full transcript

From the Ted Talk by Christopher Danielson: One is one... or is it?

Unscramble the Blue Letters


Which is correct: "A dozen eggs is?" Or "A dezon eggs are?" I remember being in elementary school, and my teachers making a big deal about the unit. And I never really got that, until one day, I was in the grocery store, and I wanted to buy an alppe, but I couldn't buy one apple. I had to buy a whole bag of apples. So I did. I bought one bag of apples, I took it home, I took one apple out of the bag, and I cut it up. And then I ate one slice. One bag, one apple, one slice. Which of these is the real "one"? Well, they all are of course, and that's what my elementary teachers were trying to tell me. Because this is the important idea behind whole number place value, decimal place value and foiarcnts. Our whole number system depends on being able to change what we count as "one". Our whole number ssetym depends on being able to chagne units. There are two ways to change utnis. We can compose, and we can partition. When we coopsme units, we take a bunch of things, we put them together to make a bigger thing, like a dozen eggs. We take 12 eggs, put them together to make a group, and we call that group a dozen. A dozen eggs is a composed unit. Other examples of composed units include a deck of cards, a pair of shoes, a jazz quartet and of course, Barbie and Ken make a couple. But think about a loaf of bread. That's not a cseopmod unit, because we don't get a bunch of slices from a bunch of different bakeries and put them together to make a loaf. No, we start with a loaf of bread and we cut it into smelalr pieces cleald secils, so each slice of bread is a poeiatirntd unit. Other examples of partitioned units include a square of a cactoohle bar, a siotcen of an orange and a scile of pizza. The important thing about units is that once we've made a new unit, we can treat it just like we did the old unit. We can compose composed units, and we can partition partitioned units. Think about toaster pastries. They come in packs of two, and then those packs get put together in sets of four to make a box. So when I buy one box of toaster pastries, am I buying one thing, four things, or eight things? It depends on the unit. One box, four packs, eight pastries. And when I sahre a slice of pzzia with a fnerid, we have to cut "it" into two smaller pieces. So a box of toaster pastries is composed of composed units, and when I siplt a slice of pizza, I'm partitioning a partitioned unit. But what does that have to do with math? In math, everything is certain. Two plus two equals four, and one is just one. But that's not really right. One isn't always one. Here's why: we start counting at one, and we count up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9, and then we get to 10, and in order to write 10, we write a one and a zero. That one means that we have one group, and the zero helps us remember that it means one group, not one thing. But 10, just like one, just like a dozen eggs, just like an egg, 10 is a unit. And 10 tens make 100. So when I think about 100, it's like the box of toaster parsetis. Is 100 one thing, 10 things or 100 things? And that depends on what "one" is, it depdens on what the unit is. So think about all the tmeis in math when you write the number one. No matter what plcae that one is in, no matter how many things that one represents, one is.

Open Cloze


Which is correct: "A dozen eggs is?" Or "A _____ eggs are?" I remember being in elementary school, and my teachers making a big deal about the unit. And I never really got that, until one day, I was in the grocery store, and I wanted to buy an _____, but I couldn't buy one apple. I had to buy a whole bag of apples. So I did. I bought one bag of apples, I took it home, I took one apple out of the bag, and I cut it up. And then I ate one slice. One bag, one apple, one slice. Which of these is the real "one"? Well, they all are of course, and that's what my elementary teachers were trying to tell me. Because this is the important idea behind whole number place value, decimal place value and _________. Our whole number system depends on being able to change what we count as "one". Our whole number ______ depends on being able to ______ units. There are two ways to change _____. We can compose, and we can partition. When we _______ units, we take a bunch of things, we put them together to make a bigger thing, like a dozen eggs. We take 12 eggs, put them together to make a group, and we call that group a dozen. A dozen eggs is a composed unit. Other examples of composed units include a deck of cards, a pair of shoes, a jazz quartet and of course, Barbie and Ken make a couple. But think about a loaf of bread. That's not a ________ unit, because we don't get a bunch of slices from a bunch of different bakeries and put them together to make a loaf. No, we start with a loaf of bread and we cut it into _______ pieces ______ ______, so each slice of bread is a ___________ unit. Other examples of partitioned units include a square of a _________ bar, a _______ of an orange and a _____ of pizza. The important thing about units is that once we've made a new unit, we can treat it just like we did the old unit. We can compose composed units, and we can partition partitioned units. Think about toaster pastries. They come in packs of two, and then those packs get put together in sets of four to make a box. So when I buy one box of toaster pastries, am I buying one thing, four things, or eight things? It depends on the unit. One box, four packs, eight pastries. And when I _____ a slice of _____ with a ______, we have to cut "it" into two smaller pieces. So a box of toaster pastries is composed of composed units, and when I _____ a slice of pizza, I'm partitioning a partitioned unit. But what does that have to do with math? In math, everything is certain. Two plus two equals four, and one is just one. But that's not really right. One isn't always one. Here's why: we start counting at one, and we count up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9, and then we get to 10, and in order to write 10, we write a one and a zero. That one means that we have one group, and the zero helps us remember that it means one group, not one thing. But 10, just like one, just like a dozen eggs, just like an egg, 10 is a unit. And 10 tens make 100. So when I think about 100, it's like the box of toaster ________. Is 100 one thing, 10 things or 100 things? And that depends on what "one" is, it _______ on what the unit is. So think about all the _____ in math when you write the number one. No matter what _____ that one is in, no matter how many things that one represents, one is.

