Download AIMS Item Specifications

AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
PO
1.
Make models that represent improper fractions.
PO CLARIFICATION
Match improper fractions to representative models.
CONCEPT
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
2.
Identify symbols, words, or models that represent improper
fractions.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 1 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
PO
3.
Use improper fractions in contextual situations.
PO CLARIFICATION
At this grade level, this PO is defined as using word problems that
do not require an operation.
CONCEPT
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Micah had two whole pizzas cut into 6 equal pieces. He ate 4 pieces of pizza. What improper
fraction represents the amount of pizza left?
A
8
4
B
C
6
2
8
6
D
12
4
Arizona Department of Education
Page 2 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
4.
Compare two proper fractions or improper fractions with like
denominators.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 3 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
5.
Order three or more unit fractions, proper or improper
fractions with like denominators, or mixed numbers with like
denominators.
CONCEPT
PO
A unit fraction has a “1” as the numerator and any number as the
1 1 1
1
denominator (e.g., , ,
,
).
2 7 23 50
PO CLARIFICATION
There are several ways to address this PO other than the
suggested sample(s) presented here.
SAMPLE MC ITEM
Which of the following lists the mixed numbers in order from least to greatest?
A
7
1
7
4
3
7
2
4
7
1
6
7
B
5
2
7
6
1
7
6
5
7
7
3
7
C
2
3
7
2
1
7
3
4
7
4
2
7
D
6
2
7
3
3
7
3
5
7
5
4
7
Arizona Department of Education
Page 4 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
6.
Compare two whole numbers, fractions, and decimals (e.g.,
1/2 to 0.6).
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
PO
7.
Order whole numbers, fractions, and decimals.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Arizona Department of Education
Page 5 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
8.
Determine the equivalency between and among fractions,
decimals, and percents in contextual situations.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
The table below shows how much of a group report each student completed.
Joe
25%
Carrie
1/3
Ben
1/4
Ally
30%
Who completed equal amounts of the report?
A
Ally and Joe
B Joe and Ben
C
Carrie and Ben
D
Ally and Carrie
Arizona Department of Education
Page 6 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
9.
Identify all whole number factors and pairs of factors for a
number.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
CONCEPT
PO
10. Recognize that 1 is neither a prime nor a composite number.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 7 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
1:
Number Sense and Operations
1:
Number Sense: Understand and apply numbers, ways of
representing numbers, the relationships among numbers and
different number systems.
PO
11. Sort whole numbers (through 50) into sets containing only
prime numbers or only composite numbers.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 8 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
1.
Select the grade-level appropriate operation to solve word
problems.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
2.
Solve word problems using grade-level appropriate operations
and numbers.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 9 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
3.
Multiply whole numbers.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
4.
Divide with whole numbers.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
CONCEPT
Arizona Department of Education
Page 10 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
5.
Demonstrate the distributive property of multiplication over
addition.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Study the expression below.
5(10 + 2)
Which of these is equivalent to the expression?
A
(5 + 10) × (5 + 2)
B
(5 × 10) × (5 × 2)
C
(5 × 10) + (5 × 2)
D
(5 + 10) + (5 + 2)
Arizona Department of Education
Page 11 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
6.
Demonstrate the addition and multiplication properties of
equality.
At this grade level, this PO is defined as demonstrating the
addition and multiplication properties of equality as follows:
PO CLARIFICATION
If a = b, then a + c = b + c
If a = b, then ac = bc
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 12 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
7.
Apply grade-level appropriate properties to assist in
computation.
PO CLARIFICATION
At this grade level, this PO is defined as using associative and
commutative properties.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
8.
Apply the symbol “[ ]” to represent grouping.
PO CLARIFICATION
No clarification needed.
CONCEPT
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 13 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
9.
Use grade-level appropriate mathematical terminology.
PO CLARIFICATION
At this grade level, this PO is defined as using the terms quotient,
divisor, sum, addend, product, factor, difference, etc.
CONCEPT
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
In the equation below, identify which number is the divisor?
25 ÷ 6 = 4 R1
A
1
B
4
C
6
D
25
STRAND
CONCEPT
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
10. Simplify fractions to lowest terms.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 14 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
11. Add or subtract proper fractions and mixed numbers with like
denominators with regrouping.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
CONCEPT
PO
12. Add or subtract decimals.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 15 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
13. Multiply decimals.
PO CLARIFICATION
No clarification needed
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
CONCEPT
PO
14. Divide decimals.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
What is the value of the expression below?
