Free Math Worksheets

- Compare \(80\,\text{cm}\) with your own height. - Think of an object that is about \(80\,\text{cm}\) long. - Could an entire class and its furniture fit in a space that length? - Might the unit have been recorded incorrectly?

1. Since \(100\,\text{cm} = 1\,\text{m}\), \(80\,\text{cm}\) is less than \(1\,\text{m}\). 2. A classroom must be long enough to hold many students, desks, and chairs. 3. Therefore, \(80\,\text{cm}\) is far too short to be the length of a classroom.

The measurement is not reasonable because \(80\,\text{cm}\) is less than \(1\,\text{m}\), while a classroom is several meters long.

- Replace numbers with nearby values that are easy to use mentally. - Compare the size of each estimate with the answer choices. - Use multiplication and division facts when they are already familiar.

1. a) Estimate \(20\times3=60\), so the matching result is \(57\). 2. b) Since \(48\) is \(6\) groups of \(8\), the matching result is \(6\). 3. c) Estimate \(400+400=800\), so the matching result is \(805\). 4. d) Estimate \(900-500=400\), so the matching result is \(409\).

a) \(57\) b) \(6\) c) \(805\) d) \(409\)

- Round to nearby tens or hundreds when helpful. - Use a known multiplication fact to estimate a division result. - Choose the option closest to your estimate.

1. a) Estimate \(40\times5=200\). The reasonable choice is \(210\). 2. b) Use the fact \(7\times8=56\). The reasonable choice is \(8\). 3. c) Estimate \(900-300=600\). The closest choice is \(580\).

a) \(210\) b) \(8\) c) \(580\)

- Round each number to a nearby ten or hundred. - Use familiar multiplication and division facts. - Match each expression with an estimate of the correct size.

1. a) Estimate \(30\times2=60\). 2. b) Since \(81\div9=9\), a reasonable estimate is \(10\). 3. c) Estimate \(400+500+100=1000\). 4. d) Estimate \(800-400=400\).

a) \(60\) b) \(10\) c) \(1000\) d) \(400\)

- When rounding to the nearest hundred, use the tens digit to decide whether to round up or down. - Use each estimate to check whether the exact difference is reasonable. - Regroup carefully when finding the exact differences.

1. Estimate: \(400-200=200\). Exact difference: \(402-199=203\). 2. Estimate: \(700-300=400\). Exact difference: \(698-301=397\). 3. Estimate: \(500-300=200\). Exact difference: \(503-275=228\).

1) Estimate: \(200\); exact difference: \(203\) 2) Estimate: \(400\); exact difference: \(397\) 3) Estimate: \(200\); exact difference: \(228\)

- Round both numbers in each difference to the nearest hundred. - Notice whether the three estimates are different or equal. - Calculate the exact differences when the estimates do not distinguish them.

1. For A), the estimate is \(800-300=500\). 2. For B), the estimate is \(900-400=500\). 3. For C), the estimate is \(700-200=500\). 4. Since all three estimates are equal, the estimates alone do not identify the greatest exact difference. 5. The exact differences are A) \(804-297=507\), B) \(901-395=506\), and C) \(702-198=504\). Therefore, A) has the greatest difference.

A) Estimate: \(500\); exact difference: \(507\) B) Estimate: \(500\); exact difference: \(506\) C) Estimate: \(500\); exact difference: \(504\) All three estimates are equal, so the estimates alone do not identify the greatest exact difference. A) has the greatest exact difference.

- Round the numbers to tens or hundreds to identify promising combinations. - Look for rounded values that total about \(1000\). - Compare each exact sum’s distance from \(1000\).

1. Estimate combinations that could be near \(1000\), such as about \(500+400+100\). 2. The combination \(482, 408,\) and \(107\) gives \(482+408+107=997\), which is \(3\) away from \(1000\). 3. Checking all three-number combinations confirms that no other sum is closer. The next closest is \(408+334+267=1009\), which is \(9\) away.

Choose \(482, 408,\) and \(107\). Their exact sum is \(482+408+107=997\).