Counting Machines Years 1 - 6

Summary The following series of activities embody the concepts of place value in a table top game. Because of the colourful, tactile nature of the material and the active hands-on modelling of sound mathematics, the games provide an excellent basis for learning about place value. Children become involved in a counting machine and discovering how it works to 'collect a point' in the chosen column parallels the way our decimal place value system works. If used over time with a variety of different 'size' machines, children abstract the key elements of place value and come to see our system as only one of many possible systems. The activity provides much more meaning for 'hundreds, tens and ones' than just manipulating symbols. Suitable for threading. Materials One Poly Plug set per pair - later, one each One set of digit cards or playing cards per pair Scrap paper

Acknowledgement

This activity was originally titled Collecting Points. It was renamed to be the same name as Maths300 Lesson 176, which it spawned. Learning can be extended even further by adapting the game to a giant plastic mat so that the children's bodies become the playing pieces. Whole body, kinaesthetic learning produces learning which lasts longer. For further information see Lovitt, C. & Clarke, D. (1988) MCTP Activity Bank Volume 1, pp 185 - 188, Curriculum Corporation, Australia. Reference to use of the plastic mat can be found at: http://www.mathematicscentre.com.au/taskcentre/mathmat.htm

Nine & Over: Adventures in Place Value from the Maths on the Move professional development library offers a full day workshop on the development of place value concepts and skills.

Machine of the Day

The height of the right hand column defines the machine of the day. It is numbered 0 to ... and the machine starts with plugs beside zero in all columns. The pack of cards of cards is modified to only contain these numbers. If wanted, a royal card can stand for zero. For example, the machine shown plays with Ace (1) to 4 and points are collected in groups of 5; if the collection group is 9, play with Ace to 8. The card pack is always one less than the collection group, just like our digit system is one less than the group size we collect for counting, ie: we collect to ten but record using digits to 9. The activity can be played in several ways: One machine between two and the person who moves the left column plug wins. For machines up to 5, the game can be played between two players each with their own red board. First to move the left hand plug wins. For machines from 6 to 10 it can be played between two teams of two players, each of which has two red boards.

Learning The Game

The key to the way the machine works is discovered when the right hand plug reaches the top of its column for the first time and has to count more points. Ask the children to tell you what might happen next. There is usually at least one who suggests that the plug in the next column has to move up one to indicate that there has been one travel up the points column.

Interestingly teachers seem to have more apprehension about this game (somehow thinking it is too complex for the kids) than do the children. Kids seem to think that the movement of a plug in one column being dependent on what happens in another column is 'kind of neat'. The slide show is of Year 1 posters explaining to someone else about the counting machine. A flick through these will convince you that children well and truly understand the supposed complexity of a counting machine.

Counting Machines in Year 1
(Use your arrow keys to change slides. Use Esc or Alt/F4 to end the show.)

Example: 0 - 2 Machine (Collecting 3 Points) Players begin with their red board masked as in the picture. That is, three blue 'people' representing zero in each column and empty spaces above them which they can move into. The board is placed on the paper and a frame is prepared as shown. It is important that zero is shown as the first row. Zero is a number. It counts the existence of nothing. The model is consistent with objects such as the odometer of a car and the counter on a video with which the children are familiar. When playing with collection groups of between 6 and 10 points, use two red boards, one placed above the other. The blue plug moves up each column as necessary to register the collection of points. When the blue plug reaches 1 in the left hand column, the player is finished.

Choosing a card always tells how many movements the machine makes in the right hand column. This amount is cumulative and when the right hand plug reaches the top and continues 'around' to zero to start again, a group of 3 is registered by moving the plug in the Groups of 3 column up one. Depending on the card chosen it may also be necessary to continue counting in the right hand column. For example the picture shown may have reached this stage by: 1 drawn on the first move. 2 drawn on the second move (which would make one group of 3 points and zero single points). 2 was drawn next to increase the collection total to one group of 3 points and 2 single points as shown. The game continues in this fashion until the first player counts a plug into the 1 space of the 3 Groups of 3 column.

Holy Rosary School, Derby ... Year 2 using 0 - 4 Machine

This player has made 3 trips to the top in the points column and is on the way to the fourth.

Four ... will that get us to the top again? More importantly, will it be enough to count up to the top and 'around' to the bottom again?

Discussion (over time)

• Lesson 176 to develop Counting Machines further.
• Lesson 35 as a 0 - 9 Machine (collecting 10 points) which includes an excellent piece of software to support the lesson.
• Lesson 169 as a human computer to model the 0 - 1 Machine.

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