Download Equations Inequalities

Development of
Equations
&
Inequalities
Mathematics | Grades 5-8
Write your name here:
Christine Robson
[email protected]
http://lead4ward.com/equations/
password: equationsrock2016
1
2
6.10 (A) model and solve one-variable, one-step equations and inequalities that represent problems,
including geometric concepts
Equation
Pictorial
Abstract
x–3=5
x – 3 = -6
-4 = x + 1
3
6.10 (A) model and solve one-variable, one-step equations and inequalities that represent problems,
including geometric concepts
Equation
Pictorial
Abstract
3x = 6
2x = -8
10 = 2x
4
6.10 (A) model and solve one-variable, one-step equations and inequalities that represent problems,
including geometric concepts
Equation
Pictorial
Abstract
-4x = 4
-6 = -2x
x
4
= -3
5
6.10 (A) model and solve one-variable, one-step equations and inequalities that represent problems,
including geometric concepts
Equation
Abstract
Number Line
x–3<5
x – 3 ≥ -6
-4 ≤ x + 1
6
6.10 (A) model and solve one-variable, one-step equations and inequalities that represent problems,
including geometric concepts
Equation
Abstract
Number Line
-2x ≥ -6
4x ≥ -8
24 ≤ -6x
7
7.11 (A) model and solve one-variable, two-step equations and inequalities
Equation
Pictorial
Abstract
2x – 5 = -1
3x – 4 = 5
8 = 4x – 4
-6 = 2x – 4
8
7.11 (A) model and solve one-variable, two-step equations and inequalities
Equation
Abstract
Number Line
2x – 5 < -1
3x – 4 ≥ 5
8 ≥ 4x – 4
-6 > 2x – 4
9
8.8(C) model and solve one-variable equations with variables on both sides of the equal sign that represent
mathematical and real-world problems using rational number coefficients and constants
Equation
Pictorial
Abstract
2x – 5 = -1 + 3x
3x - 4 = 5 – 6x
8 – ½ x = 4x – 4.75
-6 + ¾ x = 0.2x - 4
10
11
12
13
14
15
16
model and solve one‐variable, one‐step equations and inequalities that
represent problems, including geometric concepts (R)
write corresponding real‐world problems given one‐variable, one‐step
equations or inequalities (S)
6.10A
6.9C
represent one‐ and two‐step problems involving addition and
subtraction of whole numbers to 1,000 using pictorial models, number
lines, and equations (R)
represent and solve one‐ and two‐step multiplication and division
problems within 100 using arrays, strip diagrams, and equations (R)
determine the unknown whole number in a multiplication or division
equation relating three whole numbers when the unknown is either a
missing factor or product (S)
3.5A
3.5B
3.5D
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represent multi‐step problems involving the four operations with whole
numbers using strip diagrams and equations with a letter standing for
the unknown quantity (R)
4.5A
5.4B
write a corresponding real‐world problem given a one‐variable, two‐step
equation or inequality (S)
7.10C
5.4 Algebraic Reasoning. The student applies mathematical process
standards to develop concepts of expressions and equations. The
student is expected to:
(B) represent and solve multi-step problems involving the four
operations with whole numbers using equations with a letter
standing for the unknown quantity
model and solve one‐variable, two‐step equations and inequalities (R)
SE
5.4B Readiness
7.11A
TEKS
TEKS Scaffold
GRADE 5
•
•
•
•
•
•
15
Addition (sum)
Division (quotient)
Equation
Multiplication (product)
Subtraction (difference)
Variable (letter for un‐
known quantity)
Academic Vocabulary
• Students may not understand that the variable/letter has value.
a multiple step problem.
•
•
•
•
© 2014 lead4ward
Apply
Develop
Represent
Solve
Rigor Implications
• Students may not appropriately apply the use of parentheses and brackets when representing the equation of
be used since we are looking for “tickets” when any variable would be appropriate).
• Students may think that they have to use a letter that stands for the unknown quantity (i.e. the letter “t” has to
sion (i.e. 20/4; 20÷ 4).
