Examples of Math Tasks
Topic: Matrices and Transformations
Cambridge Objective: C/E7.2 Reflect simple plane figures in horizontal or vertical lines; Rotate simple plane figures about the origin, vertices or
midpoints of edges of the figures, through multiples of 90°; Construct given translations and enlargements of simple plane figures; Recognise and
describe reflections, rotations, translations and enlargements.
Learning Objective
Mathematicians will construct enlargements of shapes using various strategies and determine the relationship between the scale factor the size
of the shape.
Description of Task
How Task Was Implemented
Cognitive
Demand
(M, PNC,
Part 1: Students are given the coordinates of a
Teacher provides students with coordinate
PWC,
DM)
four-sided shape, which they are to draw on a
grid. Students begin plotting given
coordinate grid. They make a list of the original
coordinates. Teacher is assessing students’
coordinates and make a new set of coordinates
ability to plot coordinates. Students conduct
by multiplying each of the original coordinates
a buddy check on their plotted coordinates.
by 2. Students plot the resulting shape. What is
After constructing their shapes students
the result? Now, have students multiply each of
discuss with their partners what they are
the original coordinates by ½ and plot that
noticing about the relationships between
shape. Next, ask students to draw a line from the
the original shape and the enlargement.
origin to a vertex of the largest shape. Repeat for
one or two additional vertices, and ask for
How does the scale factor affect the size of
observations. What do you notice about the
the shape?
enlargement?
How do the lengths of the sides and the
Part 2: Prior to the lesson, invite students to bring a picture of a favourite TV, book,
movie, or comic strip character. They use coordinates points to create a modified
version of the picture and dilate it to form a larger or smaller character.
areas of the shapes compare when the
coordinates are multiplied by 2? What if
they are multiplied by 3 or by ½ ?
Resource: Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12, by Bay-Williams, McGatha, Kobett, and Wray
1
Examples of Math Tasks
Topic: Mensuration
Cambridge Objective: C4.4 Carry out calculations involving the volume of a cuboid, prism and cylinder and the surface area of a cuboid and a
cylinder. E4.4 Carry out calculations involving the surface area and volume of a sphere, pyramid and cone. Recognise patterns and structures in a
variety of situations, and form generalisations (A02)
Learning Objective
Mathematicians will investigate the relationship between the fixed volume of a cuboid and its surface area. Mathematicians will calculate
volume and surface area of cuboids, explaining their strategies and findings of the relationship between volume and surface area.
Description of Task
How Task Was Implemented
Cognitive
Demand
(M, PNC,
In groups of 2-3, students explore all the possible cuboid (rectangular prism)
Students are each given 12 cubes and ask to
PWC,
DM)
packaging arrangements that a company could use for their packaging given a fixed
build a cuboid using all 12 cubes.
volume (12 cubic units)
Is there more than one way to build it?
Students use the chart to organize your thinking.
Do you notice anything about the
Make a
sketch
dimensions of the cube?
Is there a difference between 1 x 1 x 12 or
12 x 1 x 1?
Students calculate surface area. Teacher is
encouraging various strategies for
determining the surface area.
Students consider different arrangements, calculating the surface area of each cuboid
formation.
Students are asked to make a conjecture about the cuboid arrangement of cubes that
requires the least packaging material.
What are you noticing about the
arrangement of cubes and how the surface
area is related?
Students are then asked to explain in their
own words, how the company should
package their product such that they use the
least amount of packaging.
Resource: Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12, by Bay-Williams, McGatha, Kobett, and Wray
2
Examples of Math Tasks
Topic: Algebra and Graphs
Cambridge Objective: C2.9 Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from
given data. E2.9 Interpret and use graphs in practical situations including travel graphs and conversion graphs; Draw graphs from given data;
Apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and deceleration; Calculate
distance travelled as area under a linear speed-time graph.
Learning Objective
Mathematicians will interpret distance-time graphs, describing possible real-life situations.
Description of Task
How Task Was Implemented
Cognitive
Demand
(M, PNC,
Students work in pairs. Each student is
Students are shown four
PWC,
DM)
given a copy of the graphs with space to
distance-time graphs. Ask
write an explanation. Students discuss with
students to identify which
their partner which graphs they believe are
two graphs are impossible
impossible and why. They each write their
and ask them to explain
own response.
why. Students are then
The pairs then find another pair to discuss
asked to describe a
explanations.
possible real-life solution
Which graphs are not possible? Why?
that is depicted by the
Explain your thinking. Describe a situation
graph.
Students are then asked to
create their own DistanceTime graph depicting a
situation of their choice.
that could be depicted by the graphs which
are possible.
Resource: Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12, by Bay-Williams, McGatha, Kobett, and Wray
3
Examples of Math Tasks
Topic: Algebra and Graphs
Cambridge Objective: C2.9 Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from
given data. E2.9 Interpret and use graphs in practical situations including travel graphs and conversion graphs; Draw graphs from given data;
Apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and deceleration; Calculate
distance travelled as area under a linear speed-time graph.
Learning Objective
Mathematicians will interpret graphs, describing possible real-life situations.
Description of Task
How Task Was Implemented
Cognitive
Demand
Filling Bottles
(M, PNC,
Teacher starts lesson by asking: ‘Did you ever
PWC,
DM)
Imagine filling each of the six bottles below, pouring water in at a constant rate.
notice that when filling some bottles, the water
For each bottle, choose the correct graph, relating the height of the water to the
all of a sudden spurts out of the top? Why does
volume of water
this happen?’
that's been
Students imagine filling each of the six bottles,
poured in.
pouring water in at a constant rate. For each
bottle, students choose the correct graph. For
For the
the remaining three graphs, students sketch
remaining three
what the bottles could look like.
graphs, sketch
After some time to work independently, the
what the bottles
teacher assigns one bottle to each pair of
should look like.
students. They discuss which graph they
assigned.
What graph did you choose and why?
Large graphs are posted around the room and
students then place their bottle by the
corresponding graph
Students watch a simulation to check responses.
Graphs that were created are shared by students
to whole group using doc cam.
Resource: Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12, by Bay-Williams, McGatha, Kobett, and Wray
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