## Description

- Overview:
- This lesson unit is intended to help teachers assess how well students are able to: form and solve linear equations involving factorizing and using the distributive law. In particular, this unit aims to help teachers identify and assist students who have difficulties in: using variables to represent quantities in a real-world or mathematical problem and solving word problems leading to equations of the form px + q = r and p(x + q) = r.

- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- License:
- Creative Commons Attribution-NonCommercial-NoDerivs 3.0
- Media Format:
- Downloadable docs, Text/HTML

# Comments

## Standards

Cluster: Use properties of operations to generate equivalent expressions

Standard: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Degree of Alignment: 3 Superior (1 user)

Cluster: Use properties of operations to generate equivalent expressions

Standard: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Degree of Alignment: 3 Superior (1 user)

Cluster: Mathematical practices

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Standard: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Degree of Alignment: Not Rated (0 users)

Standard: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Indicator: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Indicator: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example, As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Use properties of operations to generate equivalent expressions

Indicator: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Use properties of operations to generate equivalent expressions

Indicator: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%"ť is the same as "multiply by 1.05."ť

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Indicator: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Indicator: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Indicator: Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Indicator: Solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Use properties of operations to generate equivalent expressions.

Indicator: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: Use properties of operations to generate equivalent expressions.

Indicator: Recognize that algebraic expressions may have a variety of equivalent forms that reveal different information, and determine an appropriate form for a given real-world situation.

Degree of Alignment: Not Rated (0 users)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)Degree of Alignment | 3 (1 user) |

Quality of Explanation of the Subject Matter | 3 (1 user) |

Utility of Materials Designed to Support Teaching | 3 (1 user) |

Quality of Assessments | N/A |

Quality of Technological Interactivity | N/A |

Quality of Instructional and Practice Exercises | N/A |

Opportunities for Deeper Learning | N/A |

# EQuIP Rubric

Average Score (3 Points Possible)ELA | Math |

Alignment to the Rigor of the CCSS | N/A |

Key Shifts in the CCSS | N/A |

Instructional Supports | N/A |

Assessment | N/A |

Overall Rating for the Lesson/Unit | N |

Alignment to the Rigor of the CCSS | N/A |

Key Shifts in the CCSS | N/A |

Instructional Supports | N/A |

Assessment | N/A |

Overall Rating for the Lesson/Unit | N |

# Tags (10)

- Mathematics
- Algebra and Calculus
- Algebra
- CCSS
- Common Core Math
- Common Core PD
- Equations
- Factoring
- Linear Equations
- ODE Learning

لقد استفدت من هذا المصدر في طريقة عرض الدرس و استخدام أوراق العمل التي تناسب مختلف المستويات حيث لاحظت التدرج في طرح المسائل و تحويلها من اللفظية إلى الجبرية و قد كان تجاوب التلاميذ و تفاعلهم ممتازاً

ناهيك عن وجود عدة أنشطة تعليمية تخدم الدرس من بطاقات يوضح عليها خطوات حل المسائل و كذلك توظيف حل المعادلات في إيجاد المساحات و المحيط لبعض الأشكال و التي أطوالها تحتوي على مقادير جبرية

This is a lesson with an assessment. There are many teacher resources like detailed lesson plans, student worksheets, ppts, and assessments. It addresses EE.1 and EE.2. It also may take longer than suggested.