DRAFT REVISION OF THE MCPS K-8 ISM MATH CURRICULUM (v. 3/1/2001)

This revision preserves the greatest strength of the ISM curriculum -- focusing instruction on the specific math skills students are ready to learn next. It tries to remedy the principal shortcoming of the current curriculum -- the clutter of low-priority objectives that slow down student learning and distract instructional time away from more important objectives.

The major features of the revision are:

The curriculum is designed for flexible pacing. Students who are on or below grade level are expected to make at least one year's progress each year. Gifted students and others who want the added challenge are expected to progress, on average, at the rate of one-and-a-half years of math per year.

NU01A Counts objects (up to 10)

NU02A Groups objects into sets and tells how many (up to 10) are in each set

NU03A Identifies two equal sets as having the same number of objects when the objects are arranged differently (conservation)

NU04A Tells which of two sets has more (less)

NU06B Orders sets of objects (1 to 10 and 10 to 1)

NU07B Uses zero to name a set with no members

NU08B Reads and orders numerals (0 to 10 and 10 to 0)

NU09B Matches numerals to sets (0-10)

NU10B Makes two unequal sets equal by moving, adding, or taking away objects

NU13C Counts up to 30 objects

AD01B Arranges a given set of objects (5 or fewer) into subgroups in a variety of ways, describes in own words

AD02B Constructs sets with one more

AD03B Counts and names the number of objects in each of two sets, puts the sets together, and names the number of objects in the combined set (sums to 10)

GE01A Selects objects according to a single given attribute

GE02A Sorts objects using two or more attributes

TI01A Associates events with a time of day, (morning, afternoon, evening, night; 8:00 at night is bedtime, etc.)

TI02A Explores the days of the week

PS01A Makes with objects or draws a set to model a story problem (up to 10)

PS02B Acts out or makes models to solve addition problems and describes the process

PS03B Solves problems using logical reasoning ("clues")

NU05A Constructs sets with more (less) than a given set

NU11C Writes numerals (0-10)

NU12C When read to, demonstrates with objects, and describes number sentences which use "greater than" and "less than" vocabulary (0-10, no operations) (Don't have students read/write symbols)

NU14D Counts by tens to 100 and models with objects

NU15D Identifies, states, and models the value of each place and the whole number for 2-place numerals

NU16D Reads and writes 2-place numerals

NU17D Demonstrates 2-place numerals with materials (use discrete models)

NU18D Counts by fives to 100

NU19D Counts by twos to 20

NU20D Names missing numbers in a sequence orally counted as well as seen (before, after, or between given numbers up to 100, counting by ones, tens, fives, and twos)

NU21D Names and identifies objects with ordinal number names (first to tenth)

NU23E Orders whole numbers on a number line (to 100)

NU24E Names and identifies objects with ordinal number names to 31st (relate to calendar)

NU25E Locates missing whole numbers on partially labeled horizontal or vertical number lines (to 100, including skip counting)

AD04C Separates a set into two parts and states the number of the whole set and of each part (relate to addition and subtraction)

AD05C Models real-world addition situations using objects

AD06C Reads addition sentences and represents them with objects (relate to basic facts)

AD07D " Counts on" from one given number to another (to 99)

AD08D Reads and writes number sentences using + and = to express an addition situation (relates to basic facts)

AD09E Adds doubles and doubles +1

AD10E Models addition fact strategies

AD11E Models and adds tens (sums to 90)

AD12E Models and increases 2-place numbers by 10

AD13E Models sums with materials (relate to basic facts)

AD15F Adds three or four 1-digit addends

AD17F Names addition facts (Part 1)

AD24G Names addition facts (Part 2)

AD28K Names addition facts (Part 3)

SU01C Constructs sets with one less

SU02C Demonstrates take-away subtraction situations using objects

SU03C Reads subtraction sentences and demonstrates them with objects (relates to basic facts)

SU04D Distinguishes between addition and subtraction situations (use objects or pictures)

SU05D Counts back from one given number (<99) to another

SU06D Reads and writes number sentences using - and = to express a subtraction situation

SU07D Names addition and subtraction facts with no time limit

SU08E Demonstrates addition and subtraction (including comparison subtraction)

SU09E Relates subtraction facts to fact strategies

SU10E Writes all related + or - sentences for a given + or - sentence (relate to basic facts)

SU11E Models and subtracts tens (sums to 90)

SU12E Models and decreases 2-place numbers by 10

SU13E Models differences with materials (relate to basic facts)

SU14E Names + and - facts with no time limit (Part 2)

SU18G Names subtraction facts (Part 1)

SU25G Names subtraction facts (Part 2)

SU28K Names subtraction facts (Part 3)

MD6.3.4a. Demonstrate proficiency with addition and subtraction facts.

GE03B Recognizes rectangles (including squares), circles, and triangles in a variety of positions and sizes

GE04B Copies a pattern made using two objects

GE05B Copies a pattern made from three shapes or objects

GE06C Names and informally describes rectangles (including squares), circles, and triangles in various orientations

ME06B Uses terms to describe, compare, and order weights of hand-held objects (heavy, heavier, heaviest, light, etc.)

