Counting On Years K - 1

Summary Children love using Poly Plug and purposefully including dice and calculators in the activity adds to their level of engagement. In this activity the aim of the game is ...for all of us to plug the gaps in our red board, but the aim of the teacher is to encourage students to become aware of the efficiency of summing two numbers by counting on from the larger one. Initially the activity is used with a teaching group, but once learnt, children can play it on their own. One child can be the 'teacher' and roll one of the two dice as described below. Suitable for threading. Materials One Poly Plug per child One calculator per child Two large dice per group - you might like to use one numeral dice and one spot dice Acknowledgement This activity is adapted from a professional learning DVD made at Geeveston Primary School as part of the Changing Places project of the Tasmanian Aboriginal Education Unit. Procedure Players push out three rows of red plugs to make a 3 x 5 array. Place these unwanted plugs in the bag. (Some teachers find it makes the next steps more efficient if, at this point, the children also push out the same number of yellow/blue plugs and make a pile beside them for later use.) Discuss the number of gaps which have to be plugged. How do we know there are fifteen? Can we check it another way?

I have rolled five and now... ...I have to count on 2 more ... 6 ...7

Player A: Rolls two dice. (Some teachers think it adds to the atmosphere of the activity if the teacher rolls one and the student rolls the other.) Decides which is the larger number and works out the total by counting on. (Which number is larger, yours or mine?) Fingers are a fine counting tool at this point and a visible number line helps with decisions about which is larger. Plugs in the total. Use one colour (say blue) first turn and next time round use the other colour. Checks on the calculator by entering [larger number] + [counted on number] = ... Teacher asks: How many more do you need to plug all your gaps? ... Think about whether you will use one dice or two to do it. This sequence is repeated by the other players in the group.

Content 1:1 correspondence addition facts beyond 10 addition facts to 10 complementary addition conservation of number counting numeral recognition operations - whole number recording - calculator subitising subtraction visual and kinaesthetic representation of number

Play returns to Player A who uses one or two dice to try to roll exactly what is needed to plug the gaps. (Now we all need to roll the number to finish plugging in our red board.) If a roll can be used it is, even if there is still more board to fill. If two dice are used, the counting on steps from above are followed. After one attempt to finish plugging the board, play passes to the following players who also try to finish plugging their board. Play continues from person to person around the group until all boards are plugged. Teacher asks each student what numbers they rolled to make 15. The alternating colours are a record. Some students may have only needed three numbers; some may have needed four or more. Children say their total to 15 as an addition. (Mine is six and five and four to make fifteen.) Each child checks their statement on the calculator. (6 + 5 + 4 = ...15 Yea!) The game is well managed with a whole class if the children work in groups of the 3. One is the 'teacher' or game controller. The others are the players. The 'teacher' rolls the yellow dice each time and passes the white dice to the next player when needed. The 'teacher' also has to always ask the question Which dice number is bigger? and encourage counting on from the bigger one. This organisation allows the 'real' teacher plenty of time to move from group to group questioning, encouraging and gathering assessment information. There are also many informal learning opportunities within the activity. For example, using the red board as a frame means the answer to How many more do you need to plug all your gaps?, a complementary addition question, is visual and countable.

Counting On can be threaded. That is, it is rich enough to use for a few minutes a day, 3 or 4 days a week over several weeks. The structure of the activity remains the same, but the challenge changes each time the dice are rolled. This process provides time for the students to construct their understanding of the mathematics without simultaneously having to interpret the changing environment of the 'teacher's new maths game today'.

Extensions

• Students draw a picture of their board on a Poly Plug Frame and record their calculator equation.
  (Note: to save hours of pointless colouring in, encourage children to draw around the circumference of each circle with the appropriate coloured marker. It helps to model this first on your own frame.)
• Teacher records each person's sum on the board and writes their name beside it.
  Look at all the ways we made 15 today. I wonder if there will be new ones next time we play.
• Expand the game to a starting array of 4 x 5 or 5 x 5.
• Consider playing the backwards game. Start with 15 yellow plugs in the board. Roll two dice and count on as above. Remove the total to reveal gaps in the red board. How many more must you take away to show all the gaps?
• Because her children so loved this game, one teacher combined it with reading site vocabulary flash cards. Each card had a number in the corner which was the point score for that card. Cards were shuffled in a deck in the middle of the group. Players rolled one dice, and took the top card. They had to read the card, then show it to the group who also read it. Counting on was based on the roll of one dice and the point score on the card.

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