Rounding Estimation and Standard Form SUCCESS CRITERIA WHERE

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Rounding, Estimation and Standard Form

Rounding, Estimation and Standard Form

SUCCESS CRITERIA: WHERE ARE WE NOW? Learning outcomes: Why we round or estimate with

SUCCESS CRITERIA: WHERE ARE WE NOW? Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Starter: Why we round or estimate with numbers. When is rounding or estimation used

Starter: Why we round or estimate with numbers. When is rounding or estimation used in everyday life?

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Decimal places and significant figures Rounding Estimation Hyperlinks! Estimation of multi-stage calculations Calculating in

Decimal places and significant figures Rounding Estimation Hyperlinks! Estimation of multi-stage calculations Calculating in standard form Standard form Error in measurement Calculations using bounds

Rounding Learning Objective: Can I round numbers to the nearest 1, 100, 1000

Rounding Learning Objective: Can I round numbers to the nearest 1, 100, 1000

Why do we round? We round numbers to save writing too much. We also

Why do we round? We round numbers to save writing too much. We also round numbers so that they are easier to work with. When a number is rounded, it must be close to the original number.

Why do we round? It is often useful to use a short number line

Why do we round? It is often useful to use a short number line when rounding. Whichever end of the number line the number you are rounding is closer to, that is your answer. Remember: halfway always rounds up.

Rounding: Round to the nearest 10, 1000 etc. Using a number line: Let’s round

Rounding: Round to the nearest 10, 1000 etc. Using a number line: Let’s round 865 to the nearest 100. 865 is between 800 and 900. It is about here on the number line below. It is closer to 900. 800 850 Answer: 900

Rounding: Round to the nearest 10, 1000 etc. Using a number line: This time,

Rounding: Round to the nearest 10, 1000 etc. Using a number line: This time, let’s round 865 to the nearest 10. 865 is between 860 and 870. It is about here on the number line below. It’s halfway so we round up to 870. 860 865 Answer: 870

Rounding: Round to the nearest 10, 1000 etc. Round these to what’s in the

Rounding: Round to the nearest 10, 1000 etc. Round these to what’s in the brackets: 1. 487 [nearest 100] 500 2. 2346 [nearest 1000] 2000 3. 6325 [nearest 100] 6300 4. 6325 [nearest 10] 6330

Rounding to the nearest whole number: Round to the nearest 10, 1000 etc. On

Rounding to the nearest whole number: Round to the nearest 10, 1000 etc. On the number line put the whole numbers at either end. Eg. Round 7. 43 to the nearest whole number. 7. 43 7 7. 5 Answer: 7 8

Rounding: Round to the nearest 10, 1000 etc. Round these to the nearest whole

Rounding: Round to the nearest 10, 1000 etc. Round these to the nearest whole number: 1. 4. 8 5 2. 13. 4 13 3. 23. 45 23 4. 134. 69 135

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Decimal places and significant figures Learning Objective: Can I round a decimal to a

Decimal places and significant figures Learning Objective: Can I round a decimal to a given number of decimal places or significant figures?

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. What does this mean? We can round numbers to a certain number of decimal places and significant figures. Decimal places refer to how many digits we want after the decimal point. Significant figures refer to how many digits aren’t zero and not sandwiched between nonzeroes.

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Decimal places Remember that the decimal point does not move! The number needs to be “cut off” at the given number of decimal places. We then round up or down, depending on what the following number is.