ME07B Compares and describes weight of two objects on a primary balance (heavier, lighter, same, etc.) with nonstandard units

ME09C Measures and records length using nonstandard units and single-unit repetition with concrete models

ME10C Weighs and records using nonstandard units on a balance

MY01B Identifies a penny and states its value as one cent

MY02B Counts 10 or fewer pennies and states the amount in cents

MY03C Identifies a nickel and dime, stating the value of each and writing the amount using the cent symbol

MY04C Counts dimes by tens (up to 90¢) and writes the amount using the cent symbol

MY05D Counts nickels by fives (up to 95¢) and writes the amount using the cent symbol

MY06D Counts and writes the amount for a given set of pennies and nickels or pennies and dimes (up to 99¢) using the cent symbol

TI03C Uses terms yesterday, today, and tomorrow with a calendar when referring to events

TI04C Locates a given day, week, month, and the year on a calendar

TI12E Names the months of the year in order

TI13E Compares and orders days of the week and months of the year (before, after, next, last)

TI14E Names a date for a given day and names the day for a given date on a calendar

PS04C Acts out or makes a model to solve subtraction problems (separation and missing addends)

PS05C Makes a model or drawing to solve problems involving addition or subtraction and describes the process

PS07D Uses logical reasoning to solve a problem

PS08D Explores creating a story to match a simple addition or subtraction sentence

NU26F Counts by hundreds to 900 and models with objects

NU27F Demonstrates with objects, names the number, and states the value of hundreds, tens, and ones in 3-place numerals

NU28F Reads and writes 3-place numerals

NU30F Names missing numbers in a sequence orally counted as well as seen (before, after, or between given numbers up to 1,000, counting by ones, tens, fives, and twos)

NT01F Identifies numbers as odd and even

NT02H Extends and describes number patterns, such as evens, odds, triangular, etc.

MD1.3.1a. Identify and describe a trend.

MD1.3.1b. Identify, describe, extend, and create a variety of numeric and non-numeric patterns.

      • create and extend number patterns of 2’s, 5’2, 10’s and odd and even numbers

      • create and extend patterns using models (symbols, shapes, designs and pictures)

      (cf. Gr. 1)

MD6.3.3. Describe numbers as even or odd.

AD14F Models addition of 2-place numbers which require regrouping of ones or tens with materials

AD16F Adds 2-place numbers with (and without) regrouping

AD20G Models the regrouping of 3-place numerals for addition

AD21G Identifies places where regrouping is needed in addition problems

AD22G Adds 3-place numbers with (and without) regrouping

SU15F Models with materials subtraction of 2-place numbers which require regrouping

SU16F Subtracts 2-place numbers with (and without) regrouping

SU17F Computes easy addition and subtraction problems mentally

SU19G Mentally subtracts hundreds (vertical and horizontal, sums to 2,000)

SU20G Models the regrouping of 2- and 3-place numerals for subtraction

SU21G Identifies places needing regrouping in subtraction

SU22G Subtracts 2- and/or 3-place numbers with (or without) regrouping

MD6.3.5a. Add and subtract whole numbers with regrouping with sums and differences less than 1,000.

MU01F Combines equivalent sets, and names the number of the new set (initial concept of multiplication)

MU02F Models multiplication with objects

MU03F Skip counts twos, threes, fours, fives, and tens

MU04F Names easy multiplication facts (no time limit)

DI01F Separates a set of objects into subsets of a given size, and names the number of subsets (initial concept of division, sometimes called measurement concept)

DI02F Separates a set of objects into a given number of equivalent subsets, and names the number in each set (initial concept of division, sometimes called partitioning concept) (demonstrate these with large numbers--e.g., a pile of tomato seeds)

CF02B Recognizes equal (from unequal) parts of a whole

CF05D Interprets "whole" in a fraction situation using an object, region, or set

CF06D Demonstrates and states the number of equal (congruent) fractional parts needed to cover or make a whole (region or object--two halves, three thirds, four fourths)

CF07D Distinguishes among and names orally one-half, one-third, and one-fourth of a region or object

CF08D Demonstrates one-half, one-third, and one-fourth by separating a region (or folding a piece of paper)

CF09F Models unit fractions less than 1 by selecting and shading halves, thirds, fourths, and tenths of regions

CF10F Reads symbols for unit fractions shown on regions (one-half, one-third, one-fourth, one-tenth)

CF11F Compares and orders unit fractional pieces (one-half, one-third, one-fourth) from a common whole

CF12F Models fractions less than 1 by paper folding and shading regions (two-thirds, three-fourths, etc.)

CF14F Uses manipulatives to model the relationship of fractional parts to one (counting by halves, thirds, and fourths)

CF15F Counts by fractional parts to one, and then on to two, using manipulatives to validate the process (naming each whole number in two ways)

MY07F Counts and writes the amount of a given set of pennies, nickels, and dimes (up to 99¢) using the cent symbol

MY08F Identifies and states the value in cents of a quarter, half-dollar, and dollar

MY09F Counts quarters and half-dollars to make a dollar

MY10F States fractional relationship of quarters and half-dollars to a dollar; distinguishes this fractional idea from that involving regions

MY11F Selects coins to equal a given value less than a dollar

MY12F Counts money, then uses the dollar symbol and decimal point to write amounts greater than or equal to $1.00

MY13H Counts a collection of coins up to $1.00 and writes the amount using the dollar symbol and decimal point

MY16H Adds and subtracts money (dollars and cents, up to $10) in problem situations

ME18F Measures and records to the nearest centimeter (cm) with trains

ME19F Measures and records to the nearest centimeter (cm) with a ruler and relates to trains

ME21G Chooses appropriate unit, estimates, verifies, and records length in centimeters (cm) and meters (m)

