Numbers & Operations in Base 10

5th Grade students will be able to:

• Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. 

  • Example: Recognize that in the number 770, the 7 in the tens place is 1/10 the 7 in the hundreds place. 

• 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. 

  • Example 1: 4 × 102 = 400 

  • Example 2: 0.05 ÷ 103 = 0.00005 

• Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. 

  • Example: 347.392 = 300 + 40 + 7 + 0.3 + 0.09 + 0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001) 

• Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols. 

• Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place).

• Multiply multi-digit whole numbers (not to exceed three-digit by three-digit). 

• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. 

  • Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).