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What is the middle number in the list \(3\), \(5\), \(7\)?

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Explanation: The list has three numbers; the middle (\(2\)nd) is \(5\).

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Counting & Number Sense

Counting and Number Sense Practice Quiz with a Step-by-Step Interactive Lesson

Use the quiz at the top of the page for counting practice and number sense practice. You’ll build confidence with place value (tens and ones), comparing numbers, number patterns, skip counting, and odd and even numbers. If you want a quick refresher, click Start lesson to open a step-by-step guide.

How this counting and number sense practice works

1. Take the quiz: answer the questions at the top of the page.
2. Open the lesson (optional): review the method with examples and quick checks.
3. Retry: return to the quiz and apply what you reviewed.

What you’ll learn in the counting and number sense lesson

Counting & cardinality

Count objects with one-to-one matching
Understand that the last number tells “how many”
Count forward/backward and use a number line

Place value (tens and ones)

Break numbers into tens and ones (example: \(34=3\text{ tens}+4\text{ ones}\))
Identify digits in the ones, tens, and hundreds place
Use expanded form to understand digit value

Compare & order numbers

Use \(>\), \(<\), and \(=\) to compare numbers
Find the largest or smallest number in a set
Order numbers using place value reasoning

Patterns & number properties

Skip counting by 2s, 5s, and 10s (multiples)
Identify even and odd numbers
Learn the difference between prime and composite numbers

Back to the quiz

When you’re ready, return to the quiz at the top of the page and continue practicing.

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Counting &
Number Sense
Lesson

Step-by-step guide

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Counting & Number Sense Lesson

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Lesson Overview

Lesson overview

Purpose: Build strong counting skills and number sense so you can read, compare, and use numbers with confidence.

Success criteria

Count accurately and explain that the last number counted tells how many objects are in the set.
Use place value to describe numbers (ones, tens, hundreds) and read numbers correctly.
Compare numbers using \(>\), \(<\), and \(=\) and explain your thinking.
Find a missing number in a pattern (for example, skip counting by 2s, 5s, or 10s).
Identify even and odd numbers and count how many odds/evens are in a range.
Recognize multiples and understand the basics of prime and composite numbers.

Key vocabulary

Digit: a symbol 0–9 used to write numbers.
Place value: the value of a digit based on its position (ones, tens, hundreds).
Ones / tens / hundreds: place value positions in base-10 numbers.
Compare: decide which number is greater, less, or equal.
Even / odd: even numbers can be paired with no leftover; odd numbers have one leftover.
Multiple: a number you get by skip counting (for example, multiples of 5: 5, 10, 15, …).

Quick pre-check

Pre-check 1: How many tens and ones are in the number \(34\)?

3 tens and 4 ones 34 tens and 0 ones 4 tens and 3 ones 30 tens and 4 ones

Hint: \(34 = 30 + 4\). That is 3 tens and 4 ones.

Pre-check 2: What is \(1\) more than \(1\) more than \(7\)?

Hint: Start at 7. Add 1 to get 8, then add 1 again.

Counting & Cardinality

Counting objects and understanding “how many”

Learning goal: Count accurately, and explain that the last number you say tells the total.

Key idea

When you count objects, you match one number word to one object. The last number you say tells the total number of objects. This is called cardinality.

Worked example

Example: How many total items are in the lists \(2,4,6\) and \(1,3\)?

The first list has 3 items: \(2,4,6\).
The second list has 2 items: \(1,3\).
Total items: \(3+2=5\).

Try it

Try it 1: How many elements are in the set \(\{2,4,6,8,10\}\)?

Hint: Count how many numbers are inside the braces \(\{\ \}\).

Try it 2: How many numbers are in the list \(2,4,6,8,10,12\)?

5 6 7 8

Hint: Count each item once: \(2,4,6,8,10,12\).

Summary

Use one-to-one counting to avoid skipping or double counting.
The last number counted tells how many objects are in the set.

Place Value

Place value: ones, tens, and hundreds

Learning goal: Identify digits in the ones and tens place, and explain what those digits mean.

Key idea

Our number system is base 10. Each place is worth 10 times the place to its right. For example, in a two-digit number, the left digit is the tens and the right digit is the ones.

Worked example

Example: What digit is in the ones place of \(789\)?

In \(789\), the places are: hundreds \(=7\), tens \(=8\), ones \(=9\).
So, the ones digit is 9.

Quick reminder: “How many tens are in \(70\)?” means “How many groups of 10?” The answer is \(7\) tens.

Try it

Try it 1: How many tens are there in \(90\)?

Hint: \(90 = 9\times 10\). So there are 9 tens.

Try it 2: What digit is in the ones place of \(789\)?

7 8 9 0

Hint: The ones place is the digit on the far right.

Summary

Place value tells what a digit means in a number.
In a whole number, the ones digit is on the far right.

Compare & Order

Comparing numbers and finding the largest

Learning goal: Compare numbers using place value and identify the largest or smallest number in a set.

Key idea

To compare two numbers, start with the leftmost place value. If the tens are different, the number with the larger tens digit is larger. If the tens are the same, compare the ones digits.

