Math Exit Goals by Standard

 

Numbers and Operations

 

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Understand the meaning of operations and how they relate to each other

Use computational tools and strategies fluently and estimate appropriately

K

·         Writes numerals to 50

·         Counts objects to 20/count on and back

·         Uses vocabulary comparing quantities

·         Demonstrates understanding of number families to 5

·         Counts by 1's,5's, and 10's to 110

·         Skip counts by 2's to 30s

·         Understands team numbers as 10 + digit

·         Reads and sequences numbers 0-100

·         Solves problems using the operations of addition and subtraction - join/separate

·         Creates number stories

·         Communicates own thinking and reasoning strategies

·         Reads and sequences numbers 0-100

 

·         Uses calculator to explore counting and operations

1

·   Counts by 1s, 2s and 10s to 300+

·   Counts by 2s to 100

·   Counts back from 50+

·   Compares and orders numbers through 100 (>, <, =)

·   Reads relations sentences correctly (12 > 10)

·   Writes 2- and 3-digit numbers from dictation

·   Reads 2- and 3-digit numbers

·   Understands relationships among whole numbers using a number line

·   Understands fractions as equal parts of a whole(regions)

·   Names even and odd numbers

·   Uses tally marks

·   Makes largest and smallest numbers using 2 or 3 digits

·   Understands rule-based relationships between pairs of numbers

·   Defines operations in terms of part/part/total, compare, join/separate

·   Writes addition and subtraction stories

·   Connects part/part/whole language with symbolic notation

·   Communicates solution strategies for solving word problems

·   Mentally adds and subtracts 10s to/from 2-digit numbers using a 100 grid

 

·   Uses a calculator to count by 2s, 5s, 10s

·   Develops “fact power” through 20

·   Makes reasonable estimations with use of a benchmark and/or prior knowledge

 

2

·         Identifies and describes patterns using a hundreds chart

·         Counts by 1’s,2's ,10's from any 2 or 3 digit number forward and backward

·         Counts by 25's, 10's, 5's and 1's

·         Reads and writes 4 digit numbers from dictation

·         Reads, writes identifies place value to 10,000

·         Writes 1-4 digit even and odd numbers

·         Compares and orders whole numbers through 10,000

·         Knows and expresses the value of digits in 2-9 digit #s

·         Recognizes, reads, models, writes and compares fractions (halves, thirds, fourths, fifths, sixths)

·         Interprets a numerical sequence in a time line

·         Understands the relationships of numbers in a fact family for addition and subtraction(part/part/total)

 

·         Recognizes the process necessary to solve addition and subtraction problems

·         Using multi-digit addition strategies, solves 1 and 2 step problems involving 1,2,3 digit numbers

·         Solves mentally addition and subtraction “fact extensions” (____ = 17+5; 40=90-____)

·         Constructs a model to demonstrate problem solutions

·         Writes number sentences to describe problem solutions

·         Communicates mathematical thinking both orally and in writing

·         Uses a variety of strategies to solve problems

 

 

·         Has addition and subtraction "fact powers" through 20

·         Mentally adds three 1 digit numbers

·         Mentally adds 2 and 3 digit numbers

·         Adds and subtracts 3 digit numbers (with or without regrouping)

·         Extends addition and subtraction facts to tens and hundreds (50+70; 800+700)

·         Correctly estimates and predicts solutions using a variety of strategies

·         Uses calculator to add 3 or more 2 digit numbers

·         Solves single digit multiplication stories (multiples of equal groups 2-5)

 

 

3

·   Counts forward and back by 10s from a given 4-digit number

·   Counts forward and back by 100s from a given 4-digit number

·   Counts forward and back by 1000s from a given 4-digit number

·   Knows digit values of 3- and 4-ditig numbers

·   Determines place values in 4-digit numbers

·   Shows equivalent fractions with models

·   Writes 5- and 6-digit whole numbers

·   Reads 4-digit numbers as thousands, hundreds, and tens (e.g., 1600 as 16 hundreds or 160 tens)

 

·   Solves addition and subtraction multi-digit number stories

·   Understands whole-number multiplication as multiples of equal groups through a variety of problem situations.

·   Understands whole-number division as equal sharing or as making equal groups with/without a remainder though a variety of problem situations

·   Uses a calculator for skip counting and for multi-digit addition and subtraction

·   Understands addition and subtraction facts and fact-extension families

·   Estimates sums and differences of multi-digit numbers

·   Quickly recalls multiplication, division facts for 0,1,2,5,10

·   Writes multiplication facts for square numbers

 

 

Numbers and Operations (continued)

 

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Understand the meaning of operations and how they relate to each other

Use computational tools and strategies fluently and estimate appropriately

4

·         Reads, writes, orders, and estimates whole numbers to 1,000,000

·         Gives value of digit in numbers to millions

·         Identifies fractional parts of collections of objects and regions

·         Compares and orders decimals

·         Shades a percent of a region

·         Identifies and uses square numbers

·         Knows multiplication and division concepts to perform mental math on a variety of problems

