BUZZ Teachers Notes Volume 2/Number 5 (March 2009)

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Cover: Which item is missing?

Application: A reasoning problem where pupils are asked to identify shape and position and then recognise which item is missing from the shelves below. 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 shapes and describe position Can be used as an introduction to resolving confusions over left and right
Resources required: none
Learning objective taken from the Mathematics Framework: Recognising shapes, describing position. Problem solving: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
A good starting point would be to discuss a strategy for checking which items have their double on the shelves below. Will it be better to randomly search, or look for each item at a time? Should they start from the left? This is good mathematical discussion. Encourage using vocabulary such as left or right, above, below, next to, to describe the matches. This will provide opportunity to use vocabulary that gives location. To extend the activity, other observation games could be played which encourage concentration and memory skills. A tray of five shapes could be shown, then one shape removed. Ask, Which shape is missing?		Matches/ Same/ Difference Small, large Left, right Top, bottom Over/above Under/below Next to Beside
Assessment strategy By asking children to explain position and shape their vocabulary will be extended using appropriate words. Back to Top

Pages 2 and 3: Introductory puzzle: Half a sandwich, and contents

Application: The theme of Issue 5 is fractions. The Buzz cats and kids present a reasoning problem where pupils are asked to identify each sandwich shape and match its two halves. Five sandwiches are shown at the bottom and there is a table to complete. 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 shape halves and the names given to shapes
Resources required: pencil
Learning objective taken from the Mathematics Framework: Understand that two halves make a whole. Recognising shape, describing and classifying 2-D shapes according to their properties. Recognise the symmetry in simple cases. Describe positions. Problem solving: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
A discussion on the five shapes of sandwiches could help with the classification of shape, and their properties (ask, how many sides has the pentagon? The hexagon?) Ask, what is the shape Buzz is holding? The pupil might see that it is a right angled triangle, and makes a square with Ahmad’s half. Ask, what other way could Buzz cut his sandwich in half and what other shape could he make (two rectangles)? Ask, what is the difference with the triangles of Sasha and Kwok to the ones that make a square? Could they be cut in half any other way and still be symmetrical? This discussion leads to recognising lines of symmetry, and thinking about reflection. How many lines of symmetry has the circle sandwich? (infinite) Encourage discussion orally before completing the table. Sorting the matches will provide opportunity to use vocabulary that classifies shape and gives location.		Matches/ Same/ Difference Square Circle Triangle right angled triangle Pentagon Hexagon Rectangle Symmetry Mirror line Reflection Line of symmetry Left, right Top, bottom Over/above Under/below
Assessment strategy Understanding two halves make a whole. Describing position and shape their vocabulary will be extended using appropriate words. Recognising symmetry in simple cases. Back to Top

Pages 4 and 5: What is missing from the mix?

Application: The reader is asked to answer fraction questions in a variety of contexts. Each correct answer will give them a letter that spells out a word in the panel on the right. Buzz and Fizz are also 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.
Pupils look at fractions in a variety of contexts, from time to quantities.
Resources required: pencil
Learning objective taken from the Mathematics Framework: Recognise and find simple fractions in practical contexts. Using appropriate number operations and ways of calculating to solve problems. Problem solving in real life contexts and explain how: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
The fractions used in this activity are halves and quarters, used in a variety of ways to illustrate their application. Many recipes require halving or doubling to make the right amount, and a discussion could be had on the flapjack recipe and how it would change (see below). Encourage discussion orally before completing the panel. The first and fourth questions look at weight in grams. The second, looks at the number of squares in a bar of chocolate. If a pupil finds it hard to find the quarter, ask, how many squares would be half? How many quarters are in a half? The third question requires some reasoning, to see that a quarter of the whole amount of raisins (10) are on the table. Ask, How many quarters are in a whole? How many raisins are there altogether? The fifth question refers to the measure of time: ask, how many minutes in an hour? The ingredient (honey) Sasha is looking for is spelt out. To extend the activity, ask the children to find a recipe and halve it for fewer people. Or, ask, how much of each flapjack ingredient do we need for twice as many? (introducing the idea that doubling is the inverse of halving.) A simple flapjack recipe for about eight people is given here: 100g butter/margarine 250g oats 80g brown sugar 2 tablespoons honey 2 tablespoons raisins melt butter and margarine over low heat add sugar, raisins and honey (option: add a mashed banana instead of raisins) mix in oats gradually spread mixture into a non-stick baking tray bake for 20-30 minutes at gas 5 or 200 C (depending how brown required but do not over cook)		Half Quarter Three quarters Division Multiply Double Halve One hour 60 minutes Half an hour 30 minutes weight grams
Assessment strategy Being able to solve word problems and explain how to apply fraction calculations in practical contexts. Back to Top

