Math Curriculum

Kindergarten Math Objectives 2009 - 2010

Number Sense and Place Value (MK:1, MK:2, MK:7) Students represent, compare, and order whole numbers. They demonstrate one-to-one correspondence, understand the relationship between whole numbers, and make reasonable estimates.

1. Student counts to 100 by 1’s.

2. Student counts from 0 to 100 by 10’s.

3. Student counts from 0 to 50 by 5’s.

4. Student counts backwards from 20.

5. Student reads numbers to 100.

6. Student writes numbers to 100.

7. Student shows correct sequence of numbers to 50

8. Student demonstrates 1:1 correspondence with numbers 0 to 50.

9. Student names the number before and after up to 50.

10. Student identifies the first, second, or third object in a group.

11. Student knows that 13 = 10 + 3; 27 = 20 + 7

12. Student estimates and evaluates the reasonableness of solutions.

Operations and Computation (MK:3, MK:4) Students demonstrate understanding of the meaning of mathematical operations (addition, subtraction), by solving problems involving situations in which one adds to or takes from.

1. Student solves addition problems using numbers 10 or less.

2. Student solves subtraction problems using numbers 5 or less.

Geometry and Measurement Concepts (MK: 5; MK: 9; MK: 15; MK: 16; MK: 18) Students use attributes, composition, or decomposition to sort or classify objects using at least one attribute; determine elapsed and accrued time; and find and name locations with simple relationships.

1. Student recognizes and names designated shapes.

2. Student uses attributes to sort or classify objects using at least one attribute and identifies the attribute.

3. Student identifies the appropriate tool used to measure length.

4. Student identifies the appropriate tool used to measure temperature.

5. Student identifies the appropriate tool used to measure weight.

6. Student compares objects in relationship to length, weight, and capacity.

7. Student demonstrates an understanding of the concept of time.

8. Student identifies a clock and a calendar as measurement tools.

9. Student names the days of the week.

10. Student tells time to the hour using an analog and digital clock.

11. Student finds and names locations with simple spatial relationships. ( i.e.., near, far, above, below, under, next to, beside, between.)

12. Student names coins (pennies, nickels, dimes).

13. Student knows value of coins (pennies, nickels, dimes).

Functions and Algebra Concepts (MK:19) Students identify and extend to specific case a variety of patterns.

1. Student creates, identifies, and continues a three part pattern.

Data, Statistics and Probability Concepts (MK:23; MK:25) Students interpret a pictograph and display data.

1. Student compares the data in a pictograph.

2. Student represents data using concrete objects or pictures.

Mathematical Problem Solving (MK:30) Students create and use an appropriate grade level strategy to solve and communicate their approach and reasoning to problem solving.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student creates and uses a strategy and/or grade level approach to solve a problem.

2. Student represents the solution to grade level problems.

First Grade Math Objectives 2009 - 2010

Number Sense and Place Value (M1:1; M1:2, M1:5; M1:7, M1:8) Students understand ways of representing numbers and whole number relationships, including grouping in tens and ones. Students compare and order whole numbers, and understand the sequential order of the counting numbers. Students demonstrate understanding of monetary value.

1. Student counts on from a given number to 100 by 1’s, 2’s, 10’s, and 5’s.

2. Student counts backwards from 50 by 1’s.

3. Student reads and writes numbers to 199. (i.e. Write forty-six; seventeen; thirty-one, one hundred three; one hundred eighty; fifteen; ninety; one hundred sixty-four).

4. Student identifies odd and even numbers.

5. Student makes connections between ordinal and cardinal numbers.

6. Student uses expanded notation with whole numbers from 0 to 99 (i.e. 48 = 4 tens and 8 ones; 48 = 40 + 8; demonstrates understanding using base-ten blocks).

7. Student demonstrates understanding of equivalency by finding “other names for” numbers (i.e. 14 = 8 + 6; 11 + 3, 26 – 12; Write five other names for ______).

8. Student recognizes fractions 1/2 and 1/4 as parts of a whole (i.e. shaded and/or labeled parts.

9. Student demonstrates understanding of the relative magnitude of numbers from 0 to 199 by comparing whole numbers to each other (greater than, less than, equal to).

10. Student names and demonstrates understanding of value of coins (penny, nickel, dime, quarter).

11. Student understands that estimation is not a precise measurement. Estimates and evaluates the reasonableness of solutions appropriate to grade level.