ME26H Estimates, verifies, and records weight in kilograms (kg) and grams (g)

TI08D Distinguishes between the hour and minute hands on a clock with both hands

TI09D Demonstrates and describes the relative movement of the hands on a clock

TI10D Reads time on a clock (hour and half hour) and describes location of hands

TI11D Sets the geared clock on any given exact hour

TI15E States relationships; days to weeks, weeks to months, months to years

TI16F Relates fractional parts of a circle to fractions of an hour on a clock face (one-fourth, one-half)

TI18F Reads time on a standard clock in half-hour or quarter-hour intervals "after the hour"

TI19F Reads time on a clock in 5-minute intervals after the hour (relate to counting by fives)

TI20G Sets a standard clock to the time shown on a digital clock (5-minute intervals)

TI22G Writes the date using numerals

TI23G Reads a clock and writes time (in 5-minute intervals) using a.m. and p.m.

TI24G Shows elapsed time by hours on a clock

GE08D Continues a repeating geometric pattern which uses two or three shapes

GE09D Creates and describes a pattern with two shapes

GE10D Constructs a configuration of blocks given a pattern and/or numeric description (working with a group)

GE16H Solves simple geometric analogies

PS06D Solves a story problem by acting out or making a model to show halves, thirds, or fourths

PS09E Makes a drawing to solve problems involving addition and subtraction (include comparison subtraction problems)

PS10E Estimates a reasonable answer to a problem and checks it

PS11E Solves problems from a story with too much information

PS12E Identifies problems that cannot be solved because of missing information

PS13E Chooses a number sentence to express a problem (+ or -)

PS14F Creates a story problem for a picture or pictures

PS15F Solves problems from given clues using logical reasoning

PS16F Solves story problems which have more than one solution

PS17G Writes number sentences for problems using the symbols + and -

NU22E Reads and writes number sentences using >, <, and = to compare numbers (model with objects, to 1000)

NU29F Translates a modeled 3-place numeral into expanded notation

NU34H Demonstrates with objects and names the number of thousands, hundreds, tens, and ones in 4-place numerals

NU35I States the value of any digit in a 4-digit numeral

NU36I Reads and writes word names for numbers through four places

NU37I Reads and writes numerals through four places

NU38I Reads and writes 4-digit numerals in expanded notation

NU39I Rounds 4-place numerals to the nearer 10, 100, or 1000

MD1.3.2.Express numeric relationships using +, -, <, or >, or =.

      • select appropriate operational and relational symbols to express relationships

      • select appropriate symbols and operations to solve simple problems

MD6.3.1. Read, write, and represent whole numbers (cardinal and ordinal) and simple fractions using symbols, words, and models. (cf. Gr. 1,2)

      • identify number values and relationships of whole numbers and simple fractions

      • express numbers in expanded notation

MD6.3.2. Compare, order, and describe whole numbers less than 1,000 using place value concepts and the symbols <,>,=.

AD25I Adds numbers with four or more digits

AD26I Names a reasonable answer for whole number addition problems by rounding the addends

SU26I Estimates differences (4 or more digits) and then solves with a calculator

SU27I Subtracts numbers with 4 or more digits

MD6.3.5b. Estimate sums and differences less than 1,000 of whole numbers.

MU05G Models multiplication facts and relates to fact strategies

MU06G Writes a number sentence for a multiplication situation

MU08G Models and writes multiplies of 10, 100, and 1,000

MU09G Mentally multiplies 10, 100, and 1,000 by 1, 2, or 5

MU10H Multiplies 2- and 3-place factors by one-digit factors (2 and 5) with and without regrouping

MU13I Names multiplication facts (Part 1)

MU14I Demonstrates and explains multiplication using models different from repeated addition (e.g., arrays, cross products of sets, and area models)

MU16I Skip counts by 7, 8, and 9 using a number line

MU17I Lists multiples of whole numbers (0 to 9)

MU18J Names multiplication facts (Part 2)

MU24M Names multiplication facts (Part 3)

DI03G Demonstrates partition and measurement models for division with objects (facts of 1, 2, 3, and 5; relate to real-world situations; include remainders)

DI04G Expresses a division situation using division symbols (÷, /)

DI12J Names division facts related to multiplication facts (Part 1)

DI18J Names division facts related to multiplication facts (Part 2)

DI21K Names division facts related to multiplication facts (Part 3)

MD6.3.4b. Use models/manipulatives and make drawings to show multiplication and division facts. (cf. Gr. 2)

MD6.3.5c. Multiply and divide whole numbers using technology or models.

MD6.5.4. Demonstrate proficiency with multiplication and division facts.

CF16H Reads and writes symbols for fractions less than 1 shown on a given region

CF20H Uses concrete models and drawings to order (or verify the order for) common fractions (denominators of 2, 3, and 4)

CF21H Counts forward and backward by unit fractions (including mixed numbers, using a number line)

CF27J Writes fractions greater than 1 as mixed numerals and mixed numerals as fractions

MD1.3.4a. Plot points to represent whole numbers and fractions with denominators of 2, 3, and 4 on a number line.

IE01G Solves easy addition and subtraction sentences with a missing number in any position

IE03J Solves easy multiplication and division sentences with a missing number in any position (basic facts)

IE07L Simplifies expressions with parentheses

IE18O Solves linear equations having one operation

IE22O Solves linear equations having two operations, such as 2(3x+1)=x+22

MD1.3.3. Find the missing number in a number sentence using a variety of strategies.

