04-05

05-06

06-07

07-08

08-09

09-10

BENCHMARK

N-1-E(constructing number meaning and demonstrating that a number can be expressed in many different forms (e.g., standard notation, number words, number lines, geometrical representation, fractions, and decimals)

1.  Model, read, and write place value in word, standard, and expanded form for numbers through 9999

2.  Read, write, compare, and order whole numbers through 9999 using symbols (i.e., < , = , >) and models

3.  Use region and set models and symbols to represent, estimate, read, write, and show understanding of fractions through tenths

N-2-E demonstrating number sense and estimation skills, giving particular attention to common equivalent reference points (i.e., 1/4=25%=.25)

3.  Use region and set models and symbols to represent, estimate, read, write, and show understanding of fractions through tents

N-3-E reading, writing, representing, comparing, ordering, and using whole numbers in a variety of forms (e.g., standard notation, number line, and geometrical representation

2.  Read, write, compare, and order whole numbers through 9999 using symbols (i.e., < , = , >) and models

N-4-E demonstrating a conceptual understanding of the meaning of the basic arithmetic operations (add, subtract, multiply, and divide) and other relationships to each other

4.  Use the concepts of associative and commutative properties of multiplication to simplify computations

5.  Recognize and model multiplication as a rectangular array or as repeated addition

6.  Recognize and model division as separating quantities into equal subsets 9fair shares) or as repeated subtraction

7.  Recognize and apply multiplication and division as inverse operations

9.  Know basic multiplication and division facts [0s, 1s, 2s, 5s, 9s, and turnarounds (commutative facts), including multiplying by 10s]

16.  Use number sentences to represent real-life problems involving multiplication and division

N-5-E selecting appropriate operations(s) (add, subtract, multiply, and divide) for a given situation

8.  Recognize, select, connect, and use operations, operational words, and symbols (i.e., +, -, x, ÷) to solve real-life situations

N-6-E applying a knowledge of basic math facts and arithmetic operations to real-life situations

8.  Recognize, select, connect, and use operations, operational words, and symbols (i.e., +, -, x, ÷) to solve real-life situations

9.  Know basic multiplication and division facts [0s, 1s, 2s, 5s, 9s, and turnarounds (commutative facts), including multiplying by 10s]

10.  Calculate the value of a combination of bills and coins and make change up to $5.00

11.  Add and subtract numbers of 3 digits or less

N-7-E constructing, using, and explaining procedures to compute and estimate with whole numbers (e.g., mental math strategies)

4.  Use the concepts of associative and commutative properties of multiplication to simplify computations

5.  Recognize and model multiplication as a rectangular array or as repeated addition

6.  Recognize and model division as separating quantities into equal subsets (fair shares) or as repeated subtraction

11.  Add and subtract numbers of 3 digits or less

12.  Round to the nearest 1000 and identify situations in which such rounding is appropriate

N-8-E selecting and using appropriate computational methods and tools for given situations involving whole numbers (e.g., estimation, mental arithmetic, calculator, or paper and pencil)

13.  Determine when and how to estimate, and when and how to use mental math, calculators, or paper/pencil strategies to solve addition and subtraction problems

N-9-E demonstrating the connection of number and number relations to the other strands and to real-life situations

8.  Recognize, select, connect, and use operations, operational words, and symbols (i.e., +, -, x, ÷) to solve real-life situations

12.  Round to the nearest 1000 and identify situations in which such rounding is appropriate

13.  Determine when and how to estimate, and when and how to use mental math, calculators, or paper/pencil strategies to solve addition and subtraction problems

A-1-E demonstrating a conceptual understanding of variables, expressions, equations, and inequalities (e.g., use letters or boxes to represent values; understand symbols-, <, >,etc.)

14. Use the symbols < , > , and … to express inequalities

15.  Use objects, pictures, numbers, symbols, and words to represent multiplication and division problem situations

16.  Use number sentences to represent real-life problems involving multiplication and division

17.  Analyze and describe situations where proportional trades or correspondences are required (e.g., trade 2 pieces of candy for 3 pieces of gum, make equivalent actions on pans to keep balance scale in equilibrium, plan for the number of pieces of bread needed for x sandwiches

A-2-E modeling and developing strategies for solving equations and inequalities

18.  Use letters as variables in mathematical statements that represent real-life problems (e.g.,

 2 x n = 8)

A-3-E  recognizing the connection of algebra to the other strands and to real-life situations (e.g., number sentences or formulas to represent real-world problems)

M-1-E applying (measure or solve measurement problem) the concepts of length (inches, feet, yards, miles, millimeters, centimeters, decimeters, meters, kilometers), area, volume, capacity (cups, liquid pints and quarts, gallons, milliliters, liters), weight (ounces, pounds, tons, grams, kilograms), mass, time(seconds, minutes, hours, days, weeks, months, years), money, an temperature (Celsius and Fahrenheit) to real-world experiences

10.  Calculate the value of a combination of bills and coins and make change up to $5.00

19.  Measure length to the nearest yard, meter, and half-inch

20.  Measure capacity using pints and gallons

21.  Measure weight using grams and ounces

22.  Find the perimeter of a geometric shape given the length of its sides

23.  Find the area in square units of a given rectangle (including squares) drawn on grid or by covering the region with square tiles

