Counting and writing numbers to 120
Counting on from any number to 120, reading and writing numerals, and seeing every number as tens and ones
About four lessons of 40 to 50 minutes
The number chart that keeps going past 100
You already know the hundred square, ten rows of ten that stops at 100. But numbers do not stop at 100. What comes next? 101, 102, 103. The chart just keeps going. Add two more rows and you reach 120, and it would keep going forever if the paper were big enough.
Today we count past 100, we start counting from any number and carry on, we read and write the numerals all the way to 120, and we see how every one of these numbers is really just some tens and some ones. By the end, 100 will feel like the middle of the number chart, not the end of it.
- A number chart with two extra rows below 100the rows keep the same pattern: 101, 102, up to 120
- Bundles of ten straws with a few singles4 bundles and 7 singles is 47, four tens and seven ones
- Writing the numeral 114one hundred, one ten and four ones
- Start on 98 and keep counting99, 100, 101, the count rolls straight past a hundred
What students will be able to do
Students will count to 120 starting from any number, read and write numerals throughout that range, and understand a two-digit number as a bundle of tens and some ones.
- I can count to 120 out loud, past 100.
- I can start at any number and count on from there.
- I can read and write numbers up to 120.
- I can show a number as bundles of ten and some ones.
- I can say how many tens and how many ones are in a two-digit number.
Standards this unit teaches
- 1.NBT.A.1Common Core (US)Count and write to 120
Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
- 1.NBT.B.2Common Core (US)Tens and ones
Understand that the two digits of a two-digit number represent amounts of tens and ones, including that ten can be thought of as a bundle of ten ones, called a ten.
- AC9M1N01Australian Curriculum v9 (ACARA)Recognise, represent and order numbers to 1000 (Year 1)
Recognise, represent and order whole numbers to at least one thousand using physical and virtual materials, numerals and number lines. Counting and writing numbers to 120 sits inside this Year 1 range.
- AC9M1N02Australian Curriculum v9 (ACARA)Partition, regroup and rename numbers (Year 1)
Partition, regroup and rename two- and three-digit numbers in different ways, including understanding the role zero plays. The tens-and-ones partition in this unit is the start of this Year 1 place-value work.
Prior knowledge
This unit builds on skills students should already have met. Revisit any that are shaky first.
Words to teach and display
- Numeral
- the written symbol for a number, such as 47 or 113
- Ten
- a bundle of ten ones counted as one group
- Ones
- the single units, the leftover after making all the tens you can
- Tens digit
- the digit that tells how many tens, the left digit in a two-digit number
- Ones digit
- the digit that tells how many ones, the right digit
- Count on
- keep counting forward from a given number, not from 1
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, and counting past 100
ConcreteNumbers keep their pattern forever. Count on from 95 and listen: 96, 97, 98, 99, then 100, then 101, 102. Nothing strange happens at 100, the count just carries on. The scary part is imaginary. Extend a hundred chart with two more rows and count along them so the class sees 101 to 120 sitting in the same neat pattern.
Counting on from any number is the key skill. If you are told to start at 108, you do not go back to 1, you carry on: 109, 110, 111. Practise starting all over the range, especially just before a new ten and just before 100.
The tens boundaries are where care is needed. After 109 comes 110, after 119 comes 120. The ones digit rolls back to 0 and the tens tick up by one, exactly as it does lower down the chart.
- Start at 97 and count on. What comes after 99?
- What number comes right after 109?
- What is the last number we reach in this unit's chart?
2. Bundling ones into tens
ConcreteA ten is a bundle of ten ones counted as one group. Give each pair a heap of straws and have them bundle every ten with an elastic band. When the bundling stops, they are left with some full tens and a few loose ones. That is the hidden structure of every number: as many tens as you can make, then the ones left over.
Take 47 straws. Bundle tens until you cannot make another: 4 bundles, with 7 straws left loose. So 47 is 4 tens and 7 ones. The tens digit counts the bundles, the ones digit counts the loose ones.
