Grade 1 · 1.NBT.A.1

Counting, reading and writing numbers to 120

After 99 comes 100. What comes after that, how is each number said, and how is it written, all the way to 120?

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Counting, reading and writing numbers to 120

When you reach for it

A child who can count to one hundred knows the counting words up to 100 and the pattern inside them: one, two, three up to nine, then a new decade word, and the ones again. Many counts do not stop at 100, though. The mailboxes along a long apartment hallway, the bowling pins stored at the back of a bowling alley, a big pile of anything: the count runs on, and the child needs the words that come next and the way to write them.

This lesson takes the count past 100 up to 120. The child should be able to start at any number up to 120 and count on from there, say each number aloud, and read and write each numeral from 100 to 120. Counting on is the move they already have: start from a number instead of from one and keep saying the next number.

Two things are new. The words: after one hundred the count goes “one hundred one, one hundred two”, and so on. The numerals: from 100 on, every number is written with three digits. The words come easily, because they repeat a pattern the child already knows. The numerals take more care, because the spoken name has two parts (“one hundred” and “seven”) but the written number is one numeral, 107, not 100 and 7 set side by side.

The lesson runs over four days.

Day 1: counting on across 100.
Day 2: counting on across each new ten past 100, at 110 and at 120.
Day 3: reading and writing the numerals from 100 to 120.
Day 4: the hundred chart grown to 120, and counts that use all of it.

The pictures are a number path (a row of numbered squares a child can step along or touch), the hundred chart with two extra rows, and a number line.

The procedure

Day 1: counting on across one hundred

Counting on means saying a starting number and then each next number in order. Every number has exactly one number right after it, the number that is one more. That does not change at 100. What changes is only the word.

Put a number path on the table, or tape one to the floor from 90 to 120, and let the child touch or step on each square as they say its number.

Figure 1Counting on from 98 to 113. The shaded squares are where a new word starts, one hundred and one hundred ten.

Start at 98. “Ninety-eight, ninety-nine,” and then the word after ninety-nine is “one hundred”, written 100. The next number does not get a brand new kind of name. The count starts over with the small numbers, said after “one hundred”:

100,\; 101,\; 102,\; 103,\; 104,\; 105

is said “one hundred, one hundred one, one hundred two, one hundred three, one hundred four, one hundred five”. Ask the child what they hear: the “one hundred” stays the same, and after it comes one, two, three, four, five, the same words they said at the very start of counting.

Counting on also works when the child is counting real things. If Ayanda has already counted 99 bowling pins and has a few more to count, she does not start again from one. The 99 pins are already counted, so she touches each new pin and says the next word. The last word she says is how many pins there are in all, because counting on is still counting, and the last word of a count names how many.

Day 2: each new ten past one hundred

After one hundred comes one hundred one, one hundred two, and so on to one hundred nine. Then, just as nine is followed by ten, one hundred nine is followed by one hundred ten:

107,\; 108,\; 109,\; 110,\; 111,\; 112

said “one hundred seven, one hundred eight, one hundred nine, one hundred ten, one hundred eleven, one hundred twelve”. The words after “one hundred” are exactly the words the child said when counting from seven to twelve.

The same thing happens at the next ten. Just as nineteen is followed by twenty, one hundred nineteen is followed by one hundred twenty:

117,\; 118,\; 119,\; 120

So the whole count from 101 to 120 is the count from 1 to 20 again, with “one hundred” said in front of each word. A child who knows the words to twenty already knows the words to one hundred twenty, once they see this.

Watch the numerals at the same two places. From 109 to 110, the last digit goes from 9 back to 0 and the middle digit goes from 0 to 1. From 119 to 120, the last digit goes from 9 back to 0 and the middle digit goes from 1 to 2. That is the moment a new ten starts, the same moment as 19 to 20 or 49 to 50. Why the middle digit counts the tens is the business of Tens and ones; here the child only needs to notice where the change happens.

