BUZZ Teachers Notes Volume 2/Number 4 (Nov 2008)

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Cover: Which two penguins have matching scarves?

Application: A matching puzzle Twelve penguins are wearing scarves: but only two have the same pattern. 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 colour to recognize a pair.
Resources required: none
Learning objective taken from the Mathematics Framework Recognise differences in shape and pattern. Problem solving: making observations and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
A young reader may benefit by being helped to sort out this accessible problem. The differences between the scarves can be grouped and more discussion can be had about the patterns, making an opportunity to introduce useful vocabulary: ask, which one is the odd one out? (eg one that has no red), how many have diagonal stripes? (two), vertical stripes? (six), horizontal stripes? (four), could you group the scarves in any other way? Ask, how are you to go about finding the matching scarves? This is an early opportunity to introduce a systematic approach. Talk about describing the position of the penguins. How could they describe where the pair are without the numbers?		matches/ same/ difference pair count how many sort, group, type, set most fewest horizontal vertical diagonal left, right top, bottom over/above under/below
Assessment strategy Observation and ability to recognize differences. Vocabulary will be extended using appropriate words. Back to Top

Page 2: Match the crayons

Application: The main theme of this issue is multiplication. The introduction page has Buzz showing a pack of crayons, and saying how they can be described as 2 x 3 or, as Fizz adds, 3 x 2. The children are holding packs of crayons in different quantities and arrays. There is a table to fill in and the reader is asked which Buzz kid has the same number as Buzz. 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 arrays of crayons, and use multiplication to find the total number.
Resources required: pencil
Learning objective taken from the Mathematics Framework Counting in context, estimating then checking. Understanding the operation of multiplication and that it can be carried out in any order. Problem solving: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
Although this is quite a simple task, it offers the opportunity to do simple multiplication within a context. The table requires putting in the number of rows times the number of columns for the top line of Buzz kids, and the number of column times rows for the bottom line of Buzz kids, illustrating the point Fizz makes at the top of the page. For children who are not comfortable with multiplication, this makes a good exercise in looking for pairs to add, (as in Becky’s, Luke’s and Lucy’s boxes) or repeated addition generally (for example, ask, how many lots of four are in Jack’s box?), which leads to understanding that multiplication is repeated addition, and the order of the multiplication can be in any order. Extension questions: What other arrangement could be made for Yasmin’s 12 crayons? (2 x 6). Which box has an odd number of crayons? Having made up the table, Which line of Buzz kids has the most crayons? How many crayons altogether?		Rows Columns Arrangement/Array Multiplying Repeat addition Same as Altogether Total
Assessment strategy Recognizing that numbers in a multiplication can be in any order, that multiplication is repeated addition. Vocabulary will be extended using appropriate words. Back to Top

Pages 4 and 5: Number hats

Application: Verbal descriptions have to be matched to numbers, in order to discover which hat belongs to whom. The secret word Checker takes a letter from each hat to spell out two words describing the weather. The reader is invited to draw in the hats on the Buzz kids’ heads. 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 reading multiplication and additions in words. Can be used to reinforce knowledge of times tables.
Resources required: pencil, felt tips or colouring pencils
Learning objective taken from the Mathematics Framework Understand the operation of multiplication and the associated vocabulary. Know simple multiplication facts by heart and use known facts to derive answers quickly. Problem solving, reasoning and numeracy: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
This activity involves using known number facts and adding or subtracting numbers mentally. The calculation strategies such as doubling and using the five and ten times table lead to finding the 11 and 9 times tables, and this could be pointed out to a child who not comfortable with multiplication. Once the child has answered Yasmin’s ten fours minus four it could be pointed out that this is 4 x 9, for example. Ask, what other way could you get the answer 30 other than three fives doubled? (5 x 6 or 3 x 10). Talk about other multiplications that can be found by using doubling (x4, x8 for example). Doing the calculations will help with learning simple multiplications by heart and recognize the words describing operations. The hats once drawn in complete the picture, and the reader is rewarded by finding letters spell out cold snap.		Doubles Multiplication Addition Take away Minus plus left, right top, bottom row
Assessment strategy Confidence in using ten and five times tables, and combining addition or subtraction to reach an answer. More able children will begin to use the strategies for finding more difficult multiplications. By asking children to explain, their vocabulary will be extended using appropriate words. Back to Top

