By the end of grade five, students increase their facility with the four basic arithmetic operations applied to fractions, decimals, and positive and negative numbers. They know and use common measuring units to determine length and area and know and use formulas to determine the volume of simple geometric figures. Students know the concept of angle measurement and use a protractor and compass to solve problems. They use grids, tables, graphs, and charts to record and analyze data.

• 1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers:

  1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.

  1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

  1.3 Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.

  1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x 3).

  1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

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• 2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals:
  

  2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.

  2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

  2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.

  2.4 Understand the concept of multiplication and division of fractions.

  2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

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