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|Essential Question |Key Concepts |Cross Curricular Connections |

|How can analyzing patterns and relationships as well as graphing |Coordinate Systems |Religion: Use coordinate systems to plot points that create |

|points on a coordinate plane solve real world problems? |Patterns in the Coordinate Plane and Graphing Number Patterns from |sacramental signs and symbols for the Seven Sacraments. Have |

| |Rules |students connect the points to reveal the images. |

|Unit Vocabulary |Drawing Figures in the Coordinate Plane | |

|Axis |Problem Solving in the Coordinate Plane |Social Studies: Students will be graphing on a coordinate plane; |

|Coordinate |Multi-Step Word Problems |plotting points on a grid by creating a town. They will be making a |

|Coordinate pair |The Years in Review |map of the key places in their town (e.g., Church, house, school, |

|Coordinate plane | |library, restaurant and cinema). They will work with a partner to |

|Ordered pair | |exchange questions about their town and provide information about |

|Origin | |various locations using the coordinates on a plane. They will be |

| | |making a blueprint of their town. |

|*Assessments | | |

|Mid-Module Assessment: After Section B | |Art: The students will draw the town they created, but will also |

|(3 days, included in Unit Instructional Days) | |have a coordinate plane to show exact locations and distances |

|End-of-Module Assessment: after Section D (3 days, included in Unit | |between each building |

|Instructional Days) | | |

| | | |

GRADE 5 UNIT 6:  Problem Solving with the Coordinate Plane Suggested Number of Days for Entire UNIT: 40

| Unit Outcome (Focus) |

| |

|In this unit students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiar number line as an introduction to the idea of a |

|coordinate and construct two perpendicular number lines to create a coordinate system on the plane. They see that just as points on the line can be located by their distance from 0, the plane’s coordinate |

|system can be used to locate and plot points using two coordinates. They then use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the |

|rules that generate them. This study culminates in an exploration of the coordinate plane in real world applications. |

UNIT 6 SECTION A: Coordinate Systems Suggested Number of Days for SECTION: 6

|Essential Question |Key Concept |Standards for Mathematical Practice |

|How can the relationship of numbers be shown on |Construct a coordinate system on a line. |1. Make sense of problems and persevere in solving them |

|a coordinate plane? |Construct a coordinate system on a plane. |3. Construct viable arguments and critique the |

| |Name points using coordinate pairs, and use the coordinate pairs to plot points. |reasoning of others |

| |Investigate patterns in vertical and horizontal lines, and interpret points on the plane|6. Attend to precision |

| |as distances from the axes. | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In Section A, students come to realize that any | | | |

|line, regardless of orientation, can be made |5.G. 1 |Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the | |

|into a number line by first locating zero, |(DOK 1) |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,|( |

|choosing a unit length, and partitioning the | |called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one | |

|length-unit into fractional lengths as desired. | |axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names | |

|They are introduced to the concept of a | |of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | |

|coordinate as describing the distance of a point| | | |

|on the line from zero. As students construct | | | |

|these number lines in various orientations on a | | | |

|plane, they explore ways to describe the | | | |

|position of points not located on the lines. | | | |

|This discussion leads to the discovery that a | | | |

|second number line, perpendicular to the first, | | | |

|creates an efficient, precise way to describe | | | |

|the location of these points. | | | |

UNIT 6 SECTION B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules Suggested Number of Days for SECTION: 6

|Essential Question |Key Concepts |Standards for Mathematical Practice |

| |Plot points, use them to draw lines in the plane, and describe patterns within the | |

|How can students make sense of and explain |coordinate pairs. |2. Reason abstractly and quantitatively |

|the relationships in numerical patterns? |Generate a number pattern from a given rule, and plot the points. |7. Look for and make use of structure |

| |Generate two number patterns from given rules, plot the points, and analyze the patterns. |8. Look for and express regularity in repeated reasoning |

| |Compare the lines and patterns generated by addition rules and multiplication rules. | |

| |Analyze number patterns created from mixed operations. | |

| |Create a rule to generate a number pattern, and plot the points. | |

|Comments |Standard No. |Standard |Priority |

|Students move in to plotting points and using| |( Major Standard ( Supporting Standard ( Additional Standard | |

