Math Grade 5  Download an editable version (RTF file)

Standard 1: Understands and applies problem solving strategies
Interval Benchmark 1: Uses a variety of strategies to solve problems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Applies problem solving strategies   ITBS ***	pertinent or relevant information irrelevant information insufficient information act it out make or use a model find or use a pattern draw a picture guess and check make a chart, table, graph, or organized list use logical reasoning	Knows the general problem solving strategies Knows the characteristics of pertinent or relevant and irrelevant information Knows the characteristics of insufficient information Understands problem solving involves multiple steps	Extracts the main idea of a problem (ITBS) Chooses appropriate strategies to solve problems in the context of the problem situation (ITBS) Uses previously learned strategies, skills, knowledge and concepts to solve problems (ITBS) Uses number sentences to represent information (ITBS) Identifies insufficient information (ITBS) Identifies pertinent and irrelevant information (ITBS)	12 Days of Christmas Teaching Thinking Problem of the Week ABACUS Math Challenge Monthly Problems	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 2: Justifies the process used to solve a numerical problem
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Justifies a solution	justification evidence counter example verification diagram method process of elimination	Understands how to make an argument for a solution Understands the structured process of evaluating Understands how to justify results Understands how to use evidence to justify an answer Understands characteristics of a clear, organized justification	Uses logical arguments to justify a solution Writes a clear justification of the solution		AEA9 AEA16
Standard 2: Understands and applies concepts of numbers and operations
Interval Benchmark 1: Describes the properties of numbers and number systems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Applies counting rules to decimals and fractions	tenth hundredth fraction negative integer positive integer	Knows counting can be used for a variety of purposes	Counts by tenths and hundredths Counts by fractional units Counts negative and positive integers		AEA9 AEA16
b: Uses number theory concepts	factor multiple common factor greatest common factor least common multiple prime composite percent ratio	Understands the concept of factors and multiples Understands prime and composite numbers Knows multiplying by 1 does not change a number Knows multiplying a number by 0 equals 0 Knows the concept of percent as part-to-whole Knows the concept of ratio as part-to-part and part-to-whole	Applies the properties of 0 and 1 Identifies and represents factors and multiples of whole numbers Gives the common factors of two numbers Determines the greatest common factor and the least common multiple Classifies numbers as prime or composite Represents a ratio Represents a percent		AEA9 AEA16
c: Uses place value for any given number   ITBS **	billion decimal	Knows place value helps when adding or subtracting decimals	Reads and writes numbers up to a billion Recognizes place value up to a billion (ITBS) Uses place value for decimals (ITBS)	Human Decimal Activity	AEA1 AEA9 AEA10 AEA16
d: Compares and orders numbers   ITBS *	positive integer negative integer billion	Knows the number line can be expanded to include negative numbers	Compares positive and negative integers using greater than, less than, and equal to Uses a number line to locate positive and negative numbers (ITBS) Orders numbers up to a billion (ITBS)		AEA1 AEA9 AEA10 AEA16
e: Represents fractions, decimals, and percents   ITBS **	billion expanded form exponent power of 10 equivalent array percent	Understands the concept of multiples and powers of 10 Knows decimals, fractions, and percent can be written in equivalent form Knows percent represents part per hundred Knows multiplication can be represented as an array	Represents fractional amounts (ITBS) Writes numerals up to a billion Writes decimals and whole numbers in expanded form (ITBS) Uses exponents for the power of 10 Writes decimals to the ten thousandth Expresses equivalences between fractions, decimals, and percents (ITBS) Recognizes the percent sign and understands percent as per hundred Represents multiplication as an array (ITBS)	Fractions Fraction Bars Visual Fractions Fraction City	AEA9 AEA10 AEA16
f: Understands fraction concepts   ITBS *	equivalent fraction lowest terms	Knows fractions need common denominators to be added or subtracted	Recognizes equivalent fractions (ITBS) Expresses fractions in lowest terms Compares fractions with like and unlike denominators		AEA1 AEA9 AEA10 AEA16
Interval Benchmark 2: Understands the properties of operations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Applies the properties of multiplication and division   ITBS *	order of operations parentheses simplify commutative property associative property distributive property identity property inverse property	Knows changing the order of terms does not change the result in addition and multiplication statements Knows changing the order of terms does change the result in subtraction or division statements	Uses order of operations, including parentheses, to simplify numerical expressions (ITBS) Uses commutative, associative, distributive, identity, and inverse properties to simplify and perform computations (ITBS)	Properties	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 3: Computes fluently and makes reasonable estimates