Operations and Computation (M1:3; M1:4; M1:8) Students demonstrate conceptual understanding of addition and subtraction and how they relate to one another. They develop strategies to solve basic addition problems and related subtraction computation.

1. Student demonstrates conceptual understanding of mathematical operations involving addition by correctly solving grade appropriate problems.

2. Student demonstrates conceptual understanding of mathematical operations involving subtraction by correctly solving grade appropriate problems.

3. Student mentally adds and subtracts whole number facts through 10 with accuracy.

4. Student writes and solves addition number stories and sentences (situations in which one adds to, puts together, or adds).

5. Student writes and solves subtraction number stories and sentences (situations in which one takes from and takes apart).

6. Student solves number sentences (equations) with missing addends.

(______ + 3 = 8; 6 + _____ = 10; ____ + ____ = 9)

8. Student adds coins together to a value no greater than $1.00.

Geometry and Measurement Concepts (M1:9; M1:11; M1:16) Students analyze characteristics and properties of two-and three-dimensional shapes. Students compose and decompose geometric shapes, and use attributes to identify and sort polygons. Students use non-standard units of linear measurement and weight. Students tell time to the half-hour.

1. Student identifies polygons and three-dimensional shapes (a square, rectangle, triangle, circle, trapezoid, rhombus, and hexagon).

2. Student uses attributes (color, size, thickness, shape) to sort, order, compare or describe polygons (triangles, squares, rectangles, rhombi, trapezoids, and hexagons).

3. Student uses nonstandard units for linear measurement.

4. Student uses a ruler to measure to the nearest inch/centimeter.

5. Student uses nonstandard units to measure weight.

6. Student names the seasons and months of the year.

7. Student understands and uses “yesterday, today, tomorrow” appropriately.

8. Student understands that an hour is longer than a half-hour; a month is longer than a day.

9. Student reads and writes dates.

10. Student tells time to the hour and half-hour using analog and digital clocks.

Functions and Algebra Concepts (M1:19; M1:22) Students identify and extend to specific cases a variety of patterns. Students demonstrate a conceptual understanding of equality by showing equivalence between two expressions (4+1=5; 2+3=5) and by solving one-step equations.

1. Student creates and extends a simple three part pattern using numbers, letters, and shapes.

2. Student identifies the rule that generates the pattern.

3. Student uses simple concepts of function (input/output, function machine, What’s My Rule?).

4. Student finds patterns in addition using + 0, +1, +10.

5. Student finds patterns in subtraction using – 0, -1, -10.

Data, Statistics, and Probability Concepts (M1:23; M1:24; M1:25; M1:27; M1:28) Students interpret a given representation, analyze patterns or trends in data, and collect appropriate data to answer a question or hypothesis.

1. Student explains and interprets bar graphs and tally charts.

2. Student adds data to pre-made bar graphs.

3. Student makes tally charts.

4. Student organizes and displays data using diagrams, models, or tally charts through written or verbal/scribed response to answer questions related to the data and to analyze the data to formulate conclusions. (i.e. Kim did a survey of her class to see which flavor ice cream students liked. The chart below shows her results. Read the chart and answer the questions. (Problem may be read to child.)

Flavor Students

Chocolate llll llll

Vanilla llll ll

Strawberry llll

a. Which ice cream did the students like best?

b. How many students like vanilla?

c. How many more students chose chocolate than chose vanilla?

d. If a new first grader came into the class, which flavor ice cream do you think they would choose? Why?

5. Student describes the likelihood or chance of an event (using “certain,” “more likely,” “equally likely,” “less likely,” or “impossible”). (i.e. Choosing a red crayon from a bag of green crayons.)

6. In response to a question or hypothesis, student collects appropriate data to answer the question or hypothesis being tested through written or verbal/scribed response.

Mathematical Problem Solving (M1:30) Students isolate relevant information in a given mathematical problem, and apply a variety of grade appropriate strategies to solve a problem.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student solves problems by reasoning mathematically with concepts and skills expected at this grade level.

2. Student determines what the question, assignment, or problem is really asking them to do.

3. Student creates and uses a variety of strategies and approaches to solve problems, and learns approaches that other people use.

4. Student makes connections between concepts in order to solve problems.

5. Student extends concepts and generalizes the results to other situations.

6. Student makes sensible, reasonable estimates.

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Second Grade Mathematics Curriculum Objectives 2009 - 2010

Number Sense and Place Value (M2:1; M2:2; M2:5)) Students understand the base-ten numeration system (place-value concepts) and positive fractional numbers. Students understand the relative magnitude of numbers.