• Students may not understand the variety of representations for multiplication [i.e. 3 x 4; 3 • 4; 3 (4); 3t] and divi‐
problem.
• Students may not recognize equivalent equations (i.e. 75 = 35 + 2t is the same as (75-35) ÷ 2 = t).
• Students may use “key words” to determine the operation instead of understanding the context of the
Distractor Factor
In adherence to the standard, instruction should include multi-step problems involving a mixture of operations.
The focus is not just on the students being able to solve the problems but also represent them using the
appropriate equation (i.e. Marciella buys 75 tickets at a carnival. She keeps 35 tickets for herself and gives the
remaining tickets to her 2 sisters who will share them equally. How many tickets does each sister get?;
(75 -35) ÷ 2 = t). Encourage students to write more than one equation (i.e. 75 = 35 + 2t; 75-35 = t).
2
The representing and solving multi-step problems lays a strong foundation for future algebraic reasoning.
Instructional Implications
standing for the unknown
• Solve multi-step problems involving the four operations with whole numbers using equations with a letter
letter standing for the unknown
• Represent multi-step problems involving the four operations with whole numbers using equations with a
Content Builder - (See Appendix for Tree Diagram)
17
represent solutions for one‐variable, one‐step equations and
inequalities on number lines (S)
determine if the given value(s) make(s) one‐variable, one‐step
equations or inequalities true (S)
6.9B
6.10B
write one‐variable, one‐step equations and inequalities to represent
constraints or conditions within problems (S)
represent and solve multi‐step problems involving the four operations
with whole numbers using equations with a letter standing for the
unknown quantity (R)
represent multi‐step problems involving the four operations with whole
numbers using strip diagrams and equations with a letter standing for
the unknown quantity (R)
6.9A
5.4B
4.5A
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write corresponding real‐world problems given one‐variable, one‐step
equations or inequalities (S)
6.9C
6.10A
model and solve one‐variable, two‐step equations and inequalities (R)
7.11A
6.10 Expressions, Equations, and Relationships. The student
applies mathematical process standards to use equations and
inequalities to solve problems. The student is expected to:
(A) model and solve one-variable, one-step equations and in‐
equalities that represent problems, including geometric concepts
model and solve one‐variable equations with variables on both sides
of the equal sign that represent mathematical and real‐world problems
using rational number coefficients and constants (R)
SE
6.10A Readiness
8.8C
TEKS
TEKS Scaffold
GRADE 6
Instructional Implications
model one-variable, one-step equations that represent problems (including geometric concepts)
model one-variable, one-step inequalities that represent problems (including geometric concepts)
solve one-variable, one-step equations that represent problems (including geometric concepts)
solve one-variable, one-step inequalities that represent problems (including geometric concepts)
=
=
x + 3 + -3
x+3
2
5 + -3
5
2
3
4
5
1
2
3
x+3≥5
4
5
21
• equations
• inequalities
• solution
• variable
Academic Vocabulary
• Apply
• Use
© 2014 lead4ward
• Model
• Solve
Rigor Implications
instead of relying on what the symbol is communicating (i.e. 2 > x; student will shade all values to the right of 2
on the number line since that is the direction the inequality symbol is pointing).
• Students will ignore the inclusion or exclusion of solutions to inequalities and not apply it to a given point.
• Students may focus on the direction of the inequality sign to determine its representation on the number line
value.
• Students may not change the direction of the inequality symbol when multiplying or dividing by a negative
on one side of the equation.
• Students may disregard the equality/inequality symbol when solving equations and only perform an operation
Distractor Factor
As this standard addresses both equations and inequalities, students must understand that equations yield one
solution; whereas inequalities yield more than one solution.
1
x+3>5
In adherence to the standard, geometric concepts should also be applied to the representation and solving of
one-step, one-variable problems (i.e. if the area of a rectangle is 56.5 cm2 and the length measures 5 cm, what
is the width of the rectangle? would be represented by the equation 5w = 56.5). Number lines can be used to
represent the solution of inequalities.
