Counting to 100 by ones and tens
Counting on by ones, counting in tens, counting on from any number, and writing the numbers you count
About four to five lessons of 30 to 40 minutes
How many stickers are in the pile?
Tip out a big pile of stickers on the carpet and ask the class to guess how many. Now try to count them one by one. It takes forever and it is easy to lose your place. There has to be a faster way, and there is.
Push the stickers into groups of ten. Now you do not count 1, 2, 3 all the way. You count the groups: ten, twenty, thirty. Counting in tens gets you to a big number in a few quick words. Today you will count all the way to 100 by ones and by tens, start counting from any number you are given, and write the numbers you count.
- A pile of stickers pushed into groups of tencount the groups: 10, 20, 30, that is much faster than by ones
- Ten fingers held up, then again, then againeach full set of fingers is another ten: 10, 20, 30
- A hundred square, one row at a timeeach row holds ten, so ten rows make 100
- Writing the number that matches your countcount 7 blocks and write the numeral 7
What students will be able to do
Students will count to 100 by ones and by tens, count forward starting from a given number rather than always from 1, connect each spoken number to its quantity, and write numerals to record a count from 0 to 20.
- I can count out loud to 100 by ones.
- I can count to 100 by tens: 10, 20, 30, up to 100.
- I can keep counting forward when I am given a starting number, like 'carry on from 47'.
- I can make groups of ten and count them in tens.
- I can write the number that matches how many things I counted, up to 20.
Standards this unit teaches
- K.CC.A.1Common Core (US)Count to 100 by ones and by tens
Count to 100 by ones and by tens.
- K.CC.A.2Common Core (US)Count forward from a given number
Count forward beginning from a given number within the known sequence, instead of having to begin at 1.
- K.CC.A.3Common Core (US)Write numbers 0 to 20
Write numbers from 0 to 20, and represent a number of objects with a written numeral from 0 to 20.
- AC9MFN02Australian Curriculum v9 (ACARA)Count and compare to 20 (Foundation)
Count and compare collections of up to at least twenty objects, and explain the reasoning behind which group has more or fewer. The one-by-one counting in this unit is the Foundation skill it extends toward 100.
- AC9MFN06Australian Curriculum v9 (ACARA)Connect number names, numerals and quantities (Foundation)
Connect number names, numerals and quantities, and represent the count of a small collection in more than one way. Writing the numeral for a count is the recording skill this unit builds.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Count on
- keep counting forward from a number you are given, not from 1
- Ten
- a group of ten ones bundled together
- Count by tens
- count in jumps of ten: 10, 20, 30, and so on
- Numeral
- the written symbol for a number, such as 7 or 15
- Hundred square
- a chart of the numbers 1 to 100 in ten rows of ten
- How many
- the total you reach when you finish counting a group
Teach it: concrete, pictorial, abstract
The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.
1. Counting on by ones
ConcreteStart with the count everyone knows and stretch it further. Count around the circle, one number each, and keep the beat steady: 1, 2, 3, 4, 5. The big idea is that the numbers never run out, they just keep going in the same pattern. When you reach 9 the next number starts a new ten: 10. When you reach 19 the next is 20. Each new ten sounds like the count you already know with a 'ty' on the end.
Point at a hundred square as the class counts so every spoken number has a home to point to. The rows do the hard work: the first row ends on 10, the second on 20, the third on 30. The pattern down each column is the same digit every time.
The one rule that keeps a count honest is one number for one thing. Touch each sticker once as you say its number, and the last number you say tells how many there are altogether.
- What number comes right after 29?
- When we count and reach 39, what is the next number?
- Why do we touch each thing only once as we count?
2. Making tens: a group of ten ones
ConcreteHere is the move that makes big counts fast. Take ten single ones and bundle them into one group of ten. A ten is just ten ones held together. Build a few tens with the class using ten-frames or bundles of straws, so a ten is something you can see and hold, not only a word.
