BUZZ Teacherπs Notes Volume 1/Number 1 (November 2007)

Cover: Which shape matches Buzz the Cat?

Application: A shape puzzle Pupils are asked to select the shape that matches Buzz the cat, from a choice of four. The shapes have been rotated. The differences are mainly in the arms.
Pupils look at shape and rotations.
Resources required: none
Learning objective taken from the Mathematics Framework Understanding shape. Problem solving: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
This puzzle is easily engaging as it is a type that children may have come across before. It can be used to encourage using appropriate vocabulary. Works well as a collaborative activity. Ask: How would you describe the position of each shape? Help by asking: What has happened to the tail in number one? or, What is different about the arms in number two? The shape that matches Buzz is number three.		Position Under, above Top, bottom, side Left, right Beside, next to Clockwise, anti-clockwise Turns, half turn Up, down First, second, third, fourth
Assessment strategy By asking children to explain why number 3 matches Buzz and describing its position using appropriate words.

Pages 2 and 3: Who is the oldest?

Application: Who is the oldest? Pupils are asked to name the oldest member of the Buzz kids, by putting months in chronological order. There is a panel to fill in.
Consolidating knowledge of the months of the year and their order.
Resources required: pencil
Learning objective taken from the Mathematics Framework Understanding time Problem solving: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
The numbers relating to the months are included to help in memory mapping their order and notation. Ask: Who is the youngest? By how many months older is Becky than Lucy? Who is older, Kwok or Luke? In which months were none of the children born? This could lead to a discussion on the birthday months of the class, their years and ages. Which month has the most birthdays? Who is older of those in the same month? Make a chart. Ask: Which is the third month? Which is the tenth month? It may be appropriate to introduce the idea of numeric birth dates e.g. 20/08/01, 06/03/00 and so on.		Time Before After How many Seasons Birthday Oldest, youngest, younger, older than
Assessment strategy Achieving an understanding of the order of the months and their relationship to the year.

Pages 4 and 5: Sum socks

Application: Sum socks This activity looks at odd and even numbers, identifying pairs of numbers and solving a puzzle.
Counting and understanding number.
Resources required: pencil and paper. Red and blue crayons/felt-tip pens.
Learning objective taken from the Mathematics Framework Understanding number and using addition. Looking at odd and even numbers. Observe number relationships and patterns. Problem solving: making decisions deductions by elimination. Using appropriate methods to resolve the task.
Activities		Vocabulary/keywords
The first part of this activity is colouring in the socks, depending on whether they are odd or even. Ask: How would you describe an odd/even number? Encourage children to use their own words. The second part of this activity is looking for pairs of numbers to complete the table. It may be useful for children to draw a number line (1 to 16) on some scrap paper. They can use this to try out pairings and cross out numbers as they are eliminated. The three children in the main part of the picture show their socks and their numbers: these can be eliminated from the available numbers of 1 to 16. Their totals can be put in the table: 20, 16 and 15. Kwok tells us that his socks are blue and therefore are even numbers. (6 + 2). Lucy in the far right of the picture also has a total of 8, but made up of two odd numbers (red socks). This is also the case for for Jack and Sasha. By leaving Luke (who has an odd and even number) until last, there is only one possibility (9 + 16). Observations could be made on what happens when odd, even, or odd and even numbers are added together. What kind of number must a pair contain to be sure that their sum is odd? Provide some statements asking true or false. e.g. 14 + 5 = an odd number 7 + 7 = an even number 11 + 1 = an odd number What about the sum of four numbers? Five numbers?... The last puzzle is presented by a frog. It is about the spiderπs socks: we are told that each set of four numbers sum to 20, and we know that one side is odd numbers (red socks), the other even (blue socks). Using their learning experience, can they give a rule about sums of odd and even numbers for any number of additions?		Odd (has a remainder of one after dividing by two) Even (divides by two exactly) Whole numbers Remainder Division, dividing Pairs Partners. Sharing, Total Addition Add Sum
Assessment strategy Achieving an understanding of odd and even numbers and finding strategies to solve number problems.