242.2 ÷ 7
A
34.6
B
34 r6
C
340 r6
D
3.46
Arizona Department of Education
Page 16 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
1:
Number Sense and Operations
2:
Numerical Operations: Understand and apply numerical
operations and their relationship to one another
PO
15. Simplify numerical expressions using the order of operations
with grade-appropriate operations on number sets.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
1:
Number Sense and Operations
CONCEPT
3:
Estimation: Use estimation strategies reasonably and fluently.
PO
1.
Solve grade-level appropriate problems using estimation.
PO CLARIFICATION
At this grade level, this PO is defined as estimating to solve
problems, using the four basic operations with whole numbers and
decimals.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 17 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
CONCEPT
3:
Estimation: Use estimation strategies reasonably and fluently.
2.
Use estimation to verify the reasonableness of a calculation
(e.g., “Is 4.1 x 2.7 about 12?”).
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
1:
Number Sense and Operations
CONCEPT
3:
Estimation: Use estimation strategies reasonably and fluently.
PO
3.
Round to estimate quantities.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 18 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
CONCEPT
3:
Estimation: Use estimation strategies reasonably and fluently.
PO
4.
Estimate and measure for area and perimeter.
PO CLARIFICATION
At this grade level, this PO is defined as either estimating or
measuring either area or perimeter (i.e., estimate area, estimate
perimeter, measure area, and measure perimeter).
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 19 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
1:
Number Sense and Operations
CONCEPT
3:
Estimation: Use estimation strategies reasonably and fluently.
5.
Compare estimated measurements between U.S. customary
and metric systems (e.g., A yard is about a meter.).
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
PO
1.
Formulate questions to collect data in contextual situations.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Arizona Department of Education
Page 20 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
2.
Construct a double-bar graph, line plot, frequency table, or
three-set Venn diagram with appropriate labels and title from
organized data.
CONCEPT
PO
PO CLARIFICATION
At this grade level, this PO is defined as identifying correctly
constructed graphic organizers based on given data.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 21 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
3.
Interpret graphical representations and data displays including
bar graphs (including double-bar), circle graphs, frequency
tables, three-set Venn diagrams, and line graphs that display
continuous data.
CONCEPT
PO
PO CLARIFICATION
SAMPLE MC ITEM
Arizona Department of Education
At this grade level, this PO is defined as the ability to correctly
read a display, and answer questions based on that display.
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 22 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
4.
Answer questions based on graphical representations, and data
displays including bar graphs (including double-bar), circle
graphs, frequency tables, three-set Venn diagrams, and line
graphs that display continuous data.
CONCEPT
PO
PO CLARIFICATION
SAMPLE MC ITEM
Arizona Department of Education
At this grade level, this PO is defined as the ability to perform
mathematical operations based on data from a graphical
representation; and answer questions based on the outcome of
those operations.
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 23 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
PO
5.
Identify the mode(s) and mean (average) of given data.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Arizona Department of Education
Page 24 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
PO
6.
Formulate reasonable predictions from a given set of data.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Arizona Department of Education
Page 25 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
PO
7.
Compare two sets of data related to the same investigation.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
CONCEPT
No sample available
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
1:
Data Analysis (Statistics): Understand and apply data
collection, organization and representation to analyze and sort
data.
PO
8.
Solve contextual problems using graphs, charts, and tables.
PO CLARIFICATION
No clarification needed
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Arizona Department of Education
Page 26 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
PO
1.
Name the possible outcomes for a probability experiment.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Rick will spin the spinner shown below.
2
1
3
7
4
6
5
What is the possibility that the spinner will stop on an odd numbered space?
A.
certain
B.
impossible
C.
more likely to stop on an even number
D.
more likely to stop on an odd number
Arizona Department of Education
Page 27 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
2.
Describe the probability of events as being:
•
certain (represented by “1”),
•
impossible, (represented by “0”), or
•
neither certain nor impossible (represented by a fraction
less than 1).
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 28 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
3.
Predict the outcome of a grade-level appropriate probability
experiment.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 29 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
4.