|them to draw | |( Standard ends at this grade ( Fluency Standard | |

|lines in the plane in Section B (5.G.1). |5.OA.2 |Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For | |

|They investigate patterns relating the [pic]-|(DOK 1) |example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as|( |

|and [pic]-coordinates of the points on the | |large as 18932 + 921, without having to calculate the indicated sum or product. | |

|line and reason about the patterns in the | | | |

|ordered pairs, laying important groundwork | |Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered | |

|for Grade 6 proportional reasoning. Section |5.OA.3 |pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given | |

|B continues as students use given rules |(DOK 2) |the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting |( |

|(e.g., multiply by 2, then add 3) to generate| |sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why| |

|coordinate pairs, plot points, and | |this is so. | |

|investigate relationships. Patterns in the | | | |

|resultant coordinate pairs are analyzed, | |Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin)| |

|leading students to discover that such rules | |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 | |

|produce collinear sets of points. | |coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the | |

| |5.G. 1 |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|( |

| |(DOK 1) |the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | |

| | | | |

| | | | |

UNIT 6 SECTION C: Drawing Figures in the Coordinate Plane Suggested Number of Days for SECTION: 5

|Essential Question |Key Concept |Standards for Mathematical Practice |

|How can the relationship of numbers be shown on |Construct parallel line segments on a rectangular grid. |1. Make sense of problems and persevere in solving them |

|a coordinate plane? |Construct parallel line segments, and analyze relationships of the coordinate pairs. |3. Construct viable arguments and critique the |

| |Construct perpendicular line segments on a rectangular grid. |reasoning of others |

| |Construct perpendicular line segments, and analyze relationships of the coordinate |6. Attend to precision |

| |pairs. | |

| |Draw symmetric figures using distance and angle measure from the line of symmetry. | |

| |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

| |5.G. 1 |Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the | |

| |(DOK 1) |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 (e.g., x-axis and x-coordinate, y-axis and y-coordinate). | |

| | | | |

| | |Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret | |

| | |coordinate values of points in the context of the situation. | |

| |5.G. 2 | | |

| |(DOK 1) | |( |

|Comments | | | |

|Section C finds students drawing figures in the | | | |

|coordinate plane by plotting points to create | | | |

|parallel, perpendicular, and intersecting lines.| | | |

|They reason about what points are needed to | | | |

|produce such lines and angles, and then | | | |

|investigate the resultant points and their | | | |

|relationships. | | | |

|Students also reason about the relationships | | | |

|among coordinate pairs that are symmetric about | | | |

|a line (5.G.1). | | | |

UNIT 6 SECTION D: Problem Solving in the Coordinate Plane Suggested Number of Days for SECTION: 3

|Essential Question |Key Concept |Standards for Mathematical Practice |

|How can the relationship of numbers be shown on |Draw symmetric figures on the coordinate plane. |1. Make sense of problems and persevere in solving them |

|a coordinate plane? |Plot data on line graphs and analyze trends. |3. Construct viable arguments and critique the |

| |Use coordinate systems to solve real world problems. |reasoning of others |

| | |6. Attend to precision |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Problem solving in the coordinate plane is the | | | |

|focus of Section D. Students draw symmetric |5.OA.3 |Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered|( |

|figures using both angle size and distance from |(DOK 2) |pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, | |

|a given line of symmetry (5.G.2). Line graphs | |given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the | |

|are also used to explore patterns and make | |resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain| |

|predictions based on those patterns (5.G.2, | |informally why this is so. | |

|5.OA.3). To round out the topic, students use | | | |

|coordinate planes to solve real world problems. | | | |

| | |Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret | |

| |5.G. 2 |coordinate values of points in the context of the situation. |( |

| |(DOK 1) | | |

| | | | |

| | | | |

UNIT 6 SECTION E: Multi-Step Word Problems Suggested Number of Days for SECTION: 5

|Essential Question |Key Concept |Standards for Mathematical Practice |

|How can the relationship of numbers be shown on |Make sense of complex, multi-step problems and persevere in solving them. . |1. Make sense of problems and persevere in solving them |

