fraction operations to describe the fraction of shaded figures.

  43. Moving the Point: Why does moving the decimal point work when you multiply decimals?

  44. Cans and Containers: How many cans does one container hold?

  45. Decimal Diagram: Using diagrams to show factors and products.

  46. How Many Servings?: Help Demetrius and BJ decide how many servings they ate.

  47. The Meaning of 1/3: How can you explain the meaning of 1/3?

  48. Division Pattern: Looking for patterns in division.

  49. Jacob's Idea: Help decide of Jacob's idea is correct.

  50. Natasha's Idea: Help decide if Natasha's idea about dividing fractions is correct.

  51. 3 ÷ 1/ 2: Using visual models can help students better understand mathematics problems.

  52. Smaller Quotient: Determining why the quotient for one problem is smaller than the quotient of another.

  53. Exploring Division with Fractions: Exploring the similarities and differences in the steps taken to find the quotients.

  54. Exploring Multiplication with Fractions: Exploring the similarities and differences in the steps taken to find the products.

  55. Beaker Comparison: Help Sam and Morgan decide who has more liquid in their beakers.

  56. Estimating the Point: Help Miriam decide if her estimation approach will work for all decimals.

  57. What Happens When?: What happens when you multiply and divide fractions?

  58. Fractional Situations: Solving problems without using any kind of computational algorithm.

  59. Broken Calculator Problems: Solving problems with a broken calculator!

  60. Money Puzzle: Solving problems using different coin valuations.

  61. What Coins?: Using different combinations of coins.

  62. Pizza Party: Determining the greatest number of pizzas that the class can purchase.

  63. Another Folder Sale: Determining how many and at what price folders were sold.

  64. Dueling Speakers: Two speakers have different ways to divide fractions. Which one is right?

  65. Increasing Population: Which city had the greatest percentage increase in population?

  66. Fraction Situations: Working with story problems.

  67. Drink Mixes: Mixing juice while working with fractions.

  68. Laurel's Muffins: Reducing a muffin recipe.

  69. Fundraising: Comparing four fundraising group results.

  70. Representing Decimals: Using Base-10 blocks to represent decimals.

  71. Mathopia Farm: Use farm plots and crops to learn more about fractions.

  72. Bigger or Smaller?: Without calculating, determine the smaller product.

  73. Decimal Division: How are the three problems related?

  74. Mixed Up?: Using mathematics to determine if two drink recipes should taste the same.

  75. Base-Ten Block Multiplication: Thinking about student understanding of appropriate units.

  76. Two Models of Decimal Division: Explaining decimal division using various representations.

  77. Joel's Solution: Checking the validity of Joel's decimal division problem.

  78. Let's Help Ms. Lee: Considering multiple approaches to a decimal division problem.

  79. Decimals as Arrays: Representing decimal products using area models.

  80. Partial Products & Decimals: Understanding how the algorithm for multiplying decimals really works.

  81. Two Interpretations of Decimal Division: Creating story problems using two different approaches to division.

  82. Cliff or Evelyn: Address the role of place value in the algorithm for dividing decimals.

  83. Volume and Pressure: Looking at how inverse proportion relates to science.

  84. Math and Cookies: Looking at proportion in the context of a friendly argument over sharing cookies.

  85. Inversely Proportional: Exploring inverse proportion within the topic of speed and time relationships.

  86. Camera Lens Aperture: Looking at the inversely proprtional relationship between camera aperture and f-stops in photography.

  87. Boys and Girls in Class: Working a ratio problem about classroom gender compositions.

  88. Juice Containers: Using models rather than algorithms for computing with fractions.

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