Counting back says the same numbers in the opposite order: 112, 111, 110, 109, 108. Going back past 100, the count leaves the three-digit numbers: 101, 100, 99, 98. The number just before a number is the one that is one less.

Day 3: reading and writing the numerals from one hundred to one hundred twenty

Reading. Every numeral from 100 to 120 has three digits, and the first digit is 1. To read one, say “one hundred”, then read the last two digits as a number:

Numeral	Last two digits	Said
100	00	one hundred
104	04	one hundred four
110	10	one hundred ten
113	13	one hundred thirteen
120	20	one hundred twenty

When the middle digit is 0, as in 104, the last two digits are just the last digit, four, so the number is “one hundred four”. Many people say “one hundred and four” out loud. It names the same number; written words here leave the “and” out.

Writing. Writing goes the other way. Hear the name, write 1 for the “one hundred”, then write the number said after it as two digits. One hundred thirteen: 1, then 13, which gives 113. One hundred twenty: 1, then 20, which gives 120. One hundred seven: 1, then seven written as two digits, 07, which gives 107. The 0 is what keeps 107 a three-digit number: without it the numeral would be 17, seventeen. The digits are the same 0 to 9 the child already writes, placed left to right.

A good check is the count itself. Write the numerals while counting on from 100:

100,\; 101,\; 102,\; 103,

104,\; 105,\; 106,\; 107

Every one starts with 1 and 0, and only the last digit counts up. So one hundred seven, the seventh number after 100, is 107.

Seven and seventy. One hundred seven and one hundred seventy sound alike, but they are far apart. One hundred seventy is “one hundred” and then seventy, so it is written 1, then 70: 170. On the count, 107 comes 7 numbers after 100, while 170 comes 70 numbers after 100, well past the 120 this lesson reaches.

Figure 2One hundred seven is 7 steps past 100. One hundred seventy is 70 steps past it.

Day 4: the hundred chart grown to one hundred twenty

The hundred chart holds 1 to 100 in ten rows of ten. Grow it by two rows: 101 to 110 underneath, then 111 to 120.

Figure 3The hundred chart with two more rows. The new rows look like the first two rows with a 1 in front.

Moving one square to the right along a row is counting on by one, as on the number path. At the end of a row the count goes on at the start of the next row, so after 100 comes 101 at the start of the first new row, and after 110 comes 111 at the start of the second.

Lay the new rows next to the first two rows of the chart. The row 101 to 110 matches the row 1 to 10, and the row 111 to 120 matches the row 11 to 20: each new number is the old one with “one hundred” said in front, and written with a 1 in front (and a 0 in the middle when the old number had only one digit). Each column keeps the same last digit all the way down, so 7, 17, 97, 107 and 117 all sit in the same column. That is a quick way to find a square: 117 is in the second new row, in the column of numbers ending in 7.

Building the two new rows by hand, on a strip of paper with twenty squares, is a good task for a child: they write each numeral in turn and say it as they go.

Worked examples

Say every count aloud with the child, and keep a number path or the chart from Figure 3 on the table so they can touch each number as they say it.

Example 1

Day 1: Mailboxes from 98 to 113

Neema walks along an apartment hallway reading the numbers on the mailboxes. The numbers go in order, one more each time. The first mailbox she reads is 98 and the last is 113. What numbers does she read?

Solution

Each mailbox is one more than the one before, so Neema is counting on from 98. She says the starting number and then each next number until she reaches 113:

98,\; 99,\; 100,\; 101,\; 102,\; 103,

104,\; 105,\; 106,\; 107,\; 108,

109,\; 110,\; 111,\; 112,\; 113

Two places deserve a slow step. After ninety-nine comes one hundred, 100, the first number with three digits. After that the small numbers start again behind “one hundred”: one hundred one, one hundred two, up to one hundred nine. Then, as after nine comes ten, after one hundred nine comes one hundred ten, 110, and after that one hundred eleven, one hundred twelve, one hundred thirteen. Figure 1 shows the same count on a number path, with the two places shaded.

Check: the last number said is 113, the last mailbox.