=
x+3
In accordance with the standard, students model and solve one-variable, one-step equations or inequalities. Onevariable, one-step equations should include exposure to all four operations. Instruction should vary the position
of the variable (i.e. x + 3 > 5; 3 + x > 5; 5 < x + 3). Students should associate the manipulation of concrete objects to
the symbolic solving of the equation/inequality (i.e. x + 3 = 5).
•
•
•
•
Content Builder - (See Appendix for Tree Diagram)
18
model and solve one‐variable equations with variables on both sides
of the equal sign that represent mathematical and real‐world problems
using rational number coefficients and constants (R)
8.8C
write a corresponding real‐world problem given a one‐variable, two‐step
equation or inequality (S)
write one‐variable, two‐step equations and inequalities to represent
constraints or conditions within problems (S)
model and solve one‐variable, one‐step equations and inequalities that
represent problems, including geometric concepts (R)
represent solutions for one‐variable, one‐step equations and
inequalities on number lines (S)
write corresponding real‐world problems given one‐variable, one‐step
equations or inequalities (S)
write one‐variable, one‐step equations and inequalities to represent
constraints or conditions within problems (S)
determine if the given value(s) make(s) one‐variable, one‐step
equations or inequalities true (S)
represent and solve multi‐step problems involving the four operations
with whole numbers using equations with a letter standing for the
unknown quantity (R)
7.10C
7.10A
6.10A
6.9B
6.9C
6.9A
6.10B
5.4B
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determine if the given value(s) make(s) one‐variable, two‐step equations
and inequalities true (S)
7.11B
7.11A
solve linear inequalities in one variable, including those for which the
application of the distributive property is necessary and for which
variables are included on both sides (S)
A.5B
7.11 Expressions, Equations, and Relationships. The student applies
mathematical process standards to solve one-variable equations
and inequalities. The student is expected to:
(A) model and solve one-variable, two-step equations and
inequalities
solve linear equations in one variable, including those for which the
application of the distributive property is necessary and for which
variables are included on both sides (R)
SE
7.11A Readiness
A.5A
TEKS
TEKS Scaffold
GRADE 7
Instructional Implications
model one-variable, two-step equations
model one-variable, two-step inequalities
solve one-variable, two-step equations
solve one-variable, two-step inequalities
1
2÷2
5 + -3
5
2
3
4
5
1
2
3
2x + 3 ≥ 7
4
5
21
• equations
• inequalities
• solution
Academic Vocabulary
© 2014 lead4ward
• Apply
• Solve
• Model
Rigor Implications
instead of relying on what the symbol is communicating (i.e. 2 > x; student will shade all values to the right of 2
on the number line since that is the direction the inequality symbol is pointing).
• Students may ignore the inclusion or exclusion of solutions to inequalities and not correctly apply the use of
filled or open circles.
• Students may focus on the direction of the inequality sign to determine its representation on the number line
value.
• Students may not change the direction of the inequality symbol when multiplying or dividing by a negative
on one side of the equation.
• Students may disregard the equality/inequality symbol when solving equations and only perform an operation
Distractor Factor
As this standard addresses both equations and inequalities, students must understand that equations yield one
solution; whereas inequalities yield more than one solution.
1
2x + 3 > 7
Number lines can be used to represent the solution of inequalities (i.e. 2x + 3 > 7 or 2x + 3 ≥ 7). Instruction should
associate the use of open circles to represent the exclusion of the value as a solution (i.e. 2x + 3 > 7) or a filled
circle to represent the inclusion of the value as a solution to the inequality (i.e. 2x + 3 ≥ 7).
=
=
2x ÷ 2
=
=
x+3
2x + 3 + -3
2x + 3
In accordance with the standard, students model and solve one-variable, two-step equations (i.e. 2x + 3 = 5) or
inequalities (i.e. 2x + 3 > 5). One-variable, two-step equations should include exposure to all four operations
(i.e. 2x + 3 = 5; 2x - 3 = 5; X/3 + 2 = 5; 1/3x + 2 = 5). Instruction should vary the position of the variable
(i.e. 2x + 3 > 5; 3 + 2x > 5; 5 < 2x + 3). To model one-variable, two-step equations, instruction should include the
use of concrete objects (i.e. algebra tiles). Students should associate the representation and manipulation of the
concrete objects to the symbolic solving of the equation/inequality (i.e. 2x + 3 = 5; see below).
