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Math Class Regrouping
Math Class Regrouping
We recognize that every student is different and has different needs. To accommodate different learning styles and 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 at each level.
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 on the class to which students will be assigned is based on the following criterion: fourth grade placement and teacher recommendations; math placement test score based on fourth and fifth grade math standards, and Aspire, CMAS (or any other) test results from the end of fourth grade.
The fifth grade math curriculum this year is based on the Common Core State Standards for mathematics (CCSS) and the Standards of Mathematical Practice (SMP). Common Core standards were adopted by the state of Colorado and fully implemented in 2014. The CCSS standards are a significant shift from the previous set of standards in many ways. They change our instruction to be slower, at more depth and rigor, but covering fewer concepts, as opposed to many concepts covered faster and without any depth. Think of it this way: instruction is now an inch wide and a mile deep, instead of a mile wide and an inch deep.
The SMP are a set of standards of practice for mathematics. Think of these as behaviors or skills used while doing math.
For middle school, teachers will expect that these foundations are securely in place, and if they aren’t, 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.
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 and area of rectangles, triangles, and parallelograms.
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 1-12. 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. 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.
Bridges
Bridges
Welcome to Bridges in Mathematics.
Bridges in Mathematics, second edition, is a comprehensive K–5 mathematics curriculum that equips teachers to fully implement the Common Core State Standards for Mathematics in a manner that is rigorous, coherent, engaging, and accessible to all learners. The curriculum focuses on developing students’ deep understandings of mathematical concepts, proficiency with key skills, and ability to solve complex and novel problems. Bridges blends direct instruction, structured investigation, and open exploration. The program taps into the intelligence strengths of all students by presenting material that is as linguistically, visually, and kinesthetically rich as it is mathematically powerful.
Bridges Activities
A Bridges classroom features a combination of whole-group, small-group, and independent activities that are problem centered. Fifth graders engage in five major kinds of activities: Problems & Investigations, Work Places, Math Forums, Problem Strings, and Assessments.
Problems & Investigations
Problems & Investigations are whole-group activities that also incorporate periods of independent and partner work. They often begin with a problem posed by the teacher, followed by time for students to think independently, work for a period of time, and talk in pairs before reconvening to share and compare strategies and solutions as a whole class.
Work Places
Work Places are engaging, developmentally appropriate math stations that offer ongoing practice with key skills. Many Work Places are partner games, but some are independent activities or more open-ended partner work. Work Places are always introduced and practiced as a whole class, after which students have opportunities to repeat the Work Place over a period of weeks. Work Places include suggestions that enable the teacher to differentiate each activity to address students’ needs for additional support or challenge.
Math Forums
Students discuss their solutions to and strategies for solving problems in nearly every Bridges lesson. Math forums, which occur a few times in most units, are a more formal and structured time for students to share and discuss their work. Prior to conducting a forum, the teacher reviews students’ written work on a particular problem and selects specific students to share during the forum. The teacher carefully plans the order in which students will share to help the rest of the class develop a deeper understanding of the problem and the variety of strategies that can be applied to solve it. Students who are not sharing their own work are expected to listen carefully, compare their classmates’ work to their own, and ask questions to better understand each student’s ideas.
Problem Strings
Problem strings are fast-paced exercises in which the teacher presents a carefully structured sequence of problems one at a time to the entire class. Each time, students solve the problem independently using any strategy they like, and then the teacher uses a specific model (a number line or ratio table, for example) to represent students’ strategies. The goal is to help students develop more efficient ways of solving a particular kind of problem, based upon the connections they see among the problems in the string. In Bridges Grade 5, problem strings are featured in every unit, except Unit 8.
Assessments
Assessments in Grade 5 are generally completed independently. Teachers have many opportunities, especially during Work Places, to make observational assessments of students working in small groups and to adjust the activity immediately based upon those observations. Opportunities for work samples are also highlighted throughout the curriculum.
Number Corner
Number Corner is a skills program that is an essential part of the Bridges curriculum, but which can also be used to supplement any elementary math curriculum. This collection of quick daily skills activities makes use of a classroom display featuring a calendar, growing collections, and more. The display engages students and contributes to a math-rich classroom environment that promotes both procedural fluency and conceptual understanding.
For additional reading about the Bridges 5th Grade curriculum by unit, use this link.
For a link to the Bridges website, use this link.
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