Fifth Grade - Grade Level Overview - Georgia Standards

Georgia Standards of Excellence

Grade Level Curriculum Overview Mathematics

GSE Fifth Grade

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TABLE OF CONTENTS

Curriculum Map............................................................................................................................................ 3 Unpacking the Standards .............................................................................................................................. 4

? Standards for Mathematical Practice ............................................................................................... 4 ? Content Standards ............................................................................................................................ 5 Mindset and Mathematics .......................................................................................................................... .51 Vertical Understanding of the Mathematics Learning Trajectory .............................................................. 52 Research of Interest to Teachers ................................................................................................................. 53 GloSS and IKAN ........................................................................................................................................ 53 Fluency........................................................................................................................................................ 53 Arc of Lesson/Math Instructional Framework ............................................................................................ 54 Unpacking a Task ....................................................................................................................................... 55

Routines and Rituals ? Teaching Math in Context and Through Problems ........................................................................ 56 ? Use of Manipulatives ..................................................................................................................... 57 ? Use of Strategies and Effective Questioning ................................................................................. 58 ? Number Lines ................................................................................................................................ 58 ? Math Maintenance Activities ......................................................................................................... 59 o Number Corner/Calendar Time ........................................................................................ 61 o Number Talks ................................................................................................................... 62 o Estimation/Estimation 180................................................................................................ 64 ? Mathematize the World through Daily Routines ........................................................................... 67 ? Workstations and Learning Centers ............................................................................................... 67 ? Games ............................................................................................................................................ 68 ? Journaling....................................................................................................................................... 68

General Questions for Teacher Use ............................................................................................................ 69 Questions for Teacher Reflection ............................................................................................................... 70 Depth of Knowledge ................................................................................................................................... 71 Depth and Rigor Statement ......................................................................................................................... 72

Additional Resources 3-5 Problem Solving Rubric (creation of Richmond County Schools) .............................................................................. 73 Literature Resources ................................................................................................................................... 74 Technology Links ....................................................................................................................................... 74 Resources Consulted ................................................................................................................................... 75

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Georgia Department of Education

Georgia Standards of Excellence Fifth Grade

**NEW Click on the link in the table to view a video that shows instructional strategies for teaching the specified standard.

GSE Fifth Grade Curriculum Map

Unit 1

Order of Operations and Whole Numbers

Unit 2

Adding and Subtracting with Decimals

MGSE5.OA.1 MGSE5.OA.2 MGSE5.NBT.1 MGS5.NBT.2 MGSE5.NBT.5 MGSE5.NBT.6

MGSE5.NBT.1 MGSE5.NBT.3 MGSE5.NBT4 MGSE5.NBT.7

Unit 3 Multiplying and

Dividing with Decimals

MGSE5.NBT.2 MGSE5.NBT.7

Unit 4

Adding, Subtracting, Multiplying and

Dividing Fractions

MGSE5.NF.1 MGSE5.NF.2 MGSE5.NF.3 MGSE5.NF.4 MGSE5.NF.5 MGSE5.NF.6 MGSE5.NF.7 MGSE5.MD.2

Unit 5 2D Figures

MGSE5.G.3 MGSE5.G.4

Unit 6 Volume and Measurement

MGSE5.MD.1 MGSE5.MD.2 MGSE5.MD.3 MGSE5.MD.4 MGSE5.MD.5

Unit 7

Geometry and the Coordinate Plane

Unit 8

Show What We Know

MGSE5.G.1 MGSE5.G.2 MGSE5.OA.3

ALL

These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units. All units will include the Mathematical Practices and indicate skills to maintain. However, the progression of the units is at the discretion of districts. NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics.

Grades 3-5 Key: G= Geometry, MD=Measurement and Data, NBT= Number and Operations in Base Ten, NF = Number and Operations, Fractions, OA = Operations and Algebraic Thinking.

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Georgia Department of Education

STANDARDS FOR MATHEMATICAL PRACTICE Mathematical Practices are listed with each grade's mathematical content standards to reflect the need to connect the mathematical practices to mathematical content in instruction.

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

Students are expected to:

1. Make sense of problems and persevere in solving them. Students solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, "What is the most efficient way to solve the problem?", "Does this make sense?", and "Can I solve the problem in a different way?"

2. Reason abstractly and quantitatively. Fifth graders should recognize that a number represents a specific quantity. They connect quantities to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions that record calculations with numbers and represent or round numbers using place value concepts.

3. Construct viable arguments and critique the reasoning of others. In fifth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain calculations based upon models and properties of operations and rules that generate patterns. They demonstrate and explain the relationship between volume and multiplication. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like "How did you get that?" and "Why is that true?" They explain their thinking to others and respond to others' thinking.

4. Model with mathematics. Students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fifth

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Georgia Department of Education

graders should evaluate their results in the context of the situation and whether the results make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems.

5. Use appropriate tools strategically. Fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real world data.

6. Attend to precision. Students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answers in cubic units.

7. Look for and make use of structure. In fifth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate them to a rule or a graphical representation.

8. Look for and express regularity in repeated reasoning. Fifth graders use repeated reasoning to understand algorithms and make generalizations about patterns. Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digit numbers and perform all operations with decimals to hundredths. Students explore operations with fractions with visual models and begin to formulate generalizations.

***Mathematical Practices 1 and 6 should be evident in EVERY lesson***

CONTENT STANDARDS

OPERATIONS AND ALEGEBRAIC THINKING

MGSE CLUSTER #1: WRITE AND INTERPRET NUMERICAL EXPRESSIONS. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: parentheses, brackets, braces, numerical expressions. **IMPORTANT INFORMATION ON ORDER OF OPERATIONS FOUND HERE: Order of Operations: The Myth and The Math (Please read BEFORE you teach this concept.)

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