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A. NUMBER: Students use numbers in everyday and mathematical contexts to quantify or describe phenomena, develop concepts of operations with different types of numbers, use the structure and properties of numbers with operations to solve problems, and perform mathematical computations. Students develop number sense related to magnitude, estimation, and the effects of mathematical operations on different types of numbers. It is expected that students use numbers flexibly, using forms of numbers that best match a situation. Students compute efficiently and accurately. Estimation should always be used when computing with numbers or solving problems. 
WHOLE NUMBER





A.1. Students understand and use number notation and place value to 100,000 in numerals.  a. Read and write numbers up to 100,000 in numerals and words.
 Number and Numeration Goal 1: Read and write whole numbers up to 1,000,000 and decimals through thousandths: identify places in such numbers and the values of the digits in those places; translate between whole numbers and decimals represented in words and in base10 blocks. Units 2, 4, 5, and 9   classroom tests
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 b. Recognize the place value of digits in numbers to 100,000.
 Number and Numeration Goal 1: Read and write whole numbers up to 1,000,000 and decimals through thousandths: identify places in such numbers and the values of the digits in those places; translate between whole numbers and decimals represented in words and in base10 blocks. Units 2, 4, 5, and 9   classroom tests
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 c. Compare and order numbers with up to five digits.
 Number and Numeration Goal 6: Compare and order whole numbers up to 1,000,000 and decimals through thousandths; compare and order integers between100 and 0; use area models, benchmark fractions, and analyses of numerators and denominators to compare and order fractions. Units 4 and 9   classroom tests
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 d. Round numbers to the nearest 100 or 1000.
 Operations and Computation Goal 6: Make reasonable estimates for whole number and decimal adddition and subtraction problems, and whole number multiplication and division problems; explain how the estimates were obtained. Units 2, 3, 4, 5, and 9   classroom tests
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A.2. Students understand and use the concepts of factor and multiple.
 a. Determine if a singledigit number is a factor of a given whole number.
 Number and Numeration Goal 3: Find multiples of whole numbers less than 10; find wholenumber factors of numbers. Units 6 and 12
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 b. Determine if a whole number is a multiple of a given single digit number.
 Number and Numeration Goal 3: Find multiples of whole numbers less than 10; find wholenumber factors of numbers. Units 6 and 12
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 c. List the first 10 multiples of a given number.
 Number and Numeration Goal 3: Find multiples of whole numbers less than 10; find wholenumber factors of numbers. Units 6 and 12   classroom tests
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A.3. Students understand and use procedures to multiply and divide whole numbers by twodigit numbers.
 a. Multiply up to fourdigit numbers by a singledigit number.
 Operations and Computation Goal 4: Use mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the multiplication of multi digit whole numbers by 2digit whole numbers and the division of multi digit whole numbers by 1digit whole numbers; describe the strategies used and explain how they work. Units 3, 5, 6, 7, and 12   classroom tests
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 b. Multiply threedigit numbers by twodigit numbers
 Operations and Computation Goal 4: Use mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the multiplication of multi digit whole numbers by 2digit whole numbers and the division of multi digit whole numbers by 1digit whole numbers; describe the strategies used and explain how they work. Units 3, 5, 6, 7, and 12   classroom tests
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 c. Divide whole numbers up to four digits by a singledigit number and by ten (remainders may be present).
 Operations and Computation Goal 4: Use mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the multiplication of multi digit whole numbers by 2digit whole numbers and the division of multi digit whole numbers by 1digit whole numbers; describe the strategies used and explain how they work. Units 3, 5, 6, 7, and 12   classroom tests
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RATIONAL NUMBER



