## Description

- Overview:
- This lesson unit is intended to help teachers assess how well students are able to create and solve linear equations. In particular, the lesson will help you identify and help students who have the following difficulties: solving equations with one variable and solving linear equations in more than one way.

- 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), 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: Analyze and solve linear equations and pairs of simultaneous linear equations

Standard: Analyze and solve pairs of simultaneous linear equations.

Degree of Alignment: 2 Strong (1 user)

Cluster: Work with radicals and integer exponents

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Work with radicals and integer exponents

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Work with radicals and integer exponents

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Work with radicals and integer exponents

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x –1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x^2 + x + 1), and (x – 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Degree of Alignment: Not Rated (0 users)

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

Standard: 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.

Degree of Alignment: Not Rated (0 users)

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

Standard: Solve linear equations in one variable.

Degree of Alignment: Not Rated (0 users)

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

Standard: 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.

Degree of Alignment: Not Rated (0 users)

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

Standard: 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.

Degree of Alignment: Not Rated (0 users)

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

Standard: 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.

Degree of Alignment: Not Rated (0 users)

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

Standard: 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).

Degree of Alignment: Not Rated (0 users)

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

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

Degree of Alignment: Not Rated (0 users)

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

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x -1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x^2 + x + 1), and (x - 1)(x^3 + x^2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

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

Indicator: Solve linear equations in one variable.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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).

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

Standard: 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.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Expressions and Equations

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

Indicator: Analyze and solve pairs of simultaneous linear equations.

Degree of Alignment: Not Rated (0 users)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)Degree of Alignment | 2 (1 user) |

Quality of Explanation of the Subject Matter | 2 (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 |

اعجبني في هذا المصدر طريقة العرض من حيث التدرج ومراعات الفروق الفردية

ايضا هناك فرصة للعمل الجماعي في المجموعات

طريقة العرض مشوقة للطلاب خاصة في بداية مرحلة التعلم لحل المعادلات من خلال استخدام الة المدخلات والمخرجات (input -output machine)

يمكن استخدام الانشطة داخل غرفة الصف لأنه يحقق احد المعايير الخاصة بالنهج وكأنشطة إثرائية تدعم الكتاب المدرسي

This is a lesson/assessment unit. There are many resources for the teacher to aid in the lesson. There are student handouts, assessments, assessment revisited, ppt, explorations for students, suggested questions and prompts for common issues, analysis of sample student responses. This lesson looks at a solution and has student write different possible equations that would have that solution.It slightly addresses CCSS 8.EE.8 analyzing and solving pairs of simultaneous linear equations.