<h2>Teaching Find The Distance Between Two Points (Real World Problems) Easily</h2><h2>&nbsp;</h2><ol><li>Introduce the concept of distance and the <a href="https://www.bytelearn.com/math-topics/distance-formula" target="_blank" class="backlink">distance formula</a>: Explain the distance formula to the students, using the examples provided earlier in the answer. Show them how to use the formula to calculate the distance between two points in a two-dimensional coordinate plane.</li><li>Practice with worksheets: Give students practice worksheets to solve using the distance formula. Start with simpler problems and gradually increase the difficulty level.&nbsp;</li><li>Provide feedback: Provide feedback on the students' work and help them understand where they made mistakes. Point out the key concepts and formulas they used to solve the problem and how they can apply them to other problems given in the worksheet.</li></ol> &nbsp;<h2>Why Should You Use Find The Distance Between Two Points (Real World Problems) Worksheet for your students?&nbsp;</h2>&nbsp;Yours students will earn to use different formulas to find the distance between two pointsThe most common methods include: &nbsp;<ul><li>Distance formula: The distance formula is a mathematical formula used to calculate the distance between two points in a two-dimensional coordinate plane. It is given by:</li></ul>Distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points. &nbsp;<ul><li><a href="https://www.bytelearn.com/math-topics/pythagorean-theorem" target="_blank" class="backlink">Pythagorean theorem</a>: The Pythagorean theorem is used to calculate the distance between two points in a three-dimensional space. It states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.</li></ul>Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2), where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points. &nbsp;<ul><li>Manhattan distance: The Manhattan distance is used to calculate the distance between two points in a grid-like structure, such as a city. It is calculated by summing the absolute differences of their coordinates along each dimension of the space. Distance = |x2 - x1| + |y2 - y1|</li></ul>These are just some examples of distance calculation methods, depending on the problem, other methods and formulas can be used.<h2>Download Find The Distance Between Two Points (Real World Problems) Worksheets PDF</h2>&nbsp;You can download and print these super fun Basic word problems (using formula) worksheet&nbsp; 6th grade pdf from here for your students. You can also try our <a href="https://www.bytelearn.com/math-grade-6/practice-problems/find-the-distance-between-two-points-real-world-problems">Find The Distance Between Two Points (Real World Problems) Problems</a> and <a href="https://www.bytelearn.com/math-grade-6/quiz/find-the-distance-between-two-points-real-world-problems">Find The Distance Between Two Points (Real World Problems) Quiz</a> as well for a better understanding of the concepts. &nbsp;

Find the distance between two points (real world problems)

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Finding the distance between two points refers to the calculation of the straight-line distance between two points in a given space, such as a coordinate plane or a three-dimensional space. This distance is also known as the "Euclidean distance" and is represented by a line segment connecting the two points.

<h2>Important Points of the Coordinate Plane</h2>&nbsp;<ul><li>The left and the bottom part of the plane have negative x-axis and negative y-axis for negative integers. The point where the number lines intersect is called the origin.</li><li>A coordinate plane is a tool used for graphing points, lines, and other objects. It functions like a map that follows directions from one point to another.</li><li>The two number lines divide the coordinate plane into 4 regions. These regions are called Quadrants.</li><li>The first quadrant (+, +) known as the positive coordinates quadrant, is represented by the Roman numeral I.</li><li>The second quadrant (-, +) is represented by the Roman numeral II.</li><li>The third quadrant (-, -) is represented by the Roman numeral III.</li><li>The fourth quadrant (+, -) is represented by the Roman numeral IV.</li><li>The coordinates of any point are enclosed in brackets.</li></ul> &nbsp;<h2>Coordinate Plane Example</h2>&nbsp;1.&nbsp; &nbsp;&nbsp;You are at (−4, 3). Move&nbsp; 5 units right and 2 units up. Write the coordinates of the point where you reach.Ø&nbsp;Moving 5 units to the right will reach −4 + 5 = 1 on the x-axis.&nbsp;Ø&nbsp;Moving 2 units up will reach 3 + 2 = 5 on the y-axis.Ø&nbsp;So, the coordinates of the point where we reached is (1, 5).Hey teachers, if you are looking for unit tests, activities, worksheets, quiz, practice test papers that are suitable for 6th grade math, here's the compilation of lessons suitable for 6th grade to share with your students.&nbsp;A detailed understanding of coordinate plane basic concepts is essential for students. This&nbsp;coordinate plane lesson plan 6th grade&nbsp;will help teachers build a strong foundation.