•
•
•
•
Content Builder - (See Appendix for Tree Diagram)
19
write one‐variable equations or inequalities with variables on both
sides that represent problems using rational number coefficients and
constants (S)
8.8B
8.8A
write a corresponding real‐world problem given a one‐variable, two‐step
equation or inequality (S)
write one‐variable, two‐step equations and inequalities to represent
constraints or conditions within problems (S)
determine if the given value(s) make(s) one‐variable, two‐step equations
and inequalities true (S)
model and solve one‐variable, one‐step equations and inequalities that
represent problems, including geometric concepts (R)
represent solutions for one‐variable, one‐step equations and
inequalities on number lines (S)
write corresponding real‐world problems given one‐variable, one‐step
equations or inequalities (S)
write one‐variable, one‐step equations and inequalities to represent
constraints or conditions within problems (S)
7.10C
7.10A
7.11B
6.10A
6.9B
6.9C
6.9A
lead4ward.com
determine if the given value(s) make(s) one‐variable, one‐step
equations or inequalities true (S)
determine if the given value(s) make(s) one‐variable, two‐step equations
and inequalities true (S)
7.11B
6.10B
model and solve one‐variable, two‐step equations and inequalities (R)
7.11A
8.8C
write a corresponding real‐world problem when given a one‐variable
equation or inequality with variables on both sides of the equal sign
using rational number coefficients and constants (S)
A.5C
8.8 Expressions, Equations, and Relationships. The student applies
mathematical process standards to use one-variable equations or
inequalities in problem situations. The student is expected to:
(C) model and solve one-variable equations with variables on
both sides of the equal sign that represent mathematical and
real-world problems using rational number coefficients and
constants
solve systems of two linear equations with two variables for
mathematical and realworldproblems (R)
A.5A
SE
8.8C Readiness
solve linear equations in one variable, including those for which the
application of the distributive property is necessary and for which
variables are included on both sides (R)
TEKS
TEKS Scaffold
GRADE 8
3x + –2x
3x + 5 + -5
3x + 5
20
• coefficient
• constant
• equation
• rational number
• solution
• variable
Academic Vocabulary
• Apply
• Use
© 2014 lead4ward
• Model
• Solve
Rigor Implications
ity when solving an equation. The value of the expression does not change throughout the solving of equation
process.
• Students may treat unlike terms as if the terms are like terms (i.e. 2x + 3 may be misrepresented as 5x).
• Students may confuse the inverse operation for addition/subtraction and the inverse operation of multiplication/division yielding the incorrect usage of signs (i.e. -3x = 6; -3X/3 = 6/3; x = 2).
• The student may not understand that an action is replicated on both sides of the equal sign to maintain equal-
Distractor Factor
As students begin to associate the representation and manipulation of the concrete objects to the symbolic
solving of the equation, then the abstract solving of equations with rational number coefficients and constants
can be introduced.
0 –2 = x
=
=
2x + 3 + -5
2x + –2 + –2x
=
2x + 3
In accordance with the standard, students model and solve one-variable equations with variables on both sides
of the equal sign (i.e. 1/2x + 3.1 = 5 - 0.6x) using rational number coefficients and constants. To model one-variable
equations with variables on both sides of the equal sign using rational number coefficients and constants,
instruction should begin with the use of concrete objects (i.e. algebra tiles) using whole number coefficients and
constants (i.e. 2x + 3 = 3x + 5).
Instructional Implications
world problems using rational number coefficients and constants
• model and solve one-variable equations with variables on both side of the equal sign representing real-
mathematical problems using rational number coefficients and constants
• model and solve one-variable equations with variables on both side of the equal sign model representing
Content Builder - (See Appendix for Tree Diagram)
Materials
Sock pairs and safety pins
Algebra tiles
Balance scale handout
Red, green, and yellow crayons or map pencils
Teacher Note: Prompt students to use either the positive or negative tiles depending on the
equation you want to be represented. For example, tell students that the left hand side will use
positive x’s and negative units and the right hand side will use positive units or vice versa
depending on the equation.
