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Grade 2 · 2.NBT.A.1B · 2.NBT.A.2

Counting by hundreds

Craft sticks come in boxes of one hundred. How do you count a shelf of boxes without opening one, and why does only one digit change each time the count goes up by a box?

You need
Counting by tens to one hundredKindergarten
Where you are 3 in Skip counting
Number9
Counting and cardinality23
Skip counting3
Counting by hundreds
Counting by tens to one hundredCounting by twos, fives, threes and fours

When you reach for it

The art room keeps its craft sticks in boxes of one hundred. Counting the sticks in seven boxes one at a time takes seven hundred counts. Counting the boxes takes seven: “one hundred, two hundred, three hundred”. Each number said is one hundred more than the one before, because each box holds one hundred more sticks.

That is Skip counting with the biggest jump a child meets before one thousand. Jumps of two, five, three and four are in Counting by twos, fives, threes and fours, and jumps of ten are in Counting by tens to one hundred. A count by hundreds has two pictures. On a The number line marked from 0 to 1{,}000, every jump is the same long stride. With base ten blocks, every jump is one more flat.

A child reaches for a count by hundreds when:

  • counting things that come in hundreds, such as boxes of one hundred sticks or hundred flats;
  • counting on by hundreds from a number that is not a whole hundred, such as 62, 162, 262;
  • counting back by hundreds, such as 900, 800, 700, or from a number such as 845;
  • counting a pile of hundreds, tens and ones quickly, the hundreds first.

Counting by ones up to 1{,}000, with the hundred chart pages where a whole page is one hundred more, is Counting past one hundred. Reading and writing three-digit numbers is Reading and writing numbers to 1,000, and the trade of ten rods for one flat is Base ten blocks and trading ten for one. This lesson uses all three and reteaches none of them.

The procedure

The lesson is taught over two days: counting by hundreds from zero to one thousand and back on the first, counting on and back from any number on the second. Examples 1 to 3 go with Day 1, Examples 4 to 7 with Day 2.

Day 1: from zero to one thousand

One count for each hundred. Set out some boxes of one hundred craft sticks, or some hundred flats. Point at the first box and say “one hundred”. Point at the next and say “two hundred”, because two boxes hold two hundred sticks. Go on: “three hundred, four hundred, five hundred”. The words are the counting words one to nine with “hundred” after each, so a child who can count to nine can already say the whole count.

As with every skip count, the child points at exactly one box for each number said. That keeps the count tied to the boxes, and it gives a second fact for free: the number of numbers said is the number of boxes.

In digits the count is

100,\; 200,\; 300,\; 400,\; 500,\; 600,\; 700,\; 800,\; 900

Only the hundreds digit moves. The tens digit and the ones digit stay 0, because a box brings no bundles of ten and no loose sticks. The hundreds digit is the number of boxes so far.

Ten hundreds. After nine hundred, one more box makes ten hundreds, and ten hundreds is one thousand, 1{,}000, as Reading and writing numbers to 1,000 names it. So ten jumps of one hundred from 0 land on 1{,}000.

0 100 200 300 400 500 600 700 800 900 1,000 +100 +100 +100 +100 +100 +100 +100 +100 +100 +100
Figure 1Ten jumps of one hundred carry the count from 0 to 1{,}000.

On the floor number line. A number line taped along the classroom floor runs from 0 to 1{,}000, with a tall mark at every hundred. The jumping game is to hop from one hundred mark to the next, saying each number on landing. Every jump is the same length, because every jump is one hundred. The line also shows where the count ends: there are exactly ten jumps between 0 and 1{,}000.

Counting back. Counting back by hundreds says one hundred less each time:

1{,}000,\; 900,\; 800,\; 700,\; 600

On the line each jump goes to the left. With boxes, one box goes back on the shelf for each number said. From any whole hundred the count back reaches 0, and the number of jumps it takes is the hundreds digit of the start: from 600 it takes six jumps, 500, 400, 300, 200, 100, 0.