1. Student gives at least five other names for all whole numbers from 0 to 199 using equivalency and expanded notation.

2. Student recognizes the fractions 1/2, 1/4, and 1/3 as a part to a whole.

3. Student compares whole numbers from 0 to 199.

4. Student recognizes equivalent coin representations.

6. Student uses “Ball Park” estimates to evaluate the reasonableness of solutions.

Operations and Computation (M2: 3; M2: 5) Students develop quick recall of addition facts and related subtraction facts, and develop fluency with multi-digit addition and subtraction. Students understand monetary value.

1. Student solves addition problems through twenty.

2. Student solves subtraction problems through twenty.

3. Student adds 3 or more 1-digit numbers.

4. Student adds 2-digit numbers using partial-sums algorithm.

5. Student adds coins together to a value no greater than $1.99.

6. Student makes change from $1.00 or less.

Geometry and Measurement (M2:9; M2:11; M2:15; M2:16) Students analyze characteristics and properties of two- and three-dimensional geometric shapes; use symmetry to analyze mathematical situations; and use spatial reasoning and geometric modeling to solve problems. Students develop an understanding of linear measurement and facility in measuring lengths.

1. Student sorts, orders, compares, and describes objects.

2. Student identifies three-dimensional shapes and their attributes.

3. Student recognizes three-dimensional shapes in the environment.

4. Student demonstrates symmetry by flipping or rotating shapes.

5. Student determines the area and perimeter of a polygon by using models or manipulatives to surround and cover polygons.

6. Student measures in inches and centimeters accurately and consistently to the nearest whole number.

7. Student determines elapsed and accrued time as it relates to days of the week, months, and hours.

8. Student tells time to the nearest five-minute interval.

Functions and Algebra Concepts (M2:19; M2:22) Students use number patterns to extend their knowledge of properties of numbers and operations. Students demonstrate conceptual understanding of equality.

1. Student finds a missing element in a pattern.

2. Student identifies the rule that generates a pattern.

3. Student solves an open addition sentence.

4. Student solves an open subtraction sentence.

5. Student adds/subtracts multiples of ten using a number grid or line.

Data, Statistics, and Probability (M2:23; 2:24, M2:25, M2:26, M2:28) Students analyze patterns or trends in data; collect organize, and display data; and use counting techniques to solve problems.

1. Student analyzes data using “more,” less,” or “equal.”

2. Student solves problems involving combinations.

3. Student collects, organizes, and displays data.

4. Student interprets a representation to answer questions or analyze data.

Mathematical Problem Solving (M2:30) Students isolate relevant information in a given mathematical problem, and apply a variety of appropriate strategies to solve a problem.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student solves grade level problems.

2. Student determines what the problem is asking and isolates important information (data).

3. Student uses a variety of strategies and approaches.

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Third Grade Mathematics Curriculum Objectives 2009-2010

Number Sense and Place Value (M3:1, M3:3, M3:7) Students understand different ways of representing numbers and understand relationships among numbers.

1. Student gives five “other names for” numbers from 0 to 1,000.

2. Student uses expanded notation with numbers from 0 to 1,000.

3. Student understands the meaning of numerator and denominator.

4. Student identifies fractional parts of a region or set (1/2, 1/3, 1/4, and 1/8).

5. Student orders and compares whole numbers from 0 to 1,000.

6. Student uses dollar and cents notation up to $10.00.

Operations and Computation (M3:3, M3:4, M3:7, M3:8) Students understand concepts of mathematical operations and how they relate to one another. Students compute accurately and fluently and make reasonable estimates.

1. Student understands the meaning of “fact families.”

2. Student knows whole number addition facts to 20.

3. Student knows whole number subtraction facts to 20.

4. Student uses partial sum addition to solve 3-digit problems including problems with decimals.

5. Student uses trade first subtraction to solve 3-digit problems.

6. Student knows multiplication facts 0, 1, 2, 5, 10.

7. Student uses “Ball Park” estimates appropriately.

8. Student applies the commutative and associative properties to solve problems and to simplify computations.

Geometry and Measurement (M3:9, M3:11, M3:14, M3:16, M3:18) Students use properties of angles or sides to identify, describe, or distinguish among two-and three dimensional shapes. Students apply transformations (flips, slides, turns) to demonstrate conceptual understanding of congruency.

