Cover: Complete the pattern
Application: A fitthepieces puzzle This issue sends the puzzle cats
and the Buzz kids to Ancient Rome. A Roman
mosaic needs completing. Where do the three pieces belong? Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full solutions can be found in the online Answers. 


Pupils look at detail to find
difference in shape and rotation to complete a pattern. 

Resources required: none 

Learning objective taken from the Mathematics FrameworkRecognise
differences in pattern, recognising the need to rotate and transform. Recognise
reflective symmetry in 2D shapes. Problem
solving: making observations and using appropriate language to resolve the
task. 

Activities 
Vocabulary/keywords


Some
children find imagining the rotation of a pattern easier than others. This
puzzle requires sorting three missing tiles and recognising where they will
fit on the floor design. Two need to be mentally rotated to see how they
complete the symmetrical design of the mosaic. Encourage
describing the positions of each missing tile. Help could be given by sketching out the design on squared
paper and cutting out the tiles. Playing with the patterns will aid understanding of the
symmetry involved. A discussion could follow about symmetry and the lines of
symmetry (mirror lines). Extension: older children could draw their
own symmetrical mosaic designs on squared paper. They could also make copies
of their design to cut up and present to each other as puzzles. 
matches/
same/ difference stripes, lines line symmetry/ mirror line sort rotate, turn left, right top,
bottom over/above under/below 

Assessment strategy
Accurate
visualising and understanding symmetry. Vocabulary will be extended using
appropriate words. 

Page 2: Roman tiles
Application: The
introduction page uses Roman tile designs to look at ways a square can be
divided up equally and yet coloured to look different. It links to the
worksheet designed with this issue. Each Buzz
kid holds a tile. Pairs have to be found that are the same design, and there
is a table to be filled in. Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full solutions can also be found in the online Answers. 


Pupils recognise similarities of
design. 

Resources required: pencil 

Learning objective taken
from the Mathematics Framework Looking
at 2D shapes to make and describe pictures and patterns. Recognise
differences in pattern. Problem
solving: making observations and using appropriate language to resolve the
task. 

Activities

Vocabulary/keywords


Looking
at shapes and patterns with increasing accuracy encourages describing and
recognising new shapes when identical ones are put together. Encourage
describing the features of each design and the way the colouring can
emphasise division, halves and quarters. Extension: children could design their own
pairs of tile designs on squared paper, then colour them to explore the
differences that can be achieved. 
Square Rectangle Quarter Half Thirds Stripes Divided Divisions Cross L shape Equal Section 

Assessment strategy
Describing
the features of shapes and naming new shapes when identical ones are put
together. Vocabulary will be extended using appropriate words. 

Pages 4 and 5: Spot the dice
Application: The main theme of this issue is
odd and even. This
first puzzle involves completing the dots on the blank dice and finding a
secret word. Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full solutions can be found in the online Answers. 


Pupils solve a problem that
involves mental addition. 

Resources required: pencil 

Learning objective taken
from the Mathematics Framework Solving
mathematical problems or puzzles. Problem
solving, reasoning and numeracy: making decisions and using appropriate
language to resolve the task. 

Activities

Vocabulary/keywords


Dice are
a useful tool to explore looking at number, and this puzzle concentrates on
the odd and even numbers up to 6, and the possibilities of sums made with two
dice. Buzz and
Fizz give an explanation of what odd and even numbers are, but make sure the
children have understood the definition, and ask them to describe other ways
to describe odd (a number that has a remainder of 1 if halved, for example)
and even, in their own words. Children
in Year 2 and younger, may need more help with
sorting the clues. When
reading the clues, you may need to remind them that the numbers on the dice
cannot be more than 6, so it is not as difficult as they might first think. Ask them
to say the odd numbers under 6, and the even numbers up to 6. Talk about what
we mean by a ÔpairÕ (or Ôdouble`) when throwing dice. Ask who has thrown a
double and hasnÕt mentioned it (Sasha, letter s) and why we know she must
have thrown two ÔtwosÕ. Talk about the pairs of numbers that are possible
with two dice, and their sums.(This will also help
with Jack (h) and Kwok(o).) Encourage children to mentally add the numbers, then find them on the check box below. The secret word is
ÔchariotsÕ (for children who donÕt know the word, show them the dottodot
puzzle, pages 10 and 11). 
Add Half Even Odd Pair Double Sum Remainder
of 1 More than Less than Between l 

Assessment strategy
More able
will be able to calculate the sums mentally, and practise will improve this.
By asking children to explain, vocabulary will be extended using appropriate
words. 

Pages 6 and 7: Odd and even sorting
Application: Children
are asked to do additions and then complete a table, which illustrates the
properties of odd and even numbers. Buzz and
Fizz are hidden in the picture. Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full
solutions can be found in the online Answers. 


Recognising odd and even numbers
and practising addition. 

Resources required: pencil 

Learning objective taken
from the Mathematics Framework Doing
mental addition and recognising odd and even numbers. Knowing
and using number facts, counting and understanding number. Problem
solving, reasoning and numeracy: making decisions and using appropriate
language to resolve the task. Develop mathematical ideas and methods to solve
problems. 

