Number Sense Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Number Sense.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

An intuitive understanding of numbers, their relative size, and how they relate to each other and to real quantities.

Knowing that 100 is way more than 10, or that 7 is between 5 and 10.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Number sense is knowing roughly where a number sits and how it compares, without doing exact arithmetic.

Common stuck point: The procedure for number sense is the easy part; the trap is treating 'is it reasonable?' as a request for the exact answer. Asking "Am I judging the size or reasonableness of a number rather than computing an exact value?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I judging the size or reasonableness of a number rather than computing an exact value?

Worked Examples

Example 1

easy

Without calculating exactly, determine which is greater:

3 \times 99

4 \times 74

Answer

3 \times 99 > 4 \times 74

First step

Estimate each product:

3 \times 99 \approx 3 \times 100 = 300

Full solution

2
Estimate the second: $4 \times 74 \approx 4 \times 75 = 300$ . These are very close.
3
Refine: $3 \times 99 = 297$ and $4 \times 74 = 296$ . So $3 \times 99 > 4 \times 74$ .

Number sense means using benchmark estimates to compare quantities before computing exactly. When estimates are close, a small refinement is needed. This strategy avoids unnecessary full computation.

Example 2

medium

A school has 483 students. Each classroom holds about 30 students. Approximately how many classrooms are needed?

Example 3

easy

A die shows: : : How many dots without counting?

Example 4

medium

A die shows the dot pattern for 5. How many dots?

Example 5

hard

A die shows 3 dots in a slanted line. Without counting, how many?

Example 6

easy

A tens frame has the top row full and 3 dots on the bottom. How many dots in all?

Example 7

easy

A tens frame is completely full. How many dots?

Example 8

medium

Ben has 8 grapes. He eats one. How many grapes does Ben have now?

Example 9

easy

What number is halfway between

10

and

20

Example 10

easy

What number is halfway between

0

and

10

Example 11

hard

Start at

63

. Take ten less. Then take ten less again. What number do you land on?

Example 12

easy

Round

23

to the nearest ten.

Example 13

easy

Round

65

to the nearest ten.

Example 14

hard

A bake sale has

58

cupcakes in the morning and

34

more in the afternoon. About how many cupcakes are there in total? Use rounding to the nearest ten.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Place the following numbers on a mental number line from smallest to largest:

0.5

5

50

0.05

Example 2

medium

Without a calculator, is

\frac{7}{8}

closer to

\frac{1}{2}

or to

1

? Explain.

Example 3

easy

Which is larger, 19 or 91?

Example 4

easy

Is 100 closer to 10 or to 1000?

Example 5

easy

Between which two of 5 and 10 does the number 7 fall?

Example 6

easy

Order from least to greatest: 8, 3, 5.

Example 7

easy

About how many is 'a little less than 50': 48 or 75?

Example 8

easy

How many tens are in 60?

Example 9

easy

Which number is just before 10 when counting up?

Example 10

easy

Is 7 closer to 5 or to 10?

Example 11

medium

Using benchmarks, estimate whether

38 + 47

is closer to 80 or 90.

Example 12

medium

A jar holds about 100 marbles. A second jar looks 3 times as full. About how many marbles in the second jar?

Example 13

medium

Which is larger,

\frac{1}{2}

\frac{1}{3}

, using the benchmark of one whole?

Example 14

medium

Estimate

612 \div 3

to the nearest hundred.

Example 15

medium

On a number line from 0 to 100, roughly where does 25 sit?

Example 16

medium

Which is more: 1 ten and 4 ones, or 4 tens and 1 one?

Example 17

medium

Without computing exactly, is

98 \times 5

more or less than 500?

Example 18

medium

Order from greatest to least: 0, 7, 3.

Example 19

medium

A book has about 200 pages. You have read about half. Roughly how many pages remain?

Example 20

challenge

A number is between 40 and 50, and its ones digit is twice its tens digit. What is it?

Example 21

challenge

Estimate

\sqrt{50}

to the nearest whole number using perfect-square benchmarks.

Example 22

challenge

Three numbers add to 30. They are consecutive whole numbers. What are they?

Example 23

easy

Look fast! How many dots? :: :

Example 24

easy

Look fast! How many stars? *

Example 25

easy

Look fast! How many fingers up? You see 3 fingers up.

Example 26

easy

How many hearts do you see? :: ::

Example 27

medium

Look fast! Two dots in a line. How many dots?

Example 28

medium

Look fast! A line of 3 ducks. How many ducks?

Example 29

easy

A tens frame is full on top (5) and has 2 dots on the bottom. How many dots?

Example 30

easy

What is one more than 6?

Example 31

easy

What is one less than 9?

Example 32

medium

A tens frame has the top row full and 1 dot on the bottom. How many dots?

Example 33

medium

What is one less than 7?

Example 34

easy

What is ten more than

24

Example 35

easy

What is ten less than

58

Example 36

easy

What is ten more than

7

Example 37

medium

What is ten less than

36

Example 38

medium

Maya has

42

marbles. She gets

10

more. How many does she have?

Example 39

easy

Round

48

to the nearest ten.

Example 40

easy

Compute

50 + 30

in your head.

Example 41

easy

Compute

40 + 50

in your head.

Example 42

medium

Round

74

to the nearest ten.

Example 43

medium

A jar has

37

marbles. Round the number to the nearest ten.

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Related Concepts

Counting Place Value Estimation

Background Knowledge

These ideas may be useful before you work through the harder examples.

counting