
Ten Friends
Years K  1 
Summary
Children love to play this easytostate, easytostart game based on a ten frame. It involves children in predicting and checking addition facts to ten. Discussion is important and calculators are used to make a symbolic record of what is created. Children often want to extend the challenge for themselves. Suitable for threading.
Materials
 One calculator per pair
 One Poly Plug per pair
 One spot dice per pair


Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.
 Visit the Home Page for more Background.
 For this specific activity click the Learners link and on that page use Ctrl F (Cmd F on Mac) to search the task name.
Procedure


Content
Listed alphabetically.
Primary content in bold.
 1:1 correspondence
 addition facts beyond 10
 addition facts to 10
 complementary addition
 conservation of number
 counting
 estimating number
 group counting
 mathematical conversation
 place value
 problem solving
 recording  calculator
 recording  written
 subitising
 visual & kinaesthetic representation of number

 Alternatively, Player B may tell their guess then write the equation first to show they know the Ten Friend. However, a mathematician always checks things another way, so they now count in the blue plugs to confirm.
Once an hypothesis has been checked, players swap roles and play another round. They will want to continue for many rounds.
It seems teachers get excited about the activity too. These two responses appeared in the email almost immediately following a Working Mathematically with Infants workshop presented for the Mathematical Association of Victoria. You might want to find out more about our Professional Development programs.
Hi Doug,
Many of our teachers were enthusiastic after the PD. The prep team are very excited about making bug catchers. (see Aaron Peeters article below). David, one of our teachers trialled Ten Friends with his grade using glue stick holders and reversible counters.
Thanks,
Sarah, Yarraville West Primary School

Hi Douglas,
Ten Friends was awesome today. I teach Year 2s and, for some, this is knowledge that they have and they are able to readily explain their understandings. Having said that they were fully engaged and 'having a great time.' The questioning and discussions were really informative. Going to begin 'threading' this activity tomorrow.
Very excited!!!!!!!!
Carole Hall, Point Cook P9 College
Look! We Have Made...
If you choose to play the game without the calculator as a running record, then when a hypothesis has been made and checked by counting in, the children exclaim to each other: Look! We have made seven plus three equals ten. or whatever. They know which number was plugged first, because the dice hasn't moved. Then the plugs are removed and the game starts over swapping the roles of roller and guesser.

(Note: The exclamation Look! is considered important to refocus attention on the whole that has been created.)
When appropriate, using the question: Would you like to write that on your calculator? or Would you like to write that on your calculator like a mathematician?, encourages using the calculator to record that verbal statement. This form of recording is quicker than written recording and adds a visual and kinaesthetic representation of the symbol for the numbers and operation being spoken.
However, at another appropriate time, encourage written recording using the question: Would you like to draw a picture of that? or Would you like to write that like a mathematician might do it?. Illformed numerals will be part of this experience and a question like: That's a great seven you have drawn. Is it the same as the one on the calculator? helps children identify the differences and challenge themselves to try again. You also have the opportunity to ask: Would you like me to help your hand write it the way a mathematician would? 
Touch & Tell
Every Ten Friend situation is a potential discussion starter. Sometimes only, so the fun of the game isn't lost, use a completed board to generate more equations. This can be done sitting with a pair, or by using one of the children's boards as the focus of a teaching group discussion.
At the simplest level, expect children to 'touch and tell' number stories like those below. Later, expect the children to write equations which can be justified by touching the plugs in the frame. Plugs are not moved. For example, in the finished picture above you might see:
 5 + 5 = 10 (two zigzags)
 10  5 = 5 (cover one zigzag)
 10  5  5 = 0 (cover one zigzag then the other)
 2 + 2 + 2 + 2 + 2 = 10 (touch the yellow/blue pairs)
 5 x 2 = 10 (same way)
 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10 (touch each plug as you count)
 10 x 1 = 10 (same way)
 3 + 3 + 2 + 2 = 10 (first 3 blues and first 3 yellows each make a triangle and the twos are the arms of the remaining cross)
 ...
Variations
 See this activity used in a buddy situation in this Snapshot from Alexandra Primary School.
 Choose a finished board such as 6 + 4 =10 and ask children to explore and record all the ways they can arrange the plugs to still 'say' 6 + 4 =10.
 How many arrangements are there?
 How do you know when you have found them all?
Recording can simply be spots of yellow and blue in two rows of five on scrap paper, or you might design a record sheet. In either case, model the recording you want.
 Children soon begin exploring with more rows of plugs removed. Perhaps they will need two dice per pair.
 How about starting with ten plugs in the frame? Player A rolls to remove. Player B has to guess the number that's left and check by counting out.
 How do the children tell each other about what they have done now?
 How do they record it? On paper? On the calculator?
 Four red boards make 100 gaps!


Why did Aaron Peeters, Warburton Campus, Ngaanyatjarra Lands Schools, Western Australia make these Ten Friends houses. Find the answer in his story Learning to be Flexible with Numbers to 10 (PDF).

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