Math Leadership Support Network ’08-’09

ESTIMATION Review What is the difference between an estimate and a guess? What is the difference between an estimate and a guess?

Math Leadership Support Network ’08-’09 ESTIMATION Review Why estimate? Why estimate? When should we estimate? When should we estimate?

Math Leadership Support Network ’08-’09 Types of ESTIMATION: Measurement Measurement Quantity Quantity Computational Computational

Math Leadership Support Network ’08-’09 COMPUTATIONAL ESTIMATION Strategies: Front-end Front-end Clustering Clustering Rounding Rounding Compatible/Nice Numbers Compatible/Nice Numbers Special Numbers Special Numbers

Math Leadership Support Network ’08-’09 Front-end Strategy

Math Leadership Support Network ’08-’09 Front-end Strategy with adjustments

Math Leadership Support Network ’08-’09 Clustering Strategy Estimate the total attendance Monday 73,250 Tuesday63,819 Wednesday67,490 Thursday73, 180 Friday74, 918 Saturday68, 490

Math Leadership Support Network ’08-’09 Rounding Strategy

Math Leadership Support Network ’08-’09 Compatible/Nice Numbers Strategy Estimate 3388 ÷ 7 a) 3500 ÷ 7b) 3200 ÷ 7 c) 3200 ÷ 7d) 3400 ÷ 8 e) 3300 ÷ 7f) 4000 ÷ 8

Math Leadership Support Network ’08-’09 Special Numbers Strategy 7/8 + 6/13 = 9.84% of 345 = ÷ 0.98 = x 24.3 =

Math Leadership Support Network ’08-’09 WHY???? With all of the great estimation strategies out there, why do our students struggle with computational estimation?? Why do some of our students, work out the original problem and then round for their estimate?

Math Leadership Support Network ’08-’09 ESTIMATION Review How can we help students become better estimators? How can we help students become better estimators? How can we assess their ability to estimate? How can we assess their ability to estimate?

Math Leadership Support Network ’08-’09 Grade-Level Breakouts

Math Leadership Support Network ’08-’09 Middle School Breakout COMMIT TO AN OUTCOME: COMMIT TO AN OUTCOME: Terrence and his group were given this problem to estimate: 48 x 24 Terrence and his group were given this problem to estimate: 48 x x 5 17 x 5

Math Leadership Support Network ’08-’09 They each had their own method and shared their strategies (see chart). Donovan said that one of the estimates was unreasonable. Without picking up your pencil or calculator, can you quickly spot which approach is unreasonable? Why is it unreasonable?

Math Leadership Support Network ’08-’09 EXPOSE BELIEFS: EXPOSE BELIEFS: Share your choice and reasoning with Share your choice and reasoning with your group. your group. Ask someone from your group to be Ask someone from your group to be ready to share the group’s ideas with ready to share the group’s ideas with the class. the class.

Math Leadership Support Network ’08-’09 CONFRONT BELIEFS: CONFRONT BELIEFS: In your group, come up with an agreement on a good way to estimate this problem. In your group, come up with an agreement on a good way to estimate this problem. Test the proposed methods of estimation from Terence’s group. Test the proposed methods of estimation from Terence’s group. How does the result of your work compare with your original thoughts about this problem? How does the result of your work compare with your original thoughts about this problem? Prepare to share your group’s strategy with the class. Prepare to share your group’s strategy with the class.

Math Leadership Support Network ’08-’09 ACCOMMODATE THE CONCEPT ACCOMMODATE THE CONCEPT Compare your results with those of other groups. Compare your results with those of other groups. Based on what you have observed and heard, write down the strengths and weaknesses of the different approaches used for estimation. Based on what you have observed and heard, write down the strengths and weaknesses of the different approaches used for estimation. In your own words, explain an approach to estimation that makes the most sense to you and explain why you chose that approach? In your own words, explain an approach to estimation that makes the most sense to you and explain why you chose that approach?

Math Leadership Support Network ’08-’09 EXTEND THE CONCEPT EXTEND THE CONCEPT GO BEYOND GO BEYOND See Handout See Handout

Math Leadership Support Network ’08-’09 Probes and Probing Questions… What are some types of questions you can ask and activities you can provide to get at student understanding and/or misconceptions of computational estimation?

Math Leadership Support Network ’08-’09 1. Which of these products will be 100 or greater? How do you know? 54.2 x x x x x x x x x x 18.3

Math Leadership Support Network ’08-’09