Numbers to 100: Tens and Ones

A ten is a group of 10 ones. You can bundle 10 straws together to make one ten. The bundle still has 10 straws inside.

Make full groups

Imagine a pile of seeds. Move seeds into a small cup, counting each one. Stop when the cup has exactly 10. Fill more cups the same way.

You fill four cups and have two seeds left. Count the full cups in tens: “10, 20, 30, 40.” Then count the loose seeds: “41, 42.” There are 42 seeds altogether.

Four cups and two loose seeds are six things to point at. But they hold 42 seeds. Each full cup stands for ten seeds, not one.

Read the tens numbers

The number of tens tells you the whole amount:

The last number you say counts all the things in those groups. Nine full bundles of ten hold 90 things. One more full bundle makes ten tens, or 100.

Use a ten frame

A ten frame is a grid with 10 spaces. Put one dot in each space. A full frame shows one ten.

Two full frames and six extra dots show 26. Count “10, 20,” then “21, 22, 23, 24, 25, 26.” Full frames let you see the tens without counting each dot again.

Guess, then check

Before counting a pile, make an estimate, a close guess. You might say, “I think there are about 40 seeds.” Then make tens and count the loose ones. Finding 42 means your guess was close.

Check that each full group has exactly 10. A cup with nine seeds cannot be counted as a ten.

A two-digit number is written with two digits, like 64. You can build a number with base-ten blocks. A long rod shows one ten. A small cube shows one one.

Build and read a model

To build 64, take six rods and four cubes. Count the rods: “10, 20, 30, 40, 50, 60.” Count on the cubes: “61, 62, 63, 64.”

You can move the blocks around without changing their value. Put the cubes on the left or spread the rods out. You still have six tens and four ones. A rod stays worth ten wherever you put it.

Draw tens and ones

For a quick drawing, use a line for each ten. Use a dot for each one. To show 37, draw three lines and seven dots.

Each line stands for ten things. You do not need to draw all ten tiny marks. When you read the drawing, count “10, 20, 30,” then count on seven ones to reach 37.

Put the digits in their places

A place-value chart has a Tens column and a Ones column. To show 81, put 8 under Tens and 1 under Ones.

The numeral is 81. In a two-digit number, the tens digit goes on the left. The ones digit goes on the right.

Seven rods with no loose cubes show 70. Put 7 under Tens and 0 under Ones. The zero tells you there are no loose ones.

Make another ten

Sometimes a model has more than nine loose cubes. Try three rods and 14 cubes. Take 10 of the cubes and trade them for one rod.

Now there are four rods and four cubes. They show 44. You have changed the groups, but kept the same amount.

Writing 314 would join the block counts without finding their value. The 14 cubes include a whole new ten. Make that ten before writing one digit in each place.

A digit is one of the symbols 0 to 9. Its value is how much it stands for. Its place in a number tells you that value.

Same digit, different value

Look at 28. The 2 is in the tens place. It means two tens, or 20. The 8 is in the ones place. It means eight ones, or 8.

Now look at 82. The 8 means eight tens, or 80. The 2 means two ones. The digits have swapped places, so the number has changed.

In 66, both digits look the same. The left 6 is worth 60, and the right 6 is worth 6. You could say, “The first 6 counts tens. The second 6 counts ones.”

Zero keeps a place

In 60, the 0 shows no ones. It also keeps the 6 in the tens place. Six rods and no cubes show 60. A single 6 would show only six ones.

Be careful with teen names. “Eighteen” starts with the sound of “eight,” but 18 has one ten and eight ones. Write the ten first, then the ones.

One more or one ten more

Start with 46. Add a rod. Now you have five tens and six ones: 56. Take a rod from 46 instead, and you have 36.

Adding one cube gives 47. When nine loose cubes get one more cube, they make a new ten. That is why one more than 39 is 40. The ones become 0 as the new ten is made.

Ten more than 90 is 100. You now have ten groups of ten.

