1. Estimating Decimals EQ: How can I use estimation techniques? MA.6.A.3.5

2. Estimating Decimals ClusteringRoundingCompatible Numbers

3. Clustering What is clustering?

4. Clustering A method used to estimate a sum or product when all the numbers are close to the same value. When would you use clustering to estimate the solution to a problem involving decimals?

5. Clustering What is clustering? A method used to estimate a sum or product when all the numbers are close to the same value. When would you use clustering to estimate the solution to a problem involving decimals? When all the numbers are close to each other.

6. Clustering Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.) In this example, what number could represent all of the calories?

7. Clustering Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.) In this example, what number could represent all of the calories? 170

8. Clustering Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.) In this example, what number could represent all of the calories? 170

9. Clustering Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.) What operation could you use rather than adding 170 plus 170 plus 170?

10. Clustering Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling – 165.5 calories, ice skating – 177.5 calories, and water skiing – 171.5 calories.) What operation could you use rather than adding 170 plus 170 plus 170? Multiplication

11. Rounding When rounding a decimal, how do you know which digit to look at?

12. Rounding 0. 375 1000 Place a 1 under the decimal and a 0 under each value past the decimal. Read the whole number and the “spit” number

13. Rounding Explain the rules for rounding a decimal.

14. Rounding ◦ Underline the specified place value.

15. Rounding Explain the rules for rounding a decimal. ◦ Underline the specified place value. ◦ Look to the right of the underlined value.

16. Rounding Explain the rules for rounding a decimal. ◦ Underline the specified place value. ◦ Look to the right of the underlined value. ◦ 5 or more “raise the score” or 4 or less “let it rest”

17. Rounding If you rounded all the numbers “up”, how would your estimated answer compare to the actual answer to the problem?

18. Rounding If all the numbers were rounded up, the estimated answer would be an over-estimate

19. Compatible Numbers What are compatible numbers? Given the expression 33.83 · 1.98, how does the estimated product compare to the actual product? Explain. Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26? What would you use?

20. Compatible Numbers What are compatible numbers? Numbers that are close to the given numbers that make estimation or mental math easier.

21. Compatible Numbers Given the expression 33.83 · 1.98, how does the estimated product compare to the actual product? Explain.

22. Compatible Numbers Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26?

23. Compatible Numbers Given the expression 72.77 ÷ 26.14, why would you choose not to round the numbers to 73 and 26? What would you use?

24. Estimating Decimals Make the following estimations and justify your choices Estimating Decimals Clustering 31.2 · 28.7 · 30.5 Rounding 7.6 · 9.2 Compatible Numbers 18.89 · 5.11