MD1.5.2b. Use grouping symbols to evaluate expressions.

MD1.5.3. Solve for the unknown in an equation (one unknown, one operation) with whole number coefficients.

      • write simple algebraic expresions in one unknown and evaluate by substitution

ME20G Chooses appropriate unit, estimates, verifies, and records length to the nearest inch (in), foot (ft), and yard (yd)

ME22G Measures perimeters of plane figures in centimeters (cm)

ME24H Finds and records approximate areas of regular shapes by counting square units

ME27J Estimates and records approximate areas of irregular shapes by counting square units

ME29J Distinguishes between perimeter and area of a shape

ME34J States basic measurement equivalencies and makes simple conversions (within systems only)

ME39L Computes areas of squares and rectangles and names as square units

MD3.3.3a. • convert between inches, feet and yards

MD3.5.3a. Estimate and determine the perimeter of polygons and real world objects.

MD3.5.3b. Estimate and determine the area of rectangles and estimate the area within any closed figure.

MD3.5.3e. Determine and use equivalent units within the same system.

MY14H Rounds amount of money to the nearer whole dollar

MY15H Estimates sums and differences of money to nearer 10¢

MY17H Makes change from a quarter and half-dollar

MY19I Makes change for $5.00 (using fewest bills and coins)

MY20K Makes change for $10.00

MY21K Makes change for $20.00

MY16H Adds and subtracts money (dollars and cents, up to $100) in problem situations

MY22M Multiplies and divides using money

MD6.3.5d. Identify, name, compare, and determine the value of a given set of currency through one hundred dollars and use this knowledge to solve problems including adding and subtracting money and counting change.

TI25J Describes minutes on a clock, reads and writes time to the minute using a.m. and p.m.

TI26J Sets a clock to a given time and demonstrates the passage of a given interval (to show elapsed time)

TI31M Computes elapsed time

MD3.5.3d. Estimate and determine elapsed time.

PS18G Solves problems from a story with too much information

PS19G Identifies problems which cannot be solved because of missing information

PS20G Makes a drawing or diagram to solve problems involving multiplication or division facts

PS21H Solves two-step addition and subtraction problems

PS22H Solves problems from given clues using logical reasoning

PS23H Estimates a reasonable answer to a problem

PS24H Creates a story problem from given information

PS25H Solves problems using guess and check method

PS26H Uses models to solve problems involving fractions

PS47N Makes a diagram to solve problems involving area and perimeter

PS32J Makes a drawing to solve problems involving perimeter and/or area

MD6.3.4c. Write a story problem that models a mathematical expression

MD6.3.7a.Apply strategies to solve problems with whole numbers

      • use estimation to solve problems with whole numbers

      • estimate the number of objects in a set

      • use estimation to evaluate reasonableness of results

MD3.5.4. Use perimeter, area, volume, and elapsed time to solve problems.

#1: Algebra, Patterns, and Functions

MD1.3.4b. Locate points on a simple grid.

#2: Geometry

2.3.1. Describe and compare the attributes of plane and solid geometric figures and use this understanding to show relationships and solve problems

      • identify, represent, and describe one-, two-, and three-dimensional figures.

      • combine and subdivide circles, squares, triangles, rectangles and other shapes

      • describe the following relationships: rectangle/prism, circle/sphere, square/cube, triangle/pyramid

MD2.3.2 Identify right angles and compare them to other angles

MD2.3.3 Construct or draw geometric figures using tools and technology

      • sketch squares, rectangles, triangles and circles.

MD2.3.4a.Describe and demonstrate slides, flips, and turns using pictures or other simple objects.

MD2.3.4b. Identify, describe, and represent symmetry of geometric figures and real-world objects.

MD2.3.5. Identify, describe, and represent congruency of geometric figures and real-world objects.

#3: Measurement

MD3.3.1 Identify the measurable attributes (length, area, weight, volume/capacity)

MD3.3.2a. Use rulers, scales, thermometers, and clocks to measure.

MD3.3.2b. Measure in standard units (inches, feet, yard, centimeters, meters, grams, ounces, pounds, Celsius, Fahrenheit, hours and minutes) and non-standard units (i.e. paper clips).

MD3.3.3a. Estimate and measure length, weight, temperature, time and capacity

MD3.3.3b. Estimate and count to find perimeter, area, and volume of figures and real-world objects

MD3.3.4 Use length, capacity, weight, temperature, and time to solve problems

#4: Statistics

MD4.3.1. Gather relevant data and compile the results to answer a question

MD4.3.2. Organize and display data using tables, pictographs, and bar graphs.

MD4.3.3. Interpret, compare, and make predictions based on tables, pictographs, and bar graphs.

#5: Probability

MD5.3.1. List possible outcomes for an activity.

MD5.3.2a. Describe the likelihood of an activity by using certain, impossible, more likely, less likely, and equally likely.

MD5.3.2b. Determine fairness by applying the concept of equally likely.

