BUZZ    TeacherŐs Notes Volume 5/Number 14 (March 2012)

 

Cover: Match the parasol

 

Application:

 

A puzzle that requires finding which two parasols are an identical pair.

 

 

 

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 delicate parasols all look very similar at first glance. Encourage the child to look carefully at the first one and then look along the rows to spot the differences. It may be noticed that only number 5 has an empty right hand corner, as in number 1, but the bird has changed to a butterfly. This eliminates numbers 1 and 5 quickly. A systematic method will help find the pair. Suggest looking at the sections on the parasols to see the difference between numbers 6 and 10.

Ask, how would you describe the positions?

 

Matches/ Same/ Difference

Left, right

Top, bottom

Over/above

Under/below

Next to

Beside

Pair

Identical

 

 

 

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 sum pairs, and contents 

 

 

Application:

 

The theme of Issue 14 is hundreds, tens and units.

 

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

 

The Puzzle cats hold up the Japanese symbol for 5,

whilst the Buzz kids show the other symbols for 1 to 9. As well as matching pairs that make ten, there is a panel to fill in with Japanese symbols.

 

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 and draw another set of symbols for numbers: Japanese numbers are very different to Hindu-Arabic, and demonstrate how numbers have developed in other cultures. A single stroke is the earliest and most obvious way to record a unit, and can be found in many systems (Roman and Egyptian, for example) as well as in a tally.

 

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

Number

Symbol

Tally

 

 

 

 

Assessment strategy

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

 

 

 

 

 

 

 

 

 

 

Pages 4 and 5:  Round to ten

 

Application:

 

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

 

There is a panel to fill in and a chance to check the estimates with the total.

 

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, give a sensible estimate for a number of objects, understanding and using the vocabulary of estimation and approximation.

Use mental calculation strategies to solve a problem.

 

 

Activities

 

Vocabulary/keywords

Six of the Buzz kids have a speech balloon that has a box to fill in with an estimate of the number of things on the shelves. This activity will be manageable for all levels, as the numbers are easy to count, but as an exercise it introduces the idea of rounding and to make estimates. Before the children start, you could ask them to choose the box in the panel on the top right which they think has the nearest total to their guess: they could revisit their decision as they work through the speech balloons, as the estimates the Buzz kids make will help with this decision.

 

Making estimates by rounding number is an important skill, as is understanding when to round up or down, to the nearest ten. Younger children may well need help with doing this, but should be within the scope of Year 2 and 3 children. A column of boxes gives the opportunity to add all the estimates together, to compare with the guess made. As a counting exercise, can they then check how close the estimate total is to the actual number of items in the shop? It may surprise them to realise the estimate is very accurate on this occasion.

 

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 5Ős, 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? Ask how the estimate can be made (seeing three rows of three dolls plus two, for example) and talk about strategies for getting estimates.

 

 

How many

Round up

Round down

Estimate

Less than

More than

About

Nearly

Approximately

Close to

Roughly

Rows

 

 

 

 

 

 

Assessment strategy

Being able to solve word problems in practical contexts, and use the information to answer questions about estimates shows good reasoning.

 

 

 

 

 

 

 

Pages 6 and 7: Colour around

 

 

Application:

 

Moving on from rounding up to 30 with six fairly easy challenges on the previous pages, this colouring puzzle consolidates the idea and goes up to 50.

 

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.

 

 

Rounding with numbers up to 50

 

 

Resources required: coloured pens or pencils: orange, red, yellow, blue and green

 

 

Learning objective taken from the Mathematics Framework:

Round to the nearest 10, understanding and using the vocabulary of estimation and approximation.

Read and understand numbers. Know what each digit in a two 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 younger children may also be able to tackle it with a little help. Before a younger child starts, write down the numbers by each colour that he or she will have to use in the key.

 

Ask a Year 3 reader, could you round three digit numbers? Is 443 closer to 400 than 500? What do we do with numbers that end in 5, or 50 (450 for example)? The Puzzle cats on the spread help with their explanations.

