Georgia Standards of Excellence Curriculum Frameworks ...

1 These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Georgia Standards of Excellence Curriculum Frameworks GSE Fifth grade Unit 7: Geometry and the Coordinate Plane Mathematics Georgia Department of Education Georgia Standards of Excellence Framework GSE Geometry and the Coordinate Plane Unit 7 Mathematics GSE grade 5 Unit 7: Geometry and the Coordinate Plane Richard Woods, State School Superintendent July 2017 Page 2 of 69 All Rights Reserved Unit 7: Geometry and the Coordinate Plane TABLE OF CONTENTS Overview ..3 Standards for Mathematical Practice.

2 3 Standards for Mathematical Content ..4 Big Ideas ..5 Essential Questions ..5 Concepts and Skills to Maintain ..6 Strategies for Teaching and Learning ..6 Selected Terms and Symbols ..7 Tasks ..10 Intervention Table ..11 Air Traffic Controller ..20 Beads Under the Atlanta Earth Day First to Arrive ..40 What s the Better Buy? ..43 The Slow Coordinate Grid IF YOU HAVE NOT READ THE 5th grade Curriculum OVERVIEW IN ITS ENTIRETY PRIOR TO USE OF THIS UNIT, PLEASE STOP AND CLICK HERE: Return to the use of this unit once you ve completed reading the Curriculum Overview. Thank you!

3 Georgia Department of Education Georgia Standards of Excellence Framework GSE Geometry and the Coordinate Plane Unit 7 Mathematics GSE grade 5 Unit 7: Geometry and the Coordinate Plane Richard Woods, State School Superintendent July 2017 Page 3 of 69 All Rights Reserved OVERVIEW Students extend their grade 4 pattern work by working briefly with two numerical patterns that can be related and examining these relationships within sequences of ordered pairs and in the graphs in the first quadrant of the coordinate plane. This work prepares students for studying proportional relationships and functions in middle school.

4 Analyze patterns and relationships. 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: numerical patterns, rules, ordered pairs, coordinate plane. Graph points on the coordinate plane to solve real-world and mathematical problems. 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: coordinate system, coordinate plane, first quadrant, points, lines, axis/axes, x-axis, y-axis, horizontal, vertical, intersection of lines, origin, ordered pairs, coordinates, x-coordinate, y-coordinate.

5 The Critical Areas are designed to bring focus to the Standards at each grade by describing the big ideas that educators can use to build their Curriculum and to guide instruction. This cluster goes beyond the grade 5 Critical Areas of Focus to address modeling numerical relationships with the coordinate plane. Based on previous work with measurement and number lines, students develop understanding of the coordinate plane as a tool to model numerical relationships. These initial understandings provide the foundation for work with negative numbers, and ratios and proportional relationships in grade Six and functional relationships in further grades.

6 For more detailed information about unpacking the content Standards , unpacking a task, math routines and rituals, maintenance activities and more, please refer to the grade Level Overview. Standards FOR MATHEMATICAL PRACTICE This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards . The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit.

7 The list is not exhaustive and will hopefully prompt further reflection and discussion. 1. Make sense of problems and persevere in solving them. Students make sense of solving real world problems involving points on the coordinate plane. Georgia Department of Education Georgia Standards of Excellence Framework GSE Geometry and the Coordinate Plane Unit 7 Mathematics GSE grade 5 Unit 7: Geometry and the Coordinate Plane Richard Woods, State School Superintendent July 2017 Page 4 of 69 All Rights Reserved 2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning about ordered pairs with their visual representations.

8 Students consider the values of these numbers in relation to patterns and points on a coordinate plane. 3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding patterns and relationship of ordered pairs as they are plotted on a coordinate plane to represent real-world contexts. 4. Model with mathematics. Students use the coordinate plane to compare two numbers in mathematical and real-world contexts. 5. Use appropriate tools strategically. Students select and use tools such as colored pencils, number line models and the coordinate plane to represent situations involving positive numbers.

9 6. Attend to precision. Students attend to the language of real-world situations to determine how far to travel from the origin and the given direction of the coordinates being represented. 7. Look for and make use of structure. Students relate the structure of number lines to values of positive integers as they use the coordinate plane. 8. Look for and express regularity in repeated reasoning. Students relate new experiences to experiences with similar contexts when studying positive representations of distance and quantity. **Mathematical Practices 1 and 6 should be evident in EVERY lesson** Standards FOR MATHEMATICAL CONTENT Analyze patterns and relationships.

10 Generate two numerical patterns using a given rule. Identify apparent relationships between corresponding terms by completing a function table or input/output table. Using the terms created, form and graph ordered pairs on a coordinate plane. Graph points on the coordinate plane to solve real-world and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond ( , x-axis and x-coordinate, y-axis and y-coordinate).