1. Rounding and Estimating Salem School Wednesday, April 23, 2008 Wednesday, April 23, 2008

2. Components in Teaching Professional judgment knowledge experience evidence Mathematics Decide on the mathematics needed to move students on Pedagogy Decide on learning activities and focus questions Students Observe students and interpret what they do and say from First Steps in Mathematics

3. What questions do we ask ourselves about estimation?  What is the difference between rounding and estimating?  What types of rounding and estimation skills and concepts are appropriate to teach at my grade level?  What are some activities I use to teach these concepts?

4. Rounding vs. Estimating Rounding Taking a known value and making it less accurate Ex. I spent $200 for my new camera. Estimating Coming up with an inaccurate number you didn’t have in exact form to begin with Ex. I’d say there are 50 pretzels in that bowl.

5. State Standards  National & State Standards  CMT Strands  Naugatuck’s Math Power Standards  State of CT GLE’s  Your classroom…

6. CMT Strands 4. Order, Magnitude and Rounding Numbers C. Round 2-digit whole numbers in context. (Gr.3) C. Round 2- and 3- digit whole numbers in context. (Gr. 4) 10. Numerical Estimation Strategies A. Identify the best expression to find an estimate. (Gr. 3/4) 11. Estimating Solutions to Problems A. Identify a reasonable estimate to a problem. (Gr. 3) A. Identify a reasonable estimate to a problem, including estimating change from $1, $5, and $10. (Gr. 4) 15. Approximating Measures A. Estimate lengths and areas by comparing. (Gr.3/4)

7. Components in Teaching Professional judgment knowledge experience evidence Mathematics Decide on the mathematics needed to move students on Pedagogy Decide on learning activities and focus questions Students Observe students and interpret what they do and say from First Steps in Mathematics

8. School: Naugatuck District Grade: 3 Subject: Math Test: BR Math 1 Question: 9, CMT 4c 62 + 97 = If you round each number in the number sentence to the nearest ten, how would the new number sentence look? A 60 + 90 = B 60 + 100 = C 70 + 90 = D 70 + 100 = Number of students answering question:202 A 31% B 54% C 8% D 5% Blank 1%

9. School: Naugatuck District Grade: 3 Subject: Math Test: BR Math 1 Question: 20, CMT 10b Jesse bought a basketball hoop for $78 and gave the clerk $100. Which of the following would be best for Jesse to use to estimate the change? A $80 − $100 B $70 − $100 C $100 − $80 D $100 − $70 Number of students answering question:202 A 37% B 23% C 26% D 13% Blank 1%

10. School: Naugatuck District Grade: 3 Subject: Math Test: BR Math 1 Question: 22, CMT11a Mark invited 13 people to his party. Peter invited 22 people to his party. About how many more people did Peter invite to his party? A 5 B 10 C 15 D 35 Number of students answering question:202 A 2% B 55% C 13% D 27% Blank 2%

11. Components in Teaching Professional judgment knowledge experience evidence Mathematics Decide on the mathematics needed to move students on Pedagogy Decide on learning activities and focus questions Students Observe students and interpret what they do and say from First Steps in Mathematics

12. 8 Common Types Perceptual Estimation 1.Compare an unknown quantity to a known 2.Partition an unknown into known quantities 3.Use mental computation Computational 4.Front-end estimation 5.Clustering 6.Rounding 7.Compatible numbers 8.Special Numbers From Estimation and Mental Computation, 1986 Yearbook, National Council of Teachers of Mathematics

13. Strategies Rounding Skills (Strand 4) Number Lines Modified Hundreds Charts Rounding only one number Identifying the Best Expression/Solution (Strands 10 & 11) Rounding, rounding, rounding! It comes FIRST! Practice with & without word problems Make up own problems to emphasize reasonableness Measurement (Strand 15) Post It – Mark It (Alternative: Tear It-Mark It) Real Life Applications Cube Guess style learning opportunities

14. Components in Teaching Professional judgment knowledge experience evidence Mathematics Decide on the mathematics needed to move students on Pedagogy Decide on learning activities and focus questions Students Observe students and interpret what they do and say from First Steps in Mathematics

15. “Two are better than one, if two act as one.” Coach Mike Krzyzewski, Head Coach, Duke Basketball Head Coach, Duke Basketball

16. CMT Strand 4. Order, Magnitude, and Rounding Numbers 4c. Round 2-digit (3-digit Gr.4) in context. Mrs. Kruge had 38 lollipops. This number is about… o 30 o 40 o 50 o 60 The Smith family drove 234 miles to see their cousins. This number is… o A little more than 100 o A little less than 200 o A little more than 200 o A little less than 300 Matt had 13 cars. This number is CLOSEST to… o 0 o 10 o 20 o 30

17. CMT Strand 10. Numerical Estimation Strategies 10a. Identify the best expression to find an estimate. There are two third grade classes at Salem. Mrs. Lahey has 23 students. Mrs. Tamowski has 27 students. Which of the following would be the best for the teachers to estimate the total number of students in third grade? o 10 + 20 o 20 + 20 o 20 + 30 o 30 + 30 Frank bought a book at the book fair for $12.95. He gave the clerk a $20 bill. Which of the following would be the best expression for Frank to estimate his change? o $12 - $20 o $20 - $12 o $20 - $13 o $13 - $20

18. CMT Strand 11. Estimating Solutions to Problems 11a. Identify a reasonable estimate to a problem (Gr.3), including estimating change from $1, $5, and $10 (Gr.4). There are two third grade classes at Salem. Mrs. Lahey has 23 students. Mrs. Tamowski has 27 students. About how many students are in third grade? o 30 o 40 o 50 o 60 Frank bought a book at the book fair for $12.95. He gave the clerk a $20 bill. About how much change should he receive? o A little less than $10 o A little more than $10 o A little less than $20 o A little more than $20

19. About how many squares long is the car? CMT Strand 15. Approximating Measures 15a. Estimate lengths and areas by comparing. The tree is 12 feet high. About how high is the

20. “Success is not a matter of just wanting to win. It’s a matter of preparing to win – which is much more important.” Coach Mike Krzyzewski, Head Coach, Duke Basketball Head Coach, Duke Basketball