Try This First
Try this short activity before reading the lesson.
> Get a cup of dry beans or a box of paper clips. Count out ten and put them in a pile. Make as many piles of ten as you can. Then count the piles: "ten, twenty, thirty..." and count the leftovers on by ones. Say the number you land on out loud.
Math Lab: Count on past one hundred
Predict first. You are counting beads and you reach $99$. Say the next three numbers in your head before you read on.
<div class="math-model"><p><strong>Counting on across 100.</strong></p><div class="model-bar"><span class="model-cell">99</span><span class="model-cell">100</span><span class="model-cell">101</span><span class="model-cell">102</span></div></div>
Model and solve. One more than $99$ is $100$. After $100$ the counting starts again, just like the numbers you already know: one hundred one, one hundred two. You write them $101$ and $102$.
Explain. Why is one hundred one written $101$ and not $1001$?
Your turn. Count on from $97$ to $103$.
Check after trying. $97, 98, 99, 100, 101, 102, 103$.
The Big Idea
Counting is a road, and every number is the next stop on it. After $99$ the road does not stop. The next stop is $100$, then $101$, $102$, and on to $120$. The numbers after one hundred sound like "one hundred and then a small number": one hundred one, one hundred two.
Writing a number past one hundred takes three digits, no more. One hundred fourteen is $114$: a $1$ for the hundred, then $14$. It is not $10014$. Say the hundred, then write the rest in the two places after it.
You can start counting anywhere on the road. Start at $87$ and keep walking: $88$, $89$, $90$, $91$. You do not have to go back to $1$ to know what comes after $89$.
For grown-ups. Counting past 100 is where a child first meets the pattern that every later number system repeats: the ones roll from 9 back to 0 and the tens tick up by one. Students count forward from any number, read and write numerals to 120, and say how many objects are in a group that big. Place value, the hundred chart and every two-digit sum stand on this.
Words to Know
- numeral: The written number, made of digits: $114$ is the numeral for "one hundred fourteen".
- count on: Start at a number and keep counting from there instead of starting at $1$. Counting on from $87$: $88, 89, 90$.
- decade number: A number that ends in $0$: $40$, $70$, $110$. The ones start again from $1$ after each decade number.
Worked Examples and Your Turn
Study each example, then try the paired problem.
Example 1: Count on from the middle
Problem: Start at $66$ and count on to $75$.
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Solution:
- Say $66$, then the next number: $67$. Why: counting on means starting where you are, not at $1$.
- Keep going by ones: $68, 69$. The next number after a $9$ in the ones is the next decade number, $70$.
- Carry on: $71, 72, 73, 74, 75$. Stop at $75$.
Answer: $66, 67, 68, 69, 70, 71, 72, 73, 74, 75$.
> Notice: Every time the ones reach $9$, the next number ends in $0$ and the tens go up by one.
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Your Turn 1: Start at $58$ and count on to $63$.
Example 2: Past one hundred, from 87
Problem: Start at $87$ and count aloud to $120$. What are the three numbers after $99$?
Solution:
- Count up to the next decade: $87, 88, 89, 90$.
- Keep counting by ones: $91, 92, \ldots, 99$.
- After $99$ comes $100$. Why: ten tens make one hundred, and the road keeps going.
- Now the small numbers start again after the hundred: $101, 102, 103$, and so on to $110$, then $111, \ldots, 120$.
Answer: The three numbers after $99$ are $100, 101, 102$. The count ends $\ldots, 118, 119, 120$.
> Verification & Check: Each number after $100$ is $100$ plus a small number: one hundred one is $100$ and $1$ more, one hundred two is $100$ and $2$ more.
Your Turn 2: Start at $95$ and count on to $105$.
Example 3: Count a big pile by tens and ones
Problem: Noah has $6$ bags with ten crayons in each bag, and $4$ loose crayons. How many crayons?
The chapter continues in the book.
