BUZZ    Teacher’s Notes Volume 4/Number 12 (June2011)

 

Cover: Choose the silhouette

 

Application:

 

A puzzle requiring finding which shape matches Fizz,

in this circus edition.

 

 

 

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 recognise the difference in shapes and use a strategy to do the task.

 

 

Resources required: none

 

 

Learning objective taken from the Mathematics Framework:

Present solutions to puzzles in an organised way.

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

 

Activities

 

Vocabulary/keywords

 

The challenge here is to pick the silhouette that matches the image of Fizz on the trapeze. Encourage children to look at each silhouette in turn,

eliminating ones when they find a difference, such as the rope in the first box, and ask them to describe it. The most subtle difference is Box 2, where the foot is missing. Most children will be able to decide on Box 4 after close examination.

 

Matches/ Same/ Difference

Left, right

Top, bottom

Over/above

Under/below

Next to

Beside

Missing

Close

 

 

 

Assessment strategy

Confidence in solving problems involving shape. Being able to describe their features. Vocabulary will be extended using appropriate words.

 

 

 

 

Pages ­­2 and 3: Introductory puzzle: Match the clubs, and contents 

 

 

Application:

 

The theme of Issue 12 is problem solving.

The introduction puzzle starts with recognising sets that match.

 

The Buzz Kids are juggling sets of clubs and there are panels to fill 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.

 

 

 

 

Pupils look at pairs of sets.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Use mental calculation strategies to solve a problem.

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

 

 

Activities

 

Vocabulary/keywords

Strategy is needed to work out which sets match another, as skimming from one to another makes the task surprisingly difficult.

Encourage children to look at the first one and compare it with each one. Completing the panels below is good practice for checking their answers.

 

 

 

Pairs

Same as

Altogether

Match

Set

 

 

Assessment strategy

Confidence in resolving a problem and using a systematic approach.

 

 

 

 

 

 

 

 

 

 

Pages 4 and 5:  Spinning numbers

 

Application:

 

Spinning numbers requires finding pairs of numbers to fit answers given in a panel.

 

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.

 

 

 

 

Using mental arithmetic to solve a problem.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Solve simple word problems involving number and explain how the problem was solved.

Solve problems involving understanding of numbers and operations, explain and justify decisions.

Use mental calculation strategies to solve a problem.

 

 

Activities

 

Vocabulary/keywords

The Buzz kids are spinning plates with numbers on them. To find the numbers in the panel pupils will need to do some additions and subtractions and look for pairs of numbers.

 

Younger children may well need help with these questions, but should be within the scope of able Year 2 and Year 3 children.

 

Encourage children to look for numbers they think will end with the correct digit. Estimating helps in recognising what an answer should be when doing calculations. Ask, Which numbers will give a number ending in nine when summed together? (15 and 14). Which numbers will leave a zero when you subtract one from the other? (50, 40, 10, and 21 and 11).

 

Putting in the answers will help narrow down their choices as they do the puzzle.

 

Extension: What other numbers can they find with the numbers on the spinning plates?

What is the largest number they can make with two numbers? The smallest?

 

 

 

 

How many

Addition

Sum

Subtraction

Take away

 

Estimate

Less than

More than

 

 

 

 

 

Assessment strategy

Being able to solve number problems in a puzzle activity shows good mental arithmetic ability. Children achieving in this in Years 1 and 2 would be working at a high level (more expected of Year 3 and beyond).

 

 

 

 

 

 

 

Pages 6 and 7: Circus mats

 

 

Application:

 

Two of the Buzz Kids choose shapes that will make up squares.

 

Children are invited to colour in the answers.

 

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.

 

 

Problem solving using shape

 

 

Resources required: pencil, colouring felt tips or crayons (red, green, blue and yellow)

 

 

Learning objective taken from the Mathematics Framework:

Recognising properties of shape, using rotation and translation.

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

Use 2D shapes to make new shapes.

 

Activities

 

Vocabulary/keywords

This activity is accessible to Year 1 and 2 children, as the colours can be used as a strategy, but it is particularly suitable for Year 3, requiring looking at shapes that fit on a 3 x 3 grid, using rotation and translation.

 

The importance of an activity like this is that it encourages children to ask, What if?, Could I try this?

in the process of solving a puzzle. If a child needs help, suggest a shape and ask, What does this shape have to do to fit here? (slide and turn). As an exercise, it involves finding strategies and elimination.

 

Talk about how the pieces are made up: that the shapes making up each mat are made up of combining small squares. Ask, How many small squares make up each piece? For more able children, they can be asked how many sides a piece has, or how many right angles.

Sliding

Turning

Rotating

Turns

Square

L shape

T shape

Rectangle

U shape

Z shape

Angle as a measure of turn

Clockwise

Anti clockwise

Right angle

Corner

Straight sides

 

 

 

 

Assessment strategy

Confidence in describing and recognizing 2-D shapes and being able to combine shapes to make new shapes.

Discovering strategies to resolve a task.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pages 8 and 9: Circus Way

 

 

Application:

 

A maze that gives lots of opportunity to add numbers

and find strategies for finding different totals.

 

 

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 working with numbers.

 

 

Resources required: none

 

 

Learning objective taken from the Mathematics Framework:

Recognise number connections, find ways of calculating to solve problems.

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

 

Activities

 

Vocabulary/keywords

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. There is not need to cheat, as there is no wrong way! Rather than draw on the maze, encourage children to use their fingers and count as they go.

 

Once a child has found one of the routes and added the balls, he or she should be able to see there are many ways Buzz can get to the tent, and enjoy the process of ticking off the numbers found each time. This is a puzzle that can be returned to as it is both challenging and time consuming. It does not matter if the child cannot find all the routes straight away. Ask, which routes have you found easy to solve?, Can you work together to find another?

