Measurement – Pre and Post Assessment Questions Bank
The measurement questions/activities in this file may assist classroom teachers in
determining student understanding and instructional “next steps” (entry and exit) related
to the measurement strand addressed in grades K-6, Ontario Curriculum Grades 1-8,
Mathematics.
Questions have been constructed to assess students’ understanding of concepts; as well,
mathematical process expectations. These process expectations are embedded in the
achievement chart. Each of the process expectations are addressed at the beginning of
each grade level in the Ontario Curriculum Grades 1-8, Mathematics.
Knowledge and
Understanding
Concept
Understanding
Knowledge of
content
Procedural Fluency
Facts, terms,
procedural skills,
use of tools
Thinking
Application
Communication
Problem Solving
develop, select, and apply
problem-solving
strategies as students
pose and solve problems
and conduct
investigations, to help
deepen their
mathematical
understanding;
Selecting Tools and
Computational Strategies
Select and use a variety
of concrete, visual, and
electronic learning tools
and appropriate
computational strategies
to investigate
mathematical ideas and
to solve problems;
Communicating
Communicate mathematical
thinking orally, visually, and in
writing, using everyday
language, as well as
mathematical vocabulary, and a
variety of representations, and
observing basic mathematical
conventions.
Reflecting demonstrate
that students are
reflecting on and
monitoring their thinking
to help clarify their
understandings as they
complete an investigation
or solve a problem;
Connecting
Make connections among
mathematical concepts
and procedures, and
relate mathematical
ideas to situations or
phenomena drawn from
other contexts;
Representing
Reasoning and Proving
develop and apply
reasoning skills to make
and investigate
conjectures and construct
and defend arguments;
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
Create a variety of
representations of mathematical
ideas ( example: using physical
models, pictures, numbers,
variables, diagrams, graphs,
onscreen dynamic presentations)
make connections among them,
and apply them to solve
problems;
p. 1 of 11
Classroom teachers may select questions related to the measurement concepts and Big
Ideas, to assist in diagnostic, formative and summative assessment. These questions are
not meant to replace assessment tasks related to the measurement unit activities in the
primary math resource, Math Makes Sense; rather, these questions may provide
additional information to classroom teachers in assessment of and for learning.
Each grade level bank consists of questions addressing specific expectations in
measurement with classification of mathematical processes involved. In many cases, a
question can belong to more than one process.
Classroom teachers may choose to use some or all of the questions for their grade level,
depending on the overall expectations that will be addressed in a particular unit. The
same questions can be used as pre and post assessment questions, with the understanding
that these questions will not be “taken up” or reviewed with students during the course of
instruction.
Instructions for copying questions from the grade level question bank (PDF files) to
Word Perfect are enclosed in this folder.
Special thanks and acknowledgement is extended to the staff of Coe Hill Public School,
for initiating this project as well as contributing questions and activities for the grade
level assessments.
Maureen Baraniecki
Curriculum Coordinator
HPEDSB
William Lundy
SETS-Mathematics
HPEDSB
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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Grade 6 - Measurement Pre and Post Assessment
Manipulatives may be used for any assessment questions.
Communication can be assessed in all questions. Some items are identified specifically
for Communication
Mathematical Processes are identified in italic.
Overall Expectations:
•
•
•
•
Estimate, measure, and record quantities, using the metric measurement system;
Determine the relationships among units and measurable attributes, including the
area of a parallelogram, the area of a triangle, and the volume of a triangular
prism.
Demonstrate an understanding of the relationship between estimated and precise
measurements, and determine and justify when each kind is appropriate
Estimate, measure, and record length, area, mass, capacity, and volume, using the
metric measurement system.
