BUZZ    Teachers Notes Volume 1/Number 2 (March 2008)

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Cover:  What is different?

 

Application:

 

The main theme of Issue 2 of Buzz is shape and sorting.

 

The cover presents a visual reasoning problem where pupils are asked to recognise each subtle difference in the 12 pictures, comparing each one with the one at the bottom.

 

Answers are provided on page 15 of the magazine so that children can check for themselves, and a full description of all the differences can be found in the online Answers.

 

 

 

 

Pupils look at detail to find difference in shape, colour or direction

 

 

Resources required: none

 

 

Learning objective taken from the Mathematics Framework

Recognise differences.

Problem solving: making observations and using appropriate language to resolve the task.

 

Activities

 

Vocabulary/keywords

At first glance each picture may look the same, and some differences may not be as easy to find as others.

 

Encourage verbal discussion which will give opportunity to use vocabulary for location. How do you describe that Fizz has flipped her arm, that stripes are alternately coloured (in picture 4), or going in the opposite direction (picture 8)? To help, ask, How many circles on each scarf? How many have the same sleeves?

 

 

matches/ same/ difference

circles

stripes

V shape/triangle

opposite

 

left, right

top, bottom

 

over/above

under/below

 

Assessment strategy­

By asking children to explain position and shape their vocabulary will be extended using appropriate words. Back to Top

 

 

Page 2: Which shield?

 

Application:

 

A reasoning problem where pupils are asked to identify shape and position and allocate each description to each character誷 shield in a table.

 

They will also have to find the shield that matches the one Fizz has.

 

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 look at shape and describe position

Can be used as an introduction to resolving confusions over left and right

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework

Recognising shape, 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 which is your left or right, as opposed to the character誷 on the page.

 

Encourage discussion before completing the table. Sorting the descriptions will provide opportunity to use vocabulary that explains location.

 

To extend the activity, ask: What is the difference between Becky誷 shield to Fizz誷?

Which shield uses the least motifs?

How many circles can you find?

 

 

 

matches/ same/ difference

square

diamond

star

triangle

circle

waves

 

left, right

top, bottom

 

over/above

under/below

 

 

Assessment strategy­

By asking children to explain position and shape their vocabulary will be extended using appropriate words.
Back to Top

 

 

Pages 4 and 5: Crown jewels

 

Application:

 

A reasoning problem where pupils are asked to identify shape and position to complete patterns on each of the crowns.

 

They will be rewarded by finding the word treasure, spelt out, if they correctly select and ring the jewels from the row along the bottom. (The letters will not come up in order, but the word will appear in the correct sequence once all are done.)

 

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 and pattern

Can be used as an introduction to describing and recognising 2-D shapes.

 

 

Resources required: pencil/felt tips/ colouring pencils (red, blue, yellow and green colours)

 

 

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 discussion to introduce the idea behind each pattern could be useful: Is colour significant? Which patterns use 2 shapes and 2 colours? What if you extend a pattern? How could you continue the pattern on Sasha誷 crown?

Is there a pattern that uses reflection?

 

Drawing in the shapes in the spaces will provide reinforcement of shape recognition.

 

Encourage using the names of shapes and their properties. Ask if they can find where else the thin rectangle is used: look for the rotation of it on Luke誷 crown. How would you describe that? Which other shapes are used with rotations? How many sides has the hexagon? How many squares are there altogether?

 

 

 

matches /same

circle

triangle

square

rectangle

pentagon

hexagon

 

left, right

top, bottom

 

over/above

under/below

along

first, second, third, fourth, fifth

 

quarter turn, half turn

reflection

 

 

Assessment strategy

By asking children to explain position and shape their vocabulary will be extended using appropriate words. See also pages 12/13 for practise in using names of shapes. Back to Top

 

 

Pages 6 and 7: Sort the shapes

 

Application:

 

Children are asked to find, sort and draw in the shapes using a criteria. A dotty grid is provided to help in drawing in the shapes.

 

They are also asked to find two hidden characters in the scene.

 

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 and sort according to a property.

Can be used as an introduction to right angles, and other properties of 2-D shapes.

 

 

Resources required: pencil and ruler

 

 

Learning objective taken from the Mathematics Framework

Recognising shape, describe and classify according to their properties.

Understanding angle as a measure of turn. Measure in cm.

Problem solving: making decisions and using appropriate language to resolve the task.

 

 

Activities

 

Vocabulary/keywords

Most children will be able to recognise the right angles in the shapes without the tester: however this is a useful introduction to understanding angles on a straight line, (180), the important qualities of a right angle (that it is made with lines perpendicular to each other), and is defining in many shapes (e.g. a square or right-angled triangle).

