Subtracting 2 and 3 Digit Numbers (With and Without Regrouping) Using The Dot and Stick Method By Justine Buonovolonta Resource Room Teacher Wood Park Primary School

Children are able to apply and adapt acquired mathematical ideas to new situations when they develop conceptual understanding. Conceptual understanding is understanding the WHY in mathematics. Allowing students time to progress with concrete materials will develop a strong number sense and conceptual understanding. Concrete Hands-on “Doing” stage Manipulatives Pictorial Visual representations “Seeing” stage Drawings Abstract Symbols “Symbolic” stage Numbers & symbols

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38 - 5 First think about the number 38… How many tens are in 38? (3 tens) So we are going to draw 3 “sticks” to represent the 3 tens.

38 - 5 Now think about how many ones are in 38? (8 ones) So we are going to draw 8 “dots” to represent the 8 ones.

38 - 5 Now cross out the 5 dots to represent the 5 ones that are being subtracted from 38…. Important: When subtracting, you will not draw the number you are subtracting (minuend). You will only draw the number from which you are subtracting (subtrahend).

38 - 5 Now beginning with the tens, count by the VALUE (10) of the remaining sticks and the VALUE (1) of the remaining ones…. Remind learners to “touch and count”… 10, 20, 30, 31, 32, 33, So 38 – 5= 33

38 - 25 First think about the number 38… How many tens are in 38? (3 tens) How many ones? (8 ones) So we are going to draw 3 “sticks” to represent the 3 tens and 8 dots to represent the 8 ones.

38 - 25 Now we are going to subtract 25. How many tens are in 25? (2 tens) How many ones? (5 ones) So we are going to cross out 2 “sticks” to represent the 2 tens and 5 dots to represent the 5 ones.

38 - 25 Now count up all the sticks by counting the VALUE (10), and then count on by the ones… Reminding learners to touch and count… 10, 11,12, 13 So 38 - 25 =13

Subtracting With Regrouping Using Dot and Stick

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44 - 29 So here we have drawn our dots and sticks to represent 44. 44 - 29 So here we have drawn our dots and sticks to represent 44. We are going to cross out 29. Students will likely begin by crossing out the 2 tens from 29…and then have difficulty proceeding because they don’t have enough ones to subtract.

44 - 29 At this time, remind them that they can regroup a “stick” (tens) for 10 “dots” (ones), placing the 10 dots in the empty ten frame.

44 - 29 Now you will be able to cross out the 9 dots…

44 - 29 Now count up all the sticks as the value (10) and all the dots (1). 10, 11, 12,13,14, 15 So, 44 - 29 = 15.

3 Digit Subtracting With Regrouping Using Dot and Stick

264 - 29 Show 264 using “flats”, dots and sticks. 100 100

264 - 29 Think about the number 29 that we are trying to subtract… How many tens are in 29? (2 tens) Subtract the 2 tens by crossing out 2 “sticks” (tens). 100 100

Think about the number 29 that we are trying to subtract… How many ones are in 29? (9 ones) Since we do not have enough “dots” (ones) in the ones place to remove 9 “dots”, we need to regroup a “stick” into 10 “dots”. …So cross out another “stick” (ten) and regroup it into 10 “dots” (ones). 264 - 29 100 100

264 - 29 Now subtract the 9 ones by crossing out the 9 “dots” (ones). 100 100

264 - 29 Count up the remaining “flats” (hundreds), “sticks” (tens) and “dots” (ones) to determine final answer, reminding learners to “touch and count”… 100, 200, 210, 220, 230, 231, 232, 233, 234, 235 So 264 – 29= 235 100 100

467 - 185 = Show 467 using “flats”, dots and sticks.

467 - 185 = Think about the number 185 that we are trying to subtract… How many hundreds are in 185? (1 hundred) Subtract the 1 hundred by crossing out 1 “flat” (hundred).

Think about the number 185 that we are trying to subtract… How many tens are in 185? (8 tens) Since we do not have enough “sticks” (tens) in the tens place to remove 8 “sticks”, we need to regroup a “flat” into 10 “sticks”. … (There are 10 tens in 100.) So cross out another “flat” (hundred) and regroup it into 10 “sticks” (tens). 467 - 185 =

467 - 185 = Now cross out the 8 “sticks” (tens).

467 - 185 = Now cross out the 5 “dots” (ones). Keep in mind that if we did not have enough “dots” to subtract, we would simply regroup a “stick” for 10 “dots” and then subtract.

467 - 185 = Count up the remaining “flats”, “sticks” and “dots” thinking about their value and reminding learners to “touch and count”… 100, 200, 210, 220, 230, 240, 250, 260, 270, 280 281, 282… So 467-185=282

Dot and Stick is a math strategy which can be used for many problems and is a reliable foundational strategy to reinforce. Thank you for your efforts to support our classroom instruction.

Thanks for learning and lending a helping hand!