This is why two-digit numbers have two digits. The left digit is not just a shape, it counts whole bundles of ten. In 47 the 4 is worth 4 tens, which is 40, and the 7 is worth 7 ones.
You bundle 46 counters into tens. How many tens and how many ones?
- Make as many bundles of ten as you can: 4 bundles use 40 counters.
- Count what is left loose: 6 counters.
- So 46 is 4 tens and 6 ones.
Answer: 46 is 4 tens and 6 ones. The 4 is worth 40 and the 6 is worth 6.
- Bundle 25 into tens. How many bundles and how many loose ones?
- In 58, what is the tens digit worth?
- Why can we not make another full ten out of the loose ones?
3. Reading and writing numbers to 120
PictorialWriting a two-digit number is writing its tens and its ones in order: tens digit first, ones digit second. Four tens and seven ones is written 47. Say the number as you write it and the digits line up with what you say. Past 100 there are three digits: a hundreds digit, a tens digit, and a ones digit.
Match every numeral to a picture of tens and ones so the writing is never just copying. 30 is 3 tens and 0 ones, and that 0 is doing a real job: it holds the ones place to show there are no loose ones. Without it, 3 tens would look like 3.
From 100 to 120, read the hundred first: 113 is one hundred, one ten, and three ones. The pattern of the last two digits is exactly the tens-and-ones pattern the class already knows.
Write the numeral for 8 tens and 5 ones. Then write the numeral for 1 hundred, 1 ten and 4 ones.
- 8 tens and 5 ones: write the tens digit, 8, then the ones digit, 5.
- That gives 85.
- 1 hundred, 1 ten, 4 ones: write the hundreds digit 1, then tens 1, then ones 4.
- That gives 114.
Answer: 8 tens and 5 ones is 85. One hundred, one ten and four ones is 114.
- Write the number that is 5 tens and 0 ones. What job does the 0 do?
- How do you write one hundred and ten?
- Read this numeral: 106. How many hundreds, tens and ones?
4. Seeing tens and ones in a number
AbstractNow go the other way: given a numeral, say its tens and ones without any counters. Look at 72. The tens digit is 7, so there are 7 tens, worth 70. The ones digit is 2, so there are 2 ones. 72 is 70 and 2. This is the whole idea of place value: a digit's place tells you what it is worth.
Compare 72 and 27. Same two digits, different value, because the digits sit in different places. In 72 the 7 counts tens; in 27 the 7 counts ones. The place is what matters, not just the digit.
One special number to name is a whole ten like 90: that is 9 tens and 0 ones. And a ten itself, 10, is 1 ten and 0 ones, the first bundle. Reading a number as its tens and ones is what makes adding and subtracting bigger numbers possible later.
How many tens and ones are in 90? And in 108?
- 90: the tens digit is 9 and the ones digit is 0, so 9 tens and 0 ones.
- 108: the hundreds digit is 1, the tens digit is 0, the ones digit is 8.
- So 108 is 1 hundred, 0 tens and 8 ones.
Answer: 90 is 9 tens and 0 ones. 108 is 1 hundred, 0 tens and 8 ones.
- How many tens and ones are in 46?
- In 53, what is the 5 worth? What is the 3 worth?
- How is 81 different from 18?
Common misconceptions and how to address them
MisconceptionCounting stops at 100, or something odd happens at a hundred.
Why it happens: 100 is the end of the familiar hundred square, so children treat it as a wall rather than a point in the middle of a longer count.
How to address it: Extend the chart with rows for 101 to 120 and count along them. Show the pattern is unbroken: after 100 comes 101, just as after 10 comes 11.
MisconceptionIn 47 the 4 just means four, not four tens.
Why it happens: The child reads each digit as a bare number and has not connected the left place to tens.
How to address it: Bundle 47 straws and lay the 4 bundles under the tens digit. The 4 counts bundles of ten, so it is worth 40, not 4.
MisconceptionThe zero in 30 or 40 is not needed and can be dropped.