<h2 style="text-align:justify;">6th Grade Course Summary&nbsp;</h2>&nbsp;In 6th grade math, students will learn advanced mathematical concepts and perform new operations. Here is a brief overview of the 6th Grade Math Course:<h2> <a href="https://www.bytelearn.com/math-grade-6/Coordinate-Plane">Coordinate Plane</a></h2><h2><a href="https://www.bytelearn.com/math-grade-6/Expressions-Equations-Inequalities">Expressions, Equations, And Inequalities</a></h2><h2><a href="https://www.bytelearn.com/math-grade-6/Number-System">Number System</a></h2><h2><a href="https://www.bytelearn.com/math-grade-6/percent">Percents</a></h2><h2><a href="https://www.bytelearn.com/math-grade-6/Ratios-and-rates">Ratios And Rates</a></h2>

grade 6

6th-grade math is a crucial part of a student’s math education. It introduces students to key mathematical concepts while strengthening the concepts learnt in their previous grade. In&nbsp; 6-th grade math students also learn essential concepts and make a progression towards algebra for middle school.&nbsp;&nbsp;Students will learn how to explore and reason and investigate numbers. They will also delve into understanding concepts such as Ratio and Proportion, Rational Numbers which will help them build math skills for the upcoming grades. In addition to these topics, students will also continue to study how to calculate the area and perimeter of different geometric figures and work on understanding statistics and data.

Negative Numbers

A coordinate plane is a two-dimensional plane formed by the intersection of two lines called axis. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.&nbsp;The plane is called two-dimensional because anywhere on this plane where you can put your finger, the location of that point will need two things– its distance on the x-axis and its distance on the y-axis. Coordinate plane 6th grade covers all the basics of Coordinate Planes.

The plan aims to develop students' critical thinking and problem-solving skills and to enhance their ability to reason abstractly and quantitatively. Teachers can use this lesson plan to provide a comprehensive and structured approach to teaching negative numbers, reinforce classroom instruction, and assess students' understanding of the key concepts and skills related to negative numbers. The lesson plan is designed to help students meet the 6th grade Common Core Standards for Mathematics.

6th Grade Math Negative Numbers Lesson Plan

The Negative Numbers Lesson Plan is a teaching plan designed for 6th grade students in accordance with the Common Core Standards for Mathematics. This lesson plan focuses on introducing key concepts related to negative numbers, including understanding negative numbers as positions on a number line, performing operations involving negative numbers, and solving real-world problems using negative numbers.&nbsp;&nbsp;The lesson plan includes engaging activities and exercises to help students build their conceptual understanding of negative numbers, develop their proficiency in performing arithmetic operations involving negative numbers, and apply their knowledge to solve real-world problems.&nbsp;

Teachers can share this practice problem in the classroom to upgrade students’ knowledge.

Negative Number Problems is a set of exercises designed for 6th grade students in accordance with the Common Core Standards for Mathematics. These problems focus on key concepts related to negative numbers, including integer addition, subtraction, multiplication, and division. By practicing these problems, students can improve their understanding of these concepts and develop their proficiency in solving problems involving negative numbers.&nbsp;&nbsp;The problems aim to develop students' critical thinking and problem-solving skills and to enhance their ability to reason abstractly and quantitatively. Through these problems, students can deepen their knowledge of arithmetic operations and develop their ability to apply them to real-world situations. Teachers can use these problems to reinforce classroom instruction, provide additional practice, and assess students' mastery of the key concepts and skills related to negative numbers. &nbsp;

Teachers can utilise this quiz to assess their students’ knowledge of this topic.&nbsp;

Negative Number Quizzes is a series of assessments designed for 6th grade students in accordance with the Common Core Standards for Mathematics. These quizzes focus on negative numbers and their applications, including operations with negative numbers, absolute value, and real-world contexts such as temperature, money, and elevation. By taking these quizzes, students can improve their understanding of negative numbers and develop their proficiency in performing calculations and solving problems involving negative numbers.&nbsp;&nbsp;The quizzes aim to assess students' mastery of the key concepts and skills related to negative numbers and to provide feedback to teachers on areas where students may need additional support or instruction. Through these quizzes, teachers can monitor student progress, identify areas for improvement, and tailor their instruction to meet the individual needs of each student.