Pages 6 and 7: Buying in Packs

Application: Problem solving in a real life context, readers are asked to make decisions on how much to buy to fulfil the Buzz kids’ shopping list. 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.
A word problem presents a real life context that involves sorting information and doing multiplication to resolve the task.
Resources required: pencil
Learning objective taken from the Mathematics Framework Simple word problems involving real life contexts. Understand and use every day vocabulary related to packaging and shopping; choose appropriate number operations and know and use simple multiplication. 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
When tested it was found that this puzzle is complex enough to engage older children in Years 5 and 6 as it involves understanding the problem and then finding the information by reading all the speech balloons. The younger child may like help with deciding how to resolve the task: the example shows how buying more packs will be needed if the least amount required is more than an exact number of packs. The hardest is given; it would make a good talking point: ask, How many extra slices of bread would that give the Buzz kids? (4 slices) How much extra is that for each Buzz kid? (half a slice). Which items can they buy without having extras/remainders? This leads to recognizing division is the inverse operation to multiplication. There are many questions that could be put to a child to extend the activity: if they buy 16 cereal bars how many does each Buzz kid have? Will the apples divide up equally? Which item suggests one Buzz kid doesn’t like it? What have you seen in packs in the shops? What number of things is most common in packs? What if there were more Buzz kids? How would that change the shopping list?		How many Quantity Multiplication Times Repeated addition Division Remainder
Assessment strategy The ability to adapt to a real life situation, being able to think about how they go about answering the problems and what process they use. Confidence in calculating multiplication and division. Back to Top

Pages 8 and 9: Penguins and Seals

Application: A maze where four routes are to be found, using repeated addition. 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 number and calculating.
Resources required: pencil
Learning objective taken from the Mathematics Framework Knowing and using number facts, counting and understanding number. Problem solving: making decisions and using appropriate language to resolve the task.
Activities		Vocabulary/keywords
This activity is easily accessible from Year 2 up, but younger children may need help in keeping count as they go. It may be understood quite quickly that the same number of penguins are on each float, and likewise the seals. Once this is realized, the idea of using multiplication may be suggested if it has not already occurred to the child. By completing the boxes, this can be reinforced and discussed. Ask, How many penguins altogether? How many seals?		How many Quantity Repeated addition Multiplication Times Total
Assessment strategy Confidence in recognising number facts and counting leading to using multiplication. Back to Top

Pages 10 and 12: Make a line of 5

Application: A game for two players: calling out a multiplication allows a player to place a counter, with the aim of making a line of 5 in a row. Answers are not required, but the activity invites investigating other rules to develop mathematical ideas.
Pupils use multiplication and strategy.
Resources required: ten counters of each colour.
Learning objective taken from the Mathematics Framework Using multiplication. Know simple multiplication facts by heart.
Activities		Vocabulary/keywords
This game requires strategy to make lines: the more able child will look for the multiplications that lead to having several opportunities to reach the other side, requiring to make numbers such as 49 (remind the children that they can use a number twice). For those who avoid more difficult numbers, point out that there is a Product checker at the bottom which they can use to check a multiplication. Reinforce that this is not cheating: the more times they look up the answers the more likely their memories will begin to hold the number facts. This should also be used to check an answer and avoid arguments. Encourage calling out the multiplication and agreeing the answer before placing a counter. To add an element of luck to the game, a pack of numbers could be made (three sets of the numbers) or a spinner which includes 7. This way would also encourage using multiplications they might not be so confident of knowing.		How many Product Repeated addition Multiplication Times
Assessment strategy Confidence in calling out multiplications, recognizing there can be more than one way to make a product. Back to Top

Pages 12 and 13:

