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Topic: Number and Operations in Base Ten 

Common Core Mathematics 3-5

 Cluster  Use place value understanding and properties of operations to perform multi-digit arithmetic.[A range of algorithms may be used]
  Grade 3
   3.NBT.3.Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 X 80, 5 X 60) using strategies based on place value and properties of operations.
 Cluster  Generalize place value understanding for multi-digit whole numbers.
  Grade 4
   4.NBT.1.Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
   4.NBT.2.Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
   4.NBT.3.Use place value understanding to round multi-digit whole numbers to any place.
 Cluster  Use place value understanding and properties of operations to perform multi-digit arithmetic.
  Grade 4
   4.NBT.4.Fluently add and subtract multi-digit whole numbers using the standard algorithm.
   4.NBT.5.Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
   4.NBT.6.Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 Cluster  Understand the place value system.
  Grade 5
   5.NBT.1.Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
   5.NBT.2.Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
   5.NBT.3.Read, write, and compare decimals to thousandths.
   5.NBT.3.a.Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
   5.NBT.3.b.Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
   5.NBT.4.Use place value understanding to round decimals to any place.
 Cluster  Perform operations with multi-digit whole numbers and with decimals to hundredths.
  Grade 5
   5.NBT.6.Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
   5.NBT.7.Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.