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.  Read and write place value in word, standard, and expanded form through 1,000,000

2.  Read, write, compare, and order whole numbers using place value concepts, standard notation, and models through 1,000,000

3.  Illustrate with manipulative when a number is divisible by 2, 3, 5, or 10

4.  Know all basic facts for multiplication and division through 12 x 12 and 144 ÷ 12, and recognize factors of composite numbers less than 50

5.  Read, write, and relate decimals through hundredths and connect them with corresponding decimal fractions

6.  Model, read, write, compare, order, and represent fractions with denominators through twelfths using region and set models

7.  Give decimal equivalents of halves, fourths, and tenths

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

7. Give decimal equivalents of halves, fourths, and tenths

8.  Use common equivalent reference points for percents (i.e., 1/4, ½, 3/4, and 1 whole)

9.  Estimate fractional amounts through twelfths, using pictures, models, and diagrams

27.  Use unit conversions within the same system to solve real-life problems (e.g., 60 sec. = 1 min., 12 objects = 1 dozen, 12 in. = 1 ft., 100 cm = 1 m, 1 pt. = 2 cups)

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 using place value concepts, standard notation, and models through 1,000,000

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

10.  Solve multiplication and division number sentences including interpreting remainders

19.  Solve one-step equations with whole number solutions

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

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

4.  Know all basic facts for multiplication and division through 12 x 12 and 144 ÷ 12, and recognize factors of composite numbers less than 50

11.  Multiply 3-digit by 1-digit numbers, 2-digit by 2-digit numbers, and divide 3-digit numbers by 1-digit numbers, with and without remainders

12.  Count money, determine change, and solve simple word problems involving money amounts using decimal notation

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

4.  Know all basic facts for multiplication and division through 12 x 12 and 144 ÷ 12, and recognize factors of composite numbers less than 50

11.  Multiply 3-digit by 1-digit numbers, 2-digit by 2-digit numbers, and divide 3-digit numbers by 1-digit numbers, with and without remainders

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 multiplication and division problems

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

12.  Count money, determine change, and solve simple word problems involving money amounts using decimal notation

14.  Solve real-life problems, including those in which some information is not given

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.)

2.  Read, write, compare, and order whole numbers using place value concepts, standard notation, and models through 1,000,000

6.  Model, read, write, compare, order, and represent fractions with denominators through twelfths using region and set models

15.  Write number sentences or formulas containing a variable to represent real-life problems

16.  Write a related story problem for a given algebraic sentence

17.  Use manipulatives to represent the distributive property of multiplication over addition to explain multiplying numbers

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

17.  Use manipulatives to represent the distributive property of multiplication over addition to explain multiplying numbers

18.  Identify and create true/false and open/closed number sentences

19.  Solve one-step equations with whole number solutions

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)

10.  Solve multiplication and division number sentences including interpreting remainders

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

12.  Count money, determine change, and solve simple word problems involving money amounts using decimal notation

20.  Measure length to the nearest quarter-inch and mm

22.  Select and use the appropriate standard units of measure, abbreviations, and tools to measure length and perimeter (i.e., in., cm, ft., yd., mile, m, km), area (i.e. square inch, square foot, square centimeter), capacity (i.e., fl. Oz., cup, pt, qt, gal., l, mk), weight/mass (i.e., oz., lb., g, kg, ton) and volume (i.e., cubic cm, cubic in.)

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

20.  Measure length to the nearest quarter-inch and mm

21.  Describe the concept of volume, and measure volume using cubic inch and cubic cm and capacity using fluid ounces and ml

22.  Select and use the appropriate standard units of measure, abbreviations, and tools to measure length and perimeter (i.e., in., cm, ft., yd., mile, m, km), area (i.e. square inch, square foot, square centimeter), capacity (i.e., fl. Oz., cup, pt, qt, gal., l, mk), weight/mass (i.e., oz., lb., g, kg, ton) and volume (i.e., cubic cm, cubic in.)

23.  Set up, solve, and interpret elapsed time problems

24.  Recognize the attributes to be measured in a real-life situation

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

21.  Describe the concept of volume, and measure volume using cubic inch and cubic cm and capacity using fluid ounces and ml

25.  Use estimates and measurements to calculate perimeter and area of rectangular objects (including squares) in U.S. (Including square feet) and metric units

26.  Estimate the area of an irregular shape drawn on a unit grid

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.  Use unit conversions within the same system to solve real-life problems (e.g., 60 sec. = 1 min., 12 objects = 1 dozen, 12 in. = 1 ft., 100 cm = 1 m, 1 pt. = 2 cups)

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

12.  Count money, determine change, and solve simple word problems involving money amounts using decimal notation

23.  Set up, solve, and interpret elapsed time problems

24.  Recognize the attributes to be measured in a real-life situation

27.  Use unit conversions within the same system to solve real-life problems (e.g., 60 sec. = 1 min., 12 objects = 1 dozen, 12 in. = 1 ft., 100 cm = 1 m, 1 pt. = 2 cups)

G-1-E determining the relationships among shapes

28.  Identify the top, bottom, or side view of a given 3-dimensional object

32.  Draw, identify, and classify angles that are acute, right, and obtuse

G-2-E

29.  Identifying, describing, comparing, construction, an classifying two-dimensional and three-dimensional geometric shapes using a variety of materials

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

28.  Identify the top, bottom, or side view of a given 3-dimensional object

30.  Make and test predictions regarding transformations (i.e., slides, flips, and turns) of plane geometric shapes

31.  Identify, manipulate, and predict the results of rotations of 90, 180, 270, and 360 degrees on a given figure

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

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

32.  Draw, identify, and classify angles that are acute, right, and obtuse

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

33.  Specify locations of points in the first quadrant of coordinate and describe paths on maps

35.  Specify locations of points in the first quadrant of coordinate systems and describe paths on maps

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

34.  Summarize information and relationships revealed by patterns or trends in a graph, and use the information to make predictions

35.  Find and interpret the meaning of mean, mode, and median of a small set of numbers (using concrete objects) when the answer is a whole number

36.  Analyze, describe, interpret, and construct various types of charts and graphs using appropriate titles, axis labels, scales, and legends

37.  Determine which type of graph best represents a given set of discrete data

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

36.  Analyze, describe, interpret, and construct various types of charts and graphs using appropriate titles, axis labels, scales, and legends

37.  Determine which type of graph best represents a given set of discrete data

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

38.  Solve problems involving simple deductive reasoning

39.  Use lists, tables, and tree diagrams to generate and record all possible combinations for 2 sets of 3 or fewer objects (e.g., combinations of pants and shirts, days and games) and for given experiments

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

39.  Use lists, tables, and tree diagrams to generate and record all possible combinations for 2 sets of 3 or fewer objects (e.g., combinations of pants and shirts, days and games) and for given experiments

40.  Determine the total number of possible outcomes for a given experiment using lists, tables, and tree diagrams (e.g., spinning a spinner, tossing 2 coins)

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

40.  Determine the total number of possible outcomes for a given experiment using lists, tables, and tree diagrams (e.g., spinning a spinner, tossing 2 coins)

41.  Apply appropriate probabilistic reasoning in real-life contexts using games and other activities (e.g., examining fair and unfair situations)

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

41.  Apply appropriate probabilistic reasoning in real-life contexts using games and other activities (e.g., examining fair and unfair 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

42.  Find a describe patterns resulting from operations involving even and odd numbers (such as even + even = even)

43.  Identify missing elements in a number pattern

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

44.  Represent the relationship in an input-output situation using a simple equation, graph, table, or word description

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