NU40I Sequences whole numbers with up to 6 digits

NU43L Explores concept of place value periods

NU44L States the value of any digit in a 5- or 6-place numeral

MU07G Identifies factors and products in a multiplication number sentence

MU20K Multiplies 2- and 3-place factors by 10, 20, . . ., 90

MU22L Multiplies 2-, 3-, or 4-place factors by 2-place factors

MU15I Estimates products for 2- and 3-place factors by 1-digit factors

MU23M Estimates products for whole number multiplication problems and verifies with a calculator

DI05G Identifies factors and products in a division number sentence (relate division to multiplication)

DI07H Models the division of 2-place numbers by 1-digit divisors with 2-place quotients and remainders

DI08H Divides 2-place numerals by 1-digit divisors (1, 2, 5) with zero or nonzero remainders

DI11J Names all factors of a whole number (to 50)

DI17J Divides 3- and 4-place numbers by 1-digit divisors

DI19J Mentally computes simple mixed operation problems

MD6.5.5a. Multiply and divide whole numbers and interpret remainders.

CF13F Separates sets into halves, thirds, and fourths using a region with those divisions as a background and relating to a real-world situation (sharing toys, food, etc.)

CF17H Describes the concept of a set as a whole in using fractions (based on real-world situations, relate to CF13)

CF18H Models and names fractional parts of sets (denominators of 2, 3, 4, and 10, based on real-life problem situations)

CF19H Models with regions and sets, and states the name of each term of a fraction less than 1 (numerator, denominator)

CF26I Approximates the locations of fractions on a number line (including fractional names for whole numbers)

CF28J Rounds mixed numerals to the nearer whole number and explains the process

CF30J Models and labels fractional parts of sets with denominators of 2, 3, 4, 6, 8, and 10

CF31J Finds a fractional part of a 2-digit whole number

CF24I Writes and identifies equivalent names for fractions less than or equal to 1

CF29J Interprets a fraction as a division and models with objects or drawings

CF32J Adds and subtracts fractions with like denominators by manipulating models

CF33L Adds and subtracts like fractions by manipulating models and then using symbols to express

CF34L Adds and subtracts common fractions with like denominators of 2, 3, 4, 6, 8, and 10 in vertical or horizontal form and verifies answers with manipulatives (answers not requiring simplest form or regrouping)

MD6.5.1. Read, write, and represent simple fractions, decimals, and percents using symbols, words, and models. (cf. Gr. 3)

DF02J Identifies and explains the value of the tenths and hundredths places using models

DF03J Uses a model to show the relationship between a common fraction and a decimal fraction

DF04J Estimates locations for decimal fractions < 1 on a number line (tenths, hundredths)

DF05J Models and explains the comparison of two decimal fractions through hundredths (more, less)

DF06J Reads and writes decimal fractions through hundredths

DF07J Writes decimal fractions through hundredths as expanded notation

DF08J Represents the addition and subtraction of decimal fractions through hundredths on grid paper (horizontal and vertical form)

DF09K Models, reads, and writes equivalents for given decimals (through hundredths)

DF10K Compares and orders decimal fractions through hundredths

DF14K Rounds decimal fractions to the nearer whole number, tenth, or hundredth

DF15K Models addition and subtraction of decimal fractions

DF11K Models decimal fractions through thousandths

DF12K Reads and writes decimal fractions through thousandths

DF13K Writes decimal fractions through thousandths using expanded notation

DF16K Estimates, then adds and subtracts decimal fractions through thousandths and checks the reasonableness of the results

DF18L Writes common fractions for decimal fractions and decimal fractions for common fractions through thousandths (using common fractions with powers of ten as denominators)

DF19M Compares and orders decimal fractions through thousandths

MD6.5.2a. Compare and order decimals to the nearest thousandth and describe them using place value concepts.

TI27J States relationships: seconds to minutes, minutes to hours, hours to days, days to years (and leap year), weeks to years

TI29K Changes a given amount of time into smaller or larger units

SP11E Constructs and interprets simple bar graphs

SP12G Reads and uses information from simple tables

IE04J Identifies the location for an ordered pair on a coordinate graph and writes the ordered pair for a given location

SP17I Interprets and uses information from a line graph (include written interpretation) (time series only)

MD1.5.4. Represent relationships using graphs and tables

MD1.5.4(sic) Plot points on a coordinate plane

PS28I Solves problems using logical reasoning

PS29I Solves story problems which include too much information

PS30I Chooses or writes number sentences for computation problems

PS31J Solves whole number problems using guess and check

PS33J Solves problems by constructing a table or organized list

PS34J Makes a drawing or uses a model to solve problems involving comparing and ordering unit fractions

Division

DI20K Divides 3- and 4-place numbers by multiples of 10

DI22M Divides by 2-place divisors (zero and nonzero remainders)

DI23M Estimates reasonable answers for division of whole numbers before solving with a calculator

NU41L Uses exponents to express repeated factors

NU42L Converts exponential notation to whole numbers

NT07L Uses rules of divisibility for 2, 3, 5, 6, 9, and 10, and explores these rules to identify prime numbers

NT08M Determines whether a given number is prime, composite, or neither

NT09M Writes and verifies prime factorizations of numbers using exponents

CF35L Writes common factors of whole numbers to 50

CF36L Writes common fractions in simplest form (includes improper and mixed forms)

CF37L Estimates the location of any fraction on a number line

CF38M Names common multiples of two whole numbers to 10

CF39M Names an equivalent fraction with a given multiple as denominator

CF40M Adds and subtracts fractions with unlike denominators by manipulating models

CF41M Estimates sums and differences for common fractions less than one (including unlike denominators

CF45N Names common denominators and identifies the least common denominator (LCD)

CF46N Compares fractional numbers (<,>,=)

CF47P Estimates the sum of common fractions with unlike denominators (answers in simplest form)

CF48P Estimates the difference of common fractions with unlike denominators without regrouping (answers in simplest form)