In this worksheet, students will learn to represent negative numbers on a number line and understand their position relative to positive numbers. They will also learn how to add and subtract negative numbers and apply these operations to solve real-world problems.&nbsp;To begin, students will practice identifying the sign of a number and representing it on a number line. They will then move on to adding and subtracting positive and negative numbers, using the rules of signed numbers to guide their calculations.&nbsp;The worksheet also includes real-world problems that require students to apply their knowledge of negative numbers to solve them. For example, they may need to calculate the change received after a purchase or determine the temperature change over a period of time.&nbsp;By completing this worksheet, students will develop their understanding of negative numbers and become proficient in using them to solve mathematical problems. This will help them to excel in future mathematics classes and become confident problem solvers.

Welcome to the Negative Number worksheet for Grade 6 students, designed to help them understand and apply the concept of negative numbers. This worksheet aligns with the Common Core Standards for Mathematics, which aim to develop students' mathematical proficiency and help them become critical thinkers.

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 1, "x": 3, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -3, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 3, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": -7, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 8, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -7, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } ], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph >You are currently at the post office, but you need to get to the theater.<ul><li>What are the coordinates for both the post office and the theater?</li><li>What is the distance between the post office and the theater?</li></ul> <highlight data-color="#666" data-style="italic">Each square represents `1` mile.</highlight>

Math

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 1, "x": 1, "y": 9, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "graduation_cap" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 9, "y": 9, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "home" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 1, "y": 2, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 4, "x": -9, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 5, "x": 8, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 6, "x": -9, "y": 2, "show_point": false, "highlight_point": false, "highlight_point_color": "#000", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } ], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Playground", "icon": { "name": "kite" } }, { "label": "City Hall", "icon": { "name": "bank" } }, { "label": "Libray", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } }, { "label": "School", "icon": { "name": "graduation_cap" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Home", "icon": { "name": "home" } }, { "label": "Market", "icon": { "name": "shopping_cart" } } ] }}'></LineGraph >You are currently at home, but you need to get to the school.<ul><li>What are the coordinates for both home and the school?</li><li>What is the distance between home and the school?</li></ul><highlight data-color="#666" data-style="italic">Each square represents `1` mile.</highlight>

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 , "x_skip_interval": 2, "y_skip_interval": 2 }, "points": [ { "id": 1, "x": 2, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -3, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 2, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": -8, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 4, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "fire_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 7, "y":2, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "museum" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": -8, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Fire station", "icon": { "name": "fire_station" } }, { "label": "Museum", "icon": { "name": "museum" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph >You are currently at the post office, but you need to get to the police station.<ul><li>What are the coordinates for both the post office and the police station?</li><li>What is the distance between the post office and the police station?</li></ul><highlight data-color="#666" data-style="italic">Each big square represents `2` miles.</highlight>

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 , "x_skip_interval": 2, "y_skip_interval": 2 }, "points": [ { "id": 1, "x": 2, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -3, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 2, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": -8, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 7, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "fire_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 7, "y":2, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "museum" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": -8, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Fire station", "icon": { "name": "fire_station" } }, { "label": "Museum", "icon": { "name": "museum" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph >You are currently at the fire station, but you need to get to the post office.<ul><li>What are the coordinates for both the fire station and the post office?</li><li>What is the distance between the fire station and the post office?</li></ul> <highlight data-color="#666" data-style="italic">Each big square represents `2` miles.</highlight>

<LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 1, "x": 2, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -3, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 3, "y": -8, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": -7, "y": -3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 8, "y": 7, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -8, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } ], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph >You are currently at the post office, but you need to get to the bank.<ul><li>What are the coordinates for both the post office and the bank?</li><li>What is the distance between the post office and the bank?</li></ul> <highlight data-color="#666" data-style="italic">Each square represents `1` mile.</highlight>