Children may decide they can go round a route again to pick up every ball, in which case there are 28 possible routes.

 

Addition

How many

Odd (has a remainder of one after dividing by two)

Even (divides by two exactly)

Up, down, through, under, above

Top, bottom, left, right

 

 

Assessment strategy

Achieving an understanding of numbers and finding strategies to solve number problems. By asking children to explain directions their vocabulary will be extended using appropriate words.

 

 

 

 

Pages ­­10 and 11: Balancing Balls

 

 

Application:

 

Balancing puzzle that involves weights leading to a very early introduction to algebraic thinking.

 

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.

 

 

 

Working with mass (grams), and balancing numbers

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Use operations to solve a problem involving mass.

Develop mathematical ideas and methods to solve problems.

 

 

Activities

 

Vocabulary/keywords

This activity is exciting as on the first level it requires mental calculation and reasoning, inviting discussion on how to solve the problem. It also serves as a painless introduction simple algebra, where the reader has to find the value of ‘x’, given other information. It would be useful for older children who are intimidated by equations with number, as they will be able to recognise the balancing on a see saw.

 

The questions build up, using the information just acquired from the puzzle picture before. The weight is described as the number of balls, illustrating that the balancing can be understood as quantities of an object.

 

Being able to explain orally and writing a sentence showing how the problem was solved will encourage good reasoning skills.

 

The last question introduces grams, and involves looking back to the first question, where the hat is shown to weigh three balls. A simple multiplication or repeated addition is required as each ball is 50g. An extension could be to ask how many grams the other items, plus Fizz and Buzz, weigh.

 

How many

Add, addition, more, plus

Sum, make, total

Subtraction

Balance

Weigh

Grams

Multiply

Repeated addition

 

 

 

 

Assessment strategy

Calculating with number and being able to explain how the problem is solved shows good reasoning and functionality.

 

 

 

 

 

 

Pages ­­12 and 13: Even numbers

 

 

Application:

 

A ‘dot to dot’ picture with rules to follow.

 

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.

 

 

 

Use known number facts, understand the operation of simple addition

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Know simple addition facts by heart. Understanding odd and even numbers

 

 

 

Activities

 

Vocabulary/keywords

Most children from Year 1 will find adding in two’s familiar, and this dot to dot is a useful way of looking at the two times table, as well as reinforcing what even numbers are.

 

You could ask, What is an even number? What is an odd number? And encourage them to explain in their own words.

 

 

How many

Add, addition, more, plus

Sum, make, total

Multiples

Repeated addition

Factor

Even numbers

Odd numbers

 

 

Assessment strategy

Confidence in number, recognising a pattern and understanding multiples.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pages ­­14 and 15: Ice Cream Tub

 

 

Application:

 

A story where Buzz loses his change and only can buy one ice cream tub.

 

A question about the cost of an ice cream tub follow on the next page.

 

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. Throughout the magazine there has been a balloon to spot on every spread.

 

Full solutions can be found in the online Answers.

 

 

 

 

 

Pupils are presented with a problem about money in a story context.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

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

Understand the operation of addition and subtraction and related vocabulary.

 

 

Activities

 

Vocabulary/keywords

The story tells how, in Buzz’s enthusiasm to say thank you to Katto the Clown, he loses some of his money. How much is the ice cream tub?

The puzzle that follows invites some algebraic thinking, which is simple enough for most children to understand and solve, and uses a real life context.

 

 

 

 

Add, addition, more, plus

Sum, make, total

Same as

Take away

 

 

 

Assessment strategy

Confidence in making sense of problems using mental calculations, with a practical context.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Page 16: Curious Caravan

 

 

Application:

 

A picture puzzle that involves observation and reasoning. There are at least 22 different oddities to find.

 

The circus theme is completed with the curious caravan.

 

(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: could a mouse hold up 1 ton? 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 been 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.

 

 

 

 

 

 

 

Activity sheet 12: Triangle Totals (available online: see BUZZ Activity Sheets)

 

 

Application:

 

An investigation is presented by Buzz and Fizz, to place numbers in a triangle so that each side totals a given number.

 

A downlaoadable PDF of the worksheet is available online by clicking on the BUZZ button on the CIRCA Home page, go to Activity Sheets, and click on the relevant picture:

http://www.circamaths.co.uk/buzzws12.html

 

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calculations: addition

 

Resources required: pencil

 

Learning objective taken from the Mathematics Framework:

Find mental calculation strategies:

Use patterns of similar calculations

Problem solving: deciding on a method or tools to complete the task.

Understand that more than two numbers can be added together.

 

Activities

 

Vocabulary/keywords

This worksheet is designed to be accessible to several Year groups, but is particularly suitable for Year 3, who should be able to use reasoning and strategy.

 

The numbers are supplied at the bottom of the sheet so that they can be cut up and moved about. By experimenting with adding the three numbers along a side, they will gain confidence in the task, encouraging the questions, What if?, What could I try next?

 

The exercise of recording their solutions is useful:  learning how to organise one’s work will encourage a systematic approach to investigating patterns of similar calculations, and lead to mathematical understanding.

 

The challenge is given to find another number that works with just

numbers 1 to 6.  It will soon be discovered that a number higher than 12 cannot be made, but 9 can.

 

Extension: For younger children, the same puzzle could be to use the numbers 1, 2 or 3 (as often as wished) to make each side add up to 5.

 

 

Add

Subtract

Total

Patterns

Number sentence

Different

Equals

Minus

Plus

sum

 

 

 

Assessment strategy

A confidence in recognising patterns, using the relationship between numbers in addition. Discover mental calculation strategies.