A ten-frame holds exactly ten, in two rows of five. When the frame is full, that is one ten. Fill three ten-frames and you are holding three tens, which is thirty ones in total.
The reason we bundle is speed. Counting thirty single stickers is slow and easy to muddle. Counting three tens is quick: ten, twenty, thirty. Same amount, far fewer words.
- How many ones fill one ten-frame?
- If I fill two ten-frames, how many is that altogether?
- Is it faster to count thirty things by ones or by tens?
3. Counting to 100 by tens
PictorialNow count only the tens. Lay out the tens in a line and take a big jump of ten each time: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Ten jumps of ten reach exactly 100. Say it as a chant and clap on each ten so the rhythm sticks.
Notice the pattern in the words: twenty, thirty, forty, fifty. After the early ones they are the counting numbers two, three, four, five with a 'ty' sound added. The tenth jump lands on 100, the first three-digit number, which is ten tens.
Counting by tens is skip counting in steps of ten. The number line makes the equal jumps visible: every hop is the same size and covers a whole ten.
Count five bundles of ten straws. How many straws is that?
- Each bundle is one ten.
- Count the bundles by tens: 10, 20, 30, 40, 50.
- The last number you say is how many.
Answer: Five tens is 50 straws.
- Count by tens with me: 10, 20, 30, then what?
- How many tens do we jump to get all the way to 100?
- What number is ten more than 60?
4. Counting on from any number
AbstractYou do not always start a count at 1. If a friend has already counted to 47, you can carry straight on: 48, 49, 50. Counting on from a given number means starting where you are told and continuing the same pattern. Play a game where you call a starting number and the class counts on the next few.
The tricky spots are the tens boundaries. Counting on from 58 goes 59, then 60, then 61. The 9 rolls over to a fresh ten just like it does when you start from 1. Practise landing on and crossing each ten.
Counting on also works in tens. Start on 30 and count on by tens: 40, 50, 60. You do not have to go back to the start, you keep the pattern going from wherever you are.
Start at 78 and count on by ones four times. Where do you land?
- Begin on the number you are given: 78.
- Count on one at a time: 79, then 80, then 81, then 82.
- The fourth number you say is where you land.
Answer: You land on 82. Notice 79 rolled over into the new ten at 80.
- Carry on from 63: what are the next three numbers?
- Count on from 88. What number comes after 89?
- Start at 20 and count on by tens: what comes after 30?
5. Writing the number you count
AbstractCounting out loud is only half the job. When you count a group you write the numeral that matches, so the number is recorded. Count seven counters and write 7. Count fifteen and write 15. The written number stands in for the whole count.
For the numbers 0 to 9 there is one digit to write. From 10 to 20 there are two digits: a tens digit and a ones digit. Ten is written 1 then 0, and the teens are a 1 followed by the ones digit, so fourteen is 14.
Watch the reversals. Some children write 12 as 21 or flip individual digits. Say the number as you write it, tens digit first, and check it against a hundred square.
You count a group of counters and reach thirteen. Write the numeral.
- Thirteen is one ten and three ones.
- Write the tens digit first: 1.
- Then write the ones digit: 3.
Answer: Thirteen is written 13.
- How do you write the number twelve?
- Which digit do you write first in a teen number, the tens or the ones?
- Count these nine dots and write the numeral for how many.
Common misconceptions and how to address them
MisconceptionCounting by tens is just saying 'ten, twenty, thirty' without it standing for anything.
Why it happens: The chant can be learned as a rhyme with no quantity behind it, so the child cannot use it to count real groups.
How to address it: Tie every spoken ten to a full ten-frame or bundle. Say 'twenty' only when the second ten-frame is full. The word and the group must arrive together.
MisconceptionAfter 29 the next number is 'twenty-ten'.
Why it happens: The child follows the within-ten pattern and does not know that a new ten name begins.
