BUZZ    Teacher’s Notes Volume 3/Number 7 (November 2009)

 

Cover: Count the crates

 

Application:

 

A puzzle requiring finding which shape is missing from a group.

 

 

 

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 different 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 decide how to check which shape is missing from those on the floor. A systematic approach will result in finding which one it is (the spade) quickly.

Ask, how would you describe the position?

 

Matches/ Same/ Difference

Left, right

Top, bottom

Over/above

Under/below

Next to

Beside

 

 

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 Pairs, and contents 

 

 

Application:

 

The theme of Issue 7 is securing number facts.

 

The introduction puzzle starts with recognising pairs that sum to 10.

 

The Buzz Kids hold up the Egyptian hieroglyph equivalents to numbers 1 to 9 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 number pairs.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Deriving and recalling addition facts to 10, recognising pairs that sum to 10.

Retrieve data from information and organise and sort it.

Use mental calculation strategies to solve a problem.

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

 

 

Activities

 

Vocabulary/keywords

Pupils are given an opportunity to recognise another number system: hieroglyphs are interesting as they are pictorial, and demonstrate how numbers may have developed. A single stroke is the earliest and most obvious way to record a unit, and can be found in many systems (Roman and Chinese, for example) as well as in a tally.

 

One suggestion for the use of a hoop by the Egyptians is that it represents the handle of a basket (and the lines are sticks).

 

The task is to make pairs that sum to 10: knowing number pairs to 10 leads to confidence with finding pairs that sum to 20, and 100.

 

 

 

Pairs

Sum

Addition

Equivalent

Hieroglyph

Egyptian

Tally

Number

 

 

Assessment strategy

Confidence in deriving number facts, knowing pairs that sum to 10

 

 

 

 

 

 

 

 

 

 

Pages 4 and 5:  Round the museum

 

Application:

 

The reader is asked to answer problems about estimating and rounding in a real life context.

 

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.

 

 

 

 

Understand and use the vocabulary relating to estimating and rounding numbers.

 

 

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.

Round to the nearest 10, estimate a number of objects.

Use mental calculation strategies to solve a problem.

 

 

Activities

 

Vocabulary/keywords

The Buzz kids describe different quantities or measurements in their comments in the museum. To answer the questions in the panel pupils will need to source the information from the comments.

 

Making estimates by rounding number is an important skill, as is knowing when to round up or down, to the nearest ten. Younger children may well need help with these questions, but should be within the scope of Year 2 and 3 children.

The last question involves a 3 digit number, which is slightly more challenging.

 

Encourage children to orally explain their method for solving word problems, and explain why estimating helps in recognising what an answer should be when doing calculations. Ask, What number is 9 plus 19? (add 10 + 20 and adjust both by 1)

 

Extension: Talk about different strategies for getting estimates, and when to make sensible estimates: how to estimate the number of pencils in a box, marbles in a bag, words on a page (talk about visually grouping into 5’s, counting words in one line, etc). Ask, When do you round up to the nearest 100? Can you round to the nearest half an hour?

 

 

 

 

How many

Round up

Round down

Estimate

Less than

More than

About

Nearly

Approximately

Close to

Roughly

 

Measure

metric

Length

cm

 

 

 

 

Assessment strategy

Being able to solve word problems in practical contexts, and use the information to answer questions about estimates shows good reasoning. Children achieving in this understanding in Years 1 and 2 would be working at a high level (more expected of Year 3 and beyond).

 

 

 

 

 

 

 

Pages 6 and 7: Market Place

 

 

Application:

 

Six of the Buzz Kids have stalls where they are selling little pots of spice. Some have been bagged in hundreds, some in tens, and some as single pots.

 

The reader is invited to work out the Egyptian numbers and match the amounts to numbers in the table.

 

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.

 

 

Partition a number into hundreds, tens and ones 

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Know what each digit in a number represents, and partition a number into a multiple of 10 and ones, or a multiple of 100, 10 and ones. Read and write numbers. Know what each digit in a three digit number represents.

