# Classifying Solutions to Systems of Equations

الرجاء تسجيل الدخول لحفظ المواد. تسجيل الدخول

## Description

- نظرة عامة:
- This lesson unit is intended to help teachers assess how well students are able to classify solutions to a pair of linear equations by considering their graphical representations. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using substitution to complete a table of values for a linear equation; identifying a linear equation from a given table of values; and graphing and solving linear equations.

- مستوى:
- المدرسة الابتدائية القسم الأدنى, المدرسة الابتدائية القسم الأعلى, المدرسة الإعدادية, المدرسة الثانوية
- Grades:
- رياض الأطفال, الصف الأول, الصف الثاني, الصف الثالث, الصف الرابع, الصف الخامس, الصف السادس, الصف السابع, الصف الثامن, الصف التاسع, الصف العاشر, الصف الحادي عشر, الصف الثاني عشر
- نوع المادة:
- التقييم, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- الرخصة:
- Creative Commons Attribution Non-Commercial No Derivatives
- صيغة الوسائط:
- مستندات قابلة للتنزيل, نص/لغة رقم النص الفائق HTML

# تعليقات

## Standards

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

درجة المواءمة: 3 متفوق (عدد المستخدمين: 1)

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

درجة المواءمة: 3 متفوق (عدد المستخدمين: 1)

المجموعة: Work with radicals and integer exponents

مستوى: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Work with radicals and integer exponents

مستوى: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and determine that the world population is more than 20 times larger.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Work with radicals and integer exponents

مستوى: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) = 1/(3^3) = 1/27.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Work with radicals and integer exponents

مستوى: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Mathematical practices

مستوى: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Mathematical practices

مستوى: Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Mathematical practices

مستوى: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Analyze and solve pairs of simultaneous linear equations.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Solve linear equations in one variable.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Understand the connections between proportional relationships, lines, and linear equations

مستوى: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Understand the connections between proportional relationships, lines, and linear equations

مستوى: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

المجموعة: Analyze and solve linear equations and pairs of simultaneous linear equations

مستوى: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: الممارسات الرياضية

مستوى: Mathematical practices

Indicator: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: الممارسات الرياضية

مستوى: Mathematical practices

Indicator: Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Solve linear equations in one variable.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Understand the connections between proportional relationships, lines, and linear equations

Indicator: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y =mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Understand the connections between proportional relationships, lines, and linear equations

Indicator: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Work with radicals and integer exponents

Indicator: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Work with radicals and integer exponents

Indicator: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Work with radicals and integer exponents

Indicator: Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that ‰ö_2 is irrational.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Work with radicals and integer exponents

Indicator: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: التعبيرات والمعادلات

مستوى: Analyze and solve linear equations and pairs of simultaneous linear equations

Indicator: Analyze and solve pairs of simultaneous linear equations.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

حقل التعلم: الممارسات الرياضية

مستوى: Mathematical practices

Indicator: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"ť They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)درجة المواءمة | 3 (عدد المُقَيِّمين: 1) |

جودة شرح الموضوع | 2 (عدد المُقَيِّمين: 1) |

فائدة المواد المصممة لدعم التعليم | 3 (عدد المُقَيِّمين: 1) |

جودة التقييمات | غير متاح |

جودة التفاعل التكنولوجي | غير متاح |

جودة التمارين التدريسية وتمارين الممارسة | غير متاح |

فرص للتعلم على نحو أعمق | غير متاح |

This is a lesson/assessment to help students analyze systems of equations. There are many resources for teachers. Detailed lessons, ppt, assessments, card sets for students to match up. It addresses CCSS8.EE.8a more than the other CCSS standards listed. It does help students be fluent between writing a linear equation, completing a table, and graphing.

L Higashi