Copy of 2nd grade



Step 1: Objective Statement

|Standard(s) for the grade level(s) before, same content area |Standard(s) for your grade level and content area |Standard(s) for the grade level(s) after, same content area |

|Expressions and Equations--7.EE (M) |Expressions and Equations--8.EE (M) |Creating Equations★—A-CED (M) |

|Use properties of operations to generate equivalent expressions. |Analyze and solve linear equations and pairs of simultaneous linear |Create equations that describe numbers or relationships |

|Apply properties of operations as strategies to add, subtract, |equations |Create equations and inequalities in one variable and use them to |

|factor and expand linear expressions with rational coefficients. |Solve linear equations with one variable. (8.EE.7) |solve problems. Include equations arising from linear and quadratic|

|(7.EE.1) |Give examples of linear equations in one variable with one solution, |functions, and simple rational and exponential functions. (A-CED.1)|

|Understand that rewriting an expression in different forms in a |infinitely many solutions, or no solution. Show which of these |Represent constraints by equations or inequalities, and by systems |

|problem context can shed light on the problem and how the |possibilities is the case by successively transforming the given equation |of equations and/or inequalities, and interpret solutions as viable|

|quantities in it are related. For example, a + 0.05a = 1.05a |into simpler forms until an equivalent equation of the form x = a, a = a, |or non-viable options in a modeling context. For example, represent|

|means that “increase by 5%” is the same as “multiply by 1.05.” |or a = b results (where a and b are different numbers). (8.EE.7a) |inequalities describing nutritional and cost constraints on |

|(7.EE.2) |Solve linear equations with rational number coefficients, including |combinations of different foods. (A-CED.3) |

|Solve real-life and mathematical problems using numerical and |equations whose solutions require expanding expressions using the |Rearrange formulas to highlight a quantity of interest, using the |

|algebraic expressions and equations. |distributive property and collecting like terms. (8.EE.7b) |same reasoning as in solving equations. For example, rearrange |

|Solve multi-step real-life and mathematical problems posed with |Analyze and solve pairs of simultaneous linear equations. (8.EE.8) |Ohm’s law V = IR to highlight resistance R. (A-CED.4) |

|positive and negative rational numbers in any form (whole |Understand that solutions to a system of two linear equations in two |Reasoning with Equations and Inequalities--A-REI |

|numbers, fractions, and decimals), using tools strategically. |variables correspond to points of intersection of their graphs, because |Understand solving equations as a process of reasoning and explain |

|Apply properties of operations to calculate with numbers in any |points of intersection satisfy both equations simultaneously. (8.EE.8a) |reasoning. (M) |

|form; convert between forms as appropriate; and assess the |Solve systems of two linear equations in two variables algebraically, and |Explain each step in solving a simple equation as following from |

|reasonableness of answers using mental computation and estimation|estimate solutions by graphing the equations. Solve simple cases by |the equality of numbers asserted at the previous step, starting |

|strategies. For example: If a woman making $25 an hour gets a 10%|inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution |from the assumption that the original equation has a solution. |

|raise, she will make an additional 1/10 of her salary an hour, or|because 3x + 2y cannot simultaneously be 5 and 6. (8.EE.8b) |Construct a viable argument to justify a solution method. (A-REI.1)|

|$2.50, for a new salary of $27.50. If you want to place a towel |Solve real-world and mathematical problems leading to two linear equations|Solve equations and inequalities in one variable. |

|bar 9 3/4 inches long in the center of a door that is 27 1/2 |in two variables. For example, given coordinates for two pairs of points, |Solve linear equations and inequalities in one variable, including |

|inches wide, you will need to place the bar about 9 inches from |determine whether the line through the first pair of points intersects the|equations with coefficients represented by letters. (A-REI.3) |

|each edge; this estimate can be used as a check on the exact |line through the second pair. (8.EE.8c) |Solve systems of equations. |

|computation. (7.EE.3) | |Prove that, given a system of two equations in two variables, |

|Use variables to represent quantities in a real-world or |Mathematical Practices |replacing one equation by the sum of that equation and a multiple |

|mathematical problem, and construct simple equations and |3. Construct viable arguments and critique others’ reasoning. |of the other produces a system with the same solutions. (A-REI.5) |

|inequalities to solve problems by reasoning about the quantities.|4. Model with mathematics. |Solve systems of linear equations exactly and approximately (e.g., |