1. Student identifies polygons using properties of angles and sides.

2. Student identifies three-dimensional shapes.

3. Student identifies congruent shapes and polygons using flips, slides, and turns.

4. Student identifies and designs symmetrical shapes.

5. Student illustrates line symmetry in two-dimensional shapes.

6. Student finds the perimeter of polygons.

7. Student finds the area of rectangles.

8. Student identifies and uses units of measure (inch, foot, yard, and centimeter).

9. Student reads the Fahrenheit thermometer to the nearest degree.

10. Student solves problems using the coordinate grid.

11. Student tells time to five-minute intervals.

Functions and Algebra Concepts (M#;19, M3:20, M3:22) Students understand patterns and can identify the rule that generates the pattern. Students demonstrate conceptual understanding of equality by finding the value that will make an open sentence true.

1. Student identifies and extends patterns.

2. Student identifies the rule that generates a pattern.

3. Student solves open addition sentences (i.e. 5 + ___ = 13).

4. Student solves open subtraction sentences (i.e. 21 - ___ = 16).

5. Student solves open multiplication sentences (i.e. ___ x 5 = 35).

Data, Statistics, and Probability Concepts (M3:23, M3:24, M3:25, M3;27, M3:28) Students interpret a given representation to answer questions, to analyze data, or to make predictions. Students collect, organize, and display appropriate data to answer questions. They use the data to determine the likelihood of an event.

1. Student interprets a given representation (line plots, tally charts, tables, or bar graphs) to answer questions and to make predictions.

2. Student analyzes patterns, trends, or distributions in data by determining or using “most frequent,” “least frequent,” “largest,” “smallest.”

3. Student organizes and displays data to answer questions.

4. Student uses a probability event to determine the likelihood of an event.

5. Student collects appropriate data to draw conclusions.

Mathematical Problem Solving (M:30) Students solve grade appropriate problems using a variety of strategies and approaches, extend and generalize the results, and effectively communicate their solution to problems.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student solves grade appropriate problems.

2. Student determines what the problem is asking.

3. Student creates and uses a variety of strategies and approaches.

4. Student extends concepts and generalizes the results

5. Student makes sensible reasonable estimates.

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Fourth Grade Mathematics Curriculum Objectives 2009-2010

Number Sense and Place Value (M4:1, M4:2) Students compare and order positive and negative integers, positive fractions, and numbers with decimals to the hundredths place. Students understand the connection between fractions, decimals, and percentages. Students accurately round numbers.

1. Student reads, writes, compares (>, <, and =), identifies numbers to 100,000,000.

2. Student recognizes and uses the fractions 1/2, 1/3, 1/4, 1/6, 1/8, 1/10.

3. Student demonstrates understanding, through ordering and comparing,

of decimals to hundredths place, including money notation.

4. Student compares and orders positive and negative integers.

5. Student orders, compares, and identifies positive fractional numbers.

6. Student estimates and evaluates the reasonableness of solutions.

7. Student connects fractions, decimals, and percentages.

8. Student chooses appropriate increments for rounding.

Operations and Computation (M4:3, M4:4, M4:6) Students understand the meaning of mathematical operations and how they relate to one another. Students compute fluently and accurately and make reasonable estimates.

1. Student demonstrates the relationship between repeated subtraction and division.

2. Student describes the inverse relationship between multiplication and division.

3. Student adds and subtracts fractional numbers with like denominators.

4. Student solves problems involving multiple operations on numbers.

5. Student adds and subtracts decimals to the hundredths place.

6. Student applies the conventions of order of operations.

7. Student memorizes multiplication facts through 12.

8. Student memorizes division facts through 12.

Geometry and Measurement (M4:9, M4:11, M4:12, M4:13, M4:14, M4:15, M4:16, M4:17) Students use properties or attributes of angles to identify, describe, or distinguish among geometric shapes. They use properties or attributes of shapes (number of bases and number of lateral faces) to identify, compare, and describe three-dimensional shapes, they demonstrate understanding of similarity and congruency. Students solve problems involving perimeter and area.

1. Student identifies and describes polygons.

2. Student classifies angles relative to 90 degrees.

3. Student recognizes parallel, perpendicular, and intersecting lines.

4. Student identifies/describes components of three-dimensional shapes.

5. Student identifies congruency by matching congruent figures.

6. Student demonstrates understanding of similarity.

7. Student finds the perimeter of polygons on grids.

8. Student finds the area of polygons or irregular shapes on grids.

9. Student measures and uses units of measure appropriately. (Length, volume)

10. Student determines elapsed and accrued time to the 1/4 hour.

11. Student tells time to the nearest minute.

12. Student solves problems using the coordinate grid system.

Functions and Algebra Concepts (M4:19, M4:20, M4:21, M4:22) Students use a variety of patterns to generate a rule to find the next case. Students demonstrate conceptual understanding of linear relationships as a constant rate of change, demonstrate understanding of algebraic expressions and the concept of equality.