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

 

 

Activities

 

Vocabulary/keywords

This activity is accessible to Year 2 children and beyond, but particularly suitable for Year 3, as they begin to read and write three-digit numbers with confidence, and understand partitioning.

 

The additional activity of writing the Egyptian hieroglyphics lends itself well to looking at the meaning of place value, as the Egyptians used the devise of repeating a symbol for one hundred three times to show 300, and so on. It leads to looking at the way we use 0 to hold place value in our number system. Ask, why is our system more adaptable? How many symbols would you need to write 999 in Egyptian, for example?

 

Ask, How many tens are in the number 78? Write a number sentence made up of tens and units that makes 78. (70 + 8) How would you show 429 as hundreds, tens and units? (400 + 20 + 9).

How many

Numbers

Hundreds

Tens

Units

Ones

Two-digit

Three-digit

Place holder

Zero

Symbols

Represents

Place value

 

 

 

 

Assessment strategy

Confidence in reading, writing and understanding figures and partitioning 3 digit numbers.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pages 8 and 9: Pyramid maze

 

 

Application:

 

A maze that reinforces the rules about odd and even numbers.

 

Buzz and Fizz have to find a route each.

 

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 recognising odd and even numbers.

 

 

Resources required: none

 

 

Learning objective taken from the Mathematics Framework:

Recognise odd and even numbers, and understand their definitions.

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 an opportunity to talk about the shape of pyramids: Can the base be square or triangular?

Does this effect how many sides they have?

 

Most children from Year 2 will know when numbers are odd or even, but it may be useful to put questions to them which will make them think about how they know: Ask: How would you describe an odd/even number? Encourage children to use their own words. Why is 15 odd? How do you know? What happens if you add two odd numbers together? Observations could be made on what happens when odd, even or odd and even numbers are added together. How can you be sure to have an odd number made from adding two numbers?

 

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

Even (divides by two exactly)

Whole numbers

Remainder

Division, dividing

 

Up, down, through, under, above

 

Top, bottom, left, right

 

pyramid

 

Assessment strategy

Achieving an understanding of odd and even 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: Ups and downs in tens

 

 

Application:

 

A dot-to-dot activity that challenges the reader to not only count in tens, but go backwards and forwards.

 

The discovery of the ‘dotty thing’ leads to finding a hidden mummy on every spread of the magazine.

 

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.

 

 

 

Practise with numbers and the number sytem

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Describe and extend number sequences.

Count on or back in steps of 10 from any number.

Recognise a set of familiar numbers on a number line.

 

Develop mathematical ideas and methods to solve problems.

 

 

Activities

 

Vocabulary/keywords

This activity presents the familiar dot-to-dot activity that most children will know. Their impulse will be to find the 0 and join numbers adding on one from there. This is immediately more challenging as they are told to start at 500.

The number line will help establish the idea, but care needs to be taken as they search for the next number as it goes up in tens in one direction, and down in tens in the other.

Younger children will benefit by being guided to the numbers as they go, so as not to get confused which number comes next. The use of red dots will help to remind them when they are going backwards.

 

Ask, How many tens have you counted? Could you have started anywhere in the picture?

 

Count on

Count back

Tens

Sequence

How many

 

Add, addition, more, plus

 

Sum, make, total

Continue

rule

number

 

 

Assessment strategy

Knowing number and being able to recite in order, counting on and back in steps of 10 from any number.

 

 

 

 

 

 

Pages ­­12 and 13: What’s in the Pot?

 

 

Application:

 

A ‘colouring in’ 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 multiplication 

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Know simple multiplication facts by heart.

Understand the operation of multiplication and the associated vocabulary

 

 

Activities

 

Vocabulary/keywords

Not all Year 2’s will have tackled multiplication at the beginning of the school year, so the vocabulary may be new to them. Talk about repeated addition, how 3 lots of 5 is the same as 5 + 5 + 5.

