BUZZ Teacher’s Notes Volume 5/Number 13 (Nov 2011)

Cover: Complete the pattern

Application: A fit-the-pieces 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 Framework Recognise differences in pattern, recognising the need to rotate and transform. Recognise reflective symmetry in 2-D 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 2-D 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 ‘pair’ (or ‘double`) when throwing dice. Ask who has thrown a double and hasn’t mentioned it (Sasha, letter s) and why we know she must have thrown two ‘twos’. 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 ‘chariots’ (for children who don’t know the word, show them the dot-to-dot 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 coloured-in boxes. Testing showed that children in Year 3 thought the task ‘easy’ 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 4-sided 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 dot-to-dot 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 two-coloured 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 Buzz’s 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 ‘odd’ things are because they weren’t 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 snake-like 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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