 
A.4. Students understand, name, compare, illustrate, combine and use fractions.
 a. Add and subtract fractions with like denominators and use repeated addition to multiply a unit fraction by a whole number.
 Operations and Computation Goal 5: Use manipulatives, mental arithmetic, and calculators to solve problems involving the addition and subtraction of fractions with like unlike denominators; describe the strategies used. Unit 7   classroom tests
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 b. List equivalent fractions.
 Number and Numeration Goal 5: Use numerical expressions to find and represent equivalent names for fractions and decimals; use and explain a multiplication rule to find equivalent fractions; rename fourths, fifths, tenths, and hundredths as decimals and percents. Units 3, 4, 7, and 9   classroom tests
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 c. Represent fractions greater than one as mixed numbers and mixed numbers as fractions.
 Number and Numeration Goal 5: Use numerical expressions to find and represent equivalent names for fractions and decimals; use and explain a multiplication rule to find equivalent fractions; rename fourths, fifths, tenths, and hundredths as decimals and percents. Units 3, 4, 7, and 9   classroom tests
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A.5. Students understand and use number notation and place value in numbers with two decimal places in real world contexts including money.
 a. Compare, order, read, round and interpret decimals with up to two decimal places.
 Number and Numeration Goal 6 : Compare and Order whole numbers up to 1,000,000 and decimals through thousandths; compare and order integers between 100 and 0; use area models, benchmark fractions, and analyses of numerators and denominators to compare and order fractions. Unit 4 and 9   classroom tests
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 b. Add and subtract decimals with up to two decimal places.
 Operations and Computation Goal 2: Use manipulatives, mental arithmetic, paperand pencil algorithms, and calculators to solve problems involving the addition and subtraction of whole numbers and decimals through hundredths; describe the strategies used and explain how they work. Units 2, 3, 4, 5, and 6   classroom tests
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 c. Multiply and divide decimals with up to two decimal places by a onedigit whole number.
 Operations and Computation Goal 4: Use mental arithmetic, paperandpencil algorithms, and calculators to solve problems involving the multiplication of multi digit whole numbers by 2digit whole numbers and the division of multi digit whole numbers by 1digit whole numbers; describe the strategies used and explain how they work. Unit 9   classroom tests
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 d. Connect equivalent decimals and fractions for 1/10s, 1/4s and 1/2s in meaningful contexts.
 Number and Numeration Goal 5: Use numerical expressions to find and represent equivalent names for fractions and decimals; use and explain a multiplication rule to find equivalent fractions; rename fourths, fifths, tenths, and hundredths as decimals and percents. Units 3, 4, 7, and 9   classroom tests
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REAL NUMBERS





No performance indicator. Although no performance indicators are stated, students are expected to have instructional experiences in which they use only rational numbers. 




B. DATA: Students make measurements and collect, display, evaluate, analyze and compute with data to describe or model phenomena and to make decisions based on data. Students compute statistics to summarize data sets and use concepts of probability to make predictions and describe the uncertainty inherent in data collection and measurement. It is expected that when working with measurements students:
 understand that most measurements are approximations and that taking repeated measurements reveals this variability;
 understand that a number without a unit is not a measurement, and that an appropriate unit must always be attached to a number to provide a measurement;
 understand that the precision and accuracy of a measurement depends on selecting the appropriate tools and units; and use estimation comparing measures to benchmarks appropriate to the type of measure and units.

MEASUREMENT AND APPROXIMATION





B.1. Students understand and use measurement of time, capacity and temperature.
 a. Select appropriate tools and units for these measures.




 b. Solve and justify problems with these measures.




DATA ANALYSIS





B.2. Students collect and represent data in tables, line plots, and bar graphs, and read and interpret these types of data displays.

 Data and Chance Goal 1: Collect and organize data or use given data to create charts, tables, bar graphs, line plots, and line graphs. Units 2, 9, and 12 Data and Chance Goal 2: Use the maximum, minimum, range, median, mode, and graphs to ask and answer questions draw conclusions, and make predictions. Units 2, 3, 5, 8, 9, and 12   classroom tests
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PROBABILITY





No performance indicator. Although no performance indicators are stated, students are expected to have experiences with probability in grade four, but it is not expected that the knowledge will be secure.

 Data and Chance Goal 4: Predict the outcomes of experiments and test the predictions using manipulatives; summarize the results and use them to predict future events; express the probability of an event as a fraction Unit 7 Data and Chance Goal 3: Describe events using certain, very likely, likely, unlikely, impossible, and other basic probability terms; use more likely, equally likely, same chance, 50/50, less likely, and other basic probability terms to compare events; explain the choice of language. Unit 7   classroom tests
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C. GEOMETRY: Students use measurement and observation to describe objects based on their sizes and shapes; model or construct twodimensional and threedimensional objects; solve problems involving geometric properties; compute areas and volumes based on object properties and dimensions; and perform transformations on geometric figures. When making or calculating measures, students use estimation to check the reasonableness of results.

