Unit 4: Estimating, Time, and Shapes

# Topic A: Estimating

You use numbers in your everyday life. You often use **estimating **in your everyday life.

You go shopping and you only have twenty dollars, you may need to **estimate **how much your groceries are going to cost before you go to pay for them.

You commute by bus each day to work and it takes thirty-three minutes going to work and thirty-three minutes coming home at the end of the day. You would say that it takes you about one hour on the bus.

These are examples of **estimating.**

You have already learned about **rounding **numbers. You need to be able to round numbers in order to be able to **estimate**.

When you solve math problems, it is a good idea to **estimate **what the answer may be. **Estimating **the answer means finding an answer that is close to the real answer. **Estimating **helps you to see if the real answer is sensible. To **estimate **an answer, you need to round the numbers then add or subtract the rounded numbers. Remember to round to the nearest ten.

Example | Estimate |
---|---|

[latex]\begin{align}23\\+45\\ \hline \\ \end{align}[/latex] | [latex]\begin{align}20\\+50\\ \hline 70\end{align}[/latex] |

[latex]\begin{align}67\\-31\\ \hline \\ \end{align}[/latex] | [latex]\begin{align}70\\-30\\ \hline 40\end{align}[/latex] |

[latex]\begin{align}372\\+416\\ \hline\\ \end{align}[/latex] | [latex]\begin{align}370\\+420\\ \hline 790\end{align}[/latex] |

[latex]\begin{align}564\\-243\\ \hline \\ \end{align}[/latex] | [latex]\begin{align}560\\-240\\ \hline 320\end{align}[/latex] |

Exercise 1

Estimate the following answers. Be sure to round to the nearest 10 before adding. Check your work using the answer key at the end of the exercise.

- [latex]\begin{align}27\\+31\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}42\\+51\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}26\\+32\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}14\\+52\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}44\\+24\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}31\\+27\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}65\\+22\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}46\\+23\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}23\\+72\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}42\\+36\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}64\\+14\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}32\\+20\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}423\\+324\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}526\\+345\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}123\\+541\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}752\\+243\\ \hline \\ \end{align}[/latex]

**Answers to Exercise 1**

- 60
- 90
- 60
- 60
- 60
- 60
- 90
- 70
- 90
- 80
- 70
- 50
- 740
- 880
- 660
- 990

Exercise 2

Estimate the following answers. Be sure to round to the nearest 10 before adding. Check your work using the answer key at the end of the exercise.

- [latex]\begin{align}35\\-16\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}52\\-14\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}67\\-19\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}51\\-23\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}36\\-17\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}72\\-44\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}38\\-19\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}74\\-26\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}93\\-89\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}82\\-57\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}56\\-27\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}93\\-48\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}752\\-342\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}765\\-439\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}673\\-424\\ \hline \\ \end{align}[/latex]
- [latex]\begin{align}645\\-309\\ \hline \\ \end{align}[/latex]

**Answers to Exercise 2**

- 20
- 40
- 50
- 30
- 20
- 30
- 20
- 40
- 0
- 20
- 30
- 40
- 410
- 330
- 250
- 340

Exercise 3

Estimate the following answers. Be sure to round to the nearest ten before adding or subtracting.

Be sure to circle the information and underline what’s being asked.

Check your work using the answer key at the end of the exercise.

**Example:**

There are 186 people living in my apartment building. If 103 are children, how many are adults?

There are 186 people living in my apartment building. If 103 are children, how many are adults?

[latex]\begin{align}186\\-103\\ \hline \\ \end{align}[/latex]

Estimate:

[latex]\begin{align}190\\100\\ \hline 90 \end{align}[/latex]

About 90 people are adults.

- The bus has 84 passenger seats. All the seats are filled and 39 passengers are standing. How many passengers are on the bus?
- Trisha counted 67 boxes on one shelf. She counted 78 boxes on the next shelf. How many boxes were there altogether?
- The library loaned out 157 books on Monday. It loaned out 118 books on Tuesday. How many books did it loan on both days?
- Ryan worked on the computer for 78 minutes. Helen worked on the computer for 54 minutes. How much longer did Ryan work on the computer?
- The Ludlow factory has 73 people working in the factory. The Watson factory has 48 people working in their factory. How many more people work in the Ludlow factory?
- Mr. Martinez needs 257 metres of fencing. He has 125 metres. How much more fencing does he need to buy?

**Answers to Exercise 3**

- 120 passengers
- 150 boxes
- 280 books
- 30 minutes
- 20 people
- 130 metres