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Using Ten Frames to develop Number Knowledge _ Strategies

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Using Ten Frames to develop Number Knowledge _ Strategies Powered By Docstoc
					                           Possible Uses of Smart Kids
                              Magnetic Ten Frames
It is often useful to use red buttons in a yellow frame and vice versa at the beginning of use with
children. This shows a definite difference and makes the counting etc easier. Later, to assist
with visualising the same colour in the frame could be used.

0 Emergent

Making Numbers to Ten
   Place counters of the same one colour in one empty ten frames – count aloud as
    children point to each number to establish one-to-one correspondence for
    numbers (eg. 4, 6, 9)


                                    1, 2, 3, 4, 5, 6, 7, 8

   This can also be done with the Smart Kids Magnetic number arrangements.




1 One-to-One
Making Numbers and Recognising Combinations to Ten
   Place counters of one colour in one empty ten frames – count one-to-one and
    begin to also look at empty spaces that add up to make 10 (eg. 7 dots, 3 empty
    spaces altogether would make 10)




   Use the magnetic number combinations




                                       Len Cooper, Mathematics Education Consultant Auckland,
                                            developed from ideas by Lynne Petersen(McDonnell)
Instantly Recognising Numbers (Subitising to Ten)
   Use one magnetic frame with some yellow and some red buttons ten frame and
    quickly flash it and then hide it - talk about how many red dots you see, how do
    you know, how many more make 10 (eg. 8 dots… I know because I see 2 missing
    and 2 + 8 makes 10 … or I know because I see 4 on one side, 4 on the other side
    and 4 + 4 = 8)



                                Ten Frame covered to hide.

Adding and Subtracting Numbers to Ten
   Place counters on one ten frame using red colour for one number (eg. 6) and
    yellow for the second number (eg. 3) – encourage children to add the two sets
    together some children may have to move the yellow counters into the empty
    holes on the yellow frame or vice versa




   Parts of magnetic tens frames can also be used




   Place counters on one ten frame using one colour (eg. 8) and ask children to
    subtract a number from those counters (eg. 4) to solve the subtraction problem




   Parts of ten could also be used for subtraction.




2                                      Len Cooper, Mathematics Education Consultant Auckland,
                                     developed from ideas by Lynne Petersen(McDonnell)17/3/10
2 Count All from One with Materials

Adding Numbers Beyond Ten (Counting On)
   Place counters on two empty ten frames (eg. 8 of one colour on one and 4 of a
    different colour on the other) and ask children to solve an addition question like
    8 + 4 = ? – encourage children to count on from 8… again, refer to strategies
    used above if children do not “instantly” “know” there are 8 counters (if this has
    been well practised in the above stages, the children should be able to “hang on”
    to 8 and count on from there rather than needing to count out each counter to
    make 8)




                    Eight and 9, 10, 11, 12


Adding Numbers using Ten
   Place ten counters on one ten frame and more counters on another ten frame
    (eg. 10 on one and 5 on another) – repeat with various numbers involving ten +
    another 1-digit number – discuss how the children can at first count on from ten
    to find out the answer – eventually help them notice and discuss the patterns
    they see with the goal of them learning to instantly recognise patterns involving
    addition with tens.
    10 + 1 = 11
    10 + 2 = 12
    10 + 3 = 13 etc.
    (You may find it useful to record these patterns on paper.)




3                                 Len Cooper, Mathematics Education Consultant Auckland,
                                developed from ideas by Lynne Petersen(McDonnell)17/3/10
Subtracting Numbers Beyond Ten (Counting Back)
   Place counters on two empty ten frames (eg. 10 on one and 5 on the other) –
    encourage children to count remove each counter as they count down to solve a
    subtraction question such as 10 – 6 = ?




Recognising and using Doubles
   Place counters on first one empty ten frame (eg. 4 + 4) and then extend this
    onto two ten frames (eg. 7 + 7) once children are confident with doubles to ten
    to build up and practise recognising doubles to ten and then up to twenty




3 Count All from One by Imaging

Adding and Subtracting Below and Beyond Ten and Recognising Doubles
   Repeat the same activities listed in the sections above only substitute the
    empty ten frames and counters with pre-made ten frames where the children
    can not actually move the dots they see – encourage the children to talk about
    what they would do to solve the addition or subtraction questions you pose
    (which you also record horizontally on paper such as 15 – 7 =)

   Eventually, only put empty (ie. blank without any counters) ten frames in front
    of the children and have them solve addition, subtraction and doubles questions
    –encourage them to visualise and talk about what they would see on the ten
    frames if counters were there (have pre-made ten frames ready to show and
    check the children’s solutions if they have difficulty with the visualisation)




