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Math Class Regrouping
Math Class Regrouping
We recognize that every student is different and has different needs. Fifth grade students are regrouped according to learning styles and instructional needs. This is similar to how reading groups are used during literacy instruction. In each fifth grade math class, the same curriculum is used; so all students will be learning the same material. However, each class’ pace and structure is different based on the needs of the students in that group. The same academic rigor and high expectations exist in each class.
Students will be regrouped for math in the first week of school. The fifth grade teachers engage in a lengthy process to determine which math class will best serve each student's needs. The decision is based on the following criterion: math placement test score based on fourth and fifth grade math standards, fourth grade Star testing, fourth grade CMAS, and observed behaviors in class.
The fifth grade math curriculum this year is based on the Colorado State Standards for mathematics and the Standards of Mathematical Practice (SMP). These standards require depth and rigor, with special emphasis on conceptual understanding rather than rote memorization.
For middle school, teachers will expect that these foundations are securely in place, and if they are not, your child may struggle to keep up. Here is a list of grade-level skills that fifth graders are expected to have going into middle school:
Use the standard algorithms (the "old" way) for multiple-digit addition, subtraction, and multiplication.
Use place-value based algorithms for doing multiple-digit division ("partial quotients").
Divide whole numbers with 2 digit divisors, with and without remainders.
Advanced number patterns: finding factors and multiples, squares, and exponents.
Represent equivalent fractions; compare and order fractions using the appropriate symbol (<, >, and =); add, subtract, multiply and divide fractions, representing each visually.
Add, subtract, and multiply decimals using visual modeling and algorithms.
Understand the base ten number system and the role of place value in operations.
Use strategies to compute perimeter, area rectangles, and volume of rectangular prisms.
Determine strategies to solve word problems in math with one and two steps using whole numbers and decimals.
Solve algebraic sentences involving addition, subtraction, multiplication, and division.
Collect and analyze data to solve problems using graphs, tables, and charts.
Plot points on coordinate grids.
Math Facts
Math Facts
By the beginning of fifth grade, your student should have automatic mastery of all math “facts”—addition, subtraction, multiplication, and division—of numbers from 0-12. We call this automaticity, the spontaneous recall of information without conscious thought or attention. This is achieved through frequent practice and demonstrated mastery through classroom assessments. Please see this Edutopia article with information about the evolving subject of math fact fact learning; this one from Learning-Focused; and this study from Georgia Education Researcher: The Importance of Automaticity Development in Mathematics.
There are many common misconceptions about math instruction and the development of automaticity. These can be found here on the Science of Math website: Common Misconceptions: Timed Tests. To quote from the article:
No studies have determined that timed tests cause math anxiety. In fact, timed tactics improve math performance. Math anxiety is bi-directionally related to skill development—people with weaker skill proficiency report higher rates of anxiety and people reporting higher math anxiety have weaker skills.
Automaticity in basic math facts allows for cognitive space to be freed up to focus on more complex math concepts rather than simple computation tasks. As an example, learning the standard algorithms for multiplication and division is much more effective when you are not also trying to remember basic multiplication and division facts, which increases cognitive load. Additionally, efficiently and accurately adding and subtracting fractions requires up to 24 multiplication or division facts to be automatic. The focus here should be on conceptual understanding of the need for like denominators and how to develop them, not on what the multiples of 6 and 8 are - these should be automatic.
Other notable misconceptions about math are addressed in these articles from The Science of Math.
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