24.  Find elapsed time involving hours and minutes, without regrouping, and tell time to the nearest minute

M-2-E selecting and using appropriate standard and non-standard units of measure (e.g., paper clips and Cuisenaire rods) and tools for measuring length, area, capacity, weight/mass, and time for a given situation by considering the purpose and precision required for the task

25.  Select and use the appropriate standard units of measure, abbreviations, and tools to measure length and perimeter (i.e., in., cm, ft., yd., m), area (square inch, square centimeter), capacity (i.e., cup, pint, quart, gallon, liter), and weight/mass (i.e., oz., lb., g, kg, ton)       

M-3-E using estimation skills to describe, order, and compare measures of length, capacity, weight/mass, time, and temperature

26.  Order a set of measures within the same system

27.  Compare U.S. and metric measurements using approximate reference points without using conversions (e.g., a meter is longer than a yard)

28.  Estimate length, weight/mass, and capacity

M-4-E

converting from one unit of measurement to another within the same system (customary and metric); comparisons between systems should be based on intuitive reference points, not formal computations (e.g., a meter is a little longer than a yard)

27.  Compare U.S. and metric measurements using approximate reference points without using conversions (e.g., a meter is longer than a yard)

M-5-E demonstrating the connection of measurement to the other strands and to real-life situations

10.  Calculate the value of a combination of bills and coins and make change up to $5.00

24.  Find elapsed time involving hours and minutes, without regrouping, and tell time to the nearest minute

G-1-E determining the relationships among shapes

29.  Classify and describe 2- and 3- dimensional objects according to given attribute (triangle vs. quadrilateral, parallelogram vs. prism)

34.  Fold a 2-dimensional net into a 3-dimensional object

G-2-E identifying, describing, comparing, construction, an classifying two-dimensional and three-dimensional geometric shapes using a variety of materials

29.  Classify and describe 2- and 3- dimensional objects according to given attribute (triangle vs. quadrilateral, parallelogram vs. prism)

30.  Apply concepts of congruence, similarity, and symmetry in real-life situations

G-3-E making predictions regarding combinations, subdivisions, and transformations (slides, flips, turns) of simple plane geometric shapes

31.  Draw or reconstruct figures from visual memory or verbal descriptions

32.  Recognize and execute specified flips, turns, and slides of geometric figures using manipulatives and correct terminology (including clockwise and counterclockwise)

G-4-E drawing, constructing models, and comparing geometric shapes, with special attention to developing spatial sense

29.  Classify and describe 2- and 3- dimensional objects according to given attribute (triangle vs. quadrilateral, parallelogram vs. prism)

33.  Construct and draw rectangles (including squares) with given dimensions (e.g., grid paper, square tiles)

34.  Fold a 2-dimensional net into a 3-dimensional object

G-5-E identifying and drawing lines and angles and describing their relationships to each other and to the real world

35.  Identify, give properties of, and distinguish among points, lines, line segments, planes, rays, and angles

36.  Identify and draw segments, rays, and lines that are perpendicular, parallel, and intersecting

37.  Identify, describe, and draw intersecting, horizontal, vertical, parallel, diagonal, and perpendicular lines, rays, and right angles in the real world

G-6-E demonstrating the connection of geometry to the other strands and to real-life situations

37.  Identify, describe, and draw intersecting, horizontal, vertical, parallel, diagonal, and perpendicular lines, rays, and right angles in the real world

38.  Find the length of a path (that does not include diagonals) between two points on a grid

D-1-E collecting, organizing, an describing data based on real-life situations

39.   Identify categories and sort objects based on qualitative (categorical) and quantitative (numerical) characteristics

40.  Read, describe, and organize a two-circle Venn diagram

41.  Explain the word average and use it appropriately in discussing that is “typical” of a data set

D-2-E constructing, reading and interpreting data in charts, graphs, tables, etc.

40.  Read, describe, and organize a two-circle Venn diagram

42.  Match a data set to a graph, table, or chart and vice versa

D-3-E formulating and solving problems that involve the use of data

43.  Represent and solve problems using data from a variety of sources (e.g., tables, graphs, maps, advertisements)

D-4-E exploring, formulating, and solving sequence-of-pattern problems involving selection and arrangement of objects/numerals

D-5-E predicting outcomes based on probability (e.g., make predictions of same chance, more likely, or less likely; determine fair and unfair games

44.  Discuss chance situations in terms of certain/impossible and equally likely

45.  Use manipulatives to discuss the probability of an event (e.g., number cubes, spinners to determine what is most likely or least likely)

D-6-E demonstrating the connection of data analysis probability, and discrete math to other strands and real-life situations

P-1-E recognizing, describing, extending, and creating a wide variety of numerical (e.g., skip counting of whole numbers), geometrical, and statistical patterns

46.  Identify and model even and odd numbers with objects, pictures, and words

P-2-E representing and describing mathematical relationships using tables, variables, open sentences, and graphs

47.  Find patterns to complete tables, state the rule governing the shift between successive terms, and continue the pattern (including growing patterns)

P-3-E recognizing the use of patterns, relations, and functions in other strands and in real-life situations