Unpacked Content
Knowledge
Students know:
- Place value conventions (i.e., a digit in one place represents 10 times as much as it would represent in the place to its right and 1/10 of what it represents in the place to its left).
- Strategies for computing answers to complex addition, subtraction, multiplication, and division problems involving multi-digit decimals, including a standard algorithm for each operation.
Skills
Students are able to:
- Strategically choose and apply appropriate computation strategies.
- Accurately find sums, differences, products, and quotients using the standard algorithms for each operation.
Understanding
Students understand that:
- Place value patterns and values continue to the right of the decimal point and allow the standard algorithm for addition and subtraction to be applied in the same manner as with whole numbers.
- Mathematical problems can be solved using a variety of strategies, models, and representations.
- Efficient application of computation strategies is based on the numbers and operations in the problem.
- The steps used in the standard algorithms for the four operations can be justified by using properties of operations and understanding of place value.
- Among all techniques and algorithms that may be chosen for accurately performing multi-digit computations, some procedures have been chosen with which all should be fluent for efficiency, communication, and use in other mathematics situations.
Vocabulary
- Standard algorithms (addition, subtraction, multiplication, and division)
- Quotient
- Sum
- Product
- Difference
- Tenths
- Hundredths
- Thousandths
- Ten thousandths
- Hundred thousandths