Ask: are all the triangles in the scene right-angled? (the one on the curtain by Sasha誷 head in not quite). The tester will help to decide if an angle is more or less than a right angle. The dotty grid in each box will assist in drawing the shapes in accurately, though requiring a certain amount of measuring. To help arrange the shapes within the boundaries, one line has been drawn in already.

Extension: All the shapes to find are polygons, a 2-D shape with straight sides. Ask: which ones share other properties? Why is the rectangle not a square? What other ways could they sort the shapes by (e.g., number of sides)? What sort of shape is the hat Becky is wearing? (A cone).

 

 

sort

set

right angle 90

turn (half/quarter)

square

quadrilateral

4 sided

rectangle

triangle

equal sides

polygon

pentagon

straight sides

most/least

length

equal sides

left, right

top, bottom

over/above

under/below

cone

 

Assessment strategy

A confidence in recognising right angles, and how they are used a definition on many shapes: see the right angle maze on pages 8-9 for practise. Back to Top

 

 

Pages 8 and 9: The right angle maze

 

Application:

 

A shape maze where the criterion is to identify which shapes have at least one right angle.

 

The task is to discover which of the three castles is reachable.

 

 

 

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 and recognise right angles.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework

Recognising right angles in shapes.

Problem solving: making decisions and using appropriate language to resolve the task.

 

 

Activities

 

Vocabulary/keywords

This maze is challenging and some preparation will make it easier. The spread Sort the shapes on pages 6/7 will offer an introduction to recognising right angles, and the folded paper tester may help in deciding if a shape has a right angle or not. Marking shapes with a small square in the corner if they have at least one right angle (which introduces the convention) will help find the ones that do not comply. Blocks can be ringed to avoid crossing one by mistake, when doing the maze.

 

Extension: how many pentagons can you find? How many squares? Make a tally. Can you find a pentagon with a right angle? How would you describe your route?

 

right angle 90

quarter turn

square

quadrilateral

4 sided/5 sided

rectangle

triangle

equal sides

polygon

pentagon (irregular and regular)

straight sides

equal sides

left, right

up down

 

Assessment strategy

Confidence in recognising right angles and sorting. See also pages 6 and 7. Back to Top

 

 

Pages 10 and 11: The Game of Pile up 

 

 

Application:

 

A game for two players that involves counting and strategy.

 

(Full demonstration of a game in play can be found in online Answers)

 

BUZZ FACTS A few facts and figures are given on size to invite discussion. How wide is a double bed? Compare the playground to a football pitch

 

 

 

Pupils use number and strategy

Can be used as an introduction to other counting games such as Mancala

 

 

Resources required: 5 counters (penny coins will do)

 

 

Learning objective taken from the Mathematics Framework

Counting and understanding number

Problem solving: making decisions and using appropriate language to resolve the task.

 

 

Activities

 

Vocabulary/keywords

Some children may need help in understanding that counters are shared (and not won during the game) and only by making them into a pile of 5 does the game end. The rules are simple, and once the idea that the moves are dictated to by the number in the pile, should be quickly understood. A round of play does not take too long as it soon becomes apparent that there are strategies to adopt. Player One appears to have the advantage if both attempt to make piles each time. But by using the spare turret to delay a move, the control of the game can revert to Player Two. Encourage children to test out different strategies, first moves, taking turns to who starts. Ask: what rules would help avoid a stalemate? The first player could have to make a double, or a rule could be added that empty turrets can only be used if it is not possible to make a pile.

 

octagon/octagonal

direction

clockwise

anti-clockwise

turns

 

 

Assessment strategy

By asking children to explain their strategies, as to whether they can predict who will win and at what point they recognise who will win, demonstrates a high level of reasoning and understanding of number. Back to Top

 

 

Pages 12 and 13: Colour by Shape   

 

Application:

 

Children are asked to carefully colour in the picture by using a key that has shape as its criteria.

 

 

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.

Can be used as practise with classification of shape

 

 

Resources required: colouring pencils/felt tips (7 colours)

 

 

Learning objective taken from the Mathematics Framework

Recognising shape, use mathematical vocabulary.

 

 

Activities

 

Vocabulary/keywords

Neat colouring in encourages an important dexterous skill, and results in much more satisfying final results. Discussion on the difference between each shape is useful: ask, what is the difference between the square and the rectangle? How many sides has a hexagon? Suggest care is taken in recognising the hexagon and the circle, which look similar on this scale.

 

The repetitive nature of an activity like this is useful for reinforcing confidence in the vocabulary; encourage children to talk about the key, and the picture as it appears.