|(7.EE.4) | |with graphs), focusing on pairs of linear equations in two |

|Solve word problems leading to equations of the form px + q = r | |variables. (A-REI.6) |

|and p(x + q) = r, where p, q, and r are specific rational | |Solve a simple system consisting of a linear equation and a |

|numbers. Solve equations of these forms fluently. Compare an | |quadratic equation in two variables algebraically and graphically. |

|algebraic solution to an arithmetic solution, identifying the | |For example, find the points of intersection between the line y = |

|sequence of the operations used in each approach. For example, | |–3x and the circle x2 + y2 = 3. (A-REI.7) |

|the perimeter of a rectangle is 54 cm. Its length is 6 cm. What | | |

|is its width? (7.EE.4a) | | |

|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. (7.EE.4b) | | |

|Objective Statement |

|All students will be able to solve mathematical and real world problems leading to linear equations in one variable or two linear equations in two variables, and orally and in writing communicate a complete |

|response and critique the validity of others’ responses. |

Step 2: Performance Criteria

|Students consistently, independently, and accurately solve linear equations in one variable, with rational number coefficients, including those that require use of the distributive property and combining of |

|like terms. |

|Students independently solve systems of linear equations using algebraic methods, including the elimination and substitution methods and by inspection, when appropriate; students verify solutions graphically |

|and algebraically. |

|Students consistently, independently, and accurately solve real world problems by writing a system of linear equations and then solving the system graphically and/or algebraically. |

|Orally and in writing, students justify their solutions and communicate their reasoning using a logical and complete response with correct use of grade level vocabulary, symbols, and labels; students evaluate|

|and critique the validity of others’ responses. |

Learning Progression Rubric

|Limited Command |Moderate Command |Strong Command |Distinguished Command |

| | |(Performance Criteria) | |

|Students rely on support and scaffolding to solve |Students independently and with some accuracy solve |Students consistently, independently, and accurately |Students consistently, independently, |

|linear equations in one variable, with rational |linear equations in one variable, with rational |solve linear equations in one variable, with rational |accurately, and efficiently solve linear |

|number coefficients. |number coefficients, including those that require use|number coefficients, including those that require use |equations in one variable, with rational number |

| |of the distributive property and combining of like |of the distributive property and combining of like |coefficients, including those that require use |

| |terms. |terms. |of the distributive property and combining of |

| | | |like terms. |

|Students rely on support and scaffolding (e.g., |Students independently use graphical methods to solve|Students independently solve systems of linear |Students strategically choose the most efficient|

|pre-scaled graph) and/or with some accuracy |systems of linear equations written in standard and |equations using algebraic methods, including the |method to solve systems of linear equations. |

|independently use graphical methods to solve |slope intercept form; students rely on support and |elimination and substitution methods and by | |

|systems of linear equations written in slope |scaffolding (e.g., prompting to use elimination or |inspection, when appropriate; students verify | |

|intercept form. |substitution) to solve systems of linear equations |solutions graphically and algebraically. | |

| |using algebraic methods. | | |

|Students rely on support and scaffolding (e.g., |Students independently and with some accuracy write a|Students consistently, independently, and accurately |Students create real world problems that require|

|prompting of variables to represent quantities or |system of linear equations to solve real world |solve real world problems by writing a system of |writing and solving a system of linear |

|strategies focused on making sense of the problem) |problems; solve the system graphically, |linear equations and then solving the system |equations; students then solve the system of |

|to write a system of linear equations to solve real|algebraically, or by inspection. |graphically and algebraically. |linear equations to determine the solution to |

|world problems; solve the system graphically, | | |the problem. |

|algebraically, or by inspection. | | | |

| | | | |

|When given the grade-level vocabulary, symbols, and|Using academic and content language with scaffolds |Orally and in writing, students justify their |Orally and in writing, students construct and |

|labels, students orally and in writing construct a |and supports (e.g., sentence frames), students orally|solutions and communicate their reasoning using a |communicate a complete and efficient response |

|justification of their solutions. Responses may be |and in writing justify their solutions and |logical and complete response with correct use of |using a logical and complete chain of reasoning,|

|incomplete or illogical. |communicate their reasoning. Responses may be |grade level vocabulary, symbols, and labels; students |correctly using grade level vocabulary, symbols,|

| |incomplete, but include a logical progression. |evaluate and critique the validity of others’ |and labels; students evaluate and critique the |

| | |responses. |validity and efficiency of others’ responses. |

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download