 

 

How many

Numbers

Tens

Ones

Two-digit

Zero

Half way

How many

Round up

Round down

Estimate

Less than

More than

 

 

 

 

 

 

Assessment strategy

Confidence in reading and understanding rounding up or down with numbers under 100.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pages 8 and 9: Counting fish maze

 

 

Application:

 

A maze that requires finding a strategy of counting in tens.

 

Buzz and Fizz have to find a route where they have a number divisible by ten when they reach the last bridge.

 

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 fives and other pairs that make five, in order to make tens.

 

 

Resources required: none

 

 

Learning objective taken from the Mathematics Framework:

Count reliably a set of objects.

Recognise groups of five and using them in addition.

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.

Although there are a few groups of fish that are not in fives, the reader may soon use the strategy of looking for fives to make tens.

 

For older children, this introduces the concept of multiplication, 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. It also illustrates that 4 x 5 is two lots of ten. Not all Year 2Ős will have tackled multiplication at the beginning of the school year, so the vocabulary may be new to them. Talk about repeated addition, how 4 lots of 5 is the same as 5 + 5 + 5 + 5.

 

Towards the end of the maze, they will have to find two groups that make 5 (a two and a three) to make 45, enabling the boat reach the bridge with 50. Other routes are five short.

 

The question, Is your total divisible by 10? could lead to asking, How do we know when a number divides into ten exactly?

 

 

 

Count

How many

Addition

Fives

Tens

Multiply

Divisible

Exactly

 

 

 

 

 

 

 

Assessment strategy

Achieving an understanding of number 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: Sum bowls

 

 

Application:

 

This puzzle looks at adding in round hundreds (or tens) to resolve it.

 

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 system, working in hundreds.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Understand the operation of addition and related vocabulary, recognise that addition can be done in any order.

Understand that more than two numbers can be added together.

Develop mathematical ideas and methods to solve problems.

 

 

Activities

 

Vocabulary/keywords

The colour coded system of pricing the bowls by their colours is sometimes found in Sushi Bars, where the food is on a conveyer belt and the customer can choose to take a bowl off the belt.

 

Although it is usually Year 2 that tackles hundreds, with a little help younger children should also be able to tackle this activity, simply by suggesting they can think of the numbers as tens for the purpose of adding, to discover how each Buzz Kid has spent his or her money.

­­

This is an opportunity to make combinations of hundreds (or tens) to reach the additions each Buzz kid tells has been spent. There is only one way to make 400 with 4 bowls.

 

Extension: ask, what other combinations could make 400 if there was a different number of bowls (for example, 3)? Can they find a set of three bowls that could be made up in two or three different ways? (eg 3 bowls adding up to 600 could be: 3 lots of 200 or 100, 200 and 300). An investigation could be made looking at all the combinations possible with a maximum spend of 900 yen. Which totals have the most possibilities?

 

Count on

Count back

Tens­­

How many

Add, addition, more, plus

Sum, make, total

Number

Combination

Altogether

Total

Equals

 

 

 

 

Assessment strategy

Confidence with adding in hundreds or tens, problem solving and being able to add three numbers mentally.

 

 

 

 

 

 

Pages ­­12 and 13: Up in tens

 

 

Application:

 

A Ôdot to dotŐ 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 adding in tens 

 

 

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.

 

 

Activities

 

Vocabulary/keywords

 

This activity presents the familiar dot-to-dot activity that most children will know. This is immediately more challenging as they are told to start at 10 and reach 1000. They will gain practise in recognising 3 digit numbers and place value.

Younger children will benefit by being guided to the numbers as they go, so as not to get confused which number comes next, once the 100 boundary is crossed. Help them by focussing on the ÔtensŐ in the 3 digit numbers.

Ask, How many tens have you counted? Could you have started anywhere in the picture? Could you have started at 1000 and gone backwards?

 

 

 

How many

Add, addition, more, plus

Sum, make, total

Multiples

Factor

Groups of 10

10 times table

2 digit

3 digit

one hundred

one thousand

 

 

 

Assessment strategy

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pages ­­14 and 15: Bunch munch

 

 

Application:

 

A story where Buzz eats grapes, adding on one more each time.

 

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 adding on in consecutive numbers in a story context.

