full transcript

## Unscramble the Blue Letters

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 weatnd to buy an aplpe, but I couldn't buy one apple. I had to buy a whole bag of appels. 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 scile. 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, diceaml place value and fractions. Our whole nmuebr system depends on being able to change what we cuont 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 bncuh 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 dzoen eggs is a composed unit. Other eplexmas of cpmsooed 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 pnettiiorad uints include a square of a chocolate bar, a section of an orange and a slice of pizza. The irtnpomat 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 priesats. They come in pkcas 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 sarhe a slice of pizza with a friend, we have to cut "it" into two smaller peceis. 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 gurop, 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 teims 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.

## Open Cloze

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 ______ to buy an _____, but I couldn't buy one apple. I had to buy a whole bag of ______. 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 _____. 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, _______ place value and fractions. Our whole ______ system depends on being able to change what we _____ 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 _____ 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 _____ eggs is a composed unit. Other ________ of ________ 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 ___________ _____ include a square of a chocolate bar, a section of an orange and a slice of pizza. The _________ 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 ________. They come in _____ 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 pizza with a friend, we have to cut "it" into two smaller ______. 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 _____, 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 _____ 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.

1. pieces
2. packs
3. apples
4. decimal
5. examples
6. count
7. share
8. bunch
9. partitioned
10. wanted
11. group
12. composed
13. apple
14. slice
15. units
16. important
17. pastries
18. split
19. times
20. dozen
21. number

## 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
13. bunch
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