It is, in fact, nothing short of a miracle that the modern methods of instruction have not entirely strangled the holy curiosity of inquiry.

# Maths for Under 10 Year Olds

Presented by Christel (06/07/09)

*These ideas and activities are offered here as suggestions and guidelines, for you to use as you see fit. They have been developed and used in real teaching and remedial situations.*

You don't need maths curriculum until 10 or 11!

You can waste money on it but most of what you need is in your home.

Make sure that your child is thoroughly grounded in numbers (0-9) and the concepts between numbers ('before' and 'after', 'backwards' and 'forwards', 'one more', 'one less' etc).

Addition and subtraction *must* come before multiplication and division. Children don't need to do times tables at 6,7 or even 8!

### 4-5 year olds

Casually use 'math' terminology with your children (just not 'plus' and 'minus' at this stage)

- before
- after
- backwards
- forwards
- one more
- one less
- too many

**SORTING & MATCHING**

Give this age group plenty of opportunities for sorting (colours, shapes, sizes, animals, groups), playing and matching (5 dogs to 6 bones = 1 left over ("so there are too many bones?").

** LEGO** is good!

**COUNTING**

Before they know what numbers look like, COUNT: How many leaves? How many stones? Then bring adding in with the counting (one more, one less etc).

Provide children with containers full of many objects of the same type: sticks in one container, feathers in another, counters in the next, pegs....and so on. Whatever you have in your house.

Let children set the dinner table - count out how many people will be sitting at it, how many plates are needed, how many knives/forks. Count out loud all the time.

"So if Aunt Martha and Uncle Bertie are coming for lunch, then there will be how many of us?" Answer. "And how many more with Aunt Martha?" Answer. "And Uncle Bertie?" Answer. "Great work so we need 'X' plates all together".

If you'd like to make round counters try:

- Cutting up a broom handle
- Poker chips
- Punching out floor tiles

Having these round counters in 2 (and only two) colours is an advantage.

How to use them:

Initially put only a small handful of these counters on the table. Suggest something like "if we want to make it more we need to add some" or "if we want to make them less we have to take some away".

**GUESSING**

These same counters can be used for estimation.

Take a small amount and say to your child "guess how many are there".

Write yours and their guess on a white board. Then count the counters with them.

Do it *rhythmically*, taking a counter away from the main pile, one by one.

Discuss how close each person was to the actual total. Congratulate them if they were the closest!

**SEEING NUMBERS IN GROUPS**

From a handful of counters in a jumbled pile on the table ask the child to draw away a certain number of counters in one go (not by counting them away one by one). Say "take 4 away". Children begin to see groups of colours. For "4" they may see 2 of each colour, a 1 and a 3, or all 4 of the same colour, consciously or not - it doesn't matter how they see them but that they are getting practise at seeing different representations of a number. You *can* talk to them about what they saw and how they saw the counters to take away.

Incidentally you can start writing number sums down way before they are doing them themselves. So if you are in the middle of a real life learning experience of adding 4 and 3 together, take a moment to write down the sum 4+3=7.

**DOT TO DOT**

Use those that are not too busy. Not up to 100 when they are little - keep it simple.

If you have a tape measure lay it out as they do a dot-to-dot and have them see the numbers progress left to right as they follow them around the image they are connecting.

**ABACI **

Abacuses are good. It is preferable to have 10 counters of the same colours in each row (instead of those with 5 of 2 different colours) as this better represents the base 10/decimal system.

**SMARTY CARDS**

So named as the dots on these cards look like Smarty's (or Pebbles).

These are cards with dots on them in patterns representing the numbers 1-9. They are modeled on the patterns of dominoes and die. (Here are a set of cards to download)

Start by shuffling only the cards with 1-5 dots. Give the child the cards to put in order on the table working from left to right. Take the top card and put it in the order of where it would be in the continuum. Don't let them flick through the cards to find the '1' and then the '2' etc. Don't make them count (let them if they want to).