•
•
•
•
•
Pull tiles from the “L” sock. Place these tiles on the left hand side of the scale.
Next, pull tiles from the “R” sock. Place these tiles on the right hand side of the
scale.
Use the recording sheet and the colors to draw the algebra tile pictorial created
by the selected tiles.
Use the tiles and pictorial to write the equation represented by the model.
Use the tiles and pictorial to solve the equation represented by the model.
Example:
Algebra Tile Pictorial
-x
=
-x
1
1
1
1
1
1
1
1
1
Equation
1
- 2x + 4 = 6
Solution
−2 x + 4 =
6
−2 x + 4 − 4 = 6 − 4
−2 x =
2
−2 x
2
=
−2
−2
x = −1
20
6.10 (A) model and solve one-variable, one-step equations and inequalities that represent problems, including
geometric concepts
Algebra Tile Pictorial
Equation
Solution
21
7.11 (A) model and solve one-variable, two-step equations and inequalities
Algebra Tile Pictorial
Equation
Solution
22
8.8(C) model and solve one-variable equations with variables on both sides of the equal sign that represent
mathematical and real-world problems using rational number coefficients and constants
Algebra Tile Pictorial
Equation
Solution
23
24
IQ Combo
25
26
31
7.7(A)
represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the form y = mx + b
Expressions, equations, and relationships. The student applies mathematical process standards to represent linear relationships using multiple representations.
two-step
verbal description
y = mx + b
table*
value*
variables
graph*
rate*
solution
per (unit rate)*
one-variable
inequality
equation*
per (unit rate)*
independent quantity
teacher language
x-values*
y-values*
dependent quantity
linear relationship
equation*
previously introduced words
words new to grade level
other words related to the content
7.11(A)
7.7(A)
standard
important words for concept development
7.11(A) model and solve one-variable, two-step equations and inequalities
7.11 Expressions, equations, and relationships. The student applies mathematical process standards to solve one‐variable equations and inequalities.
7.10 Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent
situations.
7.7
Equations and Inequalities
32
29
IQ Analysis | Investigating the Question
SE 5.4(B)
5.4(B)
Units:
5.4(B) represent and solve multi-step problems involving the four operations with
whole numbers using equations with a letter standing for the unknown quantity
Analysis of Assessed Standards
Content
2015 – Sample Q12
RC: 2
Multi Coding
Readiness
5.1(A), 5.1(B), 5.1(D),
Process
5.1(F)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B*
C
D
State
Local
NA
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (B)
5.4(B) (New) represent and solve multi-step problems involving the four operations
with whole numbers using equations with a letter standing for the unknown
quantity
Analysis of Assessed Standards
7.2(F) (Old) select and use appropriate operations to solve problems and justify the
selections
Content
2014 – Q7
Readiness
Dual Coding
Process 5.1(G)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A*
B
C
D
State
76
7
7
10
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (A)
30
5.4(B) (New) represent and solve multi-step problems involving the four operations
with whole numbers using equations with a letter standing for the unknown
quantity
Analysis of Assessed Standards
5.6(A) (Old) select from and use diagrams and equations such as y = 5 + 3 to represent
meaningful problem situations
Content
2014 – Q40
Readiness
Dual Coding
Process 5.1(E)
Stimulus
Thinking
Related SEs
Data Analysis
Item
F
G*
H
J
State
9
72
12
7
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (G)
5.4(B) (New) represent and solve multi-step problems involving the four operations
with whole numbers using equations with a letter standing for the unknown
quantity
Analysis of Assessed Standards
7.5(B) (Old) formulate problem situations when given a simple equation and formulate an
equation when given a problem situation
Content
2014 – Q47
Readiness
Dual Coding
Process
Stimulus
Thinking
Related SEs
Data Analysis
Item
A*
B
C
D
State
58
15
19
8
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (A)
31
IQ Analysis | Investigating the Question
SE 6.9(B)
6.9(B)
Units:
6.9(B) represent solutions for one-variable, one-step equations and inequalities on
number lines
2015 – Sample Q17
RC: 2
Analysis of Assessed Standards
Content
Supporting
Process
6.1(A), 6.1(B), 6.1(D),
6.1(F)
Multi Coding
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B
C*
D
State
Local
NA
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (C)
IQ Analysis | Investigating the Question
6.9(C) write corresponding real-world problems given one-variable, one-step equations
or inequalities
SE 6.9(C)
RC: 2
Units:
No test questions 2013 – 2015
32
33
IQ Analysis | Investigating the Question
SE 7.10(A)
7.10(A)
Units:
7.10(A) (New) write one-variable, two-step equations and inequalities to represent
