Regrouping in addition
Add like places and explain why ten of a unit become one of the next unit.
Begin with the activity ↓Combining 28 and 17 leaves fifteen ones.
Combine ones with ones and tens with tens. Exchange ten ones for one ten without changing the total.
Combine 28 pencils and 17 pencils. They are two tens and eight ones, and one ten and seven ones. Together there are three tens and fifteen ones.
Exchange ten of the fifteen ones for a ten, leaving five ones. Add the new ten to the original three tens: four tens and five ones. Thus 28+17=45.
The little 1 carried into the tens column records that new ten. It is not an arbitrary rule of moving a digit: that 1 represents ten ones.
Tens can also be regrouped into a hundred. For 68+57, start with eleven tens and fifteen ones. Exchange the ones to obtain twelve tens and five ones, then exchange ten tens: one hundred, two tens and five ones, or 125.
Estimate before adding. 28 is near 30 and 17 near 20. A four-digit answer should prompt a check of the bundle values. An estimate does not replace the exact answer; it helps notice a mistake.
Listen one paragraph at a time
If you counted the carried 1 as one loose object
Label the bundle around ten ones with 10. The 1 in the next column counts one such bundle.
Now change it yourself
Choose an example, then exchange ten ones or ten tens. Watch the same amount take a new grouped form.
Both amounts are combined. Exchange a set of ten for the next place yourself.
Hundreds 0
Tens 3
Ones 15
28 + 17 = 0×100 + 3×10 + 15 = 45
Explain whether a carried 1 represents ten or a hundred, using its number of ones.
Combine like units. Regrouping does not add new objects; it repackages objects already present.
Try with paper and objects
Draw tens as rods and ones as dots. Circle ten dots and replace them with a rod.
Check your idea with another example
Check your idea 1
Check your idea 2
Try a different setting
Write an answer yourself
Return to the explanationCompare with an explanation
85 · Fifteen ones regroup to make eight tens and five ones.
Does your explanation include these ideas?
Speak, point or draw on paper. Explain the reason, not just the numerical answer.
Continue, or pause here
Unbundle tens and hundreds to subtract, including across zero, while preserving the starting amount.