1. Student describes geometric and numerical number patterns

2. Student uses numerical patterns to derive rules to solve problems.

3. Student uses rate tables to solve rate problems.

4. Student shows understanding of algebraic expressions.

5. Student shows understanding of equality using parenthesis.

6. Student shows understanding of one-step linear equations.

Data, Statistics, and Probability Concepts (M4:23, M4:24, M4:25, M4: 26, M4:27, M4: 28, M4:29) Students interpret a given representation to solve problems and analyze data using measures of central tendency. Students organize and display data to formulate or justify conclusions.

1. Student interprets a given representation.

2. Student uses measures of central tendency to analyze data.

3. Student organizes and displays given data.

4. Student solves problems (combinations and simple permutations).

5. Student determines the theoretical probability of an event.

6. Student collects and displays appropriate data.

7. Student uses experimental probability.

Mathematical Problem Solving (M4:30) Students solve grade appropriate problems using a variety of strategies and approaches, extend and generalize their results, and effectively communicate their solutions to problems.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student solves grade level problems.

2. Student determines what the problem is asking.

3. Student creates and uses a variety of strategies and approaches.

4. Student makes connections between concepts to solve problems

5. Student extends concepts and generalizes the results.

6. Student makes sensible, reasonable estimates.

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Fifth Grade Mathematics Curriculum Objectives 2009-2010

Number Sense and Place Value (M5:1, M5:2) Students demonstrate conceptual understanding of whole numbers, positive fractional numbers, and benchmark percents. Students demonstrate understanding of the relative magnitude of rational numbers, fractional numbers, and decimals.

1. Student reads, writes, compares, identifies numbers to 1 billion.

2. Student demonstrates understanding of fractional numbers.

3. Student demonstrates understanding of powers of ten.

4. Student demonstrates understanding of decimals to thousandths.

5. Student demonstrates understanding of percents.

6. Student understands the relative magnitude of numbers.

7. Student rounds mixed numbers and decimals to the nearest tenth.

Operations and Computation (M5:3, M5:4, M5:6) Students understand the meaning of operations and how they relate to one another. Students compute accurately and fluently and make reasonable estimates.

1. Student demonstrates understanding of mathematical operations.

2. Student demonstrates understanding of division with/without remainders.

3. Student solves problems involving multiple operations.

4. Student solves problems involving fractions with like denominators and decimals.

5. Student applies the conventions of order of operations.

6. Student knows multiplication facts through 12.

7. Student knows division facts through 12.

8. Student solves 3-digit multiplication problems.

9. Student solves 2 -digit division problems.

10. Student estimates the reasonableness of solutions.

Geometry and Measurement (M5:9, M5: 11, M5:12, M5:14, M5:16, M5:18) Students use properties or attributes of angles to identify, classify, describe, or distinguish among, different types of triangles or quadrilaterals. Students use properties or attributes to identify, compare, or describe three-dimensional shapes. Students understand similarity and congruency. Students understand the concepts of perimeter, area, and volume.

1. Student defines geometric terms: angle, vertex, face, polygon, obtuse, acute, right angle, parallelogram, rhombus, trapezoid, edge.

2. Student identifies quadrilaterals using properties of angles.

3. Student identifies measures, and draws angles within five degrees.

4. Student identifies, compares, describes two- dimensional shapes.

5. Student identifies, compares, or describes three-dimensional shapes.

6. Student demonstrates understanding of congruency.

7. Student demonstrates understanding of similarity.

8. Student finds the perimeter of polygons.

9. Student finds the area of rectangles or right triangles

10. Student finds the area of polygons.

11. Student finds the volume of rectangular prisms.

12. Student measures and uses units of linear measures appropriately.

13. Student determines elapsed and accrued time to the nearest minute.

Functions and Algebra Concepts (M5:19, M5:20, M5:21, M5:22) Students identify and extend a variety of patterns. They demonstrate understanding of linear relationships as a constant rate of change, understanding of algebraic expressions, and understanding of the concept of equality.