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Decimal places example: Round 83. 7649 to 1 decimal place. 8 3. 7 6 4 9 Up until the first decimal place, everything stays the same, so we can write everything up to that point. We may need to round the number in the first decimal place though. The following number is “over halfway” so we round up. Answer: 83. 8

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Another decimal places example: Round 83. 7649 to 2 decimal places. 8 3. 7 6 4 9 Up until the second decimal place, everything stays the same, so we can write everything up to that point. We may need to round the number in the second decimal place though. The following number is “under halfway” so we round down. Answer: 83. 76

S. f. : Round these numbers to the given number of decimal places Round

S. f. : Round these numbers to the given number of decimal places Round to a given number of decimal places or significant figures. 1. 2. 365 [1 dp] 2. 4 2. 6. 739 [1 dp] 6. 7 3. 13. 7328 [2 dp] 13. 73 4. 9. 9999 [1 dp] 10. 0

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Significant figures All numbers have significant figures. 1 st significant figure 6 th significant figure 7 6 0 2 3. 9 8

S. f. : Significant figures – careful with decimals Round to a given number

S. f. : Significant figures – careful with decimals Round to a given number of decimal places or significant figures. Decimals are slightly different. 1 st 5 th significant figure 0. 0 0 2 3 7 0 8 These zeroes aren’t significant This zero is significant

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Rounding to significant figures Round 4534 to 2 sf. 2 nd significant figure 4 5 3 7 The 5 is the 2 nd significant figure, so anything before that stays the same. The 3 rd significant figure is less than 5 so we round down. Fill up to the decimal point with zeroes. Answer: 4500

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Rounding to significant figures 2 Round 0. 00576 to 1 sf. 1 st significant figure 0 . 0 0 5 7 6 The 5 is the 1 st significant figure, so anything before that stays the same. The 2 nd significant figure is more than 5 so we round up. Answer: 0. 006

S. f. : Round to a given number of decimal places or significant figures.

S. f. : Round to a given number of decimal places or significant figures. Have a go at rounding these: 1. 7238 [1 sf] 7000 2. 926706 [2 sf] 930000 3. 0. 0435 [1 sf] 0. 04 4. 0. 00076498 [3 sf] 0. 000765

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Estimation Learning Objective: Can I estimate a difficult calculation?

Estimation Learning Objective: Can I estimate a difficult calculation?

Estimate: Estimate a calculation. Why do we estimate? It is easy to make a

Estimate: Estimate a calculation. Why do we estimate? It is easy to make a mistake when typing calculations into a calculator. We estimate to check that the answer we have sounds or looks sensible. The answer we get when we estimate won’t be exact but close to the right answer.

Estimate: Estimate a calculation. How do we estimate? You want the calculation to be

Estimate: Estimate a calculation. How do we estimate? You want the calculation to be as simple as possible so that you can do it in your head. Round to 1 significant figure or an easier number. Use numbers that work nicely. You must show your working or you will get no marks!

Estimate: Estimate a calculation. Two examples Example 1 Estimate 23 × 18 Example 2

Estimate: Estimate a calculation. Two examples Example 1 Estimate 23 × 18 Example 2 Estimate 32. 3 ÷ 5. 8 Round: 20 × 20 Round: 30 ÷ 6 Calculate: 400 Calculate: 5 Answer: 400 Answer: 5 Showing the workings!

Estimate: Estimate a calculation. Estimate these: 1. 7. 6 × 4. 93 8 ×

Estimate: Estimate a calculation. Estimate these: 1. 7. 6 × 4. 93 8 × 5 = 40 2. 14. 29 × 4. 41 15 × 4 = 60 3. 48. 13 ÷ 9. 7 50 ÷ 10 = 5 4. 48. 13 ÷ 7. 6 48 ÷ 8 = 6

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Estimating difficult calculations Learning Objective: Can I use estimate multi-stage calculations?

Estimating difficult calculations Learning Objective: Can I use estimate multi-stage calculations?

Estimate: Estimate difficult calculations by rounding. Remember bidmas! Sometimes you may be asked to

Estimate: Estimate difficult calculations by rounding. Remember bidmas! Sometimes you may be asked to estimate slightly more difficult calculations. Remember the rules of bidmas when you do these. Use numbers that work nicely!

Estimate: Estimate difficult calculations by rounding. An example • Show the workings!