Pages 6 and 7: Dots with fractions

Application: Two dot-to-dot pictures that use halves and then quarters. 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 adding in halves and quarters in a number line
Resources required: pencil
Learning objective taken from the Mathematics Framework: Counting and understanding number, knowing number facts and simple fractions.
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 care in remembering that each half number is in the sequence (easily forgotten when joining hard-to-find dots). With the second picture, where the pupil will discover there are six eggs, the sequence is in quarters, and it offers the opportunity to explain that 2/4 is the same as ½. This opens the discussion for more able pupils to recognise simple equivalent fractions that might be encountered.	Sequence In order Half Quarter Three quarters
Assessment strategy Confidence in adding and an understanding of number. Back to Top

Pages 8 and 9: Fields of halves

Application: A maze that requires recognising the half of a whole number. Each field has two sorts of animals or things to count. Only one route will take Buzz correctly through the fields to Fizz. 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 counting and halving.
Resources required: none
Learning objective taken from the Mathematics Framework: Recognising the halving of number. Problem solving, reasoning and numeracy: making decisions and using appropriate language to resolve the task.
Activities	Vocabulary/keywords
This maze is designed to appeal to the youngest of our readers, yet covers a useful exercise in knowing number facts and halves of numbers. Discussion could be had on odd and even numbers (a definition of an even number can be one that halves exactly). Counting items quickly requires a certain amount of strategy: does counting in twos make it easier? Estimating a number is an important skill, as is checking if the guess was correct. As with many BUZZ mazes, there are not obvious blocks or paths; the reader is required to follow rules in order to successfully complete the task.	Half Route Way Direction Distance Addition Half Odd Even Estimating About the same Too many, not enough, too few, nearly, over , under left, right up, down along
Assessment strategy Confidence in counting and knowing the half of a number. Older children will be able to estimate and recognise the numbers of things visually. By asking children to explain directions their vocabulary will be extended using appropriate words. Back to Top

Pages 10 and 11: Match the fractions

Application: A reasoning problem that extends the knowledge of fractions by looking at the activities of the eight Buzz Kids. The reader is asked to match written statements about the picture to fractions illustrated by parts of a circle or square. There are also hidden apples and pears to find. 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.
A word problem presents a real life context that involves representing fractions.
Resources required: pencil
Learning objective taken from the Mathematics Framework: Finding fractions of numbers or quantities. Comparing fractions in practical contexts. Problem solving: making decisions and using appropriate language to resolve the task. Develop mathematical ideas and methods to solve problems.
Activities		Vocabulary/keywords
This activity uses the eight Buzz Kids to illustrate fractions up to eighths. Although children below Year 4 may not encounter eighths, the progression here is not confusing, and in tests most children were able to deal comfortably with eighths in this context. The example of dancing Buzz Kids immediately addresses the fact that two out of eight is the same as ¼. Recognising the equivalence could lead to discussion of other fractions, such as halves and three quarters. The representation of fractions using shape, by dividing a circle or rectangle, will be familiar to most children and helps illustrate the fractions, stressing the concept of the whole. In this case, it should be pointed out, the whole is the group of eight Buzz Kids. Encourage children to verbalise their matching, using the names of fractions or the number out of eight. Extension (Year 3 upwards): Other fractions could be introduced. Ask, What fraction of girls are having a lolly? (2 out of 4: half) Of the children not up the tree, what fraction are eating bananas?(3 out of 6: half) and What fraction have a pony tail? (2 out of 6: a third).		Fraction Half Quarter Three quarters Eighth Part Whole Division Equivalence Equal parts Sixths Thirds
Assessment strategy Recognising fractions and the equivalence between them. By asking children to describe their answers their vocabulary will be extended using appropriate words. Back to Top

Pages 12 and 13: Colour by fraction

Application: A colouring picture that requires recognising parts of a circle to represent fractions. The image of a bull charging through a fence will reveal itself, using the simple palette to show light and dark.
Pupils use their knowledge of fractions using the shape of a circle
Resources required: colouring felt tips or crayons (blue, green, orange, brown and yellow)
Learning objective taken from the Mathematics Framework: Recognising fractions and their names.
Activities	Vocabulary/keywords
If the reader has tackled the activity on pages 10 and 11, the introduction of eighths should not be a problem to those who have not yet encountered them in class. If needed, help could be provided by drawing in the shapes in the key, alongside the number fractions. Using rules is an important discipline and preparation for following instructions. The drama of the resulting picture should be rewarding to the neat artist. The yellow could be replaced by a lighter shade of brown if available.	Matches/ Same/ Difference Fraction Half Quarter Three quarters Eighth Part Whole Shape circle
Assessment strategy Confidence in knowing fractions and recognising sections of a circle that represent them. Back to Top

