Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Understand meanings of operations and how they relate to one another
Compute fluently and make reasonable estimates
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Demonstrate an understanding of positive integerexponents, in particular, when used in powers of ten, e.g., 102, 105.
Demonstrate an understanding of place value to billions and thousandths.
Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 + 4.
Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line.
Identify and determine common equivalent fractions, mixed numbers, decimals, and percents.
Find and position integers, fractions, mixed numbers, and decimals (both positive and negative) on the number line.
Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents.
Apply number theory concepts-including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10-to the solution of problems.
Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents.
Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers.
Apply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ÷).
Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems.
Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals.
Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions.
Add and subtract integers, with the exception of subtracting negative integers.
Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates.
Exploratory Concepts and Skills
Explore the addition and subtraction of positive and negative fractions.
Investigate the concepts of ratio and proportion.
Investigate the distributive property of multiplication over addition for double-digit multipliers, e.g., 12 x (10 + 3) is equivalent to 12 x 10 + 12 x 3.