LAC 28:CXLII.1305. Algebraic Reasoning

A. Write and interpret numerical expressions. 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, attending to the order of operations and the properties of operations. a. Compare two simple expressions using >, =, or < to record the comparison of expressions limited to three operations and one grouping symbol. 2. Write simple expressions that record calculations with whole numbers, fractions, and decimals, and interpret numerical expressions without evaluating them. B. Compare whole numbers. 1. Generate and extend two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. a. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. b. Explain these relationships informally. C. Use place value understanding to apply patterns beyond whole numbers. 1. Construct a written explanation and apply patterns in the number of zeros of the product when multiplying a number by powers of 10. a. Explain and apply patterns in the values of the digits in the product or the quotient when a decimal is multiplied or divided by a power of 10. b. Use whole-number exponents to denote powers of 10. 2. Use understanding of the base-ten system. a. Read and write decimals to thousandths using base-ten numerals/standard form, written form (number names), unit form, and expanded form. b. Compare and order multi-digit whole numbers and decimals to thousandths based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons. D. Perform operations with multi-digit whole numbers with decimals to hundredths. 1. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value understanding, the properties of operations, subtracting multiples of the divisor, and/or the relationship between multiplication and division. a. Illustrate and/or explain the calculation by using equations, rectangular arrays, area models, or other strategies based on place value understanding. 2. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value understanding, properties of operations, and/or the part-whole relationship between addition and subtraction or multiplication and division. a. Justify the reasoning of methods used for calculation with a written explanation.