What should my 5th grader be learning? Are they meeting the common core standards?
When learning about fractions, students will meet the Massachusetts Frameworks through using equivalent fractions as a strategy to add and subtract fractions (see http://www.doe.mass.edu/frameworks/math/0311.pdf Number and Operations-Fractions 5.NF for more information)
*SWBAT add and subtract fractions with unlike denominators, which include mixed numbers, by replacing given fractions with equivalent fractions in order to produce an equivalent sum or difference of fractions with common denominators
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . In general, a/b + c/d = (ad + bc)/bd.
*SWBAT solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models and/or equations to represent the problem. Students will use benchmark fractions and number sense of fractions to estimate their final answer
For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2 .
What is procedural and conceptual knowledge? What is the difference between the two?
Procedural knowledge involves working out a procedure, or in other words, knowing what to do to solve a math problem. Conceptual knowledge is understanding the concepts in order to solve math problems. When students demonstrate conceptual knowledge they will understand the reasoning behind WHY a problem is solved the way it is. For example, a student may know that in order to add fractions, they need to find a common denominator, even though they do not understand WHY it is important. This would demonstrate procedural knowledge. When students master conceptual knowledge, they will realize that a common denominator is necessary so the fractions involved are in the same terms, and this is needed to add and subtract fractions.
For example, these two questions below contain the same content, but the way a student answers them determines if they are demonstrating procedural and/or conceptual knowledge.
Question that uses procedural knowledge: Find the sum of one-third, one-quarter, and one-fifth.
Question that uses conceptual knowledge: Without adding, is the sum of one-quarter, one-third, and one-fifth, bigger or smaller than one? How do you know this?
When learning about fractions, students will meet the Massachusetts Frameworks through using equivalent fractions as a strategy to add and subtract fractions (see http://www.doe.mass.edu/frameworks/math/0311.pdf Number and Operations-Fractions 5.NF for more information)
*SWBAT add and subtract fractions with unlike denominators, which include mixed numbers, by replacing given fractions with equivalent fractions in order to produce an equivalent sum or difference of fractions with common denominators
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . In general, a/b + c/d = (ad + bc)/bd.
*SWBAT solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, by using visual fraction models and/or equations to represent the problem. Students will use benchmark fractions and number sense of fractions to estimate their final answer
For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2 .
What is procedural and conceptual knowledge? What is the difference between the two?
Procedural knowledge involves working out a procedure, or in other words, knowing what to do to solve a math problem. Conceptual knowledge is understanding the concepts in order to solve math problems. When students demonstrate conceptual knowledge they will understand the reasoning behind WHY a problem is solved the way it is. For example, a student may know that in order to add fractions, they need to find a common denominator, even though they do not understand WHY it is important. This would demonstrate procedural knowledge. When students master conceptual knowledge, they will realize that a common denominator is necessary so the fractions involved are in the same terms, and this is needed to add and subtract fractions.
For example, these two questions below contain the same content, but the way a student answers them determines if they are demonstrating procedural and/or conceptual knowledge.
Question that uses procedural knowledge: Find the sum of one-third, one-quarter, and one-fifth.
Question that uses conceptual knowledge: Without adding, is the sum of one-quarter, one-third, and one-fifth, bigger or smaller than one? How do you know this?