Example 2

Day 1: Ninety-nine pins and four more

Ayanda is counting the bowling pins stored at the back of a bowling alley. She has counted 99 pins. There are 4 pins left, and she counts them on, one at a time. What is the last number she says? How many pins are there in all?

Solution

The 99 pins are already counted, so Ayanda does not start again from one. She keeps the number 99 and says the next number for each new pin, holding up a finger each time so she knows when she has counted all four:

first pin, one hundred, 100;
second pin, one hundred one, 101;
third pin, one hundred two, 102;
fourth pin, one hundred three, 103.

The last number she says is 103. Because the last number of a count says how many have been counted, there are 103 pins in all.

Check on the number path: start on 99 and take four steps, to 100, 101, 102 and 103.

Example 3

Day 2: Past one hundred nine

Refilwe counts on from 106 to 112. What does she say? Where does a new ten start?

Solution

She says each next number in turn:

106,\; 107,\; 108,\; 109,

110,\; 111,\; 112

In words: one hundred six, one hundred seven, one hundred eight, one hundred nine, one hundred ten, one hundred eleven, one hundred twelve. After “one hundred” she is saying six, seven, eight, nine, ten, eleven, twelve, the same words as counting from six to twelve.

A new ten starts at 110. In the numerals, the last digit runs 6, 7, 8, 9, then goes back to 0, and at that same step the middle digit goes from 0 to 1. After that the last digit counts up again: 111, 112.

Example 4

Day 2: Just after and just before

Say the number that comes (a) right after 99, (b) right after 119, (c) right before 111, (d) right before 100.

Solution

The number right after is the next number in the count, one more. The number right before is the number said just before it, one less, which is found by counting back one.

(a) After ninety-nine comes one hundred: 100. The numeral grows from two digits to three.
(b) After nineteen comes twenty, so after one hundred nineteen comes one hundred twenty: 120. The last digit goes from 9 to 0 and the middle digit from 1 to 2.
(c) Before eleven comes ten, so before one hundred eleven comes one hundred ten: 110.
(d) Before one hundred comes ninety-nine: 99. Counting back out of the hundreds, the numeral goes from three digits to two.

Parts (b) and (d) sit at the two edges of this lesson’s count, which is why they are worth saying aloud on the number path.

Example 5

Day 3: One hundred seven, not one hundred seventy

Refilwe’s mailbox number is one hundred seven. Which of these is it: 1007, 10\ 7, 107 or 170?

Solution

Count on from 100 and write each number: 100, 101, 102, 103, 104, 105, 106, 107. Every one of them starts with 1 and 0, and only the last digit counts up. One hundred seven is the seventh number after 100, so it is 107.

Look at why each of the others is a different number.

1007 has four digits. Every number from 100 up to 999 has three digits, and a number with four digits is at least one thousand, far past any mailbox in this hallway. The name “one hundred seven” has two parts, but it is written as one numeral, not 100 with a 7 added on the end.
10\ 7, with a gap, is two separate numbers, ten and seven.
170 reads “one hundred”, then 70, so it is one hundred seventy. On the number line in Figure 2, 107 is 7 steps past 100 and 170 is 70 steps past it.

So Refilwe’s mailbox is 107. The 0 in the middle matters: written without it, 17 is seventeen.

Example 6

Day 3: Reading and writing both ways

(a) Read aloud: 112, 101, 120. (b) Write the numerals for one hundred fifteen and one hundred ten.

Solution

(a) Say “one hundred”, then read the last two digits.

112: the last two digits are 12, twelve, so it is one hundred twelve.
101: the last two digits are 01, which is just one, so it is one hundred one.
120: the last two digits are 20, twenty, so it is one hundred twenty.

(b) Write 1 for “one hundred”, then the rest of the name as two digits.

One hundred fifteen: 1, then 15, which gives 115.
One hundred ten: 1, then 10, which gives 110.

Check (b) by counting on from 100. The tenth number after 100 is 110, and five more numbers after that, 111, 112, 113, 114, 115, end on 115.