Specific Expectations
Demonstrate an understanding of the relationship between estimated and precise
measurements, and determine and justify when each kind is appropriate (time – traveling
a distance)
Estimate, measure, and record length, area, mass, capacity and volume, using the
metric measurement system
6m33 select and justify the appropriate metric unit to measure length or distance in a
given real-life situation
6m34 solve problems requiring conversion from larger to smaller metric units
6m35 construct a rectangle, a square, a triangle, and a parallelogram, using a variety of
tools, given the area and /or perimeter
6m36 determine, through investigation using a variety of tools and strategies, the
relationship between the area of a rectangle and the areas of parallelograms and triangles,
by decomposing and composing
6m37 develop the formulas for the area of a parallelogram and the area of a triangle
using the area relationships among rectangles, parallelograms, and triangles
6m38 solve problems involving the estimation and calculation of the areas of triangles
and the areas of parallelograms
6m39 determine, using concrete materials, the relationships between units used to
measure area and apply the relationship to solve problems that involve conversions from
square metres to square centimeters
6m40 determine, through investigation using a variety to tools and strategies, the
relationship between the height, the area of the base, and the volume of a triangular
prism, and generalize to develop the formula
6m41 determine, through investigation using a variety of tools and strategies, the
surface area of rectangular and triangular prisms;
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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6m42 solve problems involving the estimation and calculation of the surface area and
volume of triangular and rectangular prisms
Manipulatives may be used for any assessment questions.
Demonstrate an understanding of the relationship between estimated and precise
measurements, and determine and justify when each kind is appropriate (time – traveling
a distance) (Knowing facts and procedures)
1. Suzanne is flying from Toronto Pearson Airport, to
Tampa Florida, USA. The flight leaves at 17:15.
A) Passengers leaving for the United States must
check in at the airport at least 1h30m before
their flights leave. Suzanne’s watch shows the
time she arrived at the airport.
Is she on time?
B) The plane is scheduled to land at 20:30. Florida
is the same time zone as Toronto. How long is
the flight?
(A) Clock face reads 1504. If plane leaves at 1715, 1.5 h earlier would be deadline of
1545. Because the present time (1504) is earlier than the dealine of 1545, she’s o.k. for
time. (Note: the clock could be read as 0304, which would give her PLENTY of time!)
(B) Assuming the plane leaves and arrives as scheduled, arrival time minus departure
time would yield the following:
20:30 – 17:15 = 3h 15 min for the flight time
Determine, through investigation using a variety of tools and strategies, the surface area
of rectangular and triangular prisms; solve problems requiring conversion from larger to
smaller metric units (Making connections )
2. Sarah has 1 square metre of
wrapping paper. Will she have
enough paper to wrap the parcel for
mailing? Explain your answer.
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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Surface area of the box:
Front face: 8 x 2 = 16 cm2
Right face: 2 x 3 = 6 cm2
Top face: 3 x 8 = 24 cm2
Sub total: 46 cm2
Doubled to allow for one face congruent to each: 92 cm2
1 m2 of paper = (100 x 100) = 10 000 cm2, which is plenty large enough for the box
(assuming the paper’s dimensions are 1m x 1m, 0.5m x 2m, etc – so that the smaller
dimension of the paper is no smaller than the largest dimension of the box).
Select and justify the appropriate metric unit to measure length or distance in a given
real-life situation (Knowledge of Facts and Procedures)
3. What unit of metric measurement would you use to
measure the perimeter of your teacher’s desk?
cm most likely; dm or hm acceptable; m could be acceptable if students are used to
seeing very large teacher desk; dam/hm/km unacceptable; mm not acceptable for
practical reasons.
Solve problems involving the estimation and calculation of the surface area and volume
of triangular and rectangular prisms. (Making connections)
4. A rectangular prism has a volume of 90 cm3. The area of its base is 45 cm2. What is its
height? How do you know?
Because volume is the product of basal area (B = LW) and height (h) (i.e., V = Bh),
90 cm3 = 45 cm2 x h. By inspection , 90 = 45 x 2, so h = 2. This is confirmed to some
degree by the diagram which shows a box that is not very high compared to its length and
width.
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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Select and justify the appropriate metric unit to measure length or distance in a given
real-life situation. (Reasoning and proving)
5. For each measure, would you use a linear, square or cubic unit? Explain your choice
and suggest an appropriate unit.
a) the area of the school playground
b) the distance between Bancroft and Toronto
c) the amount of water in a swimming pool
Area of school playground would be measured in square units; likely m2 because it would
likely be measured in metres.
The distance from Bancroft to Toronto is measured in linear units because it is a length;
because of the great distance involved, likely we would use km.