Follow a hundred chart

A hundred chart runs from 1 to 100, with ten numbers in each row. Within a row, the next square to the right is one more. The square below is ten more.

Start at 26. One square right is 27; one square down is 36. Move up from 26 to find 16. Numbers in a column have the same ones digit.

At the end of a row, counting continues at the start of the next row. After 20 comes 21.

A numeral is a number written with digits, such as 72. A number name uses words, such as “seventy-two.” Both show the same amount.

Listen for the two parts

Say “seventy-two” slowly. “Seventy” tells you there are seven tens. “Two” tells you there are two ones.

Write the tens digit first, then the ones digit:

The numeral is 72. You do not write 70 and then attach another 2. The 7 already shows the seven tens. The 2 goes straight into the ones place.

Read 72 aloud by saying its tens name, then its ones name. That gives “seventy-two.”

Hear the groups in any order

Someone may say, “Two ones and seven tens.” That still means 72. Listen for what each group is worth. The order of the spoken groups does not change the amount.

If the name is just “seventy,” write 70. It has seven tens and no ones. Leaving off zero would give 7, a much smaller number.

Tell similar names apart

“Fourteen” and “forty” sound a little alike. Their endings help:

• “Fourteen” is one ten and four ones: 14.
• “Forty” is four tens and no ones: 40.

The numbers 13 to 19 have names ending in “-teen.” They each have one ten and some ones. Eleven and twelve also have one ten and some ones, but their names have different endings.

When you hear “sixteen,” think of one ten and six ones. “Sixty” has six full tens. Say the whole word so its ending is easy to hear.

Reach one hundred

After 99 comes 100. Read it as “one hundred.” It is ten tens and is written with three digits. Keep both zeros when you write 100.

Number words let you write an amount with letters. Use the tens word and the ones word to build most two-digit names.

Learn the tens words

All these tens words end in “-ty.” A few spellings need care. “Forty” has no “u,” even though “four” does. “Fifty” begins with “fif,” and “thirty” begins with “thir.” “Eighty” keeps the “t” from “eight.” “Ninety” keeps the “e” from “nine.”

Join tens and ones

Look at 45. Its four tens give the word “forty.” Its five ones give the word “five.” Join them with a hyphen, a short joining mark: “forty-five.”

Use that joining mark for names from 21 to 99 with both parts. For example, 23 is “twenty-three” and 98 is “ninety-eight.” A full tens name, such as “fifty,” needs no hyphen.

To go the other way, read “eighty-six.” “Eighty” gives eight tens and “six” gives six ones. Write 86.

Keep the smaller names handy

The ones words are “one,” “two,” “three,” “four,” “five,” “six,” “seven,” “eight,” and “nine.” Zero is “zero,” and 10 is “ten.”

The next names are “eleven,” “twelve,” “thirteen,” “fourteen,” “fifteen,” “sixteen,” “seventeen,” “eighteen,” and “nineteen.” These are each one word, with no hyphen.

To write 100 in words, write “one hundred.” It is two words with a space between them.

To partition a number means to split it into parts. The whole is the full amount. Put all its parts back together, and you have the whole again.

Write what each digit is worth

Take 68. It has six tens and eight ones. The six tens are worth 60, so its parts are 60 and 8.

You can show this with six rods and eight cubes. Put the rods in one group and the cubes in another. No blocks have been added or taken away.

Writing 6 and 8 as the parts would lose the value of the tens. Six ones and eight ones make 14. The 6 in 68 stands for six whole tens.

Show the whole and its parts

A part-whole model uses a circle for the whole, with lines to circles for its parts. Write 68 in the whole circle. Write 60 and 8 in the two part circles.

The two lower circles show the groups you made. Follow their lines back to the whole to put them together.

Read the equal sign

The sign $=$ means “is the same amount as.” You can put the whole first or the parts first:

Both sentences say the same thing. You can also swap the parts:

The equal sign shows matching amounts on its two sides.

Fill a missing part

Suppose the whole is 92 and one part is 90. The other part must be 2. The whole has nine tens and two ones.