CF49P Checks reasonableness of answers in problems with common fractions using estimation

CF50P Adds and subtracts common fractions with unlike denominators including regrouping

DF20M Estimates sums, differences, and products of decimal fractions to the nearer whole number

DF21M Estimates, then multiplies a whole number times a decimal fraction (through thousandths))

DF22M Estimates, then multiplies a decimal fraction times a decimal fraction (through thousandths)

DF24N Divides a whole number or a decimal fraction by any whole number to obtain a decimal fraction quotient

DF25N Estimates a simple common fraction (denominator of 2, 3, 4, 5, or 10) which is 'close to' the value of a given decimal fraction between .100 and .999

RP07M Describes or models the meaning of percent

RP09N Writes decimals as percents and percents as decimals

RP13P Finds a percent of a number

RP14R Writes equivalent forms for fractions, decimals, and percents (include less than 1 percent and greater than 100 percent)

MD6.5.1. Read, write, and represent simple fractions, decimals, and percents using symbols, words, and models. (Cf. Gr. 4)

MD6.5.2b. Compare and order fractions in equivalent forms including improper fractions and mixed numbers with like and unlike denominators. (cf. Gr. 4)

MD6.5.3. Use number theory concepts of primes, factors, multiples, and rules of divisibility to show number relationships.

MD6.5.5b. Add and subtract fractions and decimals, mixed numbers and decimals and express answers in simplest form.

MD6.5.5c. Multiply and divide decimals by whole numbers.

MD6.5.7a Apply strategies to solve problems with fractions and decimals

      • use estimation to solve problems with fractions and decimals

      • Identify and describe the relationship among fractions, decimals, and percents

      • represent fractions, decimals, and percents in equivalent forms

      • compute percentages of 10, 20, 25, 50 and 100 percent of a number

      (cf. Gr. 4)

GE21I Identifies horizontal, vertical, intersecting, parallel, and perpendicular lines

GE22I Models intersecting, parallel, and perpendicular lines (geoboard, cm or dot paper)

GE39P Names, describes, and uses notation for a point, line, segment, angle, and ray

GE31L Measures and draws angles using a protractor and identifies congruent angles (including angles > 180)

MD2.5.1 • Identify parallelism and perpendicularity of geometric figures and real-world objects.

MD2.5.3 • draw, label, describe, and identify: points, lines, line segments, and rays

MD3.5.2a. Use protractors to measure angles.

SP17I Interprets and uses information from a line graph (include written interpretation) (time series and other 2-variable relationships)

SP18I Interprets and uses information from a circle graph (include written interpretation)

SP21K Models the concept of an average with sets of objects

SP22K Finds averages for given data sets

SP38O Finds and interprets mean, median, mode, and range

SP39O Constructs and analyzes histograms, stem and leaf plots, box and whisker plots, and scatter plots

MD4.5.1. Gather relevant data and compare data sets to answer a question.

MD4.5.3. Analyze and interpret stem and leaf plots, circle graphs, line plots, and line graphs. (Cf. Gr. 4)

MD4.5.4. Find the mean, median, mode, and range of a data set and explain how these measures are different.

IE05K Identifies situations where negative numbers are needed and uses symbols for integers

IE08L Extends a function table and writes a function rule from tabled values (include concept of a variable)

IE16O Translates verbal sentences to mathematical sentences

IE20O Subtracts integers (including negative integers)

IE25Q Simplifies expressions containing integers and more than one operation, such as 2(-x+8)-(-3)=2x+3

IE06K Compares and orders integers (include a number line)

IE10N Models addition of integers on a number line

IE11N Estimates sums and adds integers

IE21O Multiplies and divides integers and raises to positive power

IE17O Uses the commutative, associative, zero, identity, and inverse properties and the properties of equality

IE29R Uses the distributive property

MD1.5.1. Recognize, describe, and extend patterns and functional relationships

MD6.3.6. Use mathematical properties to solve problems

MD6.5.6. Use mathematical properties to solve problems

MD6.8.6. Explain and apply number relationships using the mathematical properties of operations, including distributive and additive inverse

PS35K Solves problems with too much information

PS36K Identifies problems that cannot be solved because of missing information and states the needed information

PS37K Works backwards to solve problems

PS38K Chooses reasonable answers for problems using any operation

PS39K Solves two-step problems

PS40K Uses patterns to solve problems

PS41K Makes a diagram to solve problems involving addition and subtraction of common fractions

PS42L Finds more than one solution for a problem that has a nonunique solution

PS43L Solves problems using logical reasoning

PS44L Solves problems using guess and check

PS45M Chooses a reasonable answer for a problem involving whole numbers, common fractions, or decimal fractions

7.0 Process of Problem Solving

#1: Algebra, Patterns, and Functions

MD1.5.2a. Write numeric expressions in equivalent forms.

#2: Geometry

MD2.5.1. Compare one-, two-, and three-dimensional figures to one another and relate them to real-world objects.

      • Classify two- and three-dimensional figures by sides, angles, edges, vertices, and faces.

      • Identify and describe the attributes of solid figures.

MD2.5.2. Identify, classify, measure, and draw acute, right, and obtuse angles.

MD2.5.3 Construct or draw geometric figures using tools and technology

      • Draw circles, squares, triangles, and rectangles given their dimensions.

MD2.5.4. Identify transformations: translations, reflections, and rotations.

#3: Measurement

MD3.5.1 Identify the appropriate measurable attribute to solve a problem

MD3.5.2b. Use standard units (yards, meters, degrees, and other units) to measure objects.

