Counting & early calculation skills workshop

• In order to be able to calculate [add, subtract, multiply, divide……] children need to be able to count accurately and meaningfully…..how can you help?

• Children need lots of practical activities to help them practice counting and calculation ..…a chance to see and try some of these……..

• Knowing “number bonds” and learning about “place value” form a key part of early calculation activities……so what is involved?....

Counting by rote

From an early age children use numbers as labels, counting out loud using number names they know.-often re-use known number names e.g. 1-2-3-4-5, 1-2-3-4-5, 1-2-3-4-5……… -progress to pointing to objects as they count, but not accurately.- say number names in order (…but not necessarily know their meaning/value). Children can often do this from quite a young age.

Use some number names and

number language, but not accurately

http://www.youtube.com/watch?v=KnBwm6U4Ibk- with a bit of adult help this child counts up to 50 - it is likely that she is actually ‘rote counting’- there is a big difference between rote counting and counting objects reliably and meaningfully

Meaningful [“rational”] counting

• Rational counting is counting that has meaning associated with it

• The child understands that the number name is connected with an actual value or amount of something – they know “how many”

• The child can not only say the numbers in order but recognise that 2 actually means 2 objects, 3 means 3 objects and so on

• Your child will need to understand several concepts before they can count rationally………

One-to-one correspondence

Children learn that each number name in the count relates to an object. “point to each object as you count” – manychildren tend to rush ahead and say the next number name faster than they point to the object. TIP 1: get them to move [count out] the objects one by one as they count.TIP 2: don’t ask your child to count more things than he can count easily and with success

http://www.youtube.com/watch?v=hgT0AwHVgxw

Count up to three or four objects by

saying one number name for each item

Dot Dice are a fun way to practice

ask your child to:

•roll the die,

•count and state the number of dots

•find that number of objects, or do the same number of jumping jacks/hops/ claps/stomps etc.

TIP:

Use 2 dice as your child progresses to higher numbers – also a great introduction to number bonds and addition concepts [more on this later]

Use Numeral Dice to help your child to recognise numerals – and match those

numerals to the correct number of objects

You: "Roll the die.“Child (rolls die) You: "What number did you roll?"Child: "Three!"You: "Can you get me three balls?“

Child: (moves balls into a group) "Here they are."You: "Great! Can you count the balls?" (This is a good way to get them to double-check what they’ve done)Child: "One, Two, Three!" (touches a ball for each number said)You: "Excellent counting! You were very careful. I like how you touched a ball each time you said a new number.“

TIP:

Use dice with higher numbers as your child progresses

’Jake, I wonder how many beetles are in the jar?’

Jake counts ‘1, 2, 3, 4’. ……

‘So how many are there in the jar?’

Jake replies, ‘1, 2, 3, 4’.

When asked the question ‘How many?’ children will initially repeat all of the numbers in the count. This can be very frustrating, but it’s totally normal.

With more experience, children will not need to count again, but will just say the last number in the count.

Cardinality: The ‘are we there yet?’ of the maths world – has this ever happened to you?.....

TIP: Get Sorted!! - Sorting is a fun way to encourage

your child to make collections of objects and say how many are in the set, giving them the vital

experience that they need. Practice makes perfect!!

Comparing numbers

Early calculation skills can be practised with your sorted setsUse sorted sets to match, compare, say which is more/less, how many more or less etc.

Or have some fun with computer games and APPs - there are so many good ones to choose from:

http://www.ictgames.com/mucky.html

Conservation of numberConservation of number is the stage where the child knows there are the

same number of objects in a group however that group is structured.

When your child makes and counts sets of

objects, re-arrange the objects and ask ‘how may now? – they will soon get the idea!!

A child who hasn’t yet developed this concept will say there are more in the second row.

Meaningful [“rational”] counting

Counting is MUCH more than remembering numbers and recognising numeralsHow you can help:Spend as much time as possible using real objects [including bodies!!] to practise and consolidate key concepts:

1:1 correspondencecardinality

conservation of number

Children need to be able to count confidently and meaningfully to do calculations.

Count reliably up to………..

everyday objects

Enough!!

……….of Heather talking……………………………

................let’s have a look at different equipment that can be used to develop counting and calculation skills……..

CountersTake a handful,– how would you use the counters to help your child practice some different counting/calculation skills?

