A Year in the Life: Ambient Math Wins the Race to the Top!
For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.” And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.
Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. Today’s post compares Grade 3 Algebra and Functions section of the California State Math Standards and the Grade 3 Operations and Algebraic Thinking section of the CCSS Math Standards.
My hope is that discerning the differences between the two will result in your making a right decision for your child, and all children for that matter. You may question the merits of the Common Core with your school, teacher, or school board if your child is in public school or homeschooling with a public charter school. Or you may decide to opt your child out of the Common Core testing.
Math By Hand is aligned with California State Math Standards and will remain so, because these standards are more effective, functional, and developmentally appropriate. (Math By Hand’s alignment, which is included in the binder in detail, is noted after each standard.)
California State Math Standards / Algebra and Functions / Grade 3
1.0) Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships.
1.1) Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.
1.2) Solve problems involving numeric equations or inequalities.
1.3) Select appropriate operational and relational symbols to make an expression true (e.g., if 4 _ 3 = 12, what operation symbol goes in the blank?
1.4) Express simple unit conversions in symbolic form (e.g., _ inches = _ feet x 12).
1.5) Recognize and use the commutative and associative properties of multiplica- tion (e.g., if 5 x 7 = 35, then what is 7 x 5? And if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).
2.0) Students represent simple functional relationships.
2.1) Solve simple problems involving a functional relationship between two quanti- ties (e.g., find the total cost of multiple items given the cost per unit).
2.2) Extend and recognize a linear pattern by its rules.
CCSS / Operations and Algebraic Thinking / Grade 3
Represent and solve problems involving multiplication and division.
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.
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
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.
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Understand properties of multiplication and the relationship between multiplication and division.
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.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100.
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.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Solve two-step word problems using the four operations. 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.
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.
Please compare the two and share your thoughts by posting a comment here. For me, the silver lining in the Common Core Cloud is that parents are becoming more involved and aware of the forces that have shaped and continue to shape educational policy, for good, ill, or nil.
Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.