GEOMETRIC FIGURES





C.1. Students identify and name angles, lines, relationships between lines, quadrilaterals, and triangles.
 a. Identify perpendicular and parallel lines and sides.
 Geometry Goal 1: Identify, draw, and describe points, intersecting and parallel line segments and lines, rays, and right, acute, and obtuse angles Units 1, 6, 8, and 11   classroom tests
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 b. Identify and sketch the following quadrilaterals: rectangle, square, parallelogram, rhombus, and trapezoid.
 Geometry Goal 2: Describe, compare, and classify plane and solid figures, including polygons, circles, spheres, cylinders, rectangular prisms, cones, cubes, and pyramids, using appropriate geometric terms including vertex, base, face, edge, and congruent Units 1, 6, 7, 8, 10 and 11   classroom tests
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 c. Identify and sketch the following triangles: isosceles, equilateral, acute, obtuse and right.
 Geometry Goal 1: Identify and name acute, obtuse, right, straight, and reflex angles. Unit 9 (B)
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GEOMETRIC MEASUREMENT





C.2. Students understand the concept of area of a figure.
 a. Find the area of shapes in nonstandard units.
 Measurement and Reference Frames Goal 2: Describe and use strategies to measure the perimeter and area of polygons, to estimate the area of irregular shapes and to find the volume of rectangular prisms Units 8 and 11   classroom tests
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 b. Find the area of squares and other rectangles in standard units.
 Measurement and Reference Frames Goal 2: Describe and use strategies to measure the perimeter and area of polygons, to estimate the area of irregular shapes and to find the volume of rectangular prisms Units 8 and 11   classroom tests
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 c. Recognize and estimate the relative sizes of one square meter and one square centimeter and one square inch and one square foot.
 Measurement and Reference Frames Goal 3: Describe relationships among U.S. customary units of length and among metric units of length Units 4, 8, and 11
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TRANSFORMATIONS





C.3. Students recognize congruent figures and line symmetry in figures.
 a. Recognize whether a line is a line of symmetry in a figure.
 Geometry Goal 3: Identify, describe, and sketch examples of reflections; identify and describe examples of translations and rotations. Units 6 and 10
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 b. Recognize congruent figures.
 Geometry Goal 2: Identify congruent figures. Draw or form a figure congruent to a given figure. Unit 10 (B)
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D. ALGEBRA: Students use symbols to represent or model quantities, patterns and relationships and use symbolic manipulation to evaluate expressions and solve equations. Students solve problems using symbols, tables, graphs and verbal rules choosing the most effective representation and converting among representations.

SYMBOLS AND EXPRESSIONS





D.1. Students create and evaluate simple expressions in the context of numbers and operations as described in Standard 2.1: Number* for this grade level. *Standard 2.1 referenced here in the language of Me. Dept. of Ed. Reg. 131 refers to Standard Aof this document.
 a. Create and evaluate expressions with no more than two variables.
 Patterns, Functions, and Algebra Goal 2: Use conventional notation to write expressions and number sentences using the basic 4 arithmetic operations; determine whether number sentences are true or false; solve open sentences and explain the solutions; write expressions and number sentences to model number stories. Units 2, 3 6, and 9 (B)   classroom tests
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EQUATIONS AND INEQUALITIES





D.2. Students find the unknown in simple equations in the context of numbers and operations as described in Standard 2.1: Number* for this grade level such as: 3 . b = 12 3 + 4 = x + 5 6 x 5 = 3 x [ ] *Standard 2.1 referenced here in the language of Me. Dept. of Ed. Reg. 131 refers to Standard Aof this document.

 Patterns, Functions, and Algebra Goal 2: Use conventional notation to write expressions and number sentences using the basic 4 arithmetic operations; determine whether number sentences are true or false; solve open sentences and explain the solutions; write expressions and number sentences to model number stories. Units 2, 3 6, and 9 (B)   classroom tests
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FUNCTIONS AND RELATIONS





D.3. Students use tables, rules, diagrams, and patterns to represent the relationship between quantities and to extend sequences.

 Data and Chance Goal 1: Collect and organize data or use given data to create charts, tables, bar graphs, line plots, and line graphs. Units 2, 9, and 12 Patterns, Functions, and Algebra Goal 1: Extend, describe, and create numeric patterns; describe rules for patterns and use them to solve problems; use words and symbols to describe rules for functions that involve the 4 basic arithmetic operations and use those rules to solve problems Units 2, 3, 5, 7, 10, 11, and 12   classroom tests
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