The amount of water in a swimming pool is measured in cubic units because the three
dimensions of length, width, and depth are involved; m3 would be a likely choice as a
pool would likely be measured in metres.
Construct a rectangle, a square, a triangle, and a parallelogram, using a variety of tools,
given the area and /or perimeter (Making Connections)
6. Draw and label two parallelograms, each with an area of 12 units2. Explain how you
figured out the areas.
Simplest parallelogram is a rectangle: i.e., a rectangle measuring 1 x 12, 2 x 6, or 3 x 4
units. Students may include a maximum of one rectangle.
Parallelograms with angled sides need to come close to having the equivalent of 12
square units: student explanations need to show how they interpreted and/or paired up
partial squares (e.g. with a parallelogram having 45 angles, the partial squares each just
happen to be half square units). Students need to be given a little “slack” here, i.e., a
difference of half a square unit between teacher determination of area and student
determination of area should be considered acceptable under the circumstances of this
question.
Construct a rectangle, a square, a triangle, and a parallelogram, using a variety of tools,
given the area and /or perimeter (Making Connections)
7. Draw and label as many as possible rectangles using whole units, each with a
perimeter of 36 units. Will the areas of these rectangles be the same or different? Explain
your answer.
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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The nine possible rectangles have dimensions (in units) of:
1 x 17 (perimeter: 1 + 17 + 1 + 17 = 36)
2 x 16
3 x 15
4 x 14
5 x 13
6 x 12
7 x 11
8 x 10
9x9
Answer may not necessarily include sketches of all of the rectangles; for example, if
student has drawn the first 3 or 4 and given dimensions only for the rest, but if it is clear
that he/she has seen the pattern and recognizes that order and position are of no
importance, then give full credit.
Determine, through investigation using a variety of tools and strategies, the relationship
between the area of a rectangle and the areas of parallelograms and triangles, by
decomposing and composing.
8. Determine the area of the parallelogram using what you know about the area of
rectangles and triangles. (Geoboards should be accessible to students)
A pair of vertical lines can decompose the parallelogram into a triangle with base 4
(along the top) and height 8, a rectangle with base 2 and height 8, and a second triangle
congruent to the first. Students might count the three areas and add them up;
alternatively, students might count the area of one triangle, double it (recognizing the
congruency), and add the area of the rectangle for the total; alternatively, students might
show in some fashion that by sliding either triangle to the opposite side, a rectangle with
base 6 and height 8 is created.
In any event, the total area is 48 units2.
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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Solve problems requiring conversion from larger to smaller metric units
9. Write each mass using at least two different units for each measure in the first column:
t
kg
g
mg
t
0.6
0.000 75
0.0024
kg
g
600 000
mg
600 000 000
750 000
2 400 000
3 200 000 000
600 kg
750 g
2400 g
3.2 t
Answer:
600 kg
750 g
2400 g
3.2 t
0.75
2.4
3200
3 200 000
Note: Because units are stated at the tops of each of the columns, it is not necessary to
state units in all of the cells.
Extraneous zeroes have been omitted (i.e., 0.6 is written rather than 0.600).
