Counting and Number Sense Practice Questions with Answers and a Guided Lesson

Counting objects and understanding "how many"

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

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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: ones, tens, and hundreds

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

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

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Summary

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

Comparing numbers and finding the largest

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

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Summary

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

Skip counting, multiples, and "nth" questions

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

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

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Summary

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

Even and odd numbers

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

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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.

Prime and composite numbers, plus a fraction idea

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

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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).

Why number sense matters

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

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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.