MathJewels math guide · Compare three-digit numbers with place-value reasoning and symbols
Adding and Comparing Three-Digit Numbers
Help a child add three-digit numbers accurately, compare the results, and keep a stated limit active while choosing a best total.
The big idea
Three-digit addition works by combining units of the same size: ones with ones, tens with tens, and hundreds with hundreds. When a place makes 10 or more, regroup 10 of that unit as 1 of the next larger unit. After finding several totals, compare the hundreds first, then the tens, then the ones.
A limit adds one more decision. First decide which totals are allowed. Only then choose the greatest or closest allowed total.
Worked example
Suppose a box can hold at most 600 cards. One pair has 248 and 337 cards.
\[ 248 + 337 = 585 \]
Another pair has 264 and 341 cards.
\[ 264 + 341 = 605 \]
The total 605 is closer to 600, but it is too large for the box. The total 585 fits, so it is the better choice when these are the only two pairs.
How children may show it
Children may use a vertical addition algorithm, expanded form, base-ten drawings, or partial sums. A table is useful when several choices must be compared because it keeps each pair, total, and yes-or-no limit check together.
Common mix-up
A child may choose the number closest to the limit without checking whether it goes over. Ask, “Which totals are allowed?” before asking, “Which allowed total is greatest?” Another common error is lining up digits by the left edge rather than by place value. Have the child name the ones, tens, and hundreds columns.
Try it together
Write four three-digit numbers on slips of paper. Choose a limit, such as 800. Make three different pairs, add each pair, and record whether it fits. Compare only the pairs that fit. Then change the limit and notice whether the best pair changes.