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Take any 2-digit number. Reverse the digits to make another 2-digit number. Add the two numbers together. How many answers do you get which are still 2-digit numbers? What do the answers have in common?
Specific Learning Outcomes Add 2-digit numbers with and without renaming
Description of Mathematics This problem practices the addition of 2-digit numbers. Encourage the students to share the methods that they use to solve the problem. For example some students may use place value while others will find it easier to use a rounding method. 91 + 19 place value: 91 + 9 + 10 rounding: 91 + 20 – 1 This problem also offers the opportunity for students to "play" with numbers. As well as practising addition the students are encouraged to look for patterns in their answers. This play encourages students to increase their understanding of numbers and how they relate to one another. It also helps develop problem solving skill and creativity. As numbers are 'reversed' they swap places. (eg. 41 to 14) It is therefore important to discuss what is happening to the place value of the numbers.
Required Resource Materials
Take any 2-digit number. Reverse the digits to make another 2-digit number. Add the two numbers together. How many answers do you get which are still 2-digit numbers? What do the answers have in common? Teaching Sequence
Extension to the problemIs there a pattern in the numbers that give 3-digit sums? SolutionThere are many patterns that can be found in this problem. Let's try a few numbers and see what we get: 13 + 31 = 44 26 + 62 = 88 47 + 74 = 121 54 + 45 = 99 68 + 86 = 154 Now we can see that if the sum of the digits in the 2-digit number is less than 10 then the sum of the reversed numbers is less than 100. 27 + 72 = 99 The sum of the digits in the 2-digit number determines the sum of the reversed numbers in the following way: If the sum is 6 the answer is 66 (24 + 42 = 66; 15 + 51 = 66 etc) If the sum is 8 then the sum of the reversed numbers is 88. You might support your students to notice that the sum in every case above is a multiple of 11. Solution to the Extension:Once again the 3-digit sums are all multiples of 11. To see this notive that 68 + 86 gives the same answer as 66 + 88. Now both 66 and 88 are multiples of 11, so the sum is too.
You can put this solution on YOUR website! Let = the tens digitLet = the units digit --------------------------
The only thing that fits here is:
because if is or less, then becomes zero or negative ------------------------------- The number is 19 ------------------- check:
OK |