Activities

Vocabulary/keywords


This
simple activity requires finding groups of objects on the table, completing a
table and doing simple addition. Where the
discovery will be made is in colouring numbers that are odd, and those that
are even. Most Year 2 children should be able to say that odd numbers have a
remainder of 1 when halved, but make sure the child has understood this fact
(see pages 4 and 5 for more help from Buzz and Fizz on definitions). Older
children should be able to complete the sentences without trouble, by looking
at their colouredin boxes. Testing showed that children in Year 3 thought
the task ÔeasyÕ until they realised they had to find conclusions! Encourage
children to investigate further, with sums of their own, to confirm their
discovery. Once they
have recognised the qualities of odd and even numbers, there are further questions
you can ask: what does an even number always end in? ( 0,
2, 4, 6 or 8). What does an odd number always end in? (1, 3, 5, 7 or 9).
Realising that adding two even numbers or adding two odd numbers, results in
an even number, is a high level of understanding. Trying out higher 2 digit
numbers will reinforce their discovery (ask, is 65 odd or even?) and is a
suitable activity for Year 3 and above. Extension: Another investigational activity
that uses odd and even numbers can be found in BUZZ issue 1 (Sum Socks pages
4 and 5). 
Add Forward Double Half Remainder Even Odd Sum Table Conclusion Investigate 

Assessment strategy
A high level of understanding is shown by making general
statements about odd and even numbers, and explaining how to recognise odd
and even numbers. 

Pages 8 and 9: Cross the town
Application: A maze
activity that requires sorting shape by the number of sides. Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full solutions can be found in the online Answers. 


Sorting shapes and solving a
puzzle. 

Resources required: pencil. 

Learning objective taken
from the Mathematics Framework Recognising
shape by the number of sides. Problem
solving: making decisions and using appropriate language to resolve the task. 

Activities 
Vocabulary/keywords 

Mazes are
always entertaining to do, but the ones in BUZZ usually also have a rule that
has to be followed, to make them more challenging. Shapes
can be sorted by deciding if they have an odd or even number of sides, and
this maze features four shapes that should be familiar to most children. You
could ask for the name of all right–angled 4sided shapes (rectangles)
and ask why the square has its own name. A
strategy to discover where the blocks are may be a helpful way to start, and can be ringed to avoid crossing one by mistake, when
doing the maze. Encouraging children to find strategies to solve a task is
helping them become real mathematicians. Encourage children to describe position and direction as they do
the maze. 
Add Forward Double Half Even Odd Back Subtract Next right angle 90¡ quarter turn square 3, 4, 5 or 6 sided rectangle triangle equal sides polygon (irregular and
regular) pentagon hexagon straight sides equal sides left, right up down 

Assessment strategy
Confidence
in recognising shapes, using strategy and appropriate vocabulary to describe
direction. 

Pages 10 and 11: Joining Dots
A
dottodot activity that uses odd and even rules. Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full solutions can be found in the online Answers. 


Practice in addition and
calculation, using number facts. 

Resources required: pencil 

Learning objective taken
from the Mathematics Framework Counting
and understanding number, knowing number facts. 

Activities 
Vocabulary/keywords 

Dot to
dot puzzles are enjoyed by a wide age range of children, and serve a useful
purpose as number recognition and sequence practice. This one requires more
care, as there are two sets to join up, one using the rule of odd numbers and
one with even numbers. The
numbers go to 100 and 99. Ask, What would be the next number on the odd
sequence? What other way could you describe the set of even numbers
(multiples of 2)? Extension:
For reinforcement of a successful activity there is
another dot to dot using odds and evens in BUZZ issue 3 (pages 12 and 13). 
Odd (has
a reminder of 1 when divided by 2) Even
(divides by two exactly) Sequence Set Remainder Whole
numbers Divide 

Assessment strategy
Confidence
in counting on in twos, recognising odd and even numbers up to 100. 

Pages 12 and 13: Odds and evens
Application: A
colouring activity that uses odd and even rules, and the orientation of
shape. Answers
are provided on page 15 of the magazine so that children can check for
themselves, and full solutions can be found in the online Answers. 


Practice in using number facts and
rotation of shape. 

Resources required: colouring pencils or crayons, 2 shades or close colours. 

Learning objective taken
from the Mathematics Framework Understanding
number, knowing number facts. Understanding
rotations of shape 

Activities

Vocabulary/keywords


Colouring
in using a set of rules is good practise for using a table, and this
colouring picture requires being careful with the orientation of different
triangles, and understanding odd and even numbers. Encourage
children to do complete the boxes in the table before they start. If they have
done the activities in the previous pages of this issue, filling in the odd
and even numbers will be easier. Younger children may need a little help with
this as mistakes can be made completing the colouring key, which will be
important in creating the picture. Care
needs to be taken in colouring the right triangles for each square, checking the orientation of the triangles to be coloured
in. As a strategy, it may be better to start with one group of numbers and
complete the triangles on those squares first. As
in other activities in this issue, encouraging children to find strategies to
solve a task is helping them become real mathematicians. The
twocoloured squares will add to the finished effect of the eagle (the emblem
used by the Roman Army). If orange and brown are not available, yellow and
red will work, or any two dark and light crayons of the same colour. 
Odd (has
a reminder of 1 when divided by 2) Even
(divides by two exactly) Sequence Set group less than more than shape triangle 

Assessment strategy
Confidence
in number and shape, using strategies to solve the task successfully.
Children younger than Year 3 will be working at a high level. 

