Appendix: Implementing District Standards
This curriculum unit is designed to provide a guide for teaching 2 digit by 2 digit multiplication for fourth grade students. It follows the newly revised 2016 standards of learning presented in the curriculum framework that are specific for the state of Virginia.
Virginia Standards of Learning (2016)
4.4 The student will
- demonstrate fluency with multiplication facts through 12 x 12, and the corresponding division facts;
- estimate and determine sums, differences, and products of whole numbers;
- create and solve single-step and multistep practical problems involving addition, subtraction, and multiplication, and single-step practical problems involving division with whole numbers.
The 2016 standards of learning were phased in during the 2017- 2018 school year, thus the third grade students were exposed to the following objectives as a foundation of learning for fourth grade.
3.4 The student will
- represent multiplication and division through 10 × 10, using a variety of approaches and models;
- create and solve single-step practical problems that involve multiplication and division through 10 x 10; and
- demonstrate fluency with multiplication facts of 0, 1, 2, 5, and 10; and
- solve single-step practical problems involving multiplication of whole numbers, where one factor is 99 or less and the second factor is 5 or less.
It is important to know the level of exposure the students have prior to arriving in fourth grade as it helps to guide instruction.
Common Core Standards
Virginia is not specifically a common core state but the standards below can also be applied to this unit.
CCSS.MATH.CONTENT.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
CCSS.MATH.CONTENT.3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
CCSS.MATH.CONTENT.3.OA.A.5 Apply properties of operations as strategies to multiply and divide.2 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.)
CCSS.MATH.CONTENT.3.OA.A.7 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 two one-digit numbers.
CCSS.MATH.CONTENT.4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
CCSS.MATH.CONTENT.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
CCSS.MATH.CONTENT.4.OA.A.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
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