constraints or conditions within problems
Analysis of Assessed Standards
7.5(B) (Old) formulate problem situations when given a simple equation and formulate an
equation when given a problem situation
2014 – Q21
RC: 2
Content
Supporting
Dual Coding
Process
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B
C*
D
State
11
15
70
4
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (C)
7.10(A) (New) write one-variable, two-step equations and inequalities to represent
constraints or conditions within problems
Analysis of Assessed Standards
7.5(B) (Old) formulate problem situations when given a simple equation and formulate an
equation when given a problem situation
2013 – Q2
Content
Supporting
Dual Coding
Process
Stimulus
Thinking
Related SEs
Data Analysis
Item
F
G*
H
J
State
14
76
8
2
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (G)
34
7.10(A) (New) write one-variable, two-step equations and inequalities to represent
constraints or conditions within problems
Analysis of Assessed Standards
7.5(B) (Old) formulate problem situations when given a simple equation and formulate an
equation when given a problem situation
2013 – Q15
Content
Supporting
Dual Coding
Process
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B
C
D*
State
22
10
12
56
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (D)
IQ Analysis | Investigating the Question
SE 7.10(B)
7.10(B)
Units:
7.10(B) represent solutions for one-variable, two-step equations and inequalities
on number lines
2015 – Sample Q10
RC: 2
Analysis of Assessed Standards
Content
Supporting
Multi Coding
Process 7.1(B), 7.1(D), 7.1(F)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A*
B
C
D
State
NA
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (A)
35
IQ Analysis | Investigating the Question
SE 7.10(C)
7.10(C)
Units:
7.10(C) (New) write a corresponding real-world problem given a one-variable, twostep equation or inequality
Analysis of Assessed Standards
A.5(C) (Old) use, translate, and make connections among algebraic, tabular, graphical, or
verbal descriptions of linear functions
2014 – Q1
RC: 2
Content
Supporting
Dual Coding
Process 7.1(D)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B
C*
D
State
13
3
74
10
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (C)
7.10(C) (New) write a corresponding real-world problem given a one-variable, twostep equation or inequality
Analysis of Assessed Standards
7.5(B) (Old) formulate problem situations when given a simple equation and formulate an
equation when given a problem situation
2014 – Q11
Content
Supporting
Dual Coding
Process 7.1(D)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B*
C
D
State
16
52
18
13
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (B)
36
IQ Analysis | Investigating the Question
SE 7.11(A)
7.11(A)
Units:
7.11(A) model and solve one-variable, two-step equations and inequalities
2015 – Sample Q11
RC: 2
Analysis of Assessed Standards
Content
Readiness
Multi Coding
Process 7.1(B), 7.1(E), 7.1(F)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A*
B
C
D
State
Local
NA
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (A)
7.11(A) (New) model and solve one-variable, two-step equations and inequalities
A.7(B) investigate methods for solving linear equations and inequalities using concrete
models, graphs, and the properties of equality, select a method, and solve the equations
and inequalities
2013 – Q16
Analysis of Assessed Standards
Content
Readiness
Dual Coding
Process
Stimulus
Thinking
Related SEs
Data Analysis
Item
F
G
H
J*
State
7
6
4
83
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (J)
37
IQ Analysis | Investigating the Question
SE 8.8(C)
8.8(C)
Units:
8.8(C) model and solve one-variable equations with variables on both sides of the
equal sign that represent mathematical and real-world problems using rational
number coefficients and constants
2015 – Sample Q10
RC: 2
Analysis of Assessed Standards
Content
Readiness
Multi Coding
Process 8.1(B), 8.1(F)
Stimulus
Thinking
Related SEs
Data Analysis
Item
A
B
C*
D
State
Local
NA
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (C)
8.8(C) (New) model and solve one-variable equations with variables on both sides
of the equal sign that represent mathematical and real-world problems using
rational number coefficients and constants
Analysis of Assessed Standards
7.5(A) (Old) use concrete and pictorial models to solve equations and use symbols to
record the actions
2014 – Q18
Content
Readiness
Dual Coding
Process 8.1(D)
Stimulus
Thinking
Related SEs
Data Analysis
Item
6
State
43
56
0
0
Local
Error Analysis
Guessing
Careless Error
Stopped too Early
Mixed Up Concepts
Implications for Instruction/Notes
* Correct answer (6)
38
Evidence of Learning
Tests
❏ Commontest(PLC)
❏ Districttest
❏ Teacher-madetest
Howdoesourtestvarythinking?