Example 7

Day 4: Finding a square on the chart to one hundred twenty

On the chart grown to 120 (Figure 3), which row is 117 in, and which square of that row? What number is in the last square of the chart?

Solution

The chart has ten numbers in a row. The first new row is 101 to 110 and the second is 111 to 120. One hundred seventeen is more than one hundred ten, so it is in the second new row, the last row of the chart. Counting along that row, 111, 112, 113, 114, 115, 116, 117, puts 117 in the seventh square.

The quick way says the same thing. The row 111 to 120 matches the row 11 to 20, where 17 is the seventh square. And 117 ends in 7, so it sits in the column with 7, 17 and 107.

The last square of the chart is the number after one hundred nineteen, which is one hundred twenty, 120.

Example 8

Day 4: Where did the count start?

Neema counts on from a number. After the starting number she says six more numbers, and the last one is 102. What was the starting number?

Solution

Work backward from the end. The six numbers she said, counted back from 102, are

102,\; 101,\; 100,\; 99,\; 98,\; 97

so in the order she said them they were 97, 98, 99, 100, 101, 102. Her starting number is the one just before the first of these, the number right before 97, which is 96.

Check by counting on: start at 96 and say six more numbers, 97, 98, 99, 100, 101, 102. The sixth is 102, as the problem says. The count crossed 100 on the way, which made no difference to how many numbers were said.

Boundaries

Stopping at 120 is where this lesson stops, not where counting stops. Every number has a next number. After 120 comes 121, and the count goes on through the hundreds in Counting past one hundred.
The pattern “one hundred, then the small number” holds from 101 to 199. It is used here only up to 120. At 200 the first word changes to “two hundred”.
Every number from 100 to 999 has three digits. Numbers below 100 (other than 0 to 9) have two, and counting back from 101 to 100 to 99 crosses from three digits to two. A numeral with four digits, such as 1007, is at least one thousand.
A 0 in the middle is needed from 101 to 109. Without it, 107 would be 17. From 110 to 119 the middle digit is 1, and at 120 it is 2.
The word “and”. “One hundred and seven” is common in speech and names the same number as “one hundred seven”. Written words in this lesson leave it out.
The matching rows on the chart work because each row holds ten. The row 101 to 110 lines up with 1 to 10 and the row 111 to 120 with 11 to 20. A row of a different length would break the matching columns.

Where this goes next

The count past 120 continues in Counting past one hundred, and reading and writing three-digit numbers in general is Reading and writing numbers to 1,000. Why the middle digit of 110 counts one ten and the last digit counts ones is Tens and ones, and the digit values in three-digit numbers are Place value. On the chart, moving down a column is ten more, and counting along the end of each row, 10, 20, 30 up to 120, is Counting by tens to one hundred. Numbers past 100 also sit on the The number line, as in Figure 2, which is where they are compared with the signs for greater and less.

Exercises

Day 1: counting on across one hundred

Count on from 96 to 104.
Count on from 99 to 107.
What number comes right after 100? What number comes right after 104?
Fill in the boxes: 98, 99, \square, \square, 102
Ayanda has counted 97 bowling pins. She counts on 5 more pins, one at a time. What numbers does she say? How many pins are there in all?

Day 2: each new ten past one hundred

Count on from 107 to 113.
Count on from 115 to 120.
What number comes right after 109? What number comes right after 116?
What number comes right before 110? Right before 101? Right before 120?
Fill in the boxes: 117, \square, 119, \square
Count back from 112 to 105.

Day 3: reading and writing

Write the numeral for each: one hundred four; one hundred eleven; one hundred eighteen.
Write each number in words: 108, 116, 103.
Refilwe’s mailbox is number one hundred six. Which of these shows it: 1006, 160, 106 or 10\ 6?
Neema writes the number that comes right after 114. Which of these does she write: 1015, 115 or 15?

Day 4: the chart to one hundred twenty

Figure 4Three rows of the chart, for Exercise 16.