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Performs operations with whole numbers, fractions, and decimals   ITBS ***	ratio percent	Knows the effects of addition, subtraction, multiplication, and division on the size of numbers	Multiplies four-digit numbers by four-digit numbers (ITBS) Divides four-digit numbers by two-digit numbers (ITBS) Adds and subtracts positive and negative integers (ITBS) Adds and subtracts mixed numbers and fractions with unlike denominators (ITBS) Multiplies and divides fractions Multiplies mixed numbers Adds and subtracts decimals (ITBS) Multiplies decimals Divides decimals Determines simple ratio (ITBS) Determines percent	Addition and Subtraction Game Virtual Manipulatives All About Addition All About Subtraction The Number Monsters Multiplying Magic Squares Multiplication Tips All About Multiplication All About Division Fractions Hungry for Math Visual Fractions	AEA1 AEA9 AEA10 AEA16
b: Applies mental strategies to perform computation   ITBS *	mental computation	Knows when to use paper and pencil and when to use mental math	Uses mental computation strategies Mentally multiplies and divides by 10, 100, or 1,000 or multiples of 10, 100 or 1,000 (ITBS)		AEA1 AEA9 AEA10 AEA16
c: Uses estimation strategies   ITBS ***	estimate sum difference rounding order of magnitude	Knows the strategy used to estimate should match how close an answer needs to be	Estimates products and quotients (ITBS) Estimates sums and differences (ITBS) Uses rounding to estimate (ITBS) Estimates decimal sums, differences, and products (ITBS) Uses estimation to add and subtract fractions and mixed numbers (ITBS) Estimates using order of magnitude (ITBS) Estimates using number sense (ITBS)	All About Estimation Rounding Off	AEA1 AEA9 AEA10 AEA16
d: Solves multiple-step problems   ITBS ***	story problem equation	Knows story problems represent situations that can be solved mathematically	Solves multiplication and division story problems (ITBS) Solves two-step story problems (ITBS) Solves equations involving multiplication and division (ITBS) Solves problems with more than one operation (ITBS)	Problem Solving Lesson Plans	AEA1 AEA9 AEA10 AEA16
Standard 3: Understands and applies concepts of measurement
Interval Benchmark 1: Understands measurable attributes and the process of measurement
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Compares and orders objects according to their measurable attributes	area volume angle obtuse angle acute angle right angle balance scale metric	Knows objects can be compared and ordered according to their attributes	Compares and orders objects according to length, area, weight, and volume Compares weights using a balance scale Compares U.S. and metric measurements	Exploration of a Balance	AEA9 AEA16
b: Applies the process of measurement   ITBS *	attribute measure unit	Knows there is a process to be used when measuring objects	Identifies the attribute to be measured Chooses an appropriate unit (ITBS) Compares the unit with the object	What We Do Adds Up All About Measurements	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 2: Uses a variety of techniques for measurement
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Selects the appropriate unit for a measurement situation   ITBS *	approximate unit precision metric standard	Knows a unit should be changed when the measurement becomes too big or too small	Uses the correct unit of metric or standard measurement for a given situation (ITBS)	What We Do Adds Up All About Measurements	AEA1 AEA9 AEA10 AEA16
b: Converts measurements within systems	convert divide multiply	Understands when converting from a smaller unit to a larger unit you divide Understands when converting from a larger unit to a smaller unit you multiply	Converts from smaller size unit to larger size unit Converts from larger size unit to small size unit		AEA9 AEA16
c: Uses appropriate techniques to make change	accuracy change	Knows accuracy is important when making change	Makes change for one dollar, 5 dollars, and larger amounts with accuracy		AEA9 AEA16
d: Calculates elapsed time   ITBS *	elapsed time	Knows how to find elapsed time when passing 12	Calculates whole hour time intervals (ITBS) Calculates elapsed time in hours passing 12		AEA1 AEA9 AEA10 AEA16
e: Uses the appropriate tool for a measurement situation	protractor angle degrees circumference radius diameter center	Knows different tools are used in different situations	Select appropriate tool to measure length, area, perimeter, circumference, angles, volume, weight, time, and temperature Uses a protractor to measure angles		AEA9 AEA16
f: Determines the perimeter of simple figures	perimeter distance circumference radius diameter	Knows perimeter is the distance around a figure Knows circumference is the perimeter of a circle	Computes the perimeter of figures Computes the circumference of circles		AEA9 AEA16