Day 2: from any number

Starting off the hundreds. A count by hundreds can start anywhere. Build 62 with blocks: 6 rods and 2 units. Put one flat beside them, and the blocks show 162. Another flat, 262. Another, 362.

62 162 262
Figure 2Each jump of one hundred adds one flat. The rods and units never move, so only the hundreds digit changes.

Why only the hundreds digit changes. Each jump adds one flat and nothing else. The rods are not touched, so the tens digit stays 6. The units are not touched, so the ones digit stays 2. The hundreds digit counts the flats: 0, then 1, 2, 3. No trade from Base ten blocks and trading ten for one is ever needed, because adding a flat never makes ten rods or ten units. The only trade a count by hundreds could ever call for is ten flats for a thousand, and that happens only past nine hundred something, at the end of the line (see Boundaries).

The hundred chart pages of Counting past one hundred show the same thing. One page holds 1 to 100, the next 101 to 200, and so on. A count by hundreds from 62 lands on the same square of each page, one page further on each time.

Saying it. Out loud the ending repeats and only the front word changes: “sixty-two, one hundred sixty-two, two hundred sixty-two, three hundred sixty-two”. The repeating “sixty-two” is how a child hears that the count is going right.

Counting back from any number. From 845, take one flat away for each jump: 845, 745, 645, 545, and on. The tens and ones stay 45 the whole way. The count stops at 45, because 45 has no flat left to take; it is less than one hundred. So the number of jumps back is the hundreds digit of the start: from 845, eight jumps.

Counting a pile. A pile of sticks in boxes of one hundred, bundles of ten and loose sticks is quickest to count biggest first: by hundreds for the boxes, then on by tens for the bundles, then on by ones for the loose sticks. Example 7 does this, and checks it by counting the other way round.

Worked examples

Every example can be built with boxes of sticks or base ten blocks, or walked on the floor number line. The figures show the line.

Example 1

Boxes on the art room shelf

Gebre finds 7 boxes of craft sticks on the art room shelf. Each box holds 100 sticks. How many sticks are there?

Solution

Each box is one hundred sticks, so count by hundreds, pointing at one box for each number:

100,\; 200,\; 300,\; 400,\; 500,\; 600,\; 700

Seven numbers were said, one for each box, and the last is 700. There are 700 craft sticks.

The hundreds digit of 700 is 7, the number of boxes: seven hundreds is 700. On the floor line, seven jumps from 0 land on the seventh hundred mark, which is 700 too.

Example 2

How many more boxes make a thousand?

Shani is building a class mural that needs 1{,}000 craft sticks. She has 4 full boxes of one hundred. How many more boxes does she need?

Solution

Four boxes are 400 sticks. Count on by hundreds from 400, putting up one finger for each box added, until the count says one thousand:

500,\; 600,\; 700,\; 800,\; 900,\; 1{,}000

Six numbers were said, so six fingers are up. Shani needs 6 more boxes.

Check with the boxes: 4 boxes she has and 6 boxes more are 10 boxes, and ten hundreds make one thousand.

Example 3

Back from nine hundred

In the jumping game, Hiroto stands on 900 on the floor number line and jumps back by hundreds to 0. What does he say? How many jumps does he make? After how many jumps is he standing on 300?

Solution

Each jump back is one hundred less:

900,\; 800,\; 700,\; 600,\; 500,\; 400,\; 300,\; 200,\; 100,\; 0

Count the jumps, not the numbers. The first number, 900, is where he starts, not where a jump lands, so the ten numbers said come from 9 jumps. That matches the rule from Day 1: from a whole hundred, the number of jumps back to 0 is the hundreds digit, and the hundreds digit of 900 is 9.

He lands on 800, 700, 600, 500, 400 and then 300: that is 6 jumps. Each jump took the hundreds digit down by one, from 9 to 3, and counting back from 9 to 3 is six steps.