 

matches/ same/ difference

triangle

square

rectangle

star

pentagon

circle

hexagon

right angle

straight sides

equal sides

left, right

top, bottom

 

 

Assessment strategy

A successful result will demonstrate an ability to concentrate and apply care, as well as confidence in using mathematical vocabulary and recognising shape.
Back to Top

 

 

Pages 14 and 15: Which Box?   

 

Application:

 

Children are invited to read a story, which then leads to a problem of matching objects and the boxes that they will best fit into.

 

 

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 look at shape and capacity, considering 3D shapes

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework

Recognising shape and measure relating to length, mass and capacity with 3 D shapes.

Problem solving: in a real-life situation, making decisions and using appropriate language to resolve the task.

 

Activities

 

Vocabulary/keywords

The story explains that Buzz has labelled all the packing boxes without checking their contents. resulting in finding the lamp and shoes instead of kettle and mugs.

To sort the larger objects should not prove difficult, but more thought will be required to match the more similarly sized things. Talk about the size of the objects: how long a box will take three mugs? Which is taller, the stool or the kettle? How deep is the television?

 

Before joining lines to the boxes, ask: Can you find ways to join each up without crossing lines?

 

Extension: Looking at the boxes, ask, which is the odd one out? (which has a curved surface?)  How many faces do the cuboids have?

What other types of containers could there be? (eg cylinders, prisms, cones).

 

matches/ same/ difference

rectangular

surface, face

right-angled

cube, cuboid, rectangular, square

edge, corner, sides

measure

size

big, small

bigger, smaller

shorter

higher

taller

longer

length

width

depth

curve

left, right, top, middle, bottom

 

Assessment strategy

By asking children to explain their decisions their understanding of size and capacity will be increased, and vocabulary improved by using the appropriate words. Back to Top

 

 

Page 16: Curious Castle

 

Application:

 

A picture puzzle that involves observation and reasoning. There are at least 24 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

Recognising reflections, 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 children should engage easily with this puzzle. Some may not be so easy to recognise: the shadows are all facing the wrong way for the position of the sun (it could be argued that there are seven examples of this, or one, that the sun is in the wrong place). and the wind is blowing in two directions at once.  The various reflections can provide an understanding of symmetry in simple cases; here there are interesting ones such as the bridge shape appearing square in the moat, the swan誷 reflection being reversed.

 

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/ difference

direction

reflection

left, right

top, bottom

position

over/above

under/below

 

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

 

 

Worksheet:  How many ways? 2a and 2b (available online)

 

Application:

 

An investigation of possible arrangements with four square tiles.

 

Buzz and Fizz present a tiling investigation: they offer a demonstration and show ways that won誸 be allowed in the investigation. Use in conjunction with  worksheet 2B which provides tiles to cut out and the squared grid to draw and/or position them on.

 

 

 

 

 

Looking at shape, pattern and recognising their features

Can introduce tessellations

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework

Solve mathematical problems, recognise patterns and relationships.

 

 

Activities

 

 

Vocabulary/keywords

Many children will know the game of dominoes, and that each domino is made of two squares joined edge to edge. The name for a polygon made up of four squares joined edge to edge is a tetromino (and a triomino is made of three squares). An introduction to this investigation could be to start with triominos as there are only two possible ways three squares can be arranged.

By experimenting with the cut out squares from worksheet 2b, the investigation will result in the children finding that there are five different ways they can arrange the squares (a  2 x 2 square, a bar (4 x 1 rectangle) T-shape, L-shape and a skew (zig zag). It may helpful to talk about what doesn誸 count as different: a reflection or rotation. (Two shapes are not considered different if one can be fitted exactly on top of the other, turning it if necessary.) It may also be necessary to remind them that at least one edge must join along the full length of the next square, as shown on the worksheet.

Investigating how many ways can be arranged with five square tiles (known as pentominoes) will result in finding 12 arrangements. There are 35 hexominoes (polygons made with 6 squares). Encourage recording their results, so that they can check for ones that are reflections or rotations.

 

Extension: Having discovered the five tetrominoes, it will be found that they all tessellate (form a continuous pattern without any gaps). By rotating and flipping the L tetromino, for example, many interesting tessellations can be found. Templates could be made of thin card and traced around to experiment with.

 

square

equal sides

polygon (a shape made of straight sides)

straight sides

equal sides

different, same

bar

T

L

skew

left, right

up down

reflection

rotation

symmetry

right angle 90

quarter turn

pattern

 

 

polyomino (a polygon made of any number of squares joined edge to edge)

domino (2 squares)

triomino (3 squares)

tetromino (4 squares)

pentomino (5 squares)

hexonimo (6 squares)

 

 

Assessment strategy

The ability to experiment and look for patterns and recognising the value of making a record of their investigations. Back to Top