## Description

- نظرة عامة:
- This lesson unit is intended to help teachers assess how well students are able to: solve linear equations in one variable with rational number coefficients; collect like terms; expand expressions using the distributive property; and categorize linear equations in one variable as having one, none, or infinitely many solutions. It also aims to encourage discussion on some common misconceptions about algebra.

- 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
- 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: Solve linear equations in one variable.

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: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

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: 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: 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)

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)

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: 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: 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: الممارسات الرياضية

مستوى: Mathematical practices

Indicator: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

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)

حقل التعلم: التعبيرات والمعادلات

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

Indicator: Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.

درجة المواءمة: غير مُقيَّم (عدد المستخدمين: 0)

## Evaluations

# Achieve OER

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

جودة شرح الموضوع | 3 (عدد المُقَيِّمين: 2) |

فائدة المواد المصممة لدعم التعليم | 2,5 (عدد المُقَيِّمين: 2) |

جودة التقييمات | 3 (عدد المُقَيِّمين: 1) |

جودة التفاعل التكنولوجي | غير متاح |

جودة التمارين التدريسية وتمارين الممارسة | 2 (عدد المُقَيِّمين: 1) |

فرص للتعلم على نحو أعمق | 1 (عدد المُقَيِّمين: 1) |

# EQuIP Rubric

Average Score (3 Points Possible)ELA | Math |

Alignment to the Rigor of the CCSS | غير متاح |

Key Shifts in the CCSS | غير متاح |

Instructional Supports | غير متاح |

التقييم | غير متاح |

Overall Rating for the Lesson/Unit | ان N |

Alignment to the Rigor of the CCSS | غير متاح |

Key Shifts in the CCSS | غير متاح |

Instructional Supports | غير متاح |

التقييم | غير متاح |

Overall Rating for the Lesson/Unit | ان N |

# وسوم (8)

- Mathematics
- الجبر
- CCSS
- Common Core Math
- Common Core PD
- الملكية التوزيعية
- المعادلات الخطية
- ODE Learning

on Sep 25, 11:21am Evaluation

## Quality of Explanation of the Subject Matter: متفوق (3)

Very clear instructions of what to do in each part of the lesson and how it connects to the overall objective

on Sep 25, 11:21am Evaluation

## Utility of Materials Designed to Support Teaching: قوي (2)

There are multiple worksheets, but I did not see a way to accommodate for a student who may not be able to do the worksheets. Also, there could be more of a variety of materials that are more interactive.

on Sep 25, 11:21am Evaluation

## Opportunities for Deeper Learning: محدود (1)

The initial engagement could be a little stronger during class time. Maybe make it more interactive or encourage them to think of linear equations in the real world.

This is a lesson/assessment tool. There are many teacher resources to aid in the lesson. There are ppt, detailed lessons, assessments, student handouts, suggestions of prompts to help students think about their work and to help guide them in the right direction. This addresses CCSS 8.EE.7 as they do solve one variable equations; analyze when an equation is Always, sometimes, or never true; and they learn and use the distributive property.