·         Uses, explains, and develops strategies to solve multiplication and division word problems

·         Explains the relationship between multiplication and division

·         Makes magnitude estimates for division and multiplication problems

·         Quickly recalls basic multiplication/division facts

·         Has a successful strategy for solving multi-digit multiplication problems

·         Divides whole numbers by 1 digit divisors

·         Uses the calculator to rename any fraction as a decimal or percent

5

·   Identifies the factors of a number

·   Determines whether a number is prime or composite, even or odd

·   Uses exponential notation; converts between exponential, expanded, and standard notation

·   Identifies place value to trillions and thousandths

·   Understands the terms numerator and denominator

·   Compares fractions

·   Identifies fractional parts of a set or region

·   Renames fractions in simplest form

·   Finds equivalent fractions

·   Converts between mixed numbers and fractions

·   Shades a hundred grid to represent a fraction or a decimal

·   Describes a percent of a region

·   Converts between fractions, decimals, percents mentally or with a calculator

·   Gives equivalencies between fractions, decimals, and percents

·   Compares and orders signed numbers (positive and negative)

·   Uses negative numbers to represent appropriate situations

·   Finds the prime factorization of a number

 

·   Has a successful strategy for adding and subtracting decimals

·   Has a successful strategy for solving multi-digit division problems

·   Has a successful strategy for adding and subtracting fractions with like/unlike denominators

·   Has a successful strategy for adding and subtracting mixed numbers

·   Uses fractions to represent ratios

·   Adds signed numbers (positive and negative)

 

 

 

 

 

 

 

 

 

 

 

 

 

Measurement

 

Understand attributes, units and systems of measurement

Apply a variety of techniques, tools, and formulas for determining measurements

K

·         Uses non-standard units to measure a variety of objects

·         Uses appropriate vocabulary to compare sizes of objects (i.e. more, less, long, longer, longest, heavy, heaviest, greater, fewer)

·         Identifies and understands value of coins -penny, nickel and dime

·         Tells time to the hour

·         Names days of week and uses ordinal numbers as they relate to time on a calendar

·         Uses correct tools for measuring -including volume, weight, length, temperature and time

·         Estimates measurements using a benchmark for comparison

 

 

1

·   Orders objects by weight and length.

·   Uses estimation in measuring situations

·   Tells time to the half-hour and hour

·   Describes penny, nickel, and dime exchanges

·   Measures using inches and centimeters

2

·         Recognizes the attributes of length, capacity, weight, area and time

·         Measures length in metric/customary units to the nearest centimeter, inch, foot

·         Measures capacity in volume, liters, cups, pints, quarts, gallons

·         Uses balance scale to measure weights and pounds

·         Recognizes Fahrenheit and Celsius as two units of measurement

·         Reads time to the half and quarter hour; reads the time at 5 minute intervals

·         Knows cent value of nickel, dime, quarter, half dollar, dollar

·         Know exchange value among U.S. coins (i.e. quarter = 5 nickels)

·         Records amounts of money using decimal quotations

·         Correctly uses measuring tools such as inch and centimeter rulers, yardstick, meter stick, analog clock, currency

·         Solves word problems involving money/time/measurement

·         Correctly estimates intervals of time

·         Demonstrates calendar concepts and skills

·         Identifies decades in a timeline

·         Compares estimated measurements to actual measurements

3

·   Understands negative numbers on a Celsius thermometer

·   Is familiar with appropriate linear metric units: cm, dm, m, km

·   Is familiar with appropriate linear U.S. customary units: in, ft, yd, mile

·   Identifies several equivalencies for linear metric units

·   Identifies equivalencies for linear U.S. customary units

·   Identifies basic U.S. customary units of weight measure: oz, lb

·   Is familiar with various scales for weight measure

·   Identifies the basic metric unit of weight measures: gm–kg

·   Is familiar with appropriate units for measuring capacity

·   Identifies several equivalencies for U.S. customary units

·   Identifies the basic metric unit of capacity: liter

·   Tells time to 5-minute interval and 1-minute intervals

·   Writes dollar and cents notation

·   Uses rulers correctly for inches and centimeters

·   Compares pairs of same unit temperatures, including negatives, as “warmer” or “colder”

4

·         Uses personal references to estimate lengths and U.S. customary units

·         Solves elapsed time problems

·         Uses coordinates to identify points on a grid

·         Uses money notations

·         Identifies location on Earth for which longitude and latitude are given

·         Uses map scale to estimate distances

5

·   Understands perimeter

·   Defines radius and diameter

·   Explains area; uses appropriate units for area measure

·   Identifies acute, obtuse, straight, reflex, and right angles

·   Draws line segments to the nearest 1/8 inch

·   Measures and draws angles with a protractor

·   Uses formulas to find areas of rectangles, parallelograms, and triangles

·   Finds the perimeters of polygons

·   Finds the diameter and radius of a circle

·   Measures to the nearest 1/16 of an inch

·   Uses a formula to find the area of the base of a prism

 

 

 

 

Geometry and Spatial Sense

 