 

The numbers they need to recognise to follow the rules are shown in the left hand panels, and can be seen as number sequences adding in steps of 5.

 

They will already recognise (multiples of) tens as numbers ending in 0, this activity will show them that steps of 5, starting with 0, go up in numbers that end in 0 or 5.

 

Year 3 children will add this to the number facts they know by heart:

multiples of 100 end in 00,

Multiples of 10 end in 0

Multiples of 5 end in 0 or 5

Multiples of 2 end in 2, 4, 6, 8

 

Ask, What is the next multiple of 5 after 175?

What do multiples of 50 end with? (00 or 50)

 

 

 

How many

Add, addition, more, plus

Sum, make, total

Multiples

Factor

Groups of

5 times table

 

 

 

Assessment strategy

Confidence in number, recognising a pattern and understanding multiples.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pages ­­14 and 15: Doubling days

 

 

Application:

 

A story where Buzz has bought an extraordinary plant that doubles in size each day.

 

Questions about doubling 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.

 

Full solutions can be found in the online Answers.

 

 

 

 

 

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

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Understand the vocabulary double, twice, use known facts.

Understand estimation and approximation, make a sensible estimation of size.

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

 

 

Activities

 

Vocabulary/keywords

The story tells the reader just how quickly numbers grow when they are doubled: quickly responding to doubling is good practise, but it is soon realised the numbers have got huge.

The following questions follow this idea on, with some comparisons to real things like double decker buses, and famous landmarks.

A discussion of estimating height could follow: how many buses piled up match the height of a house?

How many of you reach the height of a door?

 

 

 

 

Doubles

Add, addition, more, plus

Sum, make, total

Multiples

 

 

Assessment strategy

Confidence in making sense of problems relating doubling and to measure, with a practical context.

 

 

 

Page 16: Curious Ruin

 

 

Application:

 

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

 

The Ancient Egyptian theme is completed with the scene of these ruins in Egypt.

 

(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 the building with three pillars? Is there anything odd about one of the shadows? Is there anything odd about the reflections? 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 sheets 7a and 7b: Sum Fridge (available online: see BUZZ Activity Sheets)

 

 

Application:

 

An investigation is presented by Buzz and Fizz, making number sentences with fridge magnets.

 

PDF’s of both worksheets are 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/buzzws7a.html

­­­­

 

 

­­

calculations: addition and subtraction

 

Resources required: pencil

 

Learning objective taken from the Mathematics Framework:

Find mental calculation strategies:

Use patterns of similar calculations

Use the relationship between addition and subtraction

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

 

Activities

 

Vocabulary/keywords

This worksheet is designed to be accessible to several Year groups.

The first worksheet gives three numbers and asks for four number sentences (one is given), a task suitable for Year 2 and up. If using in a class or group, encourage the children to say the sentences out loud. Using mental calculation strategies, they should soon be able to see that they are working with pairs that can be written as addition and then the corresponding subtraction fact, and vice versa.

 

The second set of numbers is deliberately easy, so that they will see the pattern and gain confidence in the task.

 

The second worksheet offers scope for some real investigation: Ask, how will they use what they have learnt from Activity sheet 1? For those who aren’t sure, ask, Which pairs of numbers sum to a third number on the fridge?

 

The exercise of recording their number sentences 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.

 

Extension: There are 16 sets using three numbers from the magnets. Can they work systematically and find them all?

(they are: 1,2,3   1,3,4   1,4,5   1,5,6   1,6,7   1,7,8    1,8,9   2,3,5   2,4,6   2,5,7   2,6,8   2,7,9   3,4,7   3,5,8   3,6,9   4,5,9

 

For older children: If the number 5 was added to the set 9, 2 and 7, how many more sentences can you make? What number would you add after that? Can you make sets using two digit numbers? What mental strategy can you use to do this easily with numbers like 19, 11?(rounding and adjusting by 1)

 

Add

Subtract

Total

Patterns

Number sentence

Different

Equals

Minus

Plus

Pairs

sum

 

 

 

Assessment strategy

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