#4: Statistics

MD4.5.2. Organize and display data using stem and leaf plots, line plots, and line graphs.

MD4.5.4. Find the mode and range of a data set and explain how these measures are different.

#5: Probability

MD5.5.1. List all possible outcomes of an event with a limited number of possible results.

MD5.5.2. Find the probability of an event with equally likely outcomes and express as a fraction or ratio.

MD5.5.3. Conduct and experiment and make a prediction based on the outcomes of the experiment.

IE12N Identifies axes, origin, quadrants, and ordered pairs

IE13N Locates and names the coordinates of a given point in any of the four quadrants

IE34R Graphs a linear equation on a coordinate plane

MD1.8..4a. Graph ordered pairs in the four quadrants of a coordinate plane

      • graph linear equations on a coordinate plane

GE35M Names, describes, and distinguishes among quadrilaterals (square, parallelogram, rectangle, rhombus, and trapezoid)

GE40P Identifies complementary, supplementary, vertical, and adjacent angles

GE46Q Computes the measure of the third angle of a triangle given the other two measures

GE47Q Finds relationships among angles formed by parallel lines intersected by a transversal

ME46N Computes areas of parallelograms in square units

ME47N Relates the area formula for triangles to that of parallelograms

ME48N Computes areas of triangles and records in square units

ME53O Computes areas of quadrilaterals including trapezoid and rhombus, given formulas

ME55O Distinguishes among perimeter, area, surface area, and volume for plane and solid shapes

ME56O Estimates, and verifies by counting cubic units, the volumes of right rectangular prisms

ME57O Demonstrates the volume formula for rectangular prisms by counting cubic units in the base, relating this to the area of the base, and multiplying by the height

ME59Q Uses models or diagrams to validate the Pythagorean Theorem

ME60Q Applies the Pythagorean Theorem

GE33M Names and describes circumference, diameter, radius, center, and chord of a given circle

ME50N Explores the relationships among the radius, diameter, and circumference of a circle

ME51N Computes the circumference of a circle (p = 3.14)

ME54O Computes areas of circles using a formula

ME38O Demonstrates the volume for cylinders as the product of the area of the base and the height

MD3.5.3c. Estimate and determine the volume of a rectangular prism using manipulatives and formulas.

MD3.8.3b. Estimate and determine the area of figures by measuring, partitioning, and using formulas.

MD2.8.1. Apply properties of two- and three-dimensional figures to problem situations.

MD3.8.3a. Estimate and determine the circumference and area of circles.

MD3.8.3c. Estimate and determine the volume and surface area of cylinders

MD3.8.3d. Determine relationships between length, area, and volume and describe how a change in one measure affects the others.

CF42N Models multiplication of unit fraction times a unit fraction or a unit fraction times a whole number

CF43N Estimates the product of two common fractions or a fraction and a whole number

CF44N Multiplies two or more common fractions or a fraction times a whole number

CF51P Names and states the meaning of reciprocals for common fractions

CF52P Estimates quotients of fractions to be less than, greater than, or equal to 1

CF53P Divides common fractions

CF54P Simplifies common fraction expressions which have more than one operation

IE27Q Adds, subtracts, multiplies, and divides rational numbers

MD6.8.2. Compare, order, and describe rational numbers in equivalent forms.

MD6.8.5.Add, subtract, multiply and divide rational numbers.

PS46M Creates and solves a simpler version of a problem involving decimals or large whole numbers, then solves the original problem

PS48N Creates and/or solves two-step story problems from information given in a table or graph

PS49N Solves problems using logical reasoning

PS50N Works backwards to solve problems

PS51O Solves problems using a variety of techniques

      Logical reasoning

      Works backwards

      Guess and check

      Simpler version

PS52P Solves problems using a variety of techniques

      Logical reasoning

      Works backwards

      Guess and check

      Simpler version

      Organized list or table

      Finds/extends pattern

      Makes a diagram

      Writes equation

DF23N Uses mental arithmetic to multiply and divide decimal fractions by multiples/powers of 10

DF26N Uses a calculator to find decimal fractions for given common fractions

DF27N Estimates and uses a calculator for decimal computation

DF29P Estimates to the nearest whole number, quotients involving decimal fractions (2-digit divisor)

DF30P Estimates and divides a decimal fraction by a decimal fraction (1- or 2-digit divisor)

DF31P Simplifies expressions with decimal fractions and more than one operation

DF32P Uses a calculator to perform decimal operations

IE21O Multiplies and divides integers and raises to positive power

NU47M Multiplies and divides by powers of ten

NU49P Multiplies and divides by negative and positive powers of ten

NU50Q Multiplies and divides powers with the same base (non-negative exponents only)

NU51Q Writes scientific notation for customary notation and writes customary notation for scientific notation

NU52Q Uses scientific notation to multiply and divide with or without a calculator

NU53Q Uses scientific notation to solve multiplication or division problems involving large or small numbers

NU55Q Approximates the square root of a nonperfect square to the nearer whole number

RP01L Constructs patterns to explore the concept of ratio (1 dog for every 2 cats, etc.)

RP02L Writes the ratio for two quantities in fraction form and recognizes the differences between fractions and ratios

RP03M Uses a given scale to interpret a scale drawing

RP06M Solves for a missing term in a proportion (with and without a calculator)

GE42P Identifies corresponding parts of similar figures

MD2.8.5. Apply properties of congruence and similarity to solve problems.

