For parents
Comparing two-digit numbers: why 24 is greater than 19
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A child might say 19 is greater than 24 because nine is greater than four. Looking only at the ones misses part of each number. This activity shows why the tens need to be considered first when comparing two-digit whole numbers.
Build models of both numbers
Use blocks and small boxes. Every full box must contain exactly ten blocks. On one sheet, place two full packs and four loose blocks to represent 24. On another, place one pack and nine loose blocks for 19. Drawn groups of ten also work. Let your child check what each pack contains before comparing the quantities; a box is a group of ten blocks, not a single block.
Why the tens come first
24 has two tens, while 19 has only one. Two full packs already contain twenty blocks, which is more than nineteen. Four extra blocks increase that amount, so 24 > 19. The nine loose blocks do not yet make another ten. For two-digit whole numbers, having more tens settles the comparison even when the ones digit is smaller.
When the tens match, compare the ones
Now compare 24 and 27. Both have two tens, so those parts are equal. That leaves four ones and seven ones: four is less, so 24 < 27. Do not add the digits 2 and 4 to judge the size of 24; the 2 represents twenty here. If both tens and ones match, the numbers are equal, as in 26 = 26.
Read the symbol as a sentence
Read 24 > 19 as “twenty-four is greater than nineteen”. The open side faces the greater number and the point faces the smaller number. Swap the numbers and write 19 < 24: the relationship stays true, but you read it in the opposite order. The = sign means that both sides have the same value. Compare the amounts before choosing the symbol, rather than guessing from its shape.
Play cargo checker
Make cards for 19, 21, 24, 27 and another 24, plus cards showing the comparison signs. Pick two numbers, build their cargoes and place the appropriate sign between them. Your child explains: “I check the tens first; if they match, I check the ones.” Swap the number cards and the cargoes, then choose the sign again. There is no timer or scoring requirement. Checking the blocks is part of the game.
Four questions and mistakes to notice
1. Compare 17 and 21. 17 < 21 because one ten is fewer tens than two. 2. Compare 24 and 27. 24 < 27: the tens match and 4 < 7. 3. Compare 32 and 23. 32 > 23: three tens exceed two, despite using the same digits. 4. Compare 26 and 26. 26 = 26. If your child chooses by the last digit or the width of the writing, return to the packs. This explanation concerns two-digit whole numbers, not a rule for every notation, such as decimals.
Finish with your child’s explanation
Ask your child to invent a pair where the greater number has fewer ones, like 24 and 19, and justify it with packs. A parent can later choose a short calculation route in Otto Math and talk about the size of the answers. The app is available on the App Store. Cargo checker is an offline activity described in this guide.