<LineGraph data-props='{ "options": { "x_min": -7, "y_min": -7, "y_max": 7, "x_max": 7, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5 , "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 1, "x": -5, "y": -5, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "airport" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "train_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 4, "y": -2, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "city_hall" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": -2.5, "y": 3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -4, "y": 3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "hotel" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 2.5, "y": 3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": 6, "y": 6, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Library", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } } , { "label": "City hall", "icon": { "name": "city_hall" } }, { "label": "Shopping mall", "icon": { "name": "shopping_cart" } }, { "label": "Hotel", "icon": { "name": "hotel" } }, { "label": "Train station", "icon": { "name": "train_station" } } , { "label": "Airport", "icon": { "name": "airport" } }, { "label": "Gas station", "icon": { "name": "gas_station" } } ] }}'></LineGraph >You are currently at the library, but you need to get to the shopping mall.<ul><li>What are the coordinates for both the library and the shopping mall?</li><li>What is the distance between the library and the shopping mall?</li></ul> <highlight data-color="#666" data-style="italic">Each big square represents `1` mile.</highlight>

<LineGraph data-props='{ "options": { "x_min": -5, "y_min": -5, "y_max": 5, "x_max": 5, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5 , "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 1, "x": -4, "y": 4, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "graduation_cap" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": 3.5, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "train_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": -4, "y": -4, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 4, "y": -2, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "city_hall" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": -4.5, "y": 1, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "shopping_cart" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -4, "y": 3, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "hotel" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": -4.5, "y": -2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": 3.5, "y": 3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "gas_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Library", "icon": { "name": "books" } }, { "label": "Post office", "icon": { "name": "mailbox" } } , { "label": "City hall", "icon": { "name": "city_hall" } }, { "label": "Shopping mall", "icon": { "name": "shopping_cart" } }, { "label": "Hotel", "icon": { "name": "hotel" } }, { "label": "Train station", "icon": { "name": "train_station" } } , { "label": "School", "icon": { "name": "graduation_cap" } }, { "label": "Gas station", "icon": { "name": "gas_station" } } ] }}'></LineGraph ></LineGraph >You are currently at the train station, but you need to get to the gas station.<ul><li>What are the coordinates for both the train station and the gas station?</li><li>What is the distance between the train station and the gas station?</li></ul> <highlight data-color="#666" data-style="italic">Each big square represents `1` mile.</highlight>

<LineGraph data-props='{ "options": { "x_min": -5, "y_min": -5, "y_max": 5, "x_max": 5, "cell_size": 20, "x_interval": 0.5, "y_interval": 0.5 , "x_skip_interval": 1, "y_skip_interval": 1 }, "points": [ { "id": 1, "x": 0.5, "y": 2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#377CF6", "x_coordinate_highlight": false, "y_coordinate_highlight": false, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "bank" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 2, "x": -4, "y": -3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "theater" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 3, "x": 0.5, "y": -3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "weight_lifter" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 4, "x": 0.5, "y":4.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "books" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 5, "x": 3.5, "y": -3.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "police_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 6, "x": -4, "y": 0, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "fire_station" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 } , { "id": 7, "x": 3.5, "y":0, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "museum" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }, { "id": 8, "x": -4, "y": 2.5, "show_point": false, "highlight_point": false, "highlight_point_color": "#8000FF", "x_coordinate_highlight": false, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "legend_icon": { "icon": { "name": "mailbox" }, "highlight": true }, "x_color": "green", "y_color": "red", "x_intercept_width": 2, "y_intercept_width": 2 }], "line_segments": [], "legend_options": { "show_menu": true, "menu_position": "right", "menu_items": [ { "label": "Bank", "icon": { "name": "bank" } }, { "label": "Theater", "icon": { "name": "theater" } }, { "label": "Gym", "icon": { "name": "weight_lifter" } }, { "label": "Library", "icon": { "name": "books" } }, { "label": "Police station", "icon": { "name": "police_station" } }, { "label": "Fire station", "icon": { "name": "fire_station" } }, { "label": "Museum", "icon": { "name": "museum" } }, { "label": "Post office", "icon": { "name": "mailbox" } } ] }}'></LineGraph >Pat is currently at the fire station, but he need to get to the museum.<ul><li>What are the coordinates for the fire station and the museum?</li><li>What is the distance between the fire station and the museum?</li></ul> <highlight data-color="#666" data-style="italic">Each big square represents `1` mile.</highlight>

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