Pages 14 and 15: Fruit fractions

Application: A story where Buzz is invited to visit Fizz and her two nephews, gives the opportunity to set a puzzle about cutting apples into equal fractions. 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 are presented with a problem about fractions using a real life context.
Resources required: pencil
Learning objective taken from the Mathematics Framework: Recognise and calculate simple fractions in a practical context. Problem solving: making decisions and using appropriate language to resolve the task. Back to Top
Activities	Vocabulary/keywords
The story shows Buzz dropping an apple in his hurry to visit Fizz, which results in there not being enough apples for everyone to have one each. The reader is not told how many apples there are, but is presented with all the quarter pieces that Fizz has cut up, to share between the four cats. There are twelve pieces. Discuss what a quarter means (divided into four equal parts) and ask, what would you divide the total by to find how many wholes there are? (divide by four) The second question asks what fraction of apple each cat got: dividing 12 by 4 will give the answer 3,and a practical demonstration of three quarters of a whole is presented. The next challenge may be more difficult for some to manage: can they find a way that takes fewer cuts? You could help by talking about how two quarters make a half, which may lead many to leap to the answer: a half and a quarter each. Drawing in their answer reinforces the concept.	Fraction Half Quarter Three quarters Part Whole Equal parts/pieces Fewer divide division equivalent
Assessment strategy Confidence in making simple calculations with fractions, with a practical context. Back to Top

Page 16: Curious farm

Application: A picture puzzle that involves observation and reasoning. There are at least 22 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: what is wrong with some of the reflections in the pond? What is the horse pulling up the hill? (You may have to explain horse drawn ploughs!) Is that hay or a loaf in the cart? 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. Back to Top

Activity sheets 5 and 5b: Halving Towels (available online: see BUZZ Activity Sheets)

Application: An investigation is presented by Buzz and Fizz as they consider the stripes on their towel. Buzz recognises that the towel is coloured half yellow and half blue, and the reader is invited to explore the variations possible with four stripes. An extension recording sheet (5b) is available for the second part of the investigation, which looks at divisions into sixths.
Pupils recognise a shape that is equally divided can represent fractions. Can be used as an introduction to investigating.
Resources required: colouring pencils or felt tips in two colours
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.
Activities		Vocabulary/keywords
This is a rich investigation that begins on a simple level, but extends to far reaching levels of understanding of fractions and recognition of rotations. The first exploration is to discover how many ways the 4-striped (quarters) towel can be coloured half one colour and half another. There are six notations (BBYY, BYYB, YBBY, BYBY, but two are the same as BBYY and BYBY when turned: YYBB and YBYB). The conclusion the children should come to is that there are only four different ways. This is an opportunity to talk about rotations and symmetry. The extension sheet 5b allows for the investigation to continue with a different number of equal parts: six stripes (sixths). This also presents an opportunity to talk about thirds and sixths. This extension of the investigation is more challenging, as finding that patterns are the same when turned round will mean several will have to be rejected. Working in pairs will greatly help; both children can colour a few in, then compare discoveries and repeats. Encourage them to turn their pages around to look for matches. The 10 different colourings are: BBBYYY, BYBBYY, BYYBBY, BYYYBB, BBYBYY, BBYYBY, BYBYYB, BYBYBY, YBBYBY, and YBBBYY. The satisfaction achieved by working cooperatively will be self-evident. What if? Dividing the towel into 2 x 2 rectangles will result in slightly different findings: there are only three ways with two colours, which will be different. Enthusiastic investigators could experiment with other rectangles divided up equally, (a 2 x 2 square will only have two different arrangements, ask, why?). For older children, investigations could take them to looking at flags, scarves or even football kits. Encourage them to look for symmetry in their designs, which helps spot the ones that are rotations.		Matches/ Same/ Difference Equal parts Halves Quarters Sixths thirds Rotation Reflection symmetry Left, right position
Assessment strategy A confidence in recognising half in patterns, as well as learning to work-- together, being able to explore and make conclusions. Back to Top