rounding and estimating salem school wednesday, april 23, 2008 wednesday, april 23, 2008

Rounding and Rounding and EstimatingEstimating

Rounding and Rounding and EstimatingEstimating

Salem SchoolSalem School

Wednesday, April 23, 2008Wednesday, April 23, 2008

Components in Teaching

Professionaljudgmentknowledgeexperienceevidence

MathematicsDecide on the mathematics

needed to move students on

PedagogyDecide on

learning activitiesand focus questions

StudentsObserve students

and interpretwhat they do

and say from First Steps in Mathematics

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?

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.

State Standards National & State Standards

CMT Strands

Naugatuck’s Math Power Standards

State of CT GLE’s

Your classroom…

CMT Strands4. 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 StrategiesA. Identify the best expression to find an estimate. (Gr. 3/4)

11. Estimating Solutions to ProblemsA. 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 MeasuresA. Estimate lengths and areas by comparing. (Gr.3/4)





PedagogyDecide on





School: Naugatuck District Grade: 3Subject: 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%

School: Naugatuck District Grade: 3Subject: 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


School: Naugatuck District Grade: 3Subject: 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






PedagogyDecide on





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

StrategiesRounding 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





PedagogyDecide on





““Two are better than Two are better than one, if two act as one, if two act as

one.”one.”

““Two are better than Two are better than one, if two act as one, if two act as

one.”one.”

Coach Mike Krzyzewski,Coach Mike Krzyzewski, Head Coach , Duke BasketballHead Coach , Duke Basketball

CMT Strand 4.Order, Magnitude, and Rounding

Numbers4c. Round 2-digit (3-digit Gr.4) in context.

Mrs. Kruge had 38 lollipops. This number is about…

o30o40o50o60

The Smith family drove 234 miles to see their cousins. This number is…

oA little more than 100oA little less than 200oA little more than 200oA little less than 300

Matt had 13 cars. This number is CLOSEST to…

o0o10o20o30

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?

o10 + 20o20 + 20o20 + 30 o30 + 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 - $20o$20 - $12o$20 - $13 o$13 - $20

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?

o30o40o50 o60

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 $10o A little more than $10o A little less than $20oA little more than $20

About how manysquares 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

““Success is not a matter of just Success is not a matter of just wanting to win. It’s a matter of wanting to win. It’s a matter of

preparing to win – which is much preparing to win – which is much more important.”more important.”

““Success is not a matter of just Success is not a matter of just wanting to win. It’s a matter of wanting to win. It’s a matter of

preparing to win – which is much preparing to win – which is much more important.”more important.”

Coach Mike Krzyzewski,Coach Mike Krzyzewski, Head Coach , Duke BasketballHead Coach , Duke Basketball

rounding and estimating salem school wednesday, april 23, 2008 wednesday, april 23, 2008

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