Select and justify the appropriate metric unit to measure length or distance in a given
real-life situation. (Reasoning and proving)
10. There are two questions for each image: answer all questions
The amount of space inside this Mayan temple:
(Circle one unit)
(A) millilitres
(B) litres
(C) cubic centimetres
(D)centimetres
(E) cubic metres
In the question above, you are measuring for:
(Circle one unit)
(A) capacity
(B) distance
(C) mass
(D)perimeter
(E) volume
(Answers: space = (E) m3; measuring for (E) volume)
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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The amount of soup inside this can:
(Circle one unit)
(A) millilitres
(B) litres
(C) cubic centimetres
(D) centimetres
(E) cubic metres
In the question above, you are measuring for:
(Circle one unit)
(A) capacity
(B) distance
(C) mass
(D)perimeter
(E) volume
(Answers: soup = (A) mL; measuring for (A) capacity)
The amount of jam that was in this jar before it was re-used as a pencil holder:
(Circle one unit)
(A) millilitres
(B) litres
(C) cubic centimetres
(D)centimetres
(E) cubic metres
In the question above, you are measuring for:
(Circle one unit)
(A) capacity
(B) distance
(C) mass
(D) perimeter
(E) volume
(Answers; amount of jam = (A) cm3; measuring for (E) volume)
The amount of “Kool-Aid” in this pitcher:
(Circle one unit)
(A) millilitres
(B) litres
(C) cubic centimetres
(D) centimetres
(E) cubic metres
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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In the question above, you are measuring for:
(Circle one unit)
(A) capacity
(B) distance
(C) mass
(D) perimeter
(E) volume
(Answers: amount of “Kool-Aid” = (B) litres; measuring for (A) capacity)
The length from head to tail of this beaded snake:
(Circle one unit)
(A) millilitres
(B) litres
(C) cubic centimetres
(D) centimetres
(E) cubic metres
In the question above this image, you are measuring for:
(Circle one unit)
(A) capacity
(B) distance
(C) mass
(D) perimeter
(E) volume
(Answers: length = (D) cm; measuring for (B) distance)
The amount of sand this pail could hold:
(Circle one unit)
(A) millilitres
(B) litres
(C) cubic centimetres
(D)centimetres
(E) cubic metres
In the question above this image, you are measuring for:
(Circle one unit)
(A) capacity
(B) distance
(C) mass
(D) perimeter
(E) volume
(Answers: sand = cm3; measuring for (E) volume)
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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Gr 6 Unit Test: Measurement – Marking Guide
Question #
1
2
3
4
5 a, b, c
6
7 a, b
8
9, 10
Points to look for – see Answer and Marking Guide for additional detail
Student response for part (A) includes accurate reading of the clock face (1504), calculations
that she should have been at the airport not later than 1545; response for part (B) includes
accurate calculations to derive a flight time of 3h 15min (assuming no delays).
Shows knowledge that 1m2 of paper MAY measure 1m x 1m, but COULD be other
dimensions (e.g. 2m x ½ m); shows conceptual understanding of surface area of the parcel
(i.e. 6 faces, each with its own area, and surface area being their total, although may not use
the words “surface area” explicitly)
cm or dm most likely; mm would be too much work; m would be acceptable but not likely;
dam/hm/km unacceptable
height = 2 cm; answer should show understanding that V = Area of base x H, with 90 = 45 x
“unknown height” worked through informally
Answers: (a) square units for area; (b) linear units for distance; (c) cubic units for volume
Answers can vary but could include (max. 1) a rectangle; students need to include
explanations about how they interpret partial squares
There are 9 possible rectangles using whole units; students should indicate that 8 x 10 = 10 x
8 w.r.t. perimeter, and that orientation is immaterial to the perimeter; labeling needs to
include dimensions as a minimum; explanation/sketches may include understanding of a
pattern
Parallelogram should be decomposed into a number of rectangles and triangles, with
dimensions labeled; explanation needs to be organized in a fashion that makes it clear how
the final answer was determined from the decomposed parallelogram
see Answer and Marking Guide
Question
Category
Level One
Level Two
Level Three
Level Four
#
Knowledge and Understanding – The student demonstrates… …of content
1, 3, 9, 10 ƒ accuracy of points limited
some
considerable
thorough
ƒ completeness of
knowledge
knowledge/
knowledge/
knowledge/
calculations
/understanding understanding
understanding
understanding
/counting/conversi
ons
Thinking – The student uses planning/critical thinking skills with…
4, 7
ƒ solution/
limited
some
considerable
a high degree
explanation is
effectiveness
effectiveness
effectiveness
of
logical &
effectiveness
complete
ƒ solution/
explanation shows
alignment with
directions
Communicating – The student expresses/organizes/communicates/uses conventions and appropriate
terminology with…
4, 5, 7
ƒ explanation is
limited
some
considerable
a high degree
clear
effectiveness
effectiveness
effectiveness
of
ƒ mathematical
effectiveness
vocabulary used
Application – The student applies/transfers knowledge and makes connections with…
6, 8
ƒ shows use of
limited
some
considerable
a high degree
multi steps
effectiveness
effectiveness
effectiveness
of
ƒ information
effectiveness
logically applied
Grade 6 - Pre and Post Assessment Measurement – Teacher Edition
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