Record the data from performing a grade-level appropriate
probability experiment.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
CONCEPT
PO
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
5.
Compare the outcome of an experiment to predictions made
prior to performing the experiment.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 30 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
6.
Make predictions from the results of student-generated
experiments using objects (e.g., coins, spinners, number
cubes).
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
2:
Probability: Understand and apply the basic concepts of
probability.
7.
Compare the results of two repetitions of the same grade-level
appropriate probability experiment.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 31 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
2:
Data Analysis, Probability, and Discrete Mathematics
3:
Discrete Mathematics – Systematic Listing and Counting:
Understand and demonstrate the systematic listing and
counting of possible outcomes.
1.
Find all possible combinations when one item is selected from
each of two sets of different items, using a systematic
approach. (e.g., shirts: tee shirt, tank top, sweatshirt; pants:
shorts, jeans).
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 32 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
PO CLARIFICATION
SAMPLE MC ITEM
Arizona Department of Education
2:
Data Analysis, Probability, and Discrete Mathematics
4:
Vertex-Edge Graphs: Understand and apply vertex-edge
graphs.
1.
Color maps with the least number of colors so that no
common edges share the same color (increased complexity
throughout grade levels).
At this grade level, this PO is defined as coloring maps or pictures
with 12 or fewer sections.
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 33 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
3:
Patterns, Algebra, and Functions
1:
Patterns: Identify patterns and apply pattern recognition to
reason mathematically.
1.
Communicate a grade-level appropriate iterative pattern, using
symbols or numbers.
At this grade level, this PO is defined as:
PO CLARIFICATION
Iterative pattern, meaning a pattern generated by using an initial
value and repeatedly applying the same operation/s
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 34 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
3:
Patterns, Algebra, and Functions
1:
Patterns: Identify patterns and apply pattern recognition to
reason mathematically.
PO
2.
Extend a grade-level appropriate iterative pattern.
PO CLARIFICATION
At this grade level, this PO is defined as determining the
subsequent terms of an iterative pattern, using positive whole
numbers with one operation.
CONCEPT
(An iterative pattern is a pattern which is generated by using an
initial value and repeatedly applying the same operation.)
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Celia used a rule to make the number pattern below:
92, 88, 44, 40, 20, ___
What will be the next number in the pattern?
A
16
B
12
C
10
D
8
Arizona Department of Education
Page 35 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
3:
Patterns, Algebra, and Functions
1:
Patterns: Identify patterns and apply pattern recognition to
reason mathematically.
PO
3.
Solve grade-level appropriate iterative pattern problems.
PO CLARIFICATION
At this grade level, this PO is defined as either identifying the rule,
or applying the rule to determine a specified term using up to two
operations in an iterative pattern.
CONCEPT
(An iterative pattern is a pattern which is generated by using an
initial value and repeatedly applying the same operations.)
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 36 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
3:
Patterns, Algebra, and Functions
2:
Functions and Relationships: Describe and model functions
and their relationships.
1.
Describe the rule used in a simple grade-level appropriate
function (e.g., T-chart, input/output model).
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 37 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
3:
Patterns, Algebra, and Functions
3:
Algebraic Representations: Represent and analyze
mathematical situations and structures using algebraic
representations.
1.
Evaluate expressions involving the four basic operations by
substituting given decimals for the variable.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
What is the value of the expression below when n = 5.1?
4xn
A
9.1
B
9.5
C
20.4
D
20.5
STRAND
3:
Patterns, Algebra, and Functions
3:
Algebraic Representations: Represent and analyze
mathematical situations and structures using algebraic
representations.
PO
2.
Use variables in contextual situations.
PO CLARIFICATION
At this grade level, this PO is defined as identifying a variable in
word problems.
CONCEPT
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 38 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
3:
Patterns, Algebra, and Functions
3:
Algebraic Representations: Represent and analyze
mathematical situations and structures using algebraic
representations.
3.
Solve one-step equations with one variable represented by a
letter or symbol (e.g., 15 = 45 ÷ n).
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 39 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
3:
Patterns, Algebra, and Functions
4:
Analysis of Change: Analyze change in a variable over time
and in various contexts.
1.