Pages 14 and 15: Odd or even?
Application: Children
are invited to read a story, which involves counting the crayons from the
clues Buzz gives. Brief
answers are provided on page 15 of the magazine so that children can check
for themselves, and go back to puzzles to look at them again if they missed
something. Full
solutions can be found in the online Answers. 


Pupils do some simple calculations. 

Resources required: pencil 

Learning objective taken
from the Mathematics Framework Understanding
number, knowing number facts. Solve
problems involving time describing how the problem was solved. 

Activities

Vocabulary/keywords


This is a
simple counting story that requires reading BuzzÕs descriptions of how many
crayons he has, and remembering the numbers mentally. The colour red is the x
factor, and calculations have to be based on how many red crayons there are.
Writing down the amounts as you go could help a younger or less confident
child. If a
child tries to jot down the numbers as he or she goes, red could be shown as
x (the unknown number) so that blue = x + 1, green = x + (1 + 2) and yellow =
x + 3 +1. This brings the total
to 8 once you discover there are no red crayons. This strategy is a simple
form of algebra. 
Addition More than Numerals Sum, make, total Difference Odd Even 

Assessment strategy Younger children tackling the problem
with ease will be performing at a high level. 

Page 16: Curious Villa
Application: A picture
puzzle that involves observation and reasoning. There are at least 20
different oddities to find. (The
answers on page 15 of the magazine gives 10 things and the full list can be
found in online Answers) 


Can be used as an introduction to
keeping tallies. 

Resources required: pencil 

Learning objective taken
from the Mathematics Framework Counting,
keeping a tally, describing position. Problem
solving: making decisions and using appropriate language to resolve the task. 

Activities

Vocabulary/keywords


Some of
the curious things will be easy to spot, so all children should engage easily
with this puzzle. Some may not be so easy to recognise. Encourage children to
use language to describe why something is odd: tell them this is a villa in
ancient Rome. Many of the ÔoddÕ things are because they werenÕt invented 2000
years ago (like the TV, flipper, rubber hot water bottle, spotlight and
sunglasses). This could lead to an interesting discussion of the many things
the Romans did have (umbrellas, central heating, cosmetics, straight roads
(although the one in the picture is curious because it has a dotted line
along it) board games and socks (although not like the snakelike on in the
scene). An element of reasoning is required! Suggest
keeping a tally as each oddity is found, to keep a count of their
discoveries. Cooperation in sharing knowledge comes from comparing with each
other to see which ones may have missed. 
matches/
same/ different direction left,
right top,
bottom position over/above under/below beside next upside
down tally count number how many 

Assessment strategy
By asking
children to describe the location of the strange things they find their
vocabulary will be extended using appropriate words. Understanding how make a
record of the number they find. 

Worksheet: Half and half (available online)
Application: Buzz and
Fizz present an investigation dividing a square into two halves by pattern. Full
solutions can be found in the online Answers 


Pupils recognise a shape that is
equally divided can represent fractions. Can be used as an introduction to
investigating. 

Resources required: pencil/ two colouring crayons 

Learning objective taken
from the Mathematics Framework Recognising
and find simple fractions, and the equivalence between them. Problem
solving: suggest extensions by asking what if, investigate and find examples.
Making decisions and using appropriate language to resolve the task. Recognising
the divisions being odd or even. 

Activities

Vocabulary/keywords


This is
an investigation that begins on a simple level, but extends to an
understanding of fractions and recognition of odd and even numbers of
divisions or shapes. By giving
the children extra sheets (squared paper will help get them started) the
possibilities are limitless, but given the restrictions of continuing with
the designs provided on the worksheet, will still provide a wealth of discoveries.
Can they split the squares further? How many ways are there with each design?
How can they be sure they have divided the square into exactly half black and
white? (By counting the squares or equal shapes.) How can the last design
(showing thirds) be changed so that it can be half coloured? Suggest they
consider a diagonal line and see what shapes are created. What about a 3 x 3
grid? Can it be halved without adding more lines? Why not? What other grids
provide odd numbers of squares? Extension: see Activity 5 and 5b: Halving towels. This investigation invites
the child to explore the variations possible with just four stripes. The
conclusion the children should come to is that there are only four different
ways to colour the towel half and half. This is an opportunity to talk about
rotations and symmetry, and leads to rich further investigation. Please see
notes for BUZZ 5. 
Matches/
Same/ Difference Equal
parts Halves Quarters Eighths Odd Even Diagonal Horizontal Vertical Sixths thirds Rotation Reflection symmetry 

Assessment strategy
A
confidence in recognising half in patterns, as well as learning to work
together, being able to explore and make conclusions. 

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