Which numbers are hidden behind the letters A, B, C, D and E?
The mailboxes along a hallway are numbered in order from 101 to 120. Neema’s mailbox is 113. Ayanda’s is the next one after Neema’s. Refilwe’s is three mailboxes before Neema’s. What are the numbers on Ayanda’s and Refilwe’s mailboxes?
Ayanda counts on from 88 and stops at 102. Write the numbers she says.
Neema counts on from 95 and stops at 105. How many numbers does she say after 95?

Explain

Why does the numeral for one hundred seven have a 0 in the middle?
Count back from 102 to 97. Between which two numbers does the count go from three digits to two? Why there?
Is it true that the words from one hundred one to one hundred twenty are the words from one to twenty with “one hundred” in front? Check it with two examples.
Refilwe counts on from 113 to 120. Ayanda counts back from 120 to 113. Do they say the same numbers? What is different?

Answers

96, 97, 98, 99, 100, 101, 102, 103, 104. After ninety-nine comes one hundred, then one hundred one.
99, 100, 101, 102, 103, 104, 105, 106, 107. The count crosses 100 right after the start.
101 and 105. The number right after is one more: after one hundred comes one hundred one, and after one hundred four comes one hundred five.
100 and 101. After 99 comes 100, then 101, and then 102 as printed.
She says 98, 99, 100, 101, 102, and there are 102 pins in all. She keeps the 97 already counted and says one number for each of the 5 new pins. The last number said tells how many.
107, 108, 109, 110, 111, 112, 113. A new ten starts at 110.
115, 116, 117, 118, 119, 120. After one hundred nineteen comes one hundred twenty.
110 and 117. After one hundred nine comes one hundred ten, as ten comes after nine; after one hundred sixteen comes one hundred seventeen.
109, 100 and 119. Count back one each time: before one hundred ten is one hundred nine, before one hundred one is one hundred, and before one hundred twenty is one hundred nineteen.
118 and 120. The count goes 117, 118, 119, 120, one more each time.
112, 111, 110, 109, 108, 107, 106, 105. Counting back says each number one less.
104, 111 and 118. Write 1 for “one hundred”, then the rest as two digits: 04, 11, 18.
One hundred eight; one hundred sixteen; one hundred three. Say “one hundred”, then the last two digits: 08 is eight, 16 is sixteen, 03 is three.
106. Counting on from 100, the sixth number after it is 106. 1006 has four digits, 160 is one hundred sixty, and 10\ 6 is two numbers, ten and six.
115. After one hundred fourteen comes one hundred fifteen, written 1 then 15. 1015 has four digits, and 15 is fifteen.
A is 100, B is 103, C is 110, D is 114 and E is 120. A follows 99 at the end of the first row; B comes after 101, 102; C ends the second row after 109; D comes after 111, 112, 113; and E follows 119 at the end of the chart.
Ayanda’s is 114 and Refilwe’s is 110. The next number after 113 is 114. Counting back three mailboxes from 113 gives 112, 111, 110.
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102. The count crosses a new ten at 90 and at 100.
10 numbers: 96, 97, 98, 99, 100, 101, 102, 103, 104, 105. Touch one finger for each number after 95; ten fingers are up when she says 105.
One hundred seven is written 1 for “one hundred”, then seven as two digits, 07. The 0 keeps the number at three digits, like every number from 100 on. Without it the numeral is 17, which is seventeen.
102, 101, 100, 99, 98, 97. The change comes between 100 and 99: 100 has three digits and 99 has two. One hundred is the first number in the count that needs three digits, so every number before it has fewer.
Yes. For example, one hundred four is “one hundred” and then four, and one hundred sixteen is “one hundred” and then sixteen. Every word from one hundred one to one hundred twenty is made this way, with each of the words one to twenty used once, in the same order.
Yes, they say the same eight numbers, 113, 114, 115, 116, 117, 118, 119, 120. Refilwe says them in that order and Ayanda says them in the opposite order, starting at 120.