1. Student describes, analyzes, and extends linear and nonlinear patterns.

2. Student writes a rule in words or symbols for a linear relationship.

3. Student understands linear relationships as a constant rate of change.

4. Student uses letters as variables in linear algebraic expressions.

5. Student solves one-step linear equations ax=c, x + b=c, x-b=c, x/a=c.

6. Student solves problems using the coordinate grid system.

Data, Statistics, and Probability Concepts (M5:23, M5:24, M5: 25, M5: 26, M5:27, M5: 28, M5:28) Students collect, organize, and display relevant data to make predictions, ask new questions, or make connections. They select and use appropriate statistical methods to analyze data and solve problems. They determine the probability of an event. Students solve problems involving combinations and permutations.

1. Student interprets a given data representation to answer questions.

2. Student uses measures of central tendency to solve problems.

3. Student identifies the best display for a given set of data.

4. Student collects, organizes, and displays appropriate data to answer questions, make inferences, and predict.

5. Student solves problems involving combinations.

6. Student solves problems involving simple permutations.

7. Student determines the experimental probability of an event.

8. Student uses probability to describes the chance of an event.

Mathematical Problem Solving (M5:30) Students solve grade appropriate problems using a variety of strategies and approaches, extend and generalize their results, and effectively communicate their solutions to problems.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student solves grade level problems.

2. Student determines what the problem is asking.

3. Student creates and uses a variety of strategies and approaches.

4. Student makes connections between concepts to solve problems

5. Student extends concepts and generalizes the results.

6. Student makes sensible, reasonable estimates.

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Sixth Grade Mathematics Curriculum Objectives 2009- 2010

Number Sense and Place Value (M6:1, M6:2, M6:3, M6:7) Students demonstrate conceptual understanding of fractions and decimals, and fluently move between equivalent representations of commonly used fractions and decimals. Students demonstrate understanding of the relative magnitude of numbers by ordering or comparing numbers with whole-number bases and whole-number exponents.

1. Student reads, writes, and understands decimals to the thousandths.

2. Student connects equivalent benchmark fractions and decimals.

3. Student orders and compares whole numbers with exponents and rational numbers.

4. Student identifies the value of any digit in a number from millionths to millions.

5. Student rounds numbers to the nearest number (hundredth to thousand).

6. Student understands whole number base and whole number exponent.

7. Student uses estimates to evaluate the reasonableness of solutions.

Operations and Computation (M6:4, M6:6, M6:7) Students accurately solves problems involving single or multiple operations on fractions (proper, improper, and mixed) and decimals. Students apply the conventions of operations and the commutative and associative properties of numbers to solve problems and to simplify solutions.

1. Student solves problems involving operations on proper, improper, and mixed fractions.

2. Student solves problems involving operations on decimals.

3. Student solves problems involving percent of a whole, and as discounts, tax, or tips.

4. Student applies the conventions of order of operations with and without parenthesis.

5. Student applies properties of numbers to solve problems and to simplify computations.

6. Student mentally multiplies and divides whole numbers through twelve.

7. Student uses the commutative and associative properties of operations to solve problems and to simplify operations.

Geometry and Measurement (M6:9, M6:11, M6:12,M6:13, M6:14, M6: 15) Students use properties or attributes of angles to identify shapes. Students demonstrate understanding of congruency using transformations, properties of angles, and length of segments. Students demonstrate conceptual understanding of similarity and apply concepts of similarity and scaling to polygons and circles. Students use units of measures appropriately and consistently.

1. Student uses properties of shapes to identify them.

2. Student understands angles formed from perpendicular and parallel lines.

3. Student understands the relationship between the number of sides and the sum of the angles for regular polygons.

4. Student demonstrates congruency by subdividing, transforming, rotating, reflecting, and measuring.

5. Student understands similarity and scaling of polygons and circles.

6. Student understands perimeter and area of polygons using correct formulas and units.

7. Studnet understands the relationships of circle measures.

8. Student understands circumference and area of circles using correct formulas and units.

9. Student measures and uses units of measures appropriately.

10. Student uses properties of angle relationships resulting from two or three intersecting lines.

Functions and Algebra Concepts (M6:19, M6:20, M6:21)* Students identify and extend to specific cases a variety of patterns. Students create and interpret coordinate graphs. Students demonstrate conceptual understanding of algebraic expressions by substituting values for variables in known formulas (e.g. determine the value of y when x = 4 given y = 3x –2).

1. Student identifies and explains a variety of patterns.

2. Student substitutes values for variables in known formulas.

3. Student creates a coordinate graph and plots points.

4. Student solves problems and makes predictions using coordinate graphs.

Data, Statistics, and Probability Concepts (M6:23 M6:24, M6:25) * Students use and interpret a given visual representation to make predictions or to solve problems. Students analyze data by determining and using measures of central tendency. Students organize and display data using appropriate visual representations.