g: Determines the area of a triangle	area square units	Knows area is the amount of space on a flat surface that is measured by square units	Defines a square unit Uses a grid to measure area Computes the area of a square and rectangle		AEA9 AEA16
h: Uses appropriate strategies to estimate measurement	benchmark angle	Knows a meter is a little more than 3 feet, there are about 2.5 centimeters in an inch, and a little more than 2 kilometers in a mile Knows benchmarks can be used to estimate the measurement of angles	Estimates metric and customary equivalents Estimates weight by comparing objects of known weight Estimates length by comparing objects of known length Estimates volume by comparing objects of known volume Estimates measurement of angles using benchmarks		AEA9 AEA16
i: Makes measurement estimates and checks for accuracy	meter centimeter millimeter gram kilogram milliliter liter	Knows when it is appropriate to have a precise measurement and when to use an estimate	Estimates and makes linear measurements in yards, feet, inches, meters, centimeters, and millimeters Estimates and measures weight in pounds and ounces, grams and kilograms Estimates and measures liquid capacity in teaspoons, tablespoons, cups, pints, quarts, gallons, milliliters, and liters		AEA9 AEA16
Standard 4: Understands and applies properties of geometry
Interval Benchmark 1: Identifies basic properties of figures
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Classifies plane and solid figures according to their properties   ITBS *	tetrahedron octahedron icosahedron cube dodecahedron polyhedron polygon	Knows the names of basic solid figures	Identifies the five perfect solids (ITBS) Identifies plane figures (ITBS)	Triangles All About Geometry Creating Polygons	AEA1 AEA9 AEA10 AEA16
b: Compares triangles by their properties   ITBS *	equilateral triangle isosceles triangle scalene triangle right triangle acute angle obtuse angle right angle	Understands an isosceles triangle has two sides of equal length Understands all sides of an equilateral triangle are of equal length Understands a right triangle contains one 90-degree angle	Identifies triangles as isosceles, equilateral or right Identifies figures using properties of angles (ITBS)		AEA1 AEA9 AEA10 AEA16
Interval Benchmark 2: Uses coordinate geometry to describe relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses the four quadrants of the coordinate plane to specify locations, describe paths, and find distance between points   ITBS *	coordinate points ordered pair x-axis y-axis point of origin horizontal vertical diagonal positive number negative number	Understands positive and negative numbers can be used to identify points in four quadrants	Locates points on a coordinate plane using ordered pairs Uses the point of origin as a point of reference (ITBS) Uses the four quadrants to specify locations, describe paths Finds the distance between points on the coordinate plane Describes a path on the coordinate plane (ITBS)		AEA1 AEA9 AEA10 AEA16
Interval Benchmark 3: Applies the basic concepts of transformation and symmetry
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses transformations to show that two figures are congruent   ITBS *	transformation congruent similar	Understands transformations can be used to determine whether two figures are congruent or similar	Describes a transformation or a series of transformations to show that two figures are congruent (ITBS)	Congruence, Similarity, & Symmetry	AEA1 AEA9 AEA10 AEA16
b: Identifies line and rotational symmetry in two- and three-dimensional figures	rotational symmetry center of rotation angle of rotation three-dimensional figure	Understands a figure has rotational symmetry when it can be rotated around a point and the rotated design coincides with the original figure Understands the center of rotation is a fixed point in which a figure is rotated Understands the angle of rotation describes how far a shape has been rotated from its original point	Recognizes objects that are symmetrical about a point Rotates a shape around a fixed point to show rotational symmetry Identifies angle of rotation by the degree of rotation	Congruence, Similarity & Symmetry	AEA9 AEA16
Interval Benchmark 4: Uses geometric reasoning to solve problems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Creates mental images of two- and three-dimensional figures	two-dimensional three-dimensional net	Understands a net is a representation of a solid Understands a two-dimension drawing represents a three-dimensional object	Builds three-dimensional objects from two-dimensional representations and vice versa Constructs and folds nets of solids Examines diagrams of nets to predict which one can or cannot be folded to form a certain figure Mentally manipulates a figure to accurately produce a picture of hidden parts	Spatial Reasoning	AEA9 AEA16
b: Determines the perimeter of figures   ITBS *	perimeter distance	Knows perimeter is the distance around a figure	Computes the perimeter of figures (ITBS)	Geometry & Measurement Perimeter and Area of Polygons	AEA1 AEA9 AEA10 AEA16