Example 4

Counting on from sixty-two

Gebre starts on 62 on the floor line and jumps forward by hundreds. Fill in the boxes:

62,\; 162,\; 262,\; \square,\; \square,\; 562

Will he land on 500? Will he land on 762?

Solution

Each jump is one hundred more, which is one more flat. The tens and ones stay 62, and the hundreds digit goes up by one. After 262 come 362 and 462:

62,\; 162,\; 262,\; 362,\; 462,\; 562

The last box is right, because one hundred more than 462 is 562, the number printed.

0 100 200 300 400 500 600 700 800 900 1,000 +100 +100 +100 +100 +100 +100 +100 +100 +100
Figure 3Counting on by hundreds from 62. Every landing spot sits the same distance past a hundred mark.

He will not land on 500. Every number in this count ends in 62, and 500 ends in 00. On the line, the jump from 462 passes over the 500 mark and lands 62 past it, on 562. He will land on 762: two more jumps, 662 and then 762.

Example 5

Back from eight hundred forty-five

Shani starts on 845 and counts back by hundreds as far as the floor line lets her. What does she say? Where does she stop, and how many jumps does she make?

Solution

Each jump back takes one hundred away, which is one flat. The tens and ones stay 45, and the hundreds digit goes down by one:

845,\; 745,\; 645,\; 545,\; 445,\; 345,\; 245,\; 145,\; 45
0 100 200 300 400 500 600 700 800 900 1,000 −100 −100 −100 −100 −100 −100 −100 −100
Figure 4Counting back by hundreds from 845. Eight jumps reach 45, and there is no whole hundred left to jump.

She stops at 45. It has no hundreds, 0 flats, so there is no whole hundred left to jump back: one more jump of one hundred would go past 0, off the end of the line.

She made 8 jumps, one for each hundred in 845. The hundreds digit went 8, 7, 6, 5, 4, 3, 2, 1, 0, and each step down was one jump.

Example 6

From one hundred twenty-eight to seven hundred twenty-eight

Hiroto stands on 128. He wants to reach 728 using only jumps of one hundred. How many jumps does he need? Could he reach 1{,}000 the same way?

Solution

A jump of one hundred changes only the hundreds digit. The tens and ones of 128 and 728 are the same, 28, so jumps of one hundred can join them. The hundreds digit has to go from 1 to 7:

128,\; 228,\; 328,\; 428,\; 528,\; 628,\; 728

That is 6 jumps, the same as counting on from 1 to 7: 2, 3, 4, 5, 6, 7, six numbers.

He cannot reach 1{,}000 this way. Every landing spot ends in 28, and 1{,}000 does not. The count goes on 828, 928, and then one hundred more than 928 is past 1{,}000, off the end of the floor line. From 128, the farthest jumps of one hundred go on the line is 928.

Example 7

Counting a pile of sticks

Hiroto empties a messy drawer of craft sticks. He finds 3 boxes of one hundred, 4 bundles of ten, and 6 loose sticks. How many sticks are there?

Solution

Count the biggest groups first. By hundreds for the boxes:

100,\; 200,\; 300

Then keep going from 300 by tens, one count for each bundle:

310,\; 320,\; 330,\; 340

Then on by ones for the loose sticks: 341, 342, 343, 344, 345, 346. There are 346 sticks. The digits say the same thing: 3 hundreds, 4 tens and 6 ones.

Count the other way round to check. The loose sticks first, 1 to 6; then the bundles by tens from 6: 16, 26, 36, 46; then the boxes by hundreds from 46:

146,\; 246,\; 346

The total is 346 again, as it must be, since the same sticks were counted. The last part is a count by hundreds from a number that is not a whole hundred, and only its hundreds digit moved.