Application: A drawing shape and colouring-in activity using multiplication. Key panels are used to say which triangle to draw in. 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 multiplication, using number facts. Understanding shape and orientation, and symmetry.
Resources required: red and blue felt tips or pencils
Learning objective taken from the Mathematics Framework Know simple multiplication facts, knowing number facts. Make patterns and describe features, rotation of shape and recognise symmetry.
Activities		Vocabulary/keywords
If children have seen this activity in BUZZ issue 1, they may not need any help in knowing what the task is (the earlier version used simple addition and only two orientations of the triangle). This time it is more complex as there are four orientations of triangle to use: help by talking about the two examples that are given, and have already been put in the design. The activity is to match the product of each multiplication with the number on the design below: talk about the key panels and the triangle to draw in each time. How would they describe the triangles to differentiate their orientations? Ask, which triangle is this one? (answer could be: it has its right angle in the bottom right-hand corner). Younger children will need help and encouragement to take their time, as it is easy to get confused with the triangle’s rotation. It may be advisable to start with a pencil, before colouring, so that a mistake does not spoil the final effect. The symmetrical designs can be surprising as they do not appear until towards completion. Ask where a mirror could be placed so that it reflects the same image. Explain this is the line of symmetry.		Key Triangle Right angle Top/ bottom right-hand Top bottom left-hand Corner Rotation How many Product Multiplication Times Symmetry Line of symmetry
Assessment strategy Confidence in using simple multiplications, understanding shape and position. Back to Top

Pages 14 and 15: Snowball roll

Application: Children are invited to read a story, which involves making a big snowball to clear the path. The story finishes with the reader being asked to say which diagram matches the snowball in the story. 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 multiplication describing size.
Resources required: pencil
Learning objective taken from the Mathematics Framework Understand and use the vocabulary relating to multiplication and size. Measure: know a standard metric unit. Select by comparison.
Activities		Vocabulary/keywords
This simple story illustrates how a snowball collects snow as it rolls and gets bigger. Questions about size could come up reading this story: when is the snowball twice the size it started? How tall is Buzz if the ball is almost his height when 8 times wider than when it started? How wide is 5 cm? (How wide is your hand?) It could also lead to an interesting discussion on how to measure a snowball: by its width sliced in half (its diameter), or a circle right around it (its circumference). Ask: What other way could you measure a 3D object like a snowball? (weight) Ask: When do we describe things using a multiplication term, as in being times bigger/taller/wider/heavier? (eg comparing buildings, people, mountains). A discussion could be had on the vocabulary of opposites (eg shrinking, half the size) which is also used in everyday life.		Multiplication Times Size Width Wider 2D 3D smaller larger shorter narrower bigger larger twice as much half as much
Assessment strategy Using the vocabulary of multiplication to describe enlargement. Back to Top

Page 16: Curious forest

Application: A picture puzzle that involves observation and reasoning. There are at least 21 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 easily engage with this puzzle. Some may not be so easy to recognise. Encourage children to use language to describe why something is odd: where do parrots live usually? Can a pig climb a tree? Where are there pyramids? 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

Worksheet: Numbers with stamps BUZZ activity sheet 4 (available online)

Application: Buzz and Fizz present a investigation: at the post office there is a problem of only having 3p and 5p stamps: how do they make 11p? Can the numbers 3 and 5 be added to make any other numbers?
Looking at number, recognizing and using multiplication
Resources required: pencil
Learning objective taken from the Mathematics Framework Use knowledge of number facts, explore number with addition and multiplication
Activities		Vocabulary/keywords
This investigation is an excellent way to explore the 3 and 5 times tables. The example shows how 11p can be made using two 3p stamps and one 5p. Repeated addition can be applied to almost every number and the satisfaction in discovering this is both rewarding and illuminating. It will be found that there are a few exceptions and the challenge would be for the children to find these. Most will know straight way that they can’t make 1, 2 and 4. It is also not possible to make 7. Knowledge of the multiplications of threes and fives will be useful, but using repeated addition is fine as it will lead to understanding multiplication is a shorthand for the same thing. Having found all the numbers up to 25 suggests there will be no upper limit: challenge able children to find larger numbers; some will realize that any number can be made (with the few exceptions already discovered). Encourage continuing their investigation in a systematic way, as they will soon see patterns and short cuts.		Addition Multiplication Infinite Times Different
Assessment strategy Confidence with number, being able to explore number and see pattern and links. Back to Top