Having seen different ways that the questions involving regrouping 10s might vary, can you think of other variations you might offer students to deepen or extend their understanding?
To extend the idea of re-grouping 10’s, learners could try regrouping the tens into hundreds and then maybe even try questions requiring both tens and hundreds.
Variation reminds me of the importance of relationship between problems that Cathy Fosnot highlighted in her “number strings”, or that Akihiko Takahashi highlighted in the Tokyo Shoseki math textbook series. Carefully choose and sequence problems to highlight critical discernments. For the 2 digit regrouping, I think I might begin with problems in which numbers end in 0, then one of the numbers ending in 0, and one not, then both numbers ending in non zero digits that don’t add to ten, then numbers in which the ones add to 10, then to numbers in which the ones add to between… Read more »
Apart from regrouping using 10s, decomposition can also be used in deepening students understanding. That is breaking down tens into ones or hundreds into tens so that the required action (subtraction) can be effected.
The same idea should be extended to other place value and moreover for example
1234 can be expanded as 1000+200+30+4 by adding or subtracting one should focus on the place value position
I really like the idea of the sums to ten be stacked together for a clear visual…start with a small number of pairs (adding to ten), then increase and mix..so students have to think about the matches.
Increasing the number of tens that need regroup. Getting to the first hundred.
Different place values for older grades tenths, hundredths, thousandths etc…
To extend the idea of re-grouping 10’s, learners could try regrouping the tens into hundreds and then maybe even try questions requiring both tens and hundreds.
Students could extend understanding by applying this to other place values.
The numbers that sum to ten could be rearranged, e.g., 15 +29 +35 +21, so that students have to find the match.
Variation reminds me of the importance of relationship between problems that Cathy Fosnot highlighted in her “number strings”, or that Akihiko Takahashi highlighted in the Tokyo Shoseki math textbook series. Carefully choose and sequence problems to highlight critical discernments. For the 2 digit regrouping, I think I might begin with problems in which numbers end in 0, then one of the numbers ending in 0, and one not, then both numbers ending in non zero digits that don’t add to ten, then numbers in which the ones add to 10, then to numbers in which the ones add to between… Read more »
Extending it to include other place values.
Making the pairs that equal 10 less obvious.
By using different place value digits!
Regrouping can vary interms of a count of tens in hundreds or it can also vary when using the place value chart
Apart from regrouping using 10s, decomposition can also be used in deepening students understanding. That is breaking down tens into ones or hundreds into tens so that the required action (subtraction) can be effected.
Am thinking of regrouping 5’s at the levels or 100’s at the next level.
The numbers which sum up to 10s can be rearranged like this
11+19+38+12
This could be used to assist students in place value of numbers by breaking down various units such as from tens to ones
The same idea should be extended to other place value and moreover for example
1234 can be expanded as 1000+200+30+4 by adding or subtracting one should focus on the place value position
Extending ideas to other place values
I really like the idea of the sums to ten be stacked together for a clear visual…start with a small number of pairs (adding to ten), then increase and mix..so students have to think about the matches.