|a coordinate plane? | |3. Construct viable arguments and critique the |

| | |reasoning of others |

| | |6. Attend to precision |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|Section E provides an opportunity for students | | | |

|to encounter complex, multi-step problems | | | |

|requiring the application of concepts and skills|5.NF.2 | | |

|mastered throughout the Grade 5 curriculum. |5.NF.3 | | |

|They use all four operations with both whole |5.NF.6 | | |

|numbers and fractions in varied contexts. The |5.NF.7c | | |

|problems in Section E should offer students |5.MD.1 | | |

|opportunities for multi-step word problems that |5.MD.5 | | |

|are non-routine, requiring students to persevere|5.G.2 | | |

|in order to solve them. While wrestling with | | | |

|complexity is an important part of Section E, | | | |

|the true strength of this topic is derived from | | | |

|the time allocated for students to construct | | | |

|arguments and critique the reasoning of their |5.G. 2 | | |

|classmates. |(DOK 1) | | |

| | | | |

| | | | |

| | | | |

| | |Activities for this section can be found on Engage NY Topic E: | |

UNIT 6 SECTION F: The Years in Review: A Reflection on A Story of Units Suggested Number of Days for SECTION: 9

|Essential Question |Key Concept |Standards for Mathematical Practice |

| | | |

| |A Review and Reflection on A Story of Units K-5 Curriculum |All Standards |

| | | |

|Comments |Standard No. |Standard |Priority |

| | |( Major Standard ( Supporting Standard ( Additional Standard | |

| | |( Standard ends at this grade ( Fluency Standard | |

|In this final topic of Unit 6, and in fact, A | | | |

|Story of Units, seen on Engage NY students spend| | | |

|time producing a compendium of their learning. | |Activities for this section can be found on Engage NY Topic F: | |

|They not only reach back to recall learning from| | | |

|the very beginning of Grade 5, but they also | | | |

|expand their thinking by exploring such concepts| | | |

|as the Fibonacci sequence. Students solidify | | | |

|the year’s learning by creating and playing | | | |

|games, exploring patterns as they reflect back | | | |

|on their elementary years. All materials for | | | |

|the games and activities are then housed for | | | |

|summer use in boxes created in the final two | | | |

|lessons of the year. | | | |

|These activities can be found on Engage NY: | | | |

| | | |

|tics-module-6 | | | |

|Possible Activities |

|SHAPE INVADERS: Students are given (or shown on the overhead) a coordinate plane with shapes located at different coordinates in the first quadrant. Students write down the ordered pairs of the shapes in the |

|allotted time. The students receive points for each correct ordered pair. Player with most points at the end of three rounds wins. Coordinate graphing worksheets can be found online. Coordinate graphing |

|worksheets can be found at . Click on Ordered Pairs on the left. Mystery Graph pictures can also be located at this site. |

| |

|NEIGHBORHOOD MAPS: Students can create a coordinate graph of places in their neighborhood. First, students write in sentences where everything is in relation to their house. They should provide directions based |

|in how many blocks and in what direction. (East, West, North and South). Their house is the origin. After they complete their sentences, they will begin to plot points on the coordinate graph. Last, the students |

|will reflect on the project. Was there anything that did not make sense? |

| |

|METRIC OLYMPICS: Students complete in a Metric Olympics that includes a cotton ball throw, discus throw with paper plates, and the long jump. Five students are on each team and statistics are kept using the |

|metric system. Each event is recorded in millimeters, centimeters, and meters. Students have their own competition statistics sheet and a sheet to average the team results. Students will compare their scores to |

|the other members of their team. The group will figure a team score based on the average of all team members. The best student and the best team receive medals for each event. You can also use customary |

|measurements. |

| |

|MEASUREMENT SCENARIOS: Provide students with scenarios explaining how to measure items in millimeters, centimeters, meters, or kilometers. For example: How would the length of a book, the classroom, a small |

|eraser, the cabinet, the road, and the school’s property each be measured? Then have students estimate the lengths of each using a metric measurement. When possible compare and take actual measurements then |

|recording the measurements using three different metric units. Adapt this activity to use customary measurement, recording the events in inches, feet, and yards. |