MD3.8.4a. Use proportions, rates, and scale drawings to solve problems.

MD6.8.1. Read, write and represent rational numbers in a variety of forms, including exponents, scientific notation, and percents.

MD6.8.2. • determine the absolute value of rational numbers

MD6.8.5. • calculate powers and square roots of numbers

      • use the rules of exponents to combine rational numbers

      • multiply and divide by powers of ten

      (Cf. Gr. 6)

MD6.8.7a. Select and apply strategies and mathematical properties to solve problems with rational numbers

      • use estimation to solve problems with rational numbers

      • estimate powers and square roots to solve problems

      • estimate the value of radicals and numbers expressed with exponents to solve problems

MD6.8.7b. Apply ratios, proportions, and percents to solve problems.

      • determine equivalent ratios, decimals, and percents

      • determine ratios, rates, unit rates in the context of a problem

      • apply the concepts of ratios, rates, and percents to real-world problems including rate of increase/decrease, discount, commission, sales tax, simple interest

IE14O Simplifies expressions containing whole numbers using order of operation rules

IE15O Evaluate algebraic expressions and formulas

IE16O Translates verbal sentences to mathematical sentences

IE19O Writes the absolute value of a number

IE23O Solves one-step integer inequalities

IE24O Represents the solution set of integer equations and inequalities by roster, rule and/or graph (One-step inequalities)

IE37R Solves inequalities

IE30R Simplifies algebraic expressions by combining like terms

IE31R Simplifies algebraic expressions containing parentheses

IE32R Evaluates algebraic expressions containing parentheses and exponents

IE33R Solves linear equations having one or two operations

MD1.8.1a. Recognize, describe, and extend patterns and functional relationships

      • identify and extend a simple arithmetic or geometric sequence.

      • describe the recursive relationship of simple arithmetic and geometric sequences verbally, in a table, or a graph.

MD1.8.1b. Produce rules that explain how a change in one variable in a relationship affects the other variable.

MD1.8.1c. Determine whether functions are discrete or continuous

MD1.8.1d. Determine whether functions are linear or nonlinear when given graphic examples.

MD1.8.3b. Solve linear equations and inequalities in one variable using mathematical properties.

MD1.8.4b. Solve inequalities and graph the solutions on a number line.

MD1.8.3d. Solve problems involving direct and inverse variation

MD1.8.3e. Determine the slope of a linear function represented graphically, numerically, or algebraically.

MD1.8.2. Simplify expressions by combining like terms and applying order of operations

      • use mathematical properties to justify the steps in simplifying algebraic expressions

MD1.8.3a. Evaluate algebraic expressions and apply formulas.

MD1.8.3c. Describe a real-world situation represented by an algebraic expression or equation

NT03J Informally lists the members and subsets of a given set

NT04J Identifies members that two sets have in common

NT10N Uses standard symbols for sets and intersection and union of sets

NT11N Interprets and constructs Venn diagrams using subsets, intersection and union

SP29M Organizes given data into a table using computer spreadsheet and wordprocessor

SP36O Collects data, organizes it, chooses an appropriate type of graph, and graphs the data using computer spreadsheet

SP37O Interpolates on graphs

MD1.8.4. Represent and interpret quantitative relationships in a table or graph

MD4.8.1. Conduct and use the results of a statistical investigation to answer a question.

MD4.8.3a. Analyze and interpret frequency tables, box and whisker plots, and scatter plots.

MD4.8.3b. Make predictions about a set of linear data given the line of best fit.

MD4.8.3c Fit a line to a set of linear data and make predictions about the data.

PS53Q Solve problems using a variety of techniques, including rational numbers

Makes an organized list or a table to solve problems

Writes and solves a simpler version of a problem involving common or decimal fractions, then solves the original problem

Works backwards to solve problems

Solves problems using guess and check

Solves problems by using logical reasoning

Finds and extends patterns to solve problems

Makes a diagram to solve problems

Writes equations to solve problems

PS54R Uses a variety of problem-solving techniques to complete a given task

MD2.8.3. Construct or draw geometric figures using tools and technology

      • use a compass and straightedge to construct angles, rectangles, circles, and other geometric figures.

      • draw and analyze geometric figures on a coordinate plane

MD2.8.4. Draw and describe the results of translations, reflections, rotations, dilations, and combinations of transformations.

MD2.8.5. Apply properties of congruence to solve problems.

#3: Measurement

MD3.8.2 Select tools and units to measure accurately and determine the degree of precision.

MD3.8.3c. Estimate and determine the volume and surface area of triangular prisms and other solids.

#4: Statistics

MD4.8.2. Interpret, organize and display data using frequency tables, circle graphs, box and whisker plots, scatter plots, and histograms.

MD4.8.4. Select and justify mean, median, mode, or range of a data set as the best representation of data.

MD4.8.5. Examine the misinterpretation of statistics

      • identify factors leading to faulty interpretation or representation of data including choice of sample population, graphical display, scale, and use of statistical measures

#5: Probability

MD5.8.1. Determine outcomes of events using counting techniques including permutations and combinations.

MD5.8.2a.Find the probability of an event that does not have equally likely outcomes.

      • express the probability of an event as a ratio, decimal, or percent

MD5.8.2b. Find the probability of simple dependent and independent events using various methods including constructing a sample space.

MD5.8.3. Conduct and predict the probability of an event based on the outcomes of an actual event or a simulation.