So if the card number 3 is on top it goes in the 'middle' of the space

If 2 comes next then it comes 'before' 3

Use 'before', 'after', 'one more', 'one less', 'is it far away from 1' etc

Extend this by using numeric cards (see Fast Adding section below for download) and placing them next to the Smarty cards.

Stick with 1-5 until they are competent and then add 6-9.

Repeat the above with playing cards (not beyond 10 cards in sequence). Say "I am looking at number three", get them to point it out. Ask "who lives next door to number 3", get them to point it out or say it. "Who lives 3 doors down from number 3?". Child answers. "Who lives 2 doors up from 3?". Child answers. "So I have to jump 2 spaces to get to 5." and so on.

**SMARTY CARD VARIATION**

Use a larger surface area of card and place random groups of dots on the cards, in different places, shapes, sets, colours per card (these can be up to ten).

Show them to your child and let them tell you how many dots are on the cards.

(The set that Christel had, had 50 cards. She suggested that you wouldn't need 5 cards of the lower numbers as the random combinations are naturally less so make more cards of the higher numbers.)

Give them tactile experiences especially when they are not understanding anything at any level of mathematics.

**STAMP SHEETS**

Stamp a sheet with a few stamps each of 3-4 different items only, or use stickers. Get the child to count out how many of each same stamped image there are on that one page. Or use a book where they have to find out how many of something is on each page.

So on one 'Transportation' sheet you may stamp 4 trucks, 6 cars, 7 skateboards, 3 planes etc and would ask your child "how many cars can you see?" etc.

[INSERT IMAGE HERE]

You can do the same with 2 sets of grouped objects in a row and then a blank at the end too for the sum.

So a group of 3 apples on the left hand side and then in the middle of the card a set of 4 apples groups together, and finally on the right hand side a space.

Under each group you can have a box for the child to write in how many in each group OR use numeric cards or tiles instead (as you really wouldn't want to put your child off maths just because they dislike writing!)

This leads onto a card that in addition has the '+' symbol on it between the 2 groups of objects.

[IMAGE TO COME]

Children need to go through the "Counting all" stage (where they add 2 numbers together by starting at 1 and continuing on until they have the answer) and the "Counting on" stage (where they start with the whole value of the first number and count on from there the value of the second number to get the answer) *before* continuing on to adding and subtracting up to 5.

When a child can "count on" with ease and uses "counting on" when doing calculations, that's when you start introducing number bonds.

**SERIATION**

Different cards for getting a child to 'see' numbers 'before', 'after' and 'between'.

Card One

A card with numbers down the middle and spaces on each side so they have to say what comes before and what comes after.

_7_

_5_

_6_

_9_

_4_

_3_

_9_

_2_

Card Two

A card with numbers on the outer sides with a space in the middle, so they can say what comes between.

7_9

4_6

1_3

3_5

2_4

5_7

8_10

6_8

Card Three

A card with various amounts of items illustrated on each line that the child then still needs to add something to it to sum to a certain number.

So for the card adding up to 5 it may have the following on the left hand side (while there is a line down the middle creating a second column on the right which is blank)

xxx

x

xx

xxxx

xxxxx

x

Use counters and ask the child to add however many to the blank space on the right to add up to 5.

Card Four

Missing number card A

_ 2 3 _ 5

1 2 _ 4 _

1 _ 3 _ 5

_ 2 _ 4 _

_ 2 3 4 _

1 _ _ 4 _

1 _ _ _ 5

Card Five

Missing number card B

_ 7 8 _ 10

_ 7 8 9 _

6 _ 8 9 _

6 _ 8 _ 10

6 7 _ _ _

_ _ _ 9 10

Here are a set of the above 5 cards to download

### WHEN THEY CAN ADD up to 5 and 6 then focus on:

#### Number Bonds / Partners

Number bonds at this level are simply the relationship of the 3 numbers that together make up an addition or subtraction sum. These 3 numbers can be used in various orders and with both - and + .

ie 2+4=6 4+2=6 6-2=4 6-4=2

You want the child to see the 'bonds' or 'partners' of the equations whatever sum they are doing inside out and upside down.

