Counting up to 100 objects
In this topic you will
- Represent $2$-digit numbers using tens and ones.
- Estimate how many objects there are, then count to check.
- Count on and back in ones, twos, and tens.
Key Words
- accurate
- accurately
- collection
- order
Show Definitions
- accurate: Correct and exact, with no mistakes.
- accurately: In a correct and careful way, without making errors.
- collection: A group of things gathered together.
- order: The way things are arranged or placed in a sequence (for example, from smallest to biggest).
Estimating and Counting to 100
Now that you know the order of the numbers to $100$, you can use them to estimate how many objects there are and count them.
Counting in Tens
Counting in tens helps you to count larger collections quickly and accurately.
EXERCISES
$1$. Which tens number is missing from the grid? ______
Write the tens numbers in order, from $10$ to $100$.
👀 Show answer
The missing tens number is $70$.
In order from $10$ to $100$:
$10, 20, 30, 40, 50, 60, 70, 80, 90, 100$
$2$. Arun and Zara make some numbers.
Arun chooses the tens. Zara chooses the ones.
Write each number they make in a part whole diagram.
👀 Show answer
Blocks:$4$ tens and $5$ ones makes $45$.
Part-whole: whole $45$, parts $40$ and $5$.
Coins:$8$ tens and $7$ ones makes $87$.
Part-whole: whole $87$, parts $80$ and $7$.
Think like a Mathematician
Question: What if Zara chose zero ones? What can you say about those numbers? What if Arun chose zero tens? What can you say about those numbers?
👀 show answer
- 1: If Zara chooses $0$ ones, the number ends in $0$. It is a “tens number” like $10, 20, 30, \dots$. The whole number is exactly the same as the tens part (for example, $4$ tens makes $40$).
- 2: If Arun chooses $0$ tens, there are no tens at all, so the number is just the ones (for example, $0$ tens and $7$ ones makes $7$). These numbers are all less than $10$.
EXERCISES
$3$. How many in each collection? Estimate then count to check.
💡 Quick Math Tip
Count in tens first: Circle groups of $10$ objects. Count the groups in tens, then count the leftover ones to find how many objects are in the collection.
💡 Quick Math Tip
Count in twos: If counting by ones feels slow, you can count in $2$s (and also in $10$s) to reach the total faster.
👀 Show answer
Top collection (jelly beans): A sensible estimate is $100$. Counting the objects gives $77$.
Bottom collection (cubes): A sensible estimate is $20$. Counting the objects gives $21$.
❓ EXERCISES
$4$. Marcus counts from $0$ to $100$ in twos.
Draw a ring around any numbers he does not say.
$68$ $7$ $24$ $42$ $37$ $91$ $15$ $86$ $59$ $63$ $8$ $11$ $73$
Why doesn’t Marcus say these numbers?
👀 Show answer
Numbers Marcus does not say: $7$, $37$, $91$, $15$, $59$, $63$, $11$, $73$.
When you count in twos starting at $0$, you only say the even numbers ($0$, $2$, $4$, …, $100$). All the numbers above are odd, so they are skipped.
🧠 Think like a Mathematician
Zara draws this shape on the $100$ square. She says she always has $2$ or $3$ odd numbers in her shape.
Is Zara correct?
Convince yourself that you are correct.
Show Answers
- Is Zara correct? Yes. She will always have either $2$ or $3$ odd numbers in that cross shape.
- Why? On a $100$ square, moving left or right changes the number by $1$, so the parity (odd/even) flips each time. Moving up or down changes the number by $10$, and since $10$ is even, the parity stays the same.
- So in the cross: the centre, the square above, and the square below are all the same parity; the left and right squares are the opposite parity. If the centre is odd, there are $3$ odds. If the centre is even, there are $2$ odds.