Boundaries

  • Every jump must be one whole hundred. A box that is not full, say one holding 80 sticks, is not one more hundred. Count the full boxes by hundreds, then count the rest by tens and ones.
  • The count ends at the end of the line. From 0 or any whole hundred, a count on by hundreds reaches 1{,}000 in at most ten jumps. From a start such as 62 or 128, the last landing spot on a line that stops at 1{,}000 is nine hundred something: 962, 928. One more jump would need ten flats, which trade for a thousand cube, and the number would pass 1{,}000.
  • Counting back stops before it runs out. A count back by hundreds from 845 stops at 45, and from 900 at 0. The number of jumps back is the hundreds digit of the start.
  • A count by hundreds lands only on numbers with the same last two digits as the start. From 62 it lands on 562 but never on 500 or 560. To reach those, some tens or ones must be counted as well.
  • The last number is a total only when the count starts from things already counted. Gebre’s count of boxes started from nothing, so 700 was a number of sticks. Hiroto’s walk from 128 on the floor line is a walk; 728 is where he stands, not a total of anything.

Where this goes next

A count by hundreds is the first step toward adding and taking away one hundred in the head. The same idea for tens is Ten more and ten less; with hundreds it becomes a big jump on an open number line, and later part of Multi-digit addition and Subtracting three-digit numbers by place value, including across zero. Knowing that only the hundreds digit moves also helps in Comparing and ordering whole numbers, where two numbers with the same tens and ones are told apart by their hundreds alone, and in Expanded form, where 346 is written as its hundreds, tens and ones.

Exercises

Day 1: from zero to one thousand

  1. Count by hundreds from 100 to 1{,}000.
  2. Count back by hundreds from 1{,}000 to 400.
  3. Gebre counts 5 boxes of 100 craft sticks. How many sticks is that?
  4. Fill in the boxes: 300, 400, \square, \square, 700, \square
  5. Fill in the boxes: 800, 700, \square, \square, 400
  6. Shani counts boxes of craft sticks by hundreds and stops at 600. How many boxes are there?
  7. Hiroto stands on 200 on the floor number line and jumps forward by hundreds to 1{,}000. How many jumps does he make?
  8. Shani has 3 full boxes of one hundred craft sticks. How many more boxes would give her 1{,}000 sticks?
  9. Gebre stands on 600 and makes 4 jumps back by hundreds. Where does he land?

Day 2: from any number

  1. Count on by hundreds from 35 to 935.
  2. Count on by hundreds from 407 to 907.
  3. Count back by hundreds from 981 to 81.
  4. Fill in the boxes: 54, 154, \square, \square, 454
  5. Fill in the boxes: 873, 773, \square, \square, 473
  6. Fill in the boxes: \square, 290, 390, \square, 590
  7. Count back by hundreds from 619 as far as you can. Where does the count stop, and how many jumps does it take?
  8. Shani starts on 236 and jumps forward by hundreds. Will she land on 736? Will she land on 700?
  9. Hiroto stands on 315 and jumps by hundreds to 915. How many jumps does he make?
  10. Gebre finds 2 boxes of one hundred craft sticks, 5 bundles of ten, and 7 loose sticks. Count them, hundreds first. How many sticks are there?
0 100 200 300 400 500 600 700 800 900 1,000
Figure 5Jumps on the floor number line, for Exercise 20.
  1. What size is each jump on this floor number line? Which numbers does it land on? Where would the next jump land?
  2. Start at 73 and count on by hundreds. What is the last number you say before passing 1{,}000?