Here is set of templates [1, 2, 3, 4, 5, 6, 7 ] that can be used for worksheets for number bonds and any of the following activities. (Note: these can be used from beginning math upwards beyond 10 years old)

For number bond practise using these worksheets, fill in 2 of any 3 numbers that have a 'bond' and let the child fill in the answer.

**ADDENDS AND MINUENDS**

These can be taught *alongside* number bonds.

Start with adding just +1, +2, +3 to 0 - 9 (use the templates on the above sheets).

Trying using a dice with 1-3 2 times on it to choose your number to add.

**COUNTING ON REVISITED**

Use bingo chits to randomly select numbers to count on from (for the sheets) or polyhedral dice (different numbers on sides)(see stationery store or children's toy/game shop).

Give them a tape measure so they can count up and down and see the counting on at the same time.

**FLOWER GAME**

Roll 2 (normal) dice - if the sum (by either addition or subtraction of the dice) of one or the other answer, is on the flower, you jump to the next flower. If both answers are on the flower then jump to the next flower AND roll again. (Christel has offered to organise a colour photocopy of this board game board at cost for those who contact her.)

This game works best using die with numbers on them, not dots. Re-position the die when presenting them to the child to do the sum, so that the numbers are up the right way.

The aim of maths is to make them love numbers and manipulate any number that you give them.

**FAST ADDING CARDS (PARTNERS)**

Make yourself or download from here a sheet of numbers from 0 - 10 in 2 different colours.

Decide what number you want to drill and lay the same amount of cards on the table in front of the child, aligning them top to bottom but *not* in order.

So if the number is eight - then put down 8 cards, if six then 6 cards.

For the later example you may lay the cards down in the order: 2,6,1,5,3,4 or 4,1,6,2,5,3 etc

Give the child the second set of coloured numbers (equal to the chosen drill number so if 6 cards are laid on the table then 6 cards are also given to the child) and a number to add up to. Then they have to put the second number from their 'pack' next to the first number to add up to the given sum, as fast as they can.

You can do the same with 2 sets of coloured playing cards.

Do this all the way up to summing to 9.

### When you really get to adding and subtracting...

...then you want to drill it - you want those numbers to be stuck in their head - up to 10.

**BUBBLES 'GAME'**

Make a series of large (≈ 5 inch/12.5cm diameter) round 'bubbles' with addition and subtraction sums (up to sum of 9) written on them or download this complete addition set.

5+1

6+2

7+2

8-0

6-3

These can be used in a variety of ways.

- Put the 'bubbles' on the carpet. Get the child to throw a bean bag (or whatever you have) onto the bubble on the floor (for whatever number you call out).
- Make a set of fish with the 'answers' on them and have the child match the bubble up with the fish.
- Place a counter on which bubble equals a certain answer you call out.
- Use them as some form of Hopscotch. Call out the numbers and have the child jump from one answer to the next, or get them to jump from one to the next in numerical order of what the answers are.
- Whatever you make it!

**DOUBLE AND HALVES**

Start asking questions that require a child to double or halve something.

Initially up to 9 then up to 20, and then 30 and so on.

**TIPS **

Bring in written words for numbers only when children are getting into reading not before. Use the numeric card and get them to put the numeric card beside what they are counting instead of writing.

Natasha recommended the 'SET' Game.

Christel has packages of photocopies available for all times tables which she is offering to anyone who wants to borrow them on a cd.

Christel recommended the Smart Kids 'Smart Multiplier' for those kids who want/need to get on with maths but don't want to be held back by not knowing them thoroughly.

**Christel is more than willing to have you contact her for clarification or advice on anything that you read here or have heard her speak about.**

### Extra Unrelated Note:

*Learning to write*

Use a blackboard for children to write on as it gives resistance, with a stubby piece of chalk (so they develop a triangle grip), not a whiteboard with a marker. As with pencils on paper not a pen at a young age.

Lyra Ferby Pencils recommended by Cathy - short, triangular, thick, doesn't break, etc , etc approx $2 each from Humanity (members see the discounts page for more information).