Cluster: Multiply and divide within 100

Standard: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers.

Degree of Alignment: Not Rated (0 users)

Cluster: Understand properties of multiplication and the relationship between multiplication and division

Standard: Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic

Standard: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Degree of Alignment: Not Rated (0 users)

Cluster: Gain familiarity with factors and multiples

Standard: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Multiply and divide within 100

Indicator: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 Ö 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Gain familiarity with factors and multiples

Indicator: Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Understand properties of multiplication and the relationship between multiplication and division

Indicator: Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15 then 15 x 2 = 30, or by 5 x 2 = 10 then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.)

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Solve problems involving the four operations, and identify and explain patterns in arithmetic

Indicator: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Understand properties of multiplication and the relationship between multiplication and division

Indicator: Understand division as an unknown-factor problem. For example, divide 32 Ö 8 by finding the number that makes 32 when multiplied by 8.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Indicator: Identify arithmetic patterns and explain the relationships using properties of operations.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Understand properties of multiplication and the relationship between multiplication and division.

Indicator: Understand division as an unknown-factor problem.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Understand properties of multiplication and the relationship between multiplication and division.

Indicator: Apply properties of multiplication as strategies to multiply and divide. (Students need not use formal terms for these properties.)

Degree of Alignment: Not Rated (0 users)

Learning Domain: Operations and Algebraic Thinking

Standard: Develop understanding of factors and multiples.

Indicator: Demonstrate an understanding of factors and multiples.

Degree of Alignment: Not Rated (0 users)