Uncover Counting Years 2 - 6

Summary All children, or pairs of children, make the same array of plugs down the board, for example, rows of three. Boards are joined on a community floor space to make a 'giant' array. The floor array is covered with a cloth and revealed one row at a time after children predict the number of blue plugs that can be seen. In how many ways can you convince me that the number of blue plugs is...? Suitable for threading. Materials One Poly Plug per child One calculator for each child One piece of butcher's paper or equivalent for the teacher to cover the plugs - a small table cloth works well.

Each person's rows of three has a place in the class's rows of six.

Procedure Use the yellow/blue board and ask the children to turn over a certain number of plugs in each row. The example below is in on the assumption that each child turns over five in a row.

Content counting group (or skip) counting mathematical conversation multiples, factors & primes multiplication - array model operations - whole number order of operations pattern recognition recording - calculator recording - written times tables visual and kinaesthetic representation of number

2. Ask all the children to bring their boards to the front and line them up on the floor in twos.
   

3. Cover all the plugs with a large piece of paper or a cloth.
   

   How many blue plugs are showing now?
   Write that number on your calculator.
   OK, I am going to slide this cover back just one row. Can you guess how many blue plugs will show?

   Ask for responses (Whisper to the person next to you the number of blue plugs you think you will see.) then slide the cover back to reveal:
   

   Ask one child to count the blue plugs to check and then ask others to check the number a different way.

4. So there were zero blue plugs showing and now I have added on 10 blue plugs. How can we make the calculator add on 10?

   Check that each student presses +, 1, 0, = and gets 10 as the screen result.
5. Ask the children to predict the number of blue plugs which will show when the cover is slid back one more row. Again have the number checked by counting in more than one way.
   

   Also ask again how to make the calculator add on one more ten and ensure the children repeat the pressing of +, 1, 0, = to obtain 20 on the screen.

6. Repeat the process again sliding back the cover to reveal one more row and asking for predictions, checking of predictions and symbolic representation on the calculator.
   

7. Continue the process over and over, always encouraging the children to stretch just beyond their current confident counting limit.

At other times teachers use the calculator in parallel with the activity not for the serial counting aspect, but to symbolically represent the equations the students are suggesting when they justify the revealed number of plugs.

For example, this picture could be justified in at least the following ways:

Oral/Tactile Justification		Show Me With The calculator
Counting by 1s	...	1, +, 1, +, 1, +, 1, +, etc. =, 12
Counting by 2s	...	2, +, 2, +, 2, +, 2, +, 2, +, 2, =, 12
Counting by 3s	...	3, +, 3, +, 3, +, 3, =, 12
Grouping by 2s	...	6, x, 2, =, 12
Grouping by 3s	...	4, x, 3, =, 12
Mixed Operations A A group of 6 and three rows of 2.	...	6, +, 3, x, 2, =, 12 Try doing that on your 'average' classroom calculator!
Mixed Operations B Each half column is 5 but two have been made yellow so 3 are left. This happens 4 times.	...	Depends on your calculator but...if you have MathMates (not MathMaster) you can write 4, x, ( , 5, -, 2, ) , =, 12 with confidence. Yes you do have to press the x before entering the brackets. It is only people who know that a number next to a bracket means multiply. The calculator just 'thinks' that you wanted to enter 4 then changed your mind and entered the ( .

There is a considerable amount of informal learning that occurs as students struggle to represent on the calculator what they know they can see and say. They are Working Mathematically on an internal, personal level. Collecting data, organising it in their mind, making and testing hypotheses about how numbers behave.

The teacher doesn't have to say right or wrong. The students can see what the answer must be. If they press buttons that don't result in that answer, they try a different sequence (hypothesis). Eventually there is that 'aha' moment.

Extensions

This activity combines the physical representation of what is being counted with the symbolic representation of the count recorded on the calculator. It develops and extends a brain picture of serial counting far beyond just chanting. The technique of encouraging guessing involves the learner by requiring personal commitment to a prediction and evidence of how the hypothesised number is checked. Ask the children to begin by turning over say 3 in each row. Lined up in ones the boards then offer the opportunity to count in threes. Lined up in twos, it is counting by sixes that is represented. Counting by sevens, for example could be arranged by having Person A turn over five in a row and Person B turn over 2 in a row and then lining the boards up in twos. Use Poly Plug Grid to quickly record the 'Uncover of the Day' by sectioning off or cutting out the appropriate strip and 'spotting' the appropriate circles with colour from a marker pen or coloured pencil. Expect children to record the number of 'plugs' after each board image. Often they will then want to extend their strip pattern beyond what was recorded in the floor activity. Follow up with the Number & Computation A Picture Puzzles menu which explores the 6, 7, 8, 9, & 10 times tables using uncover counting on screen. (Note: Picture Puzzles is built around one screen, two learners, concrete materials and a challenge and requires a separate membership.) Use the activity Predict A Count, which is listed in the public access section of this site. Or, combine the two activities and ask students to count on with their calculator in the Predict A Count manner as the cover is pulled back. When children are used to the activity, reveal many rows of plugs and challenge them to find out the number of blue plugs. But I want you to do it without touching the boards. As children think they have calculated, they write their answer on a piece of paper and check it with someone else who is sure. When all children have had the chance to calculate, gather around the floor model again and discuss the strategies used. Combine the activity with Maths300 software from Lesson 97, Tackling Times Tables. The NRICH web site has a neat, software-based challenge which they call Poly Plug Pattern, which could be a partner to this activity.

From The Classroom

Photos and comments are taken (with permission) from a presentation these teachers made during a six day professional development program organised by the Canberra Goulburn Catholic Education Office.

Making 10 using three Poly Plug frames.

What is double 10? How could you add another 10?

What will the total be if we add another 10? If there's ten in every row, how many altogether?

Captivated! Absorbed! Fascinated!

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