Estimate: Estimate difficult calculations by rounding. An example • Show the workings!

Estimate: Estimate difficult calculations by rounding. Another example • Show the workings!

Estimate: Estimate difficult calculations by rounding. Another example • Show the workings!

Estimate: Estimate difficult calculations by rounding. Estimate these: •

Estimate: Estimate difficult calculations by rounding. Estimate these: •

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Standard form Learning Objective: Can I read and write numbers in standard form?

Standard form Learning Objective: Can I read and write numbers in standard form?

Read. Form: and write numbers in standard form. Standard What is standard form? •

Read. Form: and write numbers in standard form. Standard What is standard form? •

and write numbers in standard form. Standard Read Form: • Writing large numbers in

and write numbers in standard form. Standard Read Form: • Writing large numbers in standard form 7 0 0 0. How many places did the decimal point move? The decimal point is currently here The decimal point needs to move left until the number is between 1 and 10

Read. Form: and write numbers in standard form. Standard Writing small numbers in standard

Read. Form: and write numbers in standard form. Standard Writing small numbers in standard form • The decimal point is currently here 0. 0 0 2 4 The decimal point needs to move left until the number is between 1 and 10 How many places did the decimal point move?

Read. Form: and write numbers in standard form. Standard Things to remember The decimal

Read. Form: and write numbers in standard form. Standard Things to remember The decimal point moves left or right until the number lies between 1 and 10. Count how many places the decimal point has moved – that’s the power of 10. Large numbers – positive power of 10 Small numbers – negative power of 10.

Standard Form: Have a go at writing these in standard form: 1. 3000 2.

Standard Form: Have a go at writing these in standard form: 1. 3000 2. 230000 3. 0. 0004 4. 0. 00000762

Read. Form: and write numbers in standard form. Standard Now try writing these as

Read. Form: and write numbers in standard form. Standard Now try writing these as “normal” numbers: • 800, 000 42, 600, 000 0. 02 0. 000008913

Read. Form: and write numbers in standard form. Standard The other type of question

Read. Form: and write numbers in standard form. Standard The other type of question you might see: •

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Standard form - calculations Learning Objective: Can I perform calculations in standard form?

Standard form - calculations Learning Objective: Can I perform calculations in standard form?

Calculate with numbers in standard form. Standard Form: • How you calculate with standard

Calculate with numbers in standard form. Standard Form: • How you calculate with standard form:

Calculate with numbers in standard form. Standard Form: On your calculator try these, giving

Calculate with numbers in standard form. Standard Form: On your calculator try these, giving your answers in standard form: •

Calculate with numbers in standard form. Standard Form: Without a calculator: •

Calculate with numbers in standard form. Standard Form: Without a calculator: •

Calculate with numbers in standard form. Standard Form: Two examples of multiplying Example 1

Calculate with numbers in standard form. Standard Form: Two examples of multiplying Example 1 • Example 2 •

Calculate with numbers in standard form. Standard Form: Two more examples Example 3 •

Calculate with numbers in standard form. Standard Form: Two more examples Example 3 • Example 4 •

Standard Form: Calculate with numbers in standard form. Calculate these, giving your answers in

Standard Form: Calculate with numbers in standard form. Calculate these, giving your answers in standard form: •

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Error in measurement Learning Objective: Can I calculate the upper and lower bound of

Error in measurement Learning Objective: Can I calculate the upper and lower bound of a measurement?

Bounds: Calculate taking into account errors in measurement. What do you mean? Every time

Bounds: Calculate taking into account errors in measurement. What do you mean? Every time a measurement is made there is the possibility of an error either way. It all depends to what accuracy the measurement is made. So each measurement has an “upper bound” and a “lower bound”.

Bounds: Calculate taking into account errors in measurement. What does it look like? If

Bounds: Calculate taking into account errors in measurement. What does it look like? If a measurement has been taken, it could actually be half of that measure either side. Each value rounds to the measurement given. A measurement of 5 cm could be anything between 4. 5 cm and 5. 5 cm and round to 5 cm.

