Theories and goals of education don't matter a whit if you don't consider your students to be human beings.
Maths  Double Digits and beyond
Presented by Christel (03/08/09)
This is session two, following on from last month.
As an Aside Christel took metre lengths of cotton tape and marked various class sets with an arbitrary marking/stamp at a specific length. Ie a mexican boy may mark 75cm on one tape, a bunny rabbit may mark 72cm, a tree 78cm. She would get the children to go around the room and measure objects, recording their lengths in boys, rabbits or trees. A discussion would ensue about how we needed a uniform unit of measure if we were to get the same results as each other and then she'd introduce metric system.
FLASH CARD 'Speed' Carrying on from adding and subtracting up to 9, make a set of flash cards with adding and subtracting up to 10. Aim for the child to answer 30 cards in a minute. Start by using cards 05, then add in 6, then 7 etc until they get up to 9. [For addition use the 'Bubble' cards from the first session or this plain set here
Subtraction cards downloadable here It may take a child weeks to reach 30 correct answers in a minute. That's okay! Focus the child on the best score each week/session (and note it on a chart perhaps) Record the best all time score as the score to beat – if a child has a bad day and their score technically goes backwards – keep it where it is – their best score is still their best score!
FLASH CARDS II Use flash cards with a gap/box instead of one of the 2 addends (it doesn't matter whether its the first or the second. Ie 8 + □ = 10
Adding to Ten When starting to add to 10 and you are using manipulatives, make a big thing of adding what you need to get 10 and then add the rest. ie 8 + 3 => add 2 manipulatives to 8 to make 10 and then add another 1 to make 11.
Drum roll please........
Introducing 10 Take the beaded pipecleaners (see 'Number Rod Manipulatives' below) and show them 10. Show them the Flard card for 10 (described below and to download). Then for other numbers eg 33, show them that 33 is 3 ten's sticks and 3 unit's sticks Use the 30 Flard Card and the 3 Flard Card and lay the 3 over the 30 (in the one's column) allowing the child to see that the 3 in the ten's column is actually 30 not just 3.
Continue up to thousands, hundreds if you have got them, using tens, hundreds, thousands groupings of beads or unit blocks.
FLARD cards
These are cards where the numbers are positioned on the card in their appropriate columns (with 0's as placeholders) and each card is staggered in their size so the can be overlaid over each other.
0  9
10,20,30,40,...
100,200,300,400,...
Here are some that I have from a Montessori Resource that I had on my computer in two different sizes.
One, Two, Three, Four, Five, Six, Seven, Eight
NUMBER 'ROD' MANIPULATIVES
While you can buy wooden units, tens, hundreds and thousands manipulative, you can also make your own out of a length of pipe cleaner threaded with 10 beads (of the same colour) each. Make 9 or so of these and also have at least 10 single beads.
Grouping in Tens Use containers of objects that can be counted in different colours: counters, feathers, pompoms, coloured ice block sticks, carbouchons, pasta etc. (Label the name of the objects on the container so spelling isn't an issue) Get the child to group them into 10's with the units left over and then write it up on the following chart. Counters Sheet Or another chart puts it slightly differently and introduces the written number too. Tens and Ones Sheet
Counting and adding beyond 10 (up to 19 at first, not 20) Start with easy stuff 10 + 2 = 12 10 + 3 = 13 10 + 4 = Then move on to more difficult numbers eg 6 + 8
Put 8 counters on one row and 6 counters on another row. Take 2 counters from the 6 row and add it to the 8 row to make 10 Then 16+ 8 – they can see that they can make 20 + 4 etc
SUBTRACTION [Make sure that children know their doubles and halves.] ie 16 – 8 = then 16 – 7 Use the 'make a 10 card' so 16 – 7 if you take 3 from the 10 to make a 10 with the 7 then you need to add the 3 to the 6 – therefore 9 so a 10 + 9 = 19 Or go with whatever method you like!
CARDS + CARD GAMES Play lots of games: Playing cards Skipbo Phase 10 UNO Counting in 2's, 4's, 8's. 5's, 10's, 20's etc (perhaps in sets of like steps) Perhaps 2, (4), 5,10,11 (as these are all quite easy.) Colour in/put a counter down on an hundreds board to see the repeats.
Things Christel has to borrow and photocopy Maths Fun books – Christel has these if someone wants to photocopy them for themselves. We looked at scanning these but it would not be that easy to print these off again back to back to make the book.
Christel also has:

Unusual dot to dots worksheets (To Be Uploaded Still)
Starting with a certain number and counting on.  Dinosaur Digits worksheets
 Cats Tails worksheet
Worksheets from first lesson You can use these too.
Decide your 'magic number' Turn up a card. The child has to decide what number has to be added or subtracted to get the 'magic number' that day. Write sums on a board and cover an addend with a counter – child guesses then it is revealed to themselves
Calculator games 21 Two play with one calculator in pairs Child 1 punches in a number (19) and a + Child 2 another number and + Child 1 adds another and then = / + Winner is the first to get to 21
Nominate a number eg 32 B punches in a number A must punch in a number to equal 32
Place value calculator game Choose a number eg 213 What must be punched in to get 213 using only 100's, 10's and 1's.
Supermarket brochures Give them a list and let them go shopping with the items on the brochure to a certain value Or collect the back to school brochures and the list of supplies for the year and let them shop around and then go to that place to get them.
Number Monopoly (Christel has) This is hard to describe but is essentially a Monopoly board game but with various combinations of maths problems along the way, and maths choice cards in the central packs. Best that you ask Christel to see hers, as I didn't think to capture her demonstration on video on the night!
Other concepts to slip into Early Maths: Sharing (dividing) Odds and evens Rounding
Also recommended but no longer available new is “Trek” by Spears as this combines much of the Early Maths concepts covered here.