Worked example

Example: Which is the largest: \(22, 24, 23, 21\)?

All numbers have 2 tens, so compare the ones digits: \(2,4,3,1\).
The largest ones digit is 4, so the largest number is 24.

Try it

Try it 1: Which is the largest number: \(22, 24, 23, 21\)?

Hint: Compare tens first, then compare ones.

Try it 2: What number is missing in the pattern \(5, 10, 15, \dots, 25\)?

Hint: The pattern increases by 5 each time (skip counting by 5s).

Summary

Use place value to compare numbers accurately.
Patterns often follow a rule like “add 2”, “add 5”, or “add 10”.

Patterns & Multiples

Skip counting, multiples, and “nth” questions

Learning goal: Use skip counting to find multiples and answer questions like “the 3rd multiple of 5”.

Key idea

When you skip count, you count by the same amount each time. The numbers you land on are called multiples. For example, multiples of 5 are \(5, 10, 15, 20, 25, \dots\).

Worked example

Example: Which is the 3rd multiple of 5?

Count multiples of 5: 1st \(=5\), 2nd \(=10\), 3rd \(=15\).
So, the 3rd multiple of 5 is 15.

Sequence check: The sequence \(1,2,3,4,5,\dots\) increases by 1 each time, so the 6th number is \(6\).

Try it

Try it 1: Which is the \(3\)rd multiple of \(5\)?

Hint: List the multiples: \(5,10,15,\dots\).

Try it 2: How many multiples of \(2\) are there between \(1\) and \(10\)?

Hint: The multiples are \(2,4,6,8,10\). Count how many there are.

Summary

Skip counting creates a pattern of multiples.
For “how many” questions, list the numbers and count them carefully.

Even & Odd

Even and odd numbers

Learning goal: Identify even and odd numbers, and count how many odds are in a range.

Key idea

An even number can be split into pairs with no leftover. An odd number has one leftover when you make pairs. A quick check: even numbers end in \(0,2,4,6,8\).

Worked example

Example: Which of these is an odd number: \(2, 4, 5, 6\)?

\(2,4,6\) end in even digits, so they are even.
\(5\) ends in 5, so it is odd.

Try it

Try it: How many odd numbers are there between \(1\) and \(15\) inclusive?

Hint: List the odd numbers: \(1,3,5,7,9,11,13,15\). Then count them.

Worked solution

The odd numbers from 1 to 15 are:
\(1,3,5,7,9,11,13,15\).
There are \(8\) odd numbers.

Summary

Even numbers end in \(0,2,4,6,8\). Odd numbers end in \(1,3,5,7,9\).
To count odds in a range, list them or count by 2s starting at an odd number.

Primes & Fractions

Prime and composite numbers, plus a fraction idea

Learning goal: Recognize small prime and composite numbers and connect equal sharing to fractions.

Key idea

A factor of a number divides it evenly (no remainder). A prime number has exactly two positive factors: \(1\) and itself. A composite number has more than two factors. Important: \(1\) is not prime and not composite.

Worked example

Example: Which of these is not a prime: \(2\), \(3\), \(4\), or \(5\)?

\(2,3,5\) are prime.
\(4\) is not prime because \(4 = 2\times 2\). It has factors \(1,2,4\).
So, the number that is not prime is 4.

Try it

Try it 1: Which of these is not a prime: \(2\), \(3\), \(4\), or \(5\)? (Type the number.)

Hint: A prime has exactly two factors: \(1\) and itself.

Try it 2: What is one third of \(9\)?

Hint: One third means split into 3 equal groups. \(9 \div 3 = 3\).

Summary

Prime: exactly two factors. Composite: more than two factors. \(1\) is neither.
\(\tfrac{1}{3}\) of a number means divide by 3 (equal sharing into 3 groups).

Applications & Review

Why number sense matters

Learning goal: Use number sense skills to solve everyday problems and check if answers make sense.

Where you use counting and number sense

Money: counting coins and bills, and checking totals.
Time: reading clocks and counting minutes.
Measurement: counting units, comparing lengths, and estimating.
Data: reading charts, counting items, and comparing quantities.

Worked example: use tens and ones

Example: You have \(34\) stickers. That is \(3\) tens and \(4\) ones.

If you get \(10\) more stickers, you add one more ten:
\(34 + 10 = 44\). Now you have \(4\) tens and \(4\) ones.

Try it

Try it 1: If you remove the first and last digits from \(1234\), what number remains?

Hint: Removing the first digit (1) and last digit (4) leaves the middle digits.

Try it 2: Which of these is an even number?

17 18 19 21

Hint: Even numbers end in \(0,2,4,6,8\).

Final recap

Counting builds accuracy: one-to-one counting and cardinality (the last count tells the total).
Place value explains digits: ones, tens, hundreds, and expanded form.
Comparing numbers uses place value and symbols \(>\), \(<\), and \(=\).
Patterns and skip counting help with multiples (2s, 5s, 10s).
Even/odd, prime/composite, and simple fractions all connect to number sense.

Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the skill.