Explain

  1. Counting by hundreds from 147 to 947, why does the hundreds digit change but the tens and ones digits never do?
  2. A count back by hundreds from 572 stops at 72. Why can it not go one jump further? Why is the number of jumps the same as the hundreds digit of 572?
  3. Gebre counts by tens from 0 to 1{,}000, and Hiroto counts by hundreds from 0 to 1{,}000. Does Gebre say every number Hiroto says? Does Hiroto say every number Gebre says? Explain.
  4. Can a count by hundreds from 0 land on 450? Can a count by hundreds from 50? Give a reason for each.
Answers
  1. 100, 200, 300, 400, 500, 600, 700, 800, 900, 1{,}000. Ten counts; the tenth hundred is one thousand.
  2. 1{,}000, 900, 800, 700, 600, 500, 400. Each number is one hundred less than the one before.
  3. 500 sticks. One count for each box: 100, 200, 300, 400, 500, five numbers.
  4. 500, 600, 800. Each number is one hundred more: 400, 500, 600, then 700 as printed, then 800.
  5. 600, 500. Each number is one hundred less: 700, 600, 500, then 400 as printed.
  6. 6 boxes. The count was 100, 200, 300, 400, 500, 600, six numbers, one for each box.
  7. 8 jumps. He lands on 300, 400, 500, 600, 700, 800, 900, 1{,}000, eight numbers.
  8. 7 more boxes. Count on from 300: 400, 500, 600, 700, 800, 900, 1{,}000, seven numbers. Check: 3 boxes and 7 boxes are 10 boxes, ten hundreds.
  9. 200. The four jumps land on 500, 400, 300, 200.
  10. 35, 135, 235, 335, 435, 535, 635, 735, 835, 935. The tens and ones stay 35; the hundreds digit goes up from 0 to 9.
  11. 407, 507, 607, 707, 807, 907. The tens digit stays 0 and the ones digit stays 7.
  12. 981, 881, 781, 681, 581, 481, 381, 281, 181, 81. The tens and ones stay 81.
  13. 254, 354. Each number is one hundred more: 154, 254, 354, then 454 as printed.
  14. 673, 573. Each number is one hundred less: 773, 673, 573, then 473 as printed.
  15. 190, 490. One hundred less than 290 is 190; one hundred more than 390 is 490, and one hundred more than that is 590, as printed.
  16. It stops at 19 after 6 jumps: 619, 519, 419, 319, 219, 119, 19. The number 19 has no hundreds left to take, and six is the hundreds digit of 619.
  17. Yes to 736, no to 700. The count goes 236, 336, 436, 536, 636, 736; every number ends in 36, so 700, which ends in 00, never comes up.
  18. 6 jumps. He lands on 415, 515, 615, 715, 815, 915; the hundreds digit goes from 3 to 9, six steps.
  19. 257 sticks. Hundreds: 100, 200. Then tens from 200: 210, 220, 230, 240, 250. Then ones: 251, 252, 253, 254, 255, 256, 257.
  20. Jumps of 100, landing on 250, 350, 450, 550, 650. The first dot is halfway between the 200 and 300 marks, at the short mark, so it is 250; each jump covers the distance from one hundred mark to the next. The next jump would land on 750.
  21. 973. The count goes 73, 173, 273, 373, 473, 573, 673, 773, 873, 973; one hundred more than 973 is past 1{,}000.
  22. Each jump of one hundred adds one flat and nothing else. The rods stay 4 and the units stay 7, so the tens and ones digits stay 4 and 7. Only the number of flats grows, and that is the hundreds digit. No trade happens, because adding a flat never makes ten rods or ten units.
  23. The count goes 572, 472, 372, 272, 172, 72. The number 72 is less than one hundred, so it has no flat to take away; one more jump would go past 0. Each jump takes away one of the 5 flats in 572, so there are 5 jumps, the hundreds digit.
  24. Gebre says every number Hiroto says, because one hundred is ten tens: every tenth number Gebre says is a whole hundred, 100, 200, 300. The other way round is not true. Gebre says 10, 20 and 110, and Hiroto jumps over them.
  25. From 0, no: every number in the count ends in 00, and 450 ends in 50. From 50, yes: the count goes 50, 150, 250, 350, 450, keeping the 50 and moving the hundreds digit.
kg1128 · updated 2026-10-21 · CC-BY-SA-4.0