If the whole is 92 and the ones part is 2, the missing tens part is 90. It is the value of the tens, not just the digit 9.

A full tens number has zero ones, so $70=70+0$. A smaller number works too: $18=10+8$. Splitting into tens and ones is also called decomposing. Joining the parts is called composing.

The same whole can have different parts.

Trade one rod

Build 63 with six rods and three cubes. Its usual split is:

Trade one rod for 10 cubes. You now have five rods and 13 cubes. Five rods are worth 50, so the new split is:

One rod and ten cubes have the same value.

Trade again

Trade another rod for ten cubes. Five rods become four rods. The 13 loose cubes become 23 loose cubes.

Each trade takes 10 from the tens part and puts 10 into the other part. Adding just one cube would not replace a whole rod. It would leave nine ones missing.

You can keep going:

The last split has no rods left. All 63 are shown as ones.

Check the parts

To check 40 and 23, look inside 23. It has two tens and three ones. Four tens and two tens make six tens. The three ones stay loose. You are back to 63.

Try other parts

Parts do not have to be full tens and leftover ones. For 20 counters, you could make two groups of 10. You could also make groups of 12 and 8. Both pairs make the same whole.

A new split can help you work with the ones. To take eight ones from 63, first show it as 50 and 13. Take eight from the 13, leaving five. The 50 stays, giving 55.

To compare numbers, find which is greater, which is less, or whether they are equal. “Greater” means more. “Equal” means the same amount.

Look at tens first

Compare 49 and 53. The first has four tens; the second has five tens. Five tens already make 50, so 53 is greater than 49.

The 9 in 49 does not make it greater. Those nine ones are still less than another whole ten. Look at what the digits are worth, not just which digit looks biggest.

You can build the numbers to check. Four rods and nine cubes show 49. Five rods and three cubes show 53. The extra rod in 53 makes the greater amount.

Look at ones when tens match

Now compare 85 and 88. Both have eight tens, so the rods match. Look at the loose ones. Eight ones are more than five ones. That makes 88 greater than 85.

If the tens and the ones both match, the numbers are equal. Eight tens and five ones show exactly the same amount as 85.

Compare different kinds of models

You can compare a drawing with a numeral. Four lines and nine dots show 49. The numeral 53 shows five tens and three ones. Read each amount, then compare their tens.

A model may have ten or more loose cubes. Group those before comparing rods. Two rods and 17 cubes become three rods and seven cubes: 37. Four rods alone show 40, which is greater.

Counting only the two rods would miss the ten inside the loose cubes.

Say what you found

You can say, “53 is greater than 49,” or “49 is less than 53.” For objects, “fewer” works too: 49 beads are fewer than 53 beads.

Any two-digit number has at least one ten. Even 10 is greater than 9. On a number line that grows from left to right, the greater number is farther right.

Three signs help you write a comparison. Read from the number on the left to the number on the right.

Choose the sign

Compare 26 and 62. Two tens are less than six tens, so 26 is less. Write:

Read it aloud: “Twenty-six is less than sixty-two.” The open, wide side of the sign faces 62, the greater number. Its point faces 26, the smaller number.

If you swap the numbers, turn the sign too:

Now it says, “Sixty-two is greater than twenty-six.” The wide side still faces the greater number.

Use the equal sign

When the amounts match, use $=$. Twenty and nine ones make 29:

The left side and the right side have the same value. You can put 29 first too:

The equal sign does not tell you which side must hold the whole. It tells you the amounts match.

Compare a split number

For $20+9$ and 26, first find the whole shown by the parts. Twenty and nine make 29. Both 29 and 26 have two tens. Nine ones are more than six ones, so:

Check the whole sentence

A sign can face the wrong way even when you chose the greater number correctly. Read your finished sentence from left to right.

For example, “26 is greater than 62” is false. Use the sign that says “less than.” Check both the meaning you read and the number facing the wide side.

The least number is the smallest in a group. The greatest is the biggest. Check which end your order should start from.