Quick checks
Analyze/Interpret:Givestudentsavisualrepresentation(differentstimulus)
thattheyhavenotyetused.Askthemtoanalyzeand
interprethowitrelatestotheproblem.
Cause/Effect:
Howwouldyourrepresentationchangeif...
Compare:
Giventwodifferentrepresentations,compare/contrast
howtheyaresimilar/different.
Justify/Evaluate:
Givenfourdifferentrepresentations,justifywhich
representationbestrepresentsthescenario.
MakeConnections:Giventwodifferentrepresentations,compareeach.
Estimate/Predict: Givenarepresentation,predictwhat the equation would be.
Evidence
Whatotherevidencewillwecollectandevaluate?
39
Which will we use in
instruction?
Which visuals (stimuli)
were used on STAAR?
G
ANNI NG
H
DE
• M
AT
engaging experiences
Student Learning Report/Field Guide
What content are we teaching?
IQ: Released Test
UI
D E • MAT
stimulus
UI
top
NNI NG
Which activities will we select to engage learners?
G
PL
words
Academic Vocabulary/Field Guide
Which words are important for concept development?
H
PLA
40
TEKS Scaffold
What other evidence
will we collect and evaluate?
Local Assessment
How does the test
vary thinking?
Which items best
inform instruction?
IQ: Released Test
Where do we begin instruction
(prerequisite content)?
evidence
top
engaging experiences
evidence
top
stimulus
t e s t A+
summarize
sequence/order
predict/estimate
top
make connections
justify/evaluate
infer
generalize
draw conclusions
create/develop
compare/classify/
categorize
cause/effect
apply
analyze/interpret
thinking
math
topic/big idea/unit
stimulus
(visuals)
word problem
(everyday situation)
verbal description
chart/table
graph
number sentence
equation
manipulatives
diagram/image
number line
base ten blocks
algebra tiles
measurement tool
formula
geometric figures
words
41
Inequalities Circuit Grade 7 - Directions
1. Individuals each have their own recording sheet
2. Each team member is assigned a card letter showing where to begin –
everyone starts at a different card.
3. Look at the inequality on the bottom of the card and determine its
solution. Use the recording sheet to solve the inequality for that card’s
letter.
4. Use the solution you found (the value of x), to go to the card where that
value is represented on a number line.
5. Look at the inequality at the bottom of the new (found) card and continue
the solution process until you have been to all the cards.
6. Ask for the key to find all values for x and to check all recording sheets.
42
Inequalities Circuit Grade 7 Recording Sheet
Equation
A
x+3≥-5
B
4x + 10 < - 14
C
-x+3>-3
D
2x + 3 ≤ 7
E
7 – 2x > 11
F
-4x ≥ 16
G
3x + 4 ≥ 16
H
3x > -24
I
2x + 7 < -1
J
-2x + 4 < -12
Solution
Number Line
(Card # Only)
43