Pages 6 and 7: Add a design / Take away a design

Application: Pupils are asked to colour in triangles within squares after doing addition and subtraction.
Practice in addition and subtraction. Reinforcing number facts. Transformation of shapes: rotation.
Resources required: pencil, colouring pencils/felt-tip pens
Learning objective taken from the Mathematics Framework Counting and understanding number, calculations. Understanding shape. Recognising symmetry.
Activities		Vocabulary/keywords
The first design requires recognising pairs that sum to 20 and 15. It is important to stress the rotation of the triangle in the two tiles, if no mistakes are made they will create stripes across the design. The discovery that triangles can be combined to make interesting designs is rewarding. Take away a design is more challenging, as there are four different rotations to colour. It should be stressed that care should be taken in deciding the correct one. You may want to suggest that a pupil starts by looking for pairs that have a difference of 10, and put in all the tiles for those squares first. The finished design is a good example of symmetry. Ask: How many ways could the design be halved and still have both sides the same? Making the tiles up on a sheet of paper may help younger children to place their tiles on the correct squares. Ask: How do you describe which tile is which? An extension to to this activity is exploring triangles. Use 16 tiles with half coloured in triangles, and a 4 x 4 grid. Place them in different arrangements. (See also the worksheet and notes that accompanied CIRCA 36).		How many Add, addition, more, plus Sum, make, total Subtract, take away, minus Leave Difference Same as Symmetrical Line of symmetry Fold Match Mirror line, reflection Pattern Half, halved Triangle Square Clockwise, rotation, Top, bottom, left, right
Assessment strategy Performing the calculations confidently and recognising the rotation of shapes.

Pages 8 and 9: Which way?

Application: Which Way? Pupils are asked to explore routes through a maze of rooms, counting people as they go.
Practice in addition, problem solving and spatial awareness.
Resources required: pencil
Learning objective taken from the Mathematics Framework Counting and understanding number. Problem solving, reasoning and numeracy. Using everyday words to describe position. Developing mathematical ideas to solve practical problems.
Activities		Vocabulary/keywords
There is great potential here for reasoning and problem solving. As a maze, it requires spatial awareness, as you are asked to imagine passing through doorways, trapdoors and staircases, in a three dimensions. The element of counting the people you encounter offers further extension: how would you annotate each route? How many possibilities are there? Encourage using the appropriate vocabulary to explain each route. Routes exist so that Buzz can meet from 6 (least) to 19 (most) people, with the exception of 18. Can the exception be found? See Solutions for all the routes.		How many Add, addition, more, plus Sum, make, total Up, down, through, under, above Top, bottom, left, right
Assessment strategy A practical activity that invites discussion and using appropriate vocabulary. Strategies can be found for looking for other routes.

Pages 10 and 11: Spout!

Application: Spout! A game for 2 people, which can be played without any equipment other than a penny coin or small counter. Mental addition will be used when looking for end games.
Practice in addition and calculation.
Resources required: a penny or counter
Learning objective taken from the Mathematics Framework Counting and understanding number. Problem solving, reasoning and numeracy.
Activities		Vocabulary/keywords
This is an easy game to set up, as it only requires a penny coin or a counter. Children should take turns at going first. After a few games children will begin to develop strategies to get to winning positions though they will probably not grasp the underlying mathematical structure of the game/puzzle. They will notice that by looking ahead a player can take control of the end result and this encourages mental calculation. Also, they may notice that the second player has the advantage. For the spout ending on 15, multiples of 3 are key: Player 2 can adjust moving one or two places so that she always lands on multiples of 3. Adding another number to the spout gives Player 1 the advantage: the target becomes multiples of 3 + 1, e.g. 1, 4, 7, which Player 1 can control in the same way as Player 2 in the 15 game. Player 2 only has the advantage when the target number on the spout is a multiple of 3. She can always win if she plays her best game. For all other spout totals, Player 1 can win if he plays his best game.		How many Add, addition, more, plus Sum, make, total Multiples 3 times table Up, down, through, under, above Top, bottom, left, right
Assessment strategy A practical activity that invites discussion and using vocabulary. Strategies can be found, working back from the target and recognising the advantage of who goes first or second.

Pages 12 and 13: Join the dots +3, -1, +3, ä

Application: Join the dots +3, –1, +3, ä The well-known pastime of joining dots to find a picture is offered here with a more challenging number pattern to follow. A table is offered below, which will help in annotating the numbers and recognising the pattern.
Practice in addition and calculation
Resources required: pencil
Learning objective taken from the Mathematics Framework A practical activity involving counting and understanding number.
Activities		Vocabulary/keywords
The table at the bottom helps in avoiding making mistakes when joining the dots (it is quite hard to remember when to add or subtract as you go along) and can be used for checking if the picture goes wrong. Each row is a multiple of 10, and can be filled quite quickly. Children can cross out the number used as they go. Suggest using a light pencil, so that the picture can be corrected easily.		Add, addition, more, plus Sum, make, total Multiples Subtract, take away, minus
Assessment strategy Encourages mental addition and subtraction.