                         8      and     6
4                                 Len Cooper, Mathematics Education Consultant Auckland,
                                developed from ideas by Lynne Petersen(McDonnell)17/3/10
4/5/6 Advanced Counting & Part-Whole Additive
Using Part-Whole Strategies involving Combinations to Ten and Doubles to solve
Addition & Subtraction Problems up to 20
   Place counters on two empty ten frames (eg. 8 of one colour on one and 6 of a
    different colour on the other) and ask children to solve an addition question like
    8 + 6 = ? – encourage students not to count on from 8 to solve the addition but
    rather to use their knowledge of Combinations to Ten or Doubles to help them
    think about the problem in a more sophisticated manner




Examples:

Using Combinations to Ten – encourage the children to visualise moving 2 counters
from the 6 to give the ten frame with 8 which would make 10 and 4 (ie. 14) – have
the children at first actually slide the counters to see the 10 being built –
gradually move to pre-made ten frames where the children must visualise and talk
about what would be the slide – finally, use empty ten frames and have the
children merely visualise the counters and talk about the slide and numbers they
see




Using Doubles to Ten – encourage the chidren to visualise moving 1 counter from
the 8 to give to the ten frame with 6 which would make 7 and 7 (ie. 14) – repeat
the same process as listed above in the “Using Combinations to Ten”




5                                 Len Cooper, Mathematics Education Consultant Auckland,
                                developed from ideas by Lynne Petersen(McDonnell)17/3/10
   Once children are confident solving addition and subtraction questions up to 20
    visualising Combinations to Ten and Doubles to solve the problems, they are
    ready to move on to more advanced numbers. Use more than two ten frames (at
    first using pre-made ten frames and then empty ones while you record the
    numbers on paper) to pose questions for students to solve.



Example: What would 8 + 6 + 9 equal?
Encourage children to use “efficient” methods to solve the problem (ie. using
Combinations to Ten and Doubles to help) – prompt them to look for combinations
to group the numbers quickly rather than counting on from one number to add on
the others.




One possible solution to the above question might be:




Take one from the 8 to give to the 9 to make one 10. Now I have 7 + 6 + 10.
Take one from the 7 to make 6 + 6 + 1 + 10.
6 + 6 is 12 and 10 + 12 is 22 + 1 more is 23.

NOTE: There will be many other “Part-Whole Additive” thinking strategies to
solve this question. Encourage the children to think of more than one method to
solve the problem.

   At this stage, students should be recording number sentences underneath the
    ten frames to encourage them to move away from the materials and work more
    exclusively on the Numbers themselves.


Example from above:     8 + 6 + 9 = 23



6                                Len Cooper, Mathematics Education Consultant Auckland,
                               developed from ideas by Lynne Petersen(McDonnell)17/3/10
The goal is to move students from:


                    talk                       talk
CONCRETE                       IMAGES                      ABSTRACT

   Again, gradually, move away from using empty ten frames filled with counters,
    to using premade ten frames with which the children must visualise and talk
    about what they would do if they could move the counters. Place digit cards
    underneath the premade ten frames to show the numbers the children are
    visualising. Once children can confidently talk about what they would do,
    remove the premade ten frames and only place blank ten frames in front of the
    children with numbers underneath for them to add and subtract, talking about
    what they are visualising throughout the process.

Example:




Solve: 27 – 9 (Remember to place the digit cards underneath the ten frames.)

One possible solution the child might describe using the empty ten frames to help
visualise:

I took 7 from the last ten frame. I know that 7 + 2 = 9 so I took 2 more from the
middle ten frame. 8 + 2 is 10 so I have 8 left on the middle ten frame and 10 more
from the first ten frame. I have 18 left altogether. 27 – 9 = 18

   When children become confident with solving additions and subtractions by
    visualising the empty ten frames alongside the digit cards, push them to the
    next stage: encourage children to move beyond the visualisation of the ten
    frames to only operating on the numbers themselves (total abstraction). Do
    this by providing large enough numbers that it is difficult for children to
    visualise them with ten frames.

7                                Len Cooper, Mathematics Education Consultant Auckland,
                               developed from ideas by Lynne Petersen(McDonnell)17/3/10
Example: Solve 89 + 13 = ?


It is unlikely a child will be able to “hang on” to a visualisation of 89 using ten
frames. Encourage the children to talk about the numbers and what they would do
to manipulate them to make “tidier” numbers involving compatibles to ten and
doubles that they know.

One possible solution the child might describe:

I can take one from the 13 to give to the 89 and that makes 90 + 12. I know that
90 and 10 more makes 100 so I have 100 + 12 which equals 112.

At this stage the child is now operating purely on the numbers themselves. If this
does not occur, return to the earlier stage of visualising using empty ten frames.


Notes about Ten Frames:




8                                Len Cooper, Mathematics Education Consultant Auckland,
                               developed from ideas by Lynne Petersen(McDonnell)17/3/10

				
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