Why it happens: Zero ones feels like nothing, so the child thinks it can be left off.
How to address it: Show that without the 0, 30 collapses to 3. The 0 holds the ones place open to say there are 3 tens and no loose ones.
Misconception72 and 27 are the same number because they use the same digits.
Why it happens: The child attends to the digits but not to the place each one sits in.
How to address it: Build both with tens and ones. In 72 there are 7 tens; in 27 only 2 tens. Same digits, but the places give different values.
MisconceptionYou can only count starting from 1, so 'count on from 108' means start again.
Why it happens: Early counting is drilled from 1, so starting mid-sequence feels wrong, especially near 100.
How to address it: Cover the start of the chart and count on from the first visible number. Play 'carry on' with start numbers near tens and near 100.
MisconceptionOne hundred and ten is written 10010, by writing 100 then 10.
Why it happens: The child writes the parts they hear side by side instead of combining the places.
How to address it: Build it: one hundred, one ten, no ones. Write hundreds then tens then ones: 110. Read the numeral back to check it says one hundred and ten.
Guided practice (with answers)
1. Start at 96 and count on. Say the next five numbers.
Answer: 97, 98, 99, 100, 101.
2. How many tens and ones are in 47?
Answer: 4 tens and 7 ones. The 4 is worth 40 and the 7 is worth 7.
3. Write the numeral for 6 tens and 3 ones.
Answer: 63.
4. What number comes right after 119?
Answer: 120.
5. Read this number: 108. How many hundreds, tens and ones?
Answer: 1 hundred, 0 tens and 8 ones.
6. How is 81 different from 18?
Answer: In 81 the 8 counts tens (80) and the 1 counts ones. In 18 the 1 counts a ten and the 8 counts ones. Same digits, different places, different values.
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, then bundle into tens and ones.
Differentiation
- Keep real bundles of ten and loose ones on the desk so every number can be built before it is written.
- Secure counting to 100 before pushing on to 120, then add the two extra rows.
- Give a place-value mat with a tens column and a ones column so the digits land in the right place.
- For writing, provide the number split into tens and ones so the child only records the digits.
- Count on by tens from a non-zero start past 100, such as 83, 93, 103, 113.
- Rename a number a second way, such as 47 as 3 tens and 17 ones, as a bridge to regrouping.
- Write every number from 100 to 120 and describe the pattern in the ones digit.
- Compare two numbers to 120 by their tens first, then their ones.
Assessment: exit ticket
A three-question exit ticket in the last five minutes. It samples counting past 100, writing a numeral, and reading tens and ones.
1. Start at 108 and count on three numbers.
Answer: 109, 110, 111.
2. Write the numeral for 5 tens and 2 ones.
Answer: 52.
3. How many tens and ones are in 76?
Answer: 7 tens and 6 ones.
Teacher notes and timings
- Rough timing across four lessons: Lesson 1 counting on past 100 (section 1), Lesson 2 bundling into tens (section 2), Lesson 3 reading and writing numerals (section 3), Lesson 4 seeing tens and ones plus the exit ticket (section 4 and assessment).
- Language to keep saying: count on from here, a ten is a bundle of ten ones, tens digit then ones digit. These phrases pre-empt most of the misconceptions.
- Keep bundles of ten and loose ones on desks and an extended number chart on the wall. When a child is unsure, have them build the number before writing it.
- The bar-model figures partition each number into tens and ones on a shared scale, so the tens part really is worth ten times a one. Use them to show why the left digit counts bundles.
- Curriculum note: US Grade 1 (1.NBT.A.1) counts and writes to 120 and (1.NBT.B.2) names two-digit numbers as tens and ones. In ACARA v9, Year 1 (AC9M1N01) works with numbers to at least 1000 and (AC9M1N02) partitions and renames them, with the explicit tens-and-ones naming emphasised at Year 2. So this unit maps to US Grade 1 and Australian Year 1.
- Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the number chart and bar models to build numbers together.