Pages 14 and 15: Which pie?

Application: Which Pie? A strip story, which tells of Buzzπs trip to Woody, and explains why Buzz is late for Fizz. Followed by a problem to solve about time in a real life context. Answers The answers given in the magazine are very brief. For fuller solutions visit the Answers section from the BUZZ page.
Practice in calculation with measuring time.
Resources required: pencil
Learning objective taken from the Mathematics Framework Counting and understanding number. Calculations using time, measuring short periods of time Problem solving and reasoning, describing solutions.
Activities		Vocabulary/keywords
The clock face in frame two is reinforced by Buzz noting the time. A calculation can be made that Buzz should arrive at twenty minutes to one. It may be helpful to remind a younger child that half an hour is 30 minutes, and to talk about the clock face. The information in the last frame tells the pupil all that is needed to know to answer the time problem on page 15. The additional information of the miles, given on the signpost, offers extension activities. Ask: How far is it to Woody from Sum Town? How much further did Buzz drive when he missed the turn and drove to Sandy and back? How many miles did he drive altogether? For older pupils, suggest drawing a map of the routes. Ask: Where is Woody? How far is Woody to Sandy? For KS2: simple calculations, looking at time and distance, could lead to understanding that Buzz travelled at an average of 30 miles an hour.		Time Half an hour 30 minutes 60 minutes ten past twenty to 20 minutes how long will it take to? Analogue clock Late longer Add, addition, more, plus Sum, make, total difference
Assessment strategy An understanding of measuring time and taking information from a story.

Pages 16: The strange room

Application: The Strange room A picture puzzle that involves counting and reasoning.
Practice in counting and reasoning.
Resources required: pencil
Learning objective taken from the Mathematics Framework Counting and understanding number. Problem solving and reasoning, describing positions.
Activities		Vocabulary/keywords
Some of the strange things to find will be easily spotted: a slipper on a chairπs leg, the ceiling and floor swapped aroundä Answers in the magazine identify 10 but there are more than 20 things to find. Ones that might be missed are: paintbrush in the flowers, book number in different position on Volume 4, wind blowing in two directions outside, mirror reflection showing different vase and flowers, framed picture only has half a string to hang from, hat on the lamp, cup handle on the desk, and curtain pole two ways. Encourage children to describe what they find and why it is wrong, using language to describe the positions. Keeping count of the things they discover could involve making a tally.		Above Below Under In front Beside Left right Upside down Between Missing half Add, addition, more, plus Sum, make, total
Assessment strategy Keeping a count and using their own experiences to describe the peculiarities.

Worksheet: Snow sums

Application: Snow sums Pupils are challenged to complete a pyramid of numbers by using addition. They are then challenged to find the highest and lowest totals.
Number investigation.
Resources required: pencil
Learning objective taken from the Mathematics Framework Counting and understanding number. Using language to describe their discoveries and strategies.
Activities		Vocabulary/keywords
This activity leads to an investigation rich in mathematics that is easily accessible to most children. It offers scope for recognising strategies and organising results. Try to encourage a systematic approach so that children donπt repeat arrangements they have already tried. For a 5 based pile of snowballs the highest number is 61. The key to find this is choosing the best positions for 4 and 5. They should be in the middle where they be used twice (on the outside they will only be used once). Ask children to explain in their own words what they discover. It could be something like: put the highest number in the centre, then the next highest numbers besides it. Extra snowball piles are available on Worksheet 1a. Finding the lowest number (35) uses the same procedure, but needs to the strategy adapted to a new but similar situation – a real application of mathematics. Ask: what happens if the bottom row contains an even number of snowballs? Challenge: how many different top numbers can be made?		Position Under, above Top, bottom, side Left, right Beside, next to Up Add, sum, addition Row (1^st, 2^nd, 3^rd, 4^th) Arrangement
Assessment strategy Developing a strategy and a systematic approach to a mathematical investigation.

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