How to address it: Point at the hundred square as you cross 29 to 30. Show that a full row has ended and a new row, the thirties, begins. Rehearse the rollover at each tens boundary.
MisconceptionYou can only count starting from 1.
Why it happens: Early counting is always drilled from 1, so starting in the middle feels wrong.
How to address it: Play 'carry on': give a start number and have the class continue. Cover the start of a hundred square and count on from the first visible number.
MisconceptionSkipping or double-counting objects still gives the right total.
Why it happens: The one-to-one rule is not yet automatic, so the count and the pointing drift apart.
How to address it: Move each object into a 'counted' pile as it is counted, or drop it in a cup. If it has moved, it has been counted once.
MisconceptionThe teen number 13 is written 31.
Why it happens: The child writes the digits in the order the ones sound is heard, or reverses the pair.
How to address it: Say the number while writing, tens digit first. Match the written numeral against the hundred square to catch the swap.
MisconceptionCounting by tens and counting by ones give different totals for the same pile.
Why it happens: The child does not yet see that three tens and thirty ones are the same amount.
How to address it: Count one pile both ways in front of the class: by ones to 30, then bundled into tens to 30. Same pile, same total, faster the second way.
Guided practice (with answers)
1. Count on from 46 by ones. Say the next three numbers.
Answer: 47, 48, 49.
2. Count these three rows of ten by tens.
Answer: 10, 20, 30. Three tens is 30.
3. What number is ten more than 70?
Answer: 80. One jump of ten from 70 lands on 80.
4. How many tens do you count to reach 100?
Answer: Ten tens: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.
5. Count on from 89. What are the next two numbers?
Answer: 90, then 91. The 9 rolls over into a new ten at 90.
6. You count sixteen blocks. Write the numeral.
Answer: 16. One ten and six ones, so 1 then 6.
Independent practice worksheets
Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with counting by ones, then move to counting by tens and writing numerals.
Differentiation
- Stay concrete: keep real ten-frames and bundles on the desk so every ten can be held.
- Count to 30 securely before pushing on to 100, then add a decade at a time.
- Use a hundred square with a finger or a marker to keep the place while counting.
- For writing, give a numeral to trace before asking the child to write it from memory.
- Count on by tens from a non-zero start, such as 4, 14, 24, 34, and notice the ones digit stays the same.
- Start the count at any number on the hundred square and continue to the end of the row.
- Count backward by tens from 100 as a bridge to subtraction: 100, 90, 80.
- Write the numerals past 20 by reading them off the hundred square.
Assessment: exit ticket
A three-question exit check in the last five minutes. It samples counting by tens, counting on, and writing a numeral, the three pillars of the unit.
1. Count by tens from 10 to 50.
Answer: 10, 20, 30, 40, 50.
2. Start at 57 and say the next two numbers.
Answer: 58, 59.
3. Write the numeral for the number eleven.
Answer: 11.
Teacher notes and timings
- Rough timing across four to five short lessons: Lesson 1 counting on by ones (section 1), Lesson 2 making tens (section 2), Lesson 3 counting by tens (section 3), Lesson 4 counting on from any number (section 4), Lesson 5 writing numerals plus the exit check (section 5 and assessment).
- Language to keep saying: one number for one thing, a ten is ten ones, count on from here. These phrases pre-empt most of the misconceptions.
- Keep a hundred square on the wall and ten-frames on desks throughout. When a child is unsure, hand them a frame to fill or point them to the square.
- The hundred-square figure shows ten rows of ten. Use it to make each tens boundary visible: a full row is a ten, and a new row starts a new decade.
- Curriculum note: US Kindergarten counts and writes numerals to 20 (K.CC.A.3) while counting to 100 by ones and tens (K.CC.A.1). Reading and writing all the way to 100 in writing is a Grade 1 expectation (1.NBT.A.1), so keep written work within 20 here and count the larger numbers out loud.
- Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the hundred square and number line to count from together.