| |

|CONVERSION WORD PROBLEMS: Additional word problems involving conversions online. |

|Ex: The boundary between our farm and the farm to the north is 4.3 km. The boundary between our farm and the farm to the south is two hundred thirty-three meters. How much longer, in kilometers, is the boundary |

|with the farm to the north than the boundary with the farm to the south? (Answer: 4.067 km). Additional word problems involving conversions online can be found at . Click on Math Worksheets |

|under Table of Contents. Scroll down and select Metric System. Toward the bottom are great word problems involving conversions. More conversion practice can be found at . Scroll down and click |

|on Conversions Between Customary and Metric on the right. |

|Resources |

|For more brainteasers visit nrich.. Click on For Students on the right then select the age Secondary then select Collections for Secondary Students. |

| |

|Online video lessons and practice questions that align with: |

|NYS Common Core Standard 5.G.1: |

|NYS Common Core Standard 5. G. 2: |

| |

|Problem of the Week: A weekly challenge problem is located at nrich.. Click on For Students to find challenge. |

|Possible Activities |

|WORDS TO EXPRESSIONS GAME: Teacher gives three word forms of an expression verbally (or on whiteboard). The students have to match the right expression on paper, then simplify the expressions and take the |

|product of the three numbers. Students with the correct answers receive points. The student with the highest points after a certain time period wins the game. Example of a word form of an expression: Three |

|more than the product of seven and ten. Play Algebraic Expressions Millionaire (similar to Who Wants to be a Millionaire?). Great online game for one or two players. It can also be used as a whole class |

|game with the class divided into teams. Find the link to Algebraic Expression Millionaire at math-. Select Elementary Games on the left side. Select 5th Grade. Scroll down to find Algebraic |

|Expressions Millionaire Game. |

|TARGET: Great 5 minute game on order of operations. Teacher draws a bulls eye with a target number in the center and five various numbers around the outer circles on the whiteboard. Students are challenged |

|to try to use all the numbers with operations and parentheses to get the target number. If they use all numbers they get a bulls eye and receive10 points. If the students use only 4 numbers they get 4 |

|points, three numbers, 3 points etc. Students can keep track of their points over the course of multiple days. Play Algebraic Expressions Millionaire (similar to Who Wants to be a Millionaire?). Great |

|online game for one or two players. It can also be used as a whole class game with the class divided into teams. |

|COMBINING 2’S: Combine five 2’s using as many symbols and operations as you want. Try to produce all of the numbers from one through ten. |

|Ex: [(2+2) + (2x2)]/2 = 4 |

|ONE, TWO, THREE, FOUR….. Use any combination of the symbols: +, -, x, ÷ and () to make the following sentences true 1 __ 2___3 ___ 4 = 0; 1 __ 2___3 ___ 4 = 1; (the sums 2, 4, 5, 6, 10, 13, 14, 20, 21, 24 |

|can also be used). |

|Enrichment Activities |

|FAMOUS MATHEMATICIAN PROJECT: Students can research, report, and present about the famous mathematician Rene Descartes and his discoveries. |

|MAPS AND THE COORDINATE PLANE RESEARCH PROJECT: Students can complete a research project or paper on how our modern day maps were developed. |

|CREATE MYSTERY GRAPH PICTURES: Challenge students to create a mystery graph picture using the coordinate system of their own for classmates to solve. (Note: Make copies of the coordinates before they are |

|given to classmates in the event that the originals are lost or misplaced.) |

|FOUR QUADRANT GRAPHING: Students can be challenged to plot points in all quadrants of the coordinate plane. |

|BRAINTEASERS: Additional brainteasers can be found online. Ex: Use 4 four times with simple operation symbols to reach 12. (Sample Answer: 4/4 1, 4-1=3, 3X4=12) Extend: Try to get 15, 16 and 17 for the |

|answers. |

|Resources |

|For more brainteasers visit nrich.. Click on For Students on the right then select the age Secondary then select Collections for Secondary Students. |

|Online video lessons and practice questions that align with: |

|NYS Common Core Standard 5 |

|Fifth Grade Lessons: |

| |

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