Solution


  1. split
  2. share
  3. apple
  4. called
  5. section
  6. chocolate
  7. friend
  8. slices
  9. depends
  10. compose
  11. units
  12. composed
  13. dozen
  14. pizza
  15. system
  16. smaller
  17. pastries
  18. place
  19. change
  20. slice
  21. fractions
  22. times
  23. partitioned

Original Text


Which is correct: "A dozen eggs is?" Or "A dozen eggs are?" I remember being in elementary school, and my teachers making a big deal about the unit. And I never really got that, until one day, I was in the grocery store, and I wanted to buy an apple, but I couldn't buy one apple. I had to buy a whole bag of apples. So I did. I bought one bag of apples, I took it home, I took one apple out of the bag, and I cut it up. And then I ate one slice. One bag, one apple, one slice. Which of these is the real "one"? Well, they all are of course, and that's what my elementary teachers were trying to tell me. Because this is the important idea behind whole number place value, decimal place value and fractions. Our whole number system depends on being able to change what we count as "one". Our whole number system depends on being able to change units. There are two ways to change units. We can compose, and we can partition. When we compose units, we take a bunch of things, we put them together to make a bigger thing, like a dozen eggs. We take 12 eggs, put them together to make a group, and we call that group a dozen. A dozen eggs is a composed unit. Other examples of composed units include a deck of cards, a pair of shoes, a jazz quartet and of course, Barbie and Ken make a couple. But think about a loaf of bread. That's not a composed unit, because we don't get a bunch of slices from a bunch of different bakeries and put them together to make a loaf. No, we start with a loaf of bread and we cut it into smaller pieces called slices, so each slice of bread is a partitioned unit. Other examples of partitioned units include a square of a chocolate bar, a section of an orange and a slice of pizza. The important thing about units is that once we've made a new unit, we can treat it just like we did the old unit. We can compose composed units, and we can partition partitioned units. Think about toaster pastries. They come in packs of two, and then those packs get put together in sets of four to make a box. So when I buy one box of toaster pastries, am I buying one thing, four things, or eight things? It depends on the unit. One box, four packs, eight pastries. And when I share a slice of pizza with a friend, we have to cut "it" into two smaller pieces. So a box of toaster pastries is composed of composed units, and when I split a slice of pizza, I'm partitioning a partitioned unit. But what does that have to do with math? In math, everything is certain. Two plus two equals four, and one is just one. But that's not really right. One isn't always one. Here's why: we start counting at one, and we count up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9, and then we get to 10, and in order to write 10, we write a one and a zero. That one means that we have one group, and the zero helps us remember that it means one group, not one thing. But 10, just like one, just like a dozen eggs, just like an egg, 10 is a unit. And 10 tens make 100. So when I think about 100, it's like the box of toaster pastries. Is 100 one thing, 10 things or 100 things? And that depends on what "one" is, it depends on what the unit is. So think about all the times in math when you write the number one. No matter what place that one is in, no matter how many things that one represents, one is.

Frequently Occurring Word Combinations


ngrams of length 2

collocation frequency
dozen eggs 4
toaster pastries 3
number system 2
system depends 2
change units 2
units include 2
smaller pieces 2
partitioned unit 2
partitioned units 2

ngrams of length 3

collocation frequency
number system depends 2

Important Words


  1. apple
  2. apples
  3. ate
  4. bag
  5. bakeries
  6. bar
  7. barbie
  8. big
  9. bigger
  10. bought
  11. box
  12. bread
  13. bunch
  14. buy
  15. buying
  16. call
  17. called
  18. cards
  19. change
  20. chocolate
  21. compose
  22. composed
  23. count
  24. counting
  25. couple
  26. cut
  27. day
  28. deal
  29. decimal
  30. deck
  31. depends
  32. dozen
  33. egg
  34. eggs
  35. elementary
  36. equals
  37. examples
  38. fractions
  39. friend
  40. grocery
  41. group
  42. helps
  43. home
  44. idea
  45. important
  46. include
  47. jazz
  48. ken
  49. loaf
  50. making
  51. math
  52. matter
  53. means
  54. number
  55. orange
  56. order
  57. packs
  58. pair
  59. partition
  60. partitioned
  61. partitioning
  62. pastries
  63. pieces
  64. pizza
  65. place
  66. put
  67. quartet
  68. real
  69. remember
  70. represents
  71. school
  72. section
  73. sets
  74. share
  75. shoes
  76. slice
  77. slices
  78. smaller
  79. split
  80. square
  81. start
  82. store
  83. system
  84. teachers
  85. tens
  86. times
  87. toaster
  88. treat
  89. unit
  90. units
  91. wanted
  92. ways
  93. write