Describe patterns of change:
•
constant rate (speed of movement of the hands on a
clock), and
•
increasing or decreasing rate (rate of plant growth)
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 40 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4: Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
1.
Recognize regular polygons.
PO CLARIFICATION
At this grade level, this PO is defined as identifying regular
polygons having all sides congruent and all angles congruent.
CONCEPT
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Regular polygons have:
A
some congruent sides
B
some congruent angles
C
no congruent sides or no congruent angles
D
all congruent sides and all congruent angles
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
2.
Draw 2-dimensional figures by applying significant properties
of each (e.g., Draw a quadrilateral with two sets of parallel
sides and four right angles.).
CONCEPT
PO
PO CLARIFICATION
At this grade level, this PO is defined as identifying
2-dimensional figures by their attributes.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 41 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
3.
Sketch prisms, pyramids, cones, and cylinders.
PO CLARIFICATION
At this grade level, this PO is defined as identifying prisms,
pyramids, cones, and cylinders from pictures.
CONCEPT
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
4.
Identify the properties of 2- and 3-dimensional geometric
figures using appropriate terminology and vocabulary.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 42 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
5.
Draw points, lines, line segments, rays, and angles with
appropriate labels.
CONCEPT
PO
PO CLARIFICATION
At this grade level, this PO is defined as identifying points, lines,
line segments, rays, and angles from illustrations; and correctly
choosing appropriate labels.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
6.
Recognize that all pairs of vertical angles are congruent.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
CONCEPT
No sample available
Arizona Department of Education
Page 43 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
7.
Classify triangles as scalene, isosceles, or equilateral.
PO CLARIFICATION
At this grade level, this PO is defined as identifying types of
triangles.
CONCEPT
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 44 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
8.
Recognize that a circle is a 360º rotation about a point.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
CONCEPT
Study the circle below.
1
2
How many degrees are there in section 2 of the circle?
A
360°
B
270°
C
180°
D
90°
Arizona Department of Education
Page 45 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
9.
Identify the diameter, radius, and circumference of a circle.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
CONCEPT
No sample available
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
CONCEPT
PO
10. Understand that the sum of the angles of a triangle is 180°.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
CONCEPT
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
11. Draw two congruent geometric figures.
PO CLARIFICATION
At this grade level, this PO is defined as identifying two congruent
figures (i.e., same size, same shape).
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 46 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
CONCEPT
PO
12. Draw two similar geometric figures.
PO CLARIFICATION
At this grade level, this PO is defined as identifying two similar
figures (i.e., same shape, not same size).
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
CONCEPT
4:
Geometry and Measurement
1:
Geometric Properties: Analyze the attributes and properties of
2- and 3-dimensional shapes and develop mathematical
arguments about their relationships.
PO
13. Identify the lines of symmetry in a 2-dimensional shape.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 47 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
2:
Transformation of Shapes: Apply spatial reasoning to create
transformations and use symmetry to analyze mathematical
situations.
PO
1.
Demonstrate reflections using geometric figures.
PO CLARIFICATION
At this grade level, this PO is defined as identifying reflections
(flips).
CONCEPT
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 48 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
2:
Transformation of Shapes: Apply spatial reasoning to create
transformations and use symmetry to analyze mathematical
situations.
PO
2.
Describe the transformations that created a tessellation.
PO CLARIFICATION
At this grade level, this PO is defined as a tessellation having
geometric shapes that cover a plane with no gaps or overlapping.
CONCEPT
SAMPLE MC ITEM
Arizona Department of Education
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 49 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
3:
Coordinate Geometry: Specify and describe spatial
relationships using coordinate geometry and other
representational systems.
1.
Graph points in the first quadrant on a grid using ordered
pairs.
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 50 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
1.
PO
State an appropriate measure of accuracy for a contextual
situation (e.g., What unit of measurement would you use to
measure the top of your desk?).
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
2.
PO
PO CLARIFICATION
SAMPLE MC ITEM
Draw 2-dimensional figures to specifications using the
appropriate tools (e.g., Draw a circle with a 2-inch radius.).
At this grade level, this PO is defined as identifying which tool to
use (e.g., protractor, compass, ruler, etc.) or which graphic was
drawn with certain specifications.
There are several ways to address this PO other than the
suggested sample(s) presented here.