 

 

Resources required: pencil

 

 

Learning objective taken from the Mathematics Framework:

Adding, understanding that more than two numbers can be added together.

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

 

 

Activities

 

Vocabulary/keywords

The story illustrates how numbers grow when consecutive numbers are added together.

 

The question on page 15 is challenging: Year 3 children should be able to tackle this and younger ones may need to see the numbers written down and given help with handling the problem. Talk about there being one more grape each time (which corresponds to the number of trips) and remembering the total from the trip before to add on the number of grapes, say, on the fifth trip  (10 + 5) or the sixth trip (15 + 6).

 

 

 

 

Add,

addition,

more,

plus

Sum, make, total

In order

Consecutive

 

 

 

Assessment strategy

Confidence in making sense of problems relating consecutive numbers, with a practical context.

 

 

 

Page 16: Curious landscape

 

 

Application:

 

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

 

The Japanese theme is completed with the scene of an ornamental landscape. Throughout the magazine a little mechanical robot from the Japanese shop (pages 4-5) can be found.

 

(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: is that a parasol or a tyre? What can you see in trees? 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: Buzz14act1.pdf (available online: see BUZZ Activity Sheets)

 

 

Application:

 

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

 

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/buzzws14.html

 

­­­­

 

 

­­

calculations: addition and subtraction

 

Resources required: pencil

 

Learning objective taken from the Mathematics Framework:

Know by heart addition facts and understand that more than two numbers can be added together.

Use patterns of similar calculations.

Problem solving: deciding on a method or tools to complete the task and find mental calculation strategies.

 

Activities

 

Vocabulary/keywords

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

Adding three numbers together is a task suitable for Year 1, with a little help (choosing two numbers and asking them to find the third) but it would be working at a high level if they can explore all the possibilities.

 

For Years 2 and 3 this offers a good investigation and consolidating knowledge of the addition pairs of numbers under ten. If using in a class or group, encourage the children to say the sentences out loud. Working in pairs is also productive, as sharing knowledge helps both children. Using mental calculation strategies, they should soon be able to see that they are working with pairs that they will begin to know by heart (such as 2 + 3 = 5, 2 + 4 = 6). There are four sentences that use different numbers: 1 + 2 + 7, 1 + 3 + 6, 1 + 4 + 5,  2 + 3 + 5. 

 

The second challenge, allowing them to make doubles in the sentences, completes using some addition double facts they should be very familiar with by the end of Year 2. This will give them 4 extra sentences to work with (1 + 1 + 8, 2 + 2 + 6, 3 + 3 + 4, 4 + 4 + 2). Zero could also be added to the possibilities (making another 4 unique sentences, such as 7 + 0 + 3 = 10).

 

Putting the same numbers in a new order to make a different sentence is also a good exploration: can they predict how many ways each set of numbers can be rearranged? Realising there are 6 ways to write each sentence (4 ways if the sentence uses a double) will help them see a pattern and gain confidence in the task. Listing numbers in this way is looking for combinations that make 10. This consolidates the fact that addition can be done in any order.

 

The exercise of recording their number sentences is useful: it is easy to repeat a sentence, so learning how to organise oneŐs work will encourage a systematic approach to investigating patterns of similar calculations, and lead to mathematical understanding. A second print out of the worksheet will be useful, as there is the potential to find 64 sentences.

 

In the first challenge there are two numbers that canŐt be used (8 and 9), and in the second challenge only one (9). Ask them to explain why this is in their own words.

 

Extension: Using two sets of magnet numbers, can they find all the number sentences with two additions that sum to 20? (You could begin by asking the class to recall all the pairs that add to 15 (11 + 4, 10 + 5, 9 + 6, 4 + 11, 5 + 10, 6 + 9). This would be excellent practise for Years 3 and 4, and leads to knowing pairs of other two digit numbers (such as 19 + 19 = 38) and making sums to 30, 40, 50...

 

 

Add

Addition

Total

Patterns

Number sentence

Different

Equals

Plus

Pairs

Sum

Doubles

Set

Combination

 

 

 

 

Assessment strategy

A confidence in recognising addition pairs, doubles and sums to 10. Discover mental calculation strategies.