Boxmind e-lecture: Why do penguins huddle?
Help Sheet 8
Ma 1 Assessment sheet
Level 4
Level 3
Level 2
Level 1
NC
Statement:
My evidence:
I can use mathematics in an activity
I have made a ‘model’ penguin from 3 multilink
bricks.
I use objects and pictures to help me
I have drawn a penguin (or multilink penguin)
standing on its own. I have shown my teacher
the 14 cold bits.
I can discuss these
I can recognise a simple pattern
I have found a good way of counting the 14
squares.
I choose the mathematics to use
I can explain the problem in words.
I can use simple mathematical words
I know the difference between a cube and a
square. I have drawn some penguins standing
separately.
I draw diagrams in my work
I can answer “What will happen if….?”
I know what I have to count if there is more than
1 penguin standing separately.
I try different approaches
I have tried standing the penguins in lines.
I overcome some difficulties
I have explained at least one assumption I have
made of my model.
My work is organised quite well
I have put my results for penguins standing
separately in a table.
I check my results
I think about what my tables and charts show
I can see the numbers are getting larger the
more penguins you have.
I try out some examples to see if a general rule
is true
I have noticed the numbers go up in fourteens,
up to 10 penguins having 140 cold bits.
I find out what I need to solve the problem
I have completed the table for 100 and 1000
penguins.
I present my work in a clear and organised
way
I have explained the decisions I made and the
results I found.
I look for patterns
I have made statements like: “You need to
multiply the number of penguins by 14.”…
“because each side of each penguin is cold if
they are standing separately.”
I can give a reason for something I find out

From here, students must have worked on arrangements of penguins other than those standing separately.
NC
Statement:
Level 5
I obtain the information I need
I check my results making sure they are
reasonable
I explain using symbols, words and diagrams
 Wheathampstead Development Centre
http://www.thegrid.org.uk/learning/maths
My evidence:
I have considered different numbers of penguins
standing in a line. I have checked my answers.
I have put my results in a sensible table, with
column headings and have explained it.
JJWhiteman, SIAS, Hertfordshire
Page 1 of 2/12 February 2016

Level 6
NC
Statement:
I can make general statements from my work
…and give reasons for these
I have found that the number of cold bits goes
up in 8s… “because each penguin in the row
has 3 cold fronts, 3 cold backs, cold head and
cold feet…”
I break a task down to make it easier
I thought about 1 penguin, then 2 penguins…
I present information in a variety of forms
I have used tables, graphs, number machines,
mappings and equations. I have compared the
tables for penguins standing separately and
penguins in rows.
I explain my choice of diagrams
I can justify my general statements
Level 7
I test and check my reasoning
I discovered c = 8p + 6 and explained what the
letters represent. I related my rule to the penguin
situation. I tested my rules with known results.
I can extend my study, by thinking up my own
ideas
I included the average number of cold bits per
penguin. I have considered pairs of penguins…
trios of penguins…
I criticise and justify my choice of presentation
I decided which graphs to include and explained
why.
I explain improvement I make to my
presentation
I justify my solution in terms of the
mathematical structure
I understand the difference between proof and
experimental evidence
I added extra columns to one of my tables to
improve it.
I have explained all the rules I have found in
terms of the penguins. I understand the
importance of proving a rule which works for any
number of penguins rather than counting the
cold bits on a specific number of penguins.
I use a range of mathematical techniques to
help solve the problem
I have grouped the penguins in squares… or: I
have amended the model to tessellating
hexagons… (or other more complex work)
I
have used graphs, considered trends and limits,
quadratic expressions…
I use algebra consistently, clearly and
accurately
I have found and tested quadratic rules and
simplified algebraic expressions.
I consider the reasoning and logic behind my
general statements
I have related the rules to the penguins and
proved their truth.
I develop and follow alternative approaches
Level 8
My evidence:
I analyse the alternative approaches I have
used
Level EP
I give detailed reasons for following or rejecting
a particular line of enquiry
I can explore an area of mathematics with
which I am unfamiliar
I use mathematical language and symbols
accurately and efficiently in presenting a
convincing, concise, reasoned argument
I can provide a mathematically rigorous
justification or proof of my argument
I consider the conditions under which my
solution remains valid
 Wheathampstead Development Centre
http://www.thegrid.org.uk/learning/maths
JJWhiteman, SIAS, Hertfordshire
Page 2 of 2/12 February 2016