1. Student uses and interprets visual representations to solve problems.

2. Student solves problems using measures of central tendency.

3. Student organizes and displays data using appropriate visual representations.

4. Student uses data collection and analysis to solve problems.

Mathematical Problem Solving (M6:30) Students solve problems of increasing complexity. Students accurately use mathematical language and presentations to communicate their solutions and to foster understanding of mathematics.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student accurately solves grade appropriate problems.

2. Student effectively communicates problem solving steps, strategies, and solutions.

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Seventh Grade Mathematics Curriculum Objectives 2009 - 2010

Number Sense and Place Value (M7:1, M7:2, M7:7) Students demonstrate conceptual understanding of integers, and rational numbers with respect to percents and ratios. Students understand the relationships among rational numbers, percents, exponents, integers, absolute values, and scientific notation.

1. Student understands integers.

2. Student reads, writes, and understands numbers to the billions.

3. Student understands rational numbers with respect to ratios.

4. Student understands percents as a means of comparing whole amounts.

5. Student understands percents greater than 100 and less than 1.

6. Student understands the relationships among rational numbers, exponents, integers, absolute values, and scientific notation.

7. Student estimates and evaluates the reasonableness of solutions.

Operations and Computation (M7:3, M7:4, M7:8) Students demonstrate conceptual understanding of operations with integers. Students solve problems involving integers, proportional reasoning, and rates. Students apply properties of numbers to solve problems and to simplify solutions.

1. Student demonstrates understanding of operations with integers.

2. Student solves problems with integers.

3. Student solves problems involving proportional reasoning.

4. Student solves problems involving rates.

5. Student applies the conventions of order of operations.

Geometry and Measurement ( M7:11, M7:13, M7:14, M8:13)* Students identify and distinguish among three-dimensional shapes. Students solve problems involving the surface area and volume of prisms, cylinders, and pyramids. Students measure and use units of measures appropriately.

1. Student identifies and distinguishes three-dimensional shapes.

2. Student describes the impact on the volume and surface area of three-dimensional figures when increasing the dimensions by a constant scale factor.

3. Student measures and uses units of measures appropriately.

4. Student sketches three-dimensional solids and the nets of prisms, cylinders, and pyramids.

5. Student solves problems using the Cartesian coordinate system.

6. Student solves problems involving the surface area of prisms, cylinders, or pyramids.

7. Student solves problems involving the volume of prisms, cylinders, or pyramids.

8. Student measures and uses units of measures appropriately; makes conversions within systems.

Functions and Algebra Concepts (M7:19, M7:20, M7:21, M7:22) Students identify and extend a variety of linear and nonlinear patterns. Students understand linear relationships as a constant rate of change and generalize a linear relationship using words and symbols. Students evaluate algebraic expressions, and use data to make tables and graphs.

1. Student identifies and extends a variety of patterns (linear and nonlinear).

2. Given a situation, student can make a table and a coordinate graph.

3. Student generalizes a linear relationship using words and symbols.

4. Student understands linear relationships as a constant rate of change.

5. Student evaluates algebraic expressions or equations using substitutions.

Data, Statistics, and Probability Concepts (M7:26, M7:27, M7:29)* Students solve problems involving combinations, determine the experimental or theoretical probability of an even, and use probability to determine the fairness of a game. Students express probability as a ratio in the form of fractions, decimals, and percents.

1. Student determines the experimental or theoretical probability of a simple event.

2. Student uses counting techniques to solve problems involving combinations.

3. Student uses probability to determine the fairness of a game.

4. Student determines the theoretical and experimental probability of compound events.

5. Student expresses probability as a ratio in the form of fractions, decimals, and percents.

Mathematical Problem Solving (M7: 30) Students solve problems of increasing complexity. Students accurately use mathematical language and presentations to communicate their solutions and to foster understanding of mathematics.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student accurately solves grade appropriate problems.

2. Student effectively communicates problem solving steps, strategies and solutions.

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Eighth Grade Mathematics Curriculum Objectives 2009– 2010

Number Sense and Place Value (M8:2, M8:7)* Demonstrates understanding of the relative magnitude of numbers by ordering and comparing common irrational numbers. Estimates and evaluates the reasonableness of solutions appropriate to grade level.