Number fans- great for quick mental recallGreat resource in the classroom because:• Children LOVE being able to do as well as think, and all children participate (also

easy to spot those who have 'zoned out' and get them back on track). • It is easy to see if children are having trouble with a problem – they respond slower

or look around at what others have done.• Children can see what others have answered, and decide to review their work if they

think they are holding up the wrong answer. • Scaffolding/reminders about strategies can be given while children are thinking

through their answers or finding cards.• No marking is required! Things you could ask:

Counting and number recognition:How many fingers am I holding up? Show meShow me the number that comes before ? [or after ?, or between ? and ?]Hold up a number bigger than…… [also use more than and greater than]Smaller than…… [also use less than]Hold up an odd number an even numberHold up a two digit number…a three digit numberAnd calculation practice:Hold up 1 more than 7… now 1 more than that … now 1 more than that…Hold up double 6 [doubles to 10]Half of … [halves to 20]Hold up a multiple of 2, 5, 10 [other tables]

White boardsCan be used for many of the number fan counting/number recognition activities on the previous slide, but more versatile and handy for problem solving, investigative and mental calculation activities. e.g. Work with a friend and write down all the even numbers between ? & ? Which 3 numbers come between ? and ?Write the answer to the following sum [given verbally]:Work together to write down 3 different ways to make 10. Can you use more than 2 numbers? Can you use a subtraction?How many 5p coins could I swap for a 50p coin?Can 8 be shared equally between 2?

Number lines

Lines of different lengths are useful to show children that numbers go beyond 10 and to show number sequence and how numerals are written. They are a great way to practice counting on [addition] and back [subtraction] from any number

The Hundred Square

Remember this100 square? Did you have any theories about the ‘pattern’ shown?

It was actually random pairs!! - coloured in this way to practice comparing number values

For more information, click here …http://www.theschoolrun.com/greater-than-less-than-symbols

And for those of you who spotted some prime numbers in there, here’s the ‘sieve of eratosthenes’ – yet another way of using the 100 square format!!

Want these resources?

http://www.sparklebox.co.uk/maths/counting/number-lines/#.VBievpRdWE4

http://www.sparklebox.co.uk/maths/counting/number-lines/number-tracks.html#.VBie75RdWE4

http://www.sparklebox.co.uk/misc/other/cutout.html#.VBifJpRdWE4

http://www.sparklebox.co.uk/maths/numbers/number-fans.html#.VBifWZRdWE4

Number bonds provide a mental picture of the relationship between 2 numbers. These mental pictures are the key to enabling your child to do mental arithmetic. Knowing addition number bonds means that your child will understand subtraction with ease. If they know that 3+4 = 7 they will quickly realise that when they see 7-4 = ?, the answer is 3 because by a process of elimination 3 is the missing number in this number bond. It helps children to see that subtraction is a mirror image of addition. They begin to see the patterns in numbers and to learn mathematical principles rather than having to memorise each individual sum. Number bonds are the foundation blocks your child needs to progress with maths. Once they know all of the number bonds for 1-10, they will have the information they need to subtract using the numbers 1-10

Number Bonds (addition facts)

Examples

Investigations & missing number puzzles[early algebra]

How you can help

• Use real objects to allow your child to explore number relationships – find different ways to make a total

• Encourage them to write or draw what they find• Stretch and challenge – if I have 10 muffins and I

eat three, how many will be left…….etc

More ideas?http://letsplaymath.net/2007/01/13/number-bonds-

better-understanding/

Why are number bonds so useful?

• Number bonds let children see the inverse relationship between addition and subtraction.

• Frequently used during mental calculations

e.g. 32+25= or 27+17= or 45-7=

• Used to derive other facts – if 3+7=10 then 30 + 70 must equal………..

4 + 2 = 6 2 + 4 = 6 6 – 4 = 2 6 – 2 = 4

Place valueWe count using a ‘decimal’ column system

[remember “hundreds, tens, units”?]

We use the same 10 digits but their value varies depending on which column they are in.

“place value” describes the value of any digit in a number – for example in 48, the 4 is worth 40 [4 tens]

Children need to build their understanding of place value in order to be able to work with larger numbers [beyond 9]

Place Value Chart

Place value arrow cards – children can use these to build up [and partition] 2, 3 & 4 digit numbers

They are a brilliant tool for reinforcing the place value of any digit in a number – very important when they do mental [as well as written] calculations