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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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addition and subtraction, Grade 2, place value, Number Line, First Grade, whole number, mental math, number sense, how to, physical models

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posted: | 3/17/2010 |

language: | English |

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