Start with the least

Put 57, 32, 35, and 70 in order from least to greatest. Look at their tens. The numbers with three tens come before five tens and seven tens.

Two numbers have three tens: 32 and 35. Compare their ones. Two ones are less than five ones, so 32 comes first.

The order is 32, 35, 57, 70. Read it from left to right. Each number is greater than the one before it.

Ordering only by the ones would put 70 near the start because of its zero. But 70 has seven tens. It belongs after all the other numbers here.

Start with the greatest

For greatest to least, start with the biggest number. The same group goes 70, 57, 35, 32. Notice that 35 now comes before 32.

On a number line, least to greatest runs from left to right. Greatest to least runs the other way. A line can help you check that you have not swapped two neighbors.

Find numbers between

A number between two numbers is greater than the smaller one and less than the larger one. Between 68 and 72 are 69, 70, and 71.

Leave out 68 and 72. Those are the ends, not numbers between them. Asking for numbers between 72 and 68 gives the same three numbers.

Cross into the next ten

The number just after 69 is 70. Nine ones gain one more and make a new ten. The number just before 70 is 69.

That change matters when you sort nearby numbers. For 69, 71, and 70, the least-to-greatest order is 69, 70, 71. Six tens and nine ones still come before seven full tens.

A number line shows numbers in order. On these lines, numbers get bigger from left to right. Equal number gaps take up equal spaces.

Find the size of a jump

Read the labels before counting. A line labeled 0, 10, 20, 30 has jumps of ten between those marks. One jump from 20 lands on 30.

A line can also show jumps of one. From 60, one jump lands on 61, the next on 62, and so on.

If there are two equal jumps from 80 to 90, each jump is five. The mark in the middle is 85. Do not assume every line counts by ones.

Count spaces, not the starting mark

To find 66 on a line marked in ones, start at 60. Keep your finger there before you count. Move to the next mark as you say “61.” Continue: “62, 63, 64, 65, 66.”

You have made six jumps. Counting the starting mark as your first jump would stop you one mark too soon.

From 60 to 70 there are ten jumps of one. There are nine marks strictly between them, labeled 61 through 69. The spaces and the marks are different things to count.

Fill in a missing label

Suppose equally spaced marks read 20, 30, a blank, then 50. Each jump is ten. The blank is 40.

If a dot sits two jumps after 90 on a line marked in ones, count “91, 92.” The dot shows 92. A nearby labeled ten is a landmark, a helpful place to start.

Draw the places you need

An empty number line starts without marks. Add useful numbers in order. To show 20, 25, and 30, mark 20 on the left and 30 farther right. Put 25 halfway between them.

Keep equal number gaps equally spaced. The gap from 20 to 25 is five, just like the gap from 25 to 30.

To estimate a position means to make a close guess. You use the labels and spaces to decide where a number belongs. You do not need to count every tiny step.

Start with the ends

On a line from 0 to 100, 50 is exactly halfway. Numbers below 50 go in the left half. Numbers above 50 go in the right half.

To place 54, first find the middle. It is a little more than 50, so put it just right of the middle. Putting it near 100 would leave too much space between 50 and 54.

A number such as 6 belongs close to 0. A number such as 97 belongs close to 100. Their distance from the nearest end is small.

Use nearby tens

Think about 83. It is between 80 and 90. It is three past 80 and seven before 90, so its place is closer to 80.

Find where those tens belong, then put 83 a little right of 80. This gives a closer guess than just saying it belongs in the right half.

Read an arrow

You can estimate a number from an arrow's place too. An arrow halfway between 30 and 40 points to about 35. An arrow just right of 90 could point to about 92.

Look at both nearby labels. “Just right of 90” means the number is more than 90 and still near it. A guess of 80 would be on the wrong side.

Check the line you have

The ends decide where the middle is. On a line from 0 to 20, 10 is halfway. On a line from 0 to 100, 10 belongs near the left end.

Before placing a number, read both ends. Then use the middle and nearby tens to check your guess. A number greater than 50 cannot go left of halfway on a line from 0 to 100.