| 2.2 Understand and Apply Concepts Related
to Computation and Estimation |
2.2 Grade 3
(Computation and Estimation) |
2.2 Grade 5
(Computation and Estimation) |
2.2 Grade 8
(Computation and Estimation) |
2.2 Grade 11
(Computation and Estimation) |
| A. Basic functions (addition, subtraction, multiplication,
and division) |
A1. Apply addition and subtraction situations using concrete
objects. |
A1. Add, subtract, multiply, and divide whole numbers with and
without calculators. |
A1. Complete calculations by applying the order of operations. |
A1. Develop and use computation concepts, operations, and procedures
on real numbers in problem solving situations. |
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A2. Solve single and double digit addition and subtraction problems
with regrouping in vertical form. |
A2. Create and solve word problems involving addition, subtraction,
multiplication, and division of whole numbers. |
A2. Add, subtract, multiply, and divide different kinds and
forms of rational numbers including integers, decimal fractions, percents,
and proper and improper fractions. |
A2. Use estimation to solve problems for which exact answer
is not needed. |
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A3. Demonstrate concepts of multiplication as repeated addition
and arrays. |
A3. Develop and apply algorithms to solve word problems that
involve addition, subtraction, and/or multiplication with decimals with
and without regrouping, fractions and mixed numbers, that include like
and unlike denominators. |
A3. Solve word problems using ratio and proportion. |
A3. Construct and apply mathematical models, including lines
and curves of best fit, to estimate values of related quantities. |
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A4. Demonstrate concept of division as repeated subtraction
and as sharing. |
A4. Use +, -, x, ¸, /, , $, ¢, %, and (decimal
point) correctly in number sentences and expressions. |
A4. Estimate amount of tips and discounts using ratios, proportions,
and percents. |
A4. Describe and explain the amount of error that may exist
in a computation using estimates. |
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A5. Count, compare, and make change using a collection of coins
and one-dollar bills. |
A5. Use recall, mental computations, pencil and paper, measuring
devices, math texts, manipulatives, calculators, etc., as appropriate,
to achieve solutions. |
A5. Demonstrate appropriateness of overestimating or underestimating
in computation. |
A5. Recognize that the degree of precision needed in calculating
a number depends on how the results will be used and the instruments used
to generate the measure. |
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A6. Demonstrate knowledge of basic facts in four basic operations. |
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A6. Identify the difference between exact value and approximations
and determine which is appropriate for a given situation. |
A6. Demonstrate skills for using computer spreadsheets and scientific
and graphing calculators. |
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A7. Explain addition and subtraction algorithms with regrouping. |
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A7. Estimate the value of irrational numbers. |
| B. Reasonableness of answers |
B1. Estimate, approximate, or use exact numbers as appropriate. |
B1. Demonstrate the ability to round numbers. |
B1. Check the reasonableness of an answer. |
B1. Check the reasonableness of an answer. |
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B2. Use estimation skills to arrive at conclusions. |
B2. Determine through estimations the reasonableness of answers
to problems involving addition, subtraction, multiplication, and division
of whole numbers. |
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B3. Know and be able to apply the rules of rounding. |
B3. Apply estimation strategies to a variety of problems including
time and money. |
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B4. Determine the reasonableness of calculated answers. |
B4. Estimate numerically and spatially. |
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| C. Calculators |
C1. Use estimation skills to arrive at conclusions. |
C1. Demonstrate skills for using fraction calculators to verify
conjectures, confirm computations, and explore complex problem solving
situations. |
C1. Use scientific and/or graphing calculators to assist in
problem solving. |
C1. Continue the use of graphing calculators to assist in problem
solving. |
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C2. Know four basic functions of calculators (+, -, x, ÷). |
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C3. Be able to check answers with calculator for adding, subtracting,
and multiplying. |
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C4. Use calculators for problem solving. |
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