Analyze characteristics and properties of 2 and 3 dimensional geometric objects

Select and use different representational systems, including coordinate geometry and graph theory

Recognizes the usefulness of transformations and symmetry in analyzing mathematical situations

Uses visualization and spatial reasoning to solve problems both within and outside of mathematics

K

·         Identifies and uses pattern blocks

·         Finds and names shapes in our environment

·         Uses appropriate "position vocabulary" to describe the location of a given object (i.e. next, far, above, below)

 

 

 

1

·   Recognizes, names, and describes two- and three-dimensional shapes

·   Describes attributes and parts of two- and three-dimensional shapes

 

 

 

2

·         Explores, sorts, describes 2 and 3 dimensional objects

·         Identifies, models, draws, classifies 2 and 3 dimensional figures such as prisms, cylinders, pyramids, cones, spheres

 

·         Draws given line segments

·         Finds and names locations with simple relations (i.e. near to) and coordinate systems (maps)

·         Correctly identifies directions

 

·         Describes the similarities and differences between pairs of 2 and 3 dimensional shapes on the basis of their characteristics

·         Identifies and explains congruent figures

·         Identifies and explains symmetry in simple figures

·         Constructs symmetrical figures

·         Draws logical conclusions base on properties of shape

·         Communicates reasoning about simple geometric figures and patterns using concrete materials, diagrams and technology

3

·   Identifies similarities and differences among 3-D shapes

·   Recognizes right angles

·   Constructs and names polygons

 

 

 

4

·         Identifies and describes right angles and parallel lines

·         Identifies lines of symmetry

·         Describes properties of a parallelogram

·         Names and draws angles, triangles, quadrangles

·         Names, draws and labels line segments, lines and rays

·         Uses a transparent mirror to draw the reflection of a figure

 

 

 

5

·   Identifies and describes parallel lines

·   Sorts polygons according to their properties

·   Identifies and compares properties of geometric solids

 

·   Plots and reads ordered number pairs in the positive quadrant

 

 

 

Patterns Functions and Algebra

 

Understand various types of patterns and functional relationships

Use symbolic forms to represent and analyze mathematical situations and structures

Use mathematical models to analyze change in both real and abstract contexts

K

·         Recognizes arrays on dominoes, dice, cards without counting

·         Sees/Utilizes patterns in “what’s my rule?”

·         Identifies, extends and creates 2 and 3 part patterns with a variety of objects

·          

 

1

·   Sorts groups by attributes

·   Fills in missing numbers in a sequence (up to 100)

·   Extends a repeating and growing pattern

 

·   Writes equivalent names or expressions for 2-digit numbers (name boxes: 16 = 8+8= 9+7 etc.)

 

 

 

2

·         Recognizes, creates, analyzes and extends counting patterns

·         Identifies whole numbers as even or odd with an explanation of reasoning

 

 

 

·         Describes basic arithmetic operations (add, subtract and start multiplication, division)

·         Understands concept of equivalent names and expressions for 2 and 3 digit numbers (45=35+7+3; 345=3 hundreds, 4 tens and 3 ones)

·         Writes addition "turnarounds" (8+7 = 7+8) for given facts and extend addition facts

 

·         Describes basic arithmetic operations (add, subtract, multiply, divide) in writing and with concrete materials and drawings

3

·   Using four basic operations; understands equivalent expressions for numbers

 

·         Writes “turnarounds” for given multiplication facts

·         Determine missing factors in simple multiplication/division equations

 

4

 

 

 

 

5

·         Finds equivalent expressions for numbers

·   Uses parentheses in number sentences to specify the order of operations

·   Determines whether number sentences containing parentheses are true or false

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data Analysis, Statistics and Probability

 

Pose questions and collect, organize, and represent data to answer those questions       

Interpret data using methods of exploratory data analysis

Develop and evaluate inferences, predictions and arguments that are based on data

Understand and apply basic notions of chance and probability

K

·         Uses survey instrument to collect and analyze data

·         Participates in creating a graph to answer a question or to compare data

 

·         Collects, organizes and describes data related to real experiences using pictures, tallies and graphs

 

 

 

1

·   Gathers data about themselves and their surroundings to answer questions

·   Represents data to convey results at a glance using concrete objects, pictures or numbers

 

 

 

2

·         Constructs and reads graphs (bar, picture, circle, rectangle, Venn etc.)

 

·         Interprets and compares graphs (bar, picture, circle, rectangle, Venn, etc.)

·         Solves a problem or answers a question of interest by collecting and representing data

·         Makes a predictions based on given data

 

3

 

·   Independently conducts survey: collects, organizes, analyzes and represents data

·   Finds the median for a data set

 

 

4

·         Uses rate tables to solve problems

 

·         Uses the statistical landmarks, maximum and minimum

·         Makes predictions and decisions based on data - communicates reasoning

 

5

·   Collects and organizes data

·   Constructs bar graphs

·   Interprets data

·   Interprets bar graphs

·   Finds the statistical landmarks (median, mode, range) of a set of data

 

·         Uses appropriate vocabulary to describe the probability of chance events