Unit 5: Expressions & Equations
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In this unit students will begin with extending graphing skills that were taught at the end of 5th grade. Students will then dive into algebra. They will learn that a variable is used when a number is unknown. The order of operations will be reviewed so that students can evaluate expressions. Students will learn to solve for the value of a variable in an equation and an inequality using inverse operations. Students will learn how to graph the solution to an inequality on a number line. Finally, students will also be expected to be able to create expressions and equations that include a variable from a given situation.
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Learning Target |
NYS Standard |
Engage NY |
Textbook Resources |
1: I can plot coordinate pairs on a coordinate plane. |
5.G.1 6.NS.8 |
CMP3 Variables and Patterns Go Math 12.1 |
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2: I can determine a pattern in a table or graph. |
5.G.2 |
CMP3 Variable and Patterns Go Math 12.3 Go Math 12.4 |
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3: I can identify dependent and independent variables and describe how they are related. |
5.G.2 6.EE.9 |
CMP3 Variables and Patterns Go Math 12.2 |
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4: I can evaluate a numerical or algebraic expression. |
6.EE.1 6.EE.2b 6.EE.2c |
CMP3 Variables and Patterns Go Math Module 9 Go Math 10.2 |
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5: I can write a numerical or algebraic expression to represent a given situation. |
5.OA.3 6.EE.2a 6.EE.6 |
CMP3 Variables and Patterns Go Math 10.1 |
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6: I can generate equivalent expressions. |
6.EE.3 6.EE.4 6.NS.4 |
CMP3 Variables and Patterns Go Math 10.3 |
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7: I can solve a 1-step or 2-step algebraic equation. |
6.EE.5 |
CMP3 Variables and Patterns Go Math 11.2 Go Math 11.3 |
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8: I can create a 1-step or 2-step algebraic equation from a given word problem |
6.EE.5 6.EE.7 |
CMP3 Variables and Patterns Go Math 11.1 |
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9: I can solve and graph a 1-step or 2-step algebraic inequality. |
6.EE.8 |
CMP3 Variables and Patterns Go Math 11.4 |
Learning Target 1: I can plot coordinate pairs on the coordinate plane.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.1.A: I can identify parts of a graph. (axes, quadrants, intervals) |
(1) |
(1) |
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5.1.B: I can write and plot coordinate pairs. |
(1) Plotting the points backwards (y,x) X-axis value comes first and indicates placement horizontallY, Y-axis values comes second and indicates placement vertically |
(1)SPED coordinate_plane_exit_slip.docx |
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5.1.C: I can calculate the distance between points on the coordinate plane. |
(1) Not counting the zero as a space when moving from negative to positive |
(1) |
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5.1: I can plot coordinate pairs on the coordinate plane. |
(1) |
(1) |
Learning Target 2: I can determine a pattern from a table or graph.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.2.A: I can analyze a data table and identify the pattern through the unit rate. |
(1) Students don’t check the unit rate throughout the whole table Student’s think a table has a constant rate of change if the first couple of paired points have the same unit rate |
(1) |
(1) |
5.2.B: I can analyze a graph and identify the pattern through the unit rate. |
(1) Students don’t check the unit rate throughout the whole graph Students think a graph has a constant rate of change if the majority of the line is straight |
(1) |
Value |
5.2: I can identify a pattern from a table or graph. |
Value |
Learning Target 3: I can identify the dependent and independent variable and describe how they are related.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.3.A: I can identify the dependent and independent variables. |
(1) Students reverse variables. It is necessary for students to ask themselves the question: does variable a depend on variable b, or does variable b depend on a. The one that depends on the other is the dependent/other is independent |
(1) |
(1) |
5.3.B: I can describe how the dependent and independent variables are related. |
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(1) |
Value |
5.3: I can identify the dependent and independent variables and describe how they are related. |
Value |
(1) |
Unit 5 Mastery Quiz 1: see assessment tabs
Learning Target 4: I can evaluate a numerical or algebraic expression.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.4.A: I can identify and evaluate a numerical expression following the order of operations. |
(1) Students use the exponents as the number to multiply the base with An exponent is used to multiply the base that many times (2) Students do not go left to right when multiplication/division and addition/subtraction are together When addition/subtraction and multiplication/division are together in an expression, you evaluate from left to right |
(1) |
(1) |
5.4.B: I can identify the parts of an algebraic expression. (coefficient, variable, constant, term) |
(1) |
(1) |
Value |
5.4.C: I can use substitution to evaluate an algebraic expression given a value for the variable. |
(1) Students fail to put parentheses around the substitution |
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5.4: I can evaluate numerical or algebraic expressions. |
Learning Target 5: I can write a numerical or algebraic expression to represent a given situation.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.5.A: I can relate algebraic expressions to real world situations. |
Value |
(1) |
(1) |
5.5.B: I can create an algebraic expression from a real world situation. |
(1) |
(1) |
Value |
5.5: I can write a numerical or algebraic expression to represent a given situation. |
(1) |
Learning Target 6: I can generate equivalent expressions.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.6.A: I can explain the mathematical properties: commutative, associate, distributive, identity and inverse. |
(1) |
(1) |
(1) |
5.6.B: I can use the properties to prove that two expressions are equivalent. |
(1) |
(1) |
Value |
5.6.C: I can identify and combine like terms. |
(1) Students combine bases with different exponents; x with x squared Combine same variables with the same exponents together (2) Students evaluate operations with variables incorrectly; x + x+ x as x cubed |
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5.6: I can generate equivalent expressions. |
Value |
Unit 5 Mastery Quiz 2: see assessment tab
Learning Target 7: I can solve a 1-step or 2-step algebraic equation.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.7.A: I can identify algebraic equations and inverse operations. |
Value |
(1) |
(1) |
5.7.B: I can apply inverse operations to solve for a variable in a 1 or 2 step algebraic equation. |
(1) Students fail to get rid of the constant first in a 2 step algebraic equation Students may follow the order of operations instead of inverse operations |
(1) |
Value |
5.7: I can solve 1-step or 2-step algebraic equations. |
(1) |
Learning Target 8: I can create and solve a 1-step or 2-step algebraic equation from a real world situation.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.8.A: I can write an algebraic equation from a given real world situation. |
Value |
(1) |
(1) |
5.8.B: I can create an algebraic equation using the area formulas for a rectangle or triangle to calculate a missing dimension of a polygon. |
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(1) |
Value |
5.8: I can create and solve a 1-step or 2-step algebraic equation from a real world situation (given as a word problem, table or graph). |
(1) |
Learning Target 9: I can solve and graph a 1-step or 2-step algebraic inequality.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
5.9.A: I can graph a given inequality. |
(1) Students put an open circle on four and shade to the left for greater than or equal to 4 Students fail to recognize that it should be a shaded circle because the value is greater than OR equal to four, so it can be four OR greater than four. They also fail to understand that all the possible values are greater than 4, so it should be shaded to the right |
(1) |
(1) |
5.9.B: I can solve and graph an algebraic inequality. |
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(1) |
Value |
5.9.C: I can create and solve an algebraic inequality from a given word problem. |
(1) |
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5.9: I can solve and graph a 1-step or 2-step algebraic inequality. |