1. Student orders and compares common irrational numbers.

2. Student estimates and evaluates the reasonableness of solutions.

3. Student uses properties (commutative, associative, and distributive) to solve problems and to simplify computations.

Operations and Computation (M8:4) Students accurately solve problems involving squares, cubes, and square roots.

1. Student solves problems involving squares, cubes, and square roots.

Geometry and Measurement (M8:10, M8:13, M8:15)* Students apply the Pythagorean Theorem in problem-solving situations. Students describe the impact on the volume and surface area of a three-dimensional figure when dimensions are multiplied by a constant scale factor. Students measure and use units of measurement appropriately.

1. Student applies the Pythagorean theorem to find a missing side of a right triangle.

2. Student describes the impact on the volume and surface area of three-dimensional figures when increasing the dimensions by a constant scale factor.

3. Student applies concepts of similarity by making scale drawings.

4. Student measures and uses units of measures appropriately.

Functions and Algebra Concepts (M8:19, M8:20, M8:21, M8:22) Students generalize linear and nonlinear relationships. Students demonstrates conceptual understanding of linear relationships as a constant rate of change. Students evaluate and simplify algebraic expressions, and solve multi-step linear equations.

1. Student generalizes a linear relationship with an equation.

2. Student demonstrates conceptual understanding of slope as rate of change.

3. Student distinguishes between linear and nonlinear relationships.

4. Student describes how change in the value of one variable relates to change in the value of a second variable.

5. Student evaluates algebraic expressions within an equation.

6. Student solves multi-step linear equations with integer coefficients.

7. Student uses rates of change to sketch graphs for and match graphs to given situations.

8. Student writes an equation for a line given two points.

9. Student determines the line or curve of best fit given a set of data.

Data, Statistics, and Probability Concepts (M8:23, M8:26)* Students use a variety of strategies to solve problems involving combinations. Given a data set students create and interpret box and whisker plots.

1. Student solves problems involving a variety of representations including permutations and combinations using a variety of strategies.

2. Student creates and interprets box and whisker plots given a set of data.

3. For a probability event student determines the possible outcomes as a fraction, decimal, and percent.

Mathematical Problem Solving (M8:30) Students solve problems of increasing complexity. Students accurately use mathematical language and presentations to communicate their solutions and to foster understanding of mathematics.

“Problem solving is not a distinct topic, but a process that should permeate the entire [math] program.” NCTM

1. Student accurately solves grade appropriate problems.

2. Student effectively communicates problem solving steps, strategies, and solutions.

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Algebra I Curriculum Objectives 2009 - 2010

Critical Skills

1. Student demonstrates basic computation skills with rational numbers

2. Student uses variables and constants to create mathematical models

3. Student uses order of operations to simplify expressions

4. Student simplifies expressions involving fractions

5. Student translates words into mathematical models

Properties of Real Numbers

1. Student uses rules of +/- numbers to simplify expressions

2. Student places numbers on the real number line

3. Student evaluates expressions using absolute value

4. Student uses distributive, associative, and commutative properties

5. Student squares and cubes numbers

6. Student simplifies square roots and cube roots

Solving Linear Equations, Inequalities, and Quadratics

1. Student solves equations using addition and subtraction

2. Student solves equations using multiplication and division

3. Student solves multi-step equations

4. Student solves equations with variables on both sides

5. Student solves equations using ratios and rates

6. Student solves equations involving percents

7. Student solves multi-step linear inequalities

8. Student solves systems of linear inequalities by graphing.

9. Student solves quadratic equations by factoring and finding roots

Linear Models

1. Student names ordered pairs in the coordinate plane

2. Student plots points in the coordinate plane

3. Student graphs linear equations using a table of values

4. Student graphs and finds equations for horizontal and vertical lines

5.  Student finds slope given two points or given graph

6.  Student uses data to find slope-intercept form of equation

7.  Student uses data to find line of best fit

8.  Student uses calculator with data to find regression equation

9.  Student writes linear equations given two points or, given one point and the slope

10. Student develops linear model from problem/situation

11. Student uses interpolation/extrapolation to make predictions

Systems of linear equations

1. Student graphs systems of two linear equations (Deleted)

2. Student solves systems of two linear equations by graphing

3. Student solves systems of two linear equations by substitution and elimination

4. Student develops a mathematical model and its solution from a word problem

Exponents

1.  Student uses rules of exponents to simplify expressions

2.  Student uses zero and negative exponents to simplify expressions

3.  Student uses scientific notation to represent large and small numbers

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