To measure the size of an angle you would use:
A
compass
B
protractor
C
ruler
D
thermometer
Arizona Department of Education
Page 51 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
3.
PO
Determine relationships including volume (e.g., pints and
quarts, milliliters and liters).
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
4.
PO
Convert measurement units to equivalent units within a given
system (U.S. customary and metric) (e.g., 12 inches = 1 foot;
10 decimeters = 1 meter).
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
The ceiling in Ms. Alexander’s classroom is 7 feet high. How high is the ceiling in inches?
7 feet = _?_ inches
A
14
B 21
C
49
D
84
Arizona Department of Education
Page 52 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
PO
5.
PO CLARIFICATION
At this grade level, this PO is defined as convex polygons having
all diagonals lie inside of the polygon.
SAMPLE MC ITEM
Arizona Department of Education
Solve problems involving the perimeter of convex polygons.
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 53 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
PO
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
6.
Determine the area of figures composed of two or more
rectangles on a grid.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
Arizona Department of Education
Page 54 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
PO
7.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
Solve problems involving the area of simple polygons.
No sample available
STRAND
4:
Geometry and Measurement
4:
Measurement - Units of Measure
- Geometric Objects
CONCEPT
PO
Understand and apply appropriate units of measure,
measurement techniques, and formulas to determine
measurements.
8.
Describe the change in perimeter or area when one attribute
(length, width) of a rectangle is altered.
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 55 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
CONCEPT
PO
PO CLARIFICATION
SAMPLE MC ITEM
Arizona Department of Education
5:
Structure and Logic
1:
Algorithms and Algorithmic Thinking: Use reasoning to solve
mathematical problems in contextual situations.
1.
Discriminate necessary information from unnecessary
information in a given grade-level appropriate word problem.
At this grade level, this PO is defined as using the four basic
operations with whole numbers or decimals to determine the
suitability of information in a word problem.
There are several ways to address this PO other than the
suggested sample(s) presented here.
Page 56 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
5:
Structure and Logic
1:
Algorithms and Algorithmic Thinking: Use reasoning to solve
mathematical problems in contextual situations.
PO
2.
Design simple algorithms using whole numbers.
PO CLARIFICATION
At this grade level, this PO is defined as identifying algorithms.
SAMPLE MC ITEM
No sample item is available for this PO.
CONCEPT
No sample available
STRAND
CONCEPT
PO
5:
Structure and Logic
1:
Algorithms and Algorithmic Thinking: Use reasoning to solve
mathematical problems in contextual situations.
3.
Develop an algorithm or formula to calculate areas of simple
polygons.
PO CLARIFICATION
At this grade level, this PO is defined as identifying algorithms or
formulas from word problems.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 57 of 58
March 6, 2007
AIMS Item Specifications
5th Grade Mathematics
STRAND
5:
Structure and Logic
2:
Logic, Reasoning, Arguments, and Mathematical Proof:
Evaluate situations, select problem-solving strategies, draw
logical conclusions, develop and describe solutions and
recognize their applications.
PO
1.
Construct if…then statements.
PO CLARIFICATION
At this grade level, this PO is defined as identifying or completing
the correct if…then statement when given the condition (if).
CONCEPT
SAMPLE MC ITEM
There are several ways to address this PO other than the
suggested sample(s) presented here.
All the students in Mr. Tate’s class brought chips to school on Monday. Luis brought only an
apple to school on Monday. Based on this information, which of the following is true?
A
If Luis brought only an apple, then he was not in school on Monday.
B
If Luis brought only an apple, then he is in Mr. May’s class.
C
If Luis brought only an apple, then he is in Mr. Tate’s class
D
If Luis brought only an apple, then he is not in Mr. Tate’s class.
STRAND
5:
Structure and Logic
2:
Logic, Reasoning, Arguments, and Mathematical Proof:
Evaluate situations, select problem-solving strategies, draw
logical conclusions, develop and describe solutions and
recognize their applications.
2.
Identify simple valid arguments using if … then statements
based on graphic organizers (e.g., 3-set Venn diagrams and
pictures).
CONCEPT
PO
PO CLARIFICATION
No clarification needed.
SAMPLE MC ITEM
No sample item is available for this PO.
No sample available
Arizona Department of Education
Page 58 of 58
March 6, 2007