There are many possible questions for any given answer'

1

• There are many possible questions for any given
  answer.
• There are many different ways to represent any
  amount.

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• Numbers do not begin with zero.
• Negative numbers are numbers whose values are
  less than zero.

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• We write negative numbers with signs that look
  like minus signs, but there is no space between
  the negative sign and the number in a negative
  number. There is always a space between a minus
  sign and a number. For example
• -8º F is a negative number.

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• The numbers to the left of zero on the number
  line are negative numbers.
• The larger the digits in a negative number, the
  smaller the number.

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• Numbers are grouped in periods or families. The
  number families are ones, thousands, millions,
  etc. There are three places in each number
  family ones, tens, and hundreds.
• Our number system is a decimal system because it
  is based on ten, and decem is the Latin word
  for ten.

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• Each place is ten times as big as the place to
  its right. For example, 1 thousand 10 hundreds.

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• When you get ten ones, you regroup them as one
  ten and when you get ten tens, you regroup them
  as one hundred, ten hundreds as one thousand, ten
  thousands as one ten thousand, and ten ten
  thousands as one hundred thousand.

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• We use place value when we say and write number
  names.
• A whole number name is spoken without and in
  between the place values. For example, 863,472
  is eight hundred sixty-three thousand, four
  hundred seventy-two, NOT eight hundred and
  sixty-three thousand, four hundred and
  seventy-two.

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• The thousand family name is said after the one
  thousands and before the hundreds. For example,
  863,472 is eight hundred sixty-three thousand,
  four hundred seventy-two.

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• Expanded notation is the number written as the
  amount in each place value added together. For
  example, 800,000 60,000 3,000 400 70 2
  is the expanded notation for eight hundred
  sixty-three thousand, four hundred seventy-two.

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• Standard form is the usual or common form used to
  write numbers. For example, 863,472 is in
  standard form, which is the sum of the amounts in
  each place value.

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• The place that is ten times as big as the hundred
  thousands place is the millions place. In other
  words, one million is ten hundred thousands.

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• Place value and the digit determine the size of
  the number. For example, a 9 in the tens place
  is smaller than 1 in the hundreds place, because
  9 tens 90 and 1 hundred 100, and 90 is
  smaller than 100.

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• lt (is less than), (is equal to), and gt (is
  greater than) are symbols used in comparing
  amounts, such as 635,763 gt 243,836 or 243,836 lt
  635,763.

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• We compare and order numbers by looking at the
  largest place value first and then smaller place
  values until we find a place with different
  digits to compare.

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• We use symbols to order and compare amounts. lt
  means is less than and gt means is greater
  than. For example, 5 gt 4 and 5 lt 9. Just
  remember that the mouth opens towards the
  biggest number. It is a greedy mouth.

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• Place value and the digit determine the size of
  the number. For example, a 9 in the tens place
  is smaller than a 1 in the hundreds place because
  9 tens 90 and 1 hundred 100, and 90 is
  smaller than 100.

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• To make the largest possible number, place the
  largest digits in the largest places.
• To make the smallest possible number, place the
  smallest digits in the largest possible places.

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• ? is the symbol that means one amount is about
  as much as another amount. For example, 97 ?
  100 means 97 is about 100.
• Estimates are used to decide whether numbers in
  written material, answers to math problems, and
  calculator answers are reasonable.

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• An estimate is a good guess or an educated guess
  at an answer, not a wild guess.
• Number sense is just common sense in mathematics.
• Answers in estimation will vary depending on the
  strategy and thinking used, so any answer that is
  in the right ballpark is acceptable.

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• You use different estimation strategies depending
  on the problem and which strategies you are most
  comfortable using. Since thee are different ways
  to estimate, there can be different estimates for
  the same problem which are all good estimates.

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• Front end estimation is just a special kind of
  number sense estimation. First, you use the
  largest digits to make a rough estimate, then you
  use the rest of the digits, and then you combine
  the two sums to adjust the estimate.

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• The compatible numbers strategy is also just a
  special kind of number sense estimation. You
  look for numbers that seem to fit together to
  make a number that is easy to work with. For
  example, to estimate 3 7 9 2 3, look for
  pairs of numbers whose sums are close to 5 or 10.
  3 7 10, 9 is about 10, and 2 3 5, so the
  estimate is about 25 because 10 10 5 25.

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• Rounded numbers end in one or more zeros.
• The symbol that means is rounded to is a
  right-pointing arrow like ?.

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• To round a number, underline the place you want
  to round to. Look at the place to the right. If
  the digit is 5 or more, round up. If it is less
  than 5, round down. Put zeros in the places to
  the right of the underlined number.

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• If we carefully follow the rule for rounding, we
  will get a good estimate. This is rigid
  rounding, by the rule rounding. Actually, in
  real life we use flexible rounding.

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• The more data we have, the more educated our
  guesses and the more reasonable our estimates
  will be.
• We really need to organize data to discover
  important facts about it.
• We can predict future data based on information
  gathered from previous data.

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• The operations you can do to solve problems with
  numbers are addition, subtraction,
  multiplication, and division.
• When we are working with whole numbers, we use
  division and subtraction to get a smaller number
  and multiplication and addition to get a larger
  number. Be sure to emphasize that this is only
  true when we are using whole numbers.

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• The accepted order of operations is to work from
  left to right in a series of operations, first
  doing all the operations inside parentheses (if
  there are any), next doing all the multiplication
  or division problems, and then doing all the
  addition or subtraction problems.

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