Bounds: Calculate taking into account errors in measurement. Some examples: 50 metres measured to

Bounds: Calculate taking into account errors in measurement. Some examples: 50 metres measured to the nearest 10 metres: Half of 10 Upper bound: 55 metres is Lower bound: 45 metres 14 kg measured to the nearest kg: Upper bound: 14. 5 kg Lower bound: 13. 5 kg Half of 1 kg is 0. 5 kg

Bounds: Calculate taking into account errors in measurement. Find the upper and lower bounds

Bounds: Calculate taking into account errors in measurement. Find the upper and lower bounds of these measurements: 1. 2300 kg measured to the nearest 100 kg. Upper bound: 2350 kg Lower bound: 2250 kg 2. 60 metres measured to the nearest metre. Upper bound: 60. 5 m Lower bound: 59. 5 m 3. 7. 58 m measured to the nearest centimetre. Upper bound: 7. 585 m Lower bound: 7. 575 m

Bounds: Calculate taking into account errors in measurement. One last thing… The measurement may

Bounds: Calculate taking into account errors in measurement. One last thing… The measurement may have been rounded to a certain number of decimal places or significant figures. Your answer just needs to go “on one further”.

Bounds: Calculate taking into account errors in measurement. Two examples: Example 1 Example 2

Bounds: Calculate taking into account errors in measurement. Two examples: Example 1 Example 2 Give the upper and lower bound of 3. 4 which has been rounded to 1 dp. Give the upper and lower bound of 5700 which has been rounded to 2 sf. Upper bound: 3. 45 Lower bound: 3. 35 Upper bound: 5750 Lower bound: 5650

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Bounds and calculations Learning Objective: Can I perform calculations by taking errors in measurement

Bounds and calculations Learning Objective: Can I perform calculations by taking errors in measurement into account?

Bounds: Use bounds to calculate whether a calculation is possible. All measurements have an

Bounds: Use bounds to calculate whether a calculation is possible. All measurements have an upper and lower bound. This means that you can get maximum and minimum values of a calculation. Think carefully about which bound you use!

Bounds: Use bounds to calculate whether a calculation is possible. An example: A floor

Bounds: Use bounds to calculate whether a calculation is possible. An example: A floor needs carpeting. The floor measures 4. 2 m by 3. 7 m to the nearest 0. 1 m. What are the upper and lower bounds of the floor’s area? The two upper bounds To find the upper bound: 4. 25 × 3. 75 = 15. 9375 m² To find the lower bound: 4. 15 × 3. 65 = The two lower 15. 1475 m² bounds

Bounds: Use bounds to calculate whether a calculation is possible. Another example - be

Bounds: Use bounds to calculate whether a calculation is possible. Another example - be careful! • Upper bound Lower bound Upper bound

Bounds: Use bounds to calculate whether a calculation is possible. Have a go at

Bounds: Use bounds to calculate whether a calculation is possible. Have a go at this: A bike that is 1. 5 metres long (to the nearest 0. 1 m) needs to go in a shed that is 2 metres long (to the nearest metre). Will the bike definitely fit in the shed? (Explain your answer) No, because the upper bound of the length of the bike is 1. 55 metres and the lower bound of the length of the shed is 1. 5 metres.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not.

Usefulness Debate if rounding is useful or not.

Usefulness Debate if rounding is useful or not.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers.

Rounding, Estimation and Standard Form Learning outcomes: Why we round or estimate with numbers. Round to the nearest 10, 1000 etc. Round to a given number of decimal places or significant figures. Estimate a calculation. Estimate difficult calculations by rounding. Read and write numbers in standard form. Calculate with numbers in standard form. Calculate taking into account errors in measurement. Use bounds to calculate whether a calculation is possible. Debate if rounding is useful or not. WWW? EBI?