c: Determines the area of figures   ITBS *	area square units	Knows area is the amount of space on a flat surface that is measured by square units	Defines a square unit Uses a grid to measure area (ITBS)	Geometry & Measurement Perimeter and Area of Polygons	AEA1 AEA9 AEA10 AEA16
Standard 5: Understands and applies concepts of data analysis and probability
Interval Benchmark 1: Collects, organizes, and displays data to answer a question
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Gathers data to answer questions	survey data sample population	Understands technology helps gather data Knows the purpose of sampling	Selects and uses data collection methods Uses a survey to collect data		AEA9 AEA16
b: Represents data to convey results	line plot stem-and-leaf diagram line graphs data	Knows the functions of stem-and-leaf diagrams, line plots, and line graphs	Uses line plots, line graphs, and stem-and-leaf diagrams to represent data Questions inappropriate statements about the data		AEA9 AEA16
Interval Benchmark 2: Uses statistical methods to describe data
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Compares two data sets using central tendency   ITBS *	mean median mode shape	Knows the difference between the measures of mean, median, and mode Knows two sets of data can be compared using central tendency	Describes the shape and measures of center in a set of data (ITBS) Finds the mean or average (ITBS) Uses the measures of center to describe data (ITBS)	Comparing Fast Food Calories Create a Graph Let's Graph Virtual Manipulatives Measures	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 3: Reads and interprets data
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Reads information from graphs and tables   ITBS **	circle graph ratio double bar graph	Knows that a circle graph represents 100% Knows how to use a legend to read information Knows how to read amounts between labeled amounts on a bar graph	Reads amounts on the scales of double bar graphs, pictographs, and line graphs (ITBS) Determine the rank order of data in a table (ITBS)	Adventures in Statistics Collecting & Examining Weather Data	AEA1 AEA9 AEA10 AEA16
b: Interprets information from graphs   ITBS ***	interpret sectors compare trend functional relationship	Knows how to compare amounts show on a double bar graph Knows data can have underlying functional relationships Understands ratio statements regarding data	Uses line or bar graphs to answer multiple step questions (ITBS) Interprets the value of sectors in a circle graph Compares items on a graph as a ratio (ITBS) Draws conclusions that are based on data (ITBS) Interprets a trend in data (ITBS) Compares amounts on a bar graph or pictograph (ITBS) Finds functional relationships in data in a graph or table (ITBS)	Adventures in Statistics Collecting & Examining Weather Data Something Fishy Distance, Speed & Time Relationships	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 4: Uses basic probability concepts to describe events
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Understands the meaning of statistical predictions   ITBS *	sample space counting rules	Knows statistical predictions are not certain events but possibilities Understands the concept of sample and how it can affect results Understands how to find a group of numbers using set numbers of digits	Describes the sample space for an event Represents the likelihood of an event using numbers (ITBS) States the likelihood of an event as certain, likely, very likely, or impossible (ITBS) Uses counting rules to find a set of numbers possible to be formed from a number of digits (ITBS)	Virtual Manipulatives Playing to Win	AEA1 AEA9 AEA10 AEA16
Standard 6: Understands and applies concepts of algebra and functions
Interval Benchmark 1: Recognizes patterns and the rules that explain them
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Makes generalizations about patterns   ITBS *	numeric pattern generalization	Understands the previous quantities determine the next in a linear pattern Understands how a linear pattern can be used to make a generalization about number relationships	States a rule that explains a numeric pattern Predicts number(s) that would and would not be part of a sequence (ITBS) Identifies and extends patterns (ITBS)	The Million $ Mission Virtual Manipulatives Gauss	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 2: Understands the basic concept of a function
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Describes a function by its rule   ITBS *	functional relationship	Understands functions are expressions of regularity and patterns Understands functions can be used to describe relationships	Shows how the rule determines the next term in a function Uses a rule to describe a function (ITBS) Identifies rules of functions		AEA9 AEA10 AEA16
Interval Benchmark 3: Uses expressions and symbols to represent mathematical relationships
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses variables and numbers interchangeably   ITBS *	substitution	Uses a variable to express arithmetic operations for a situation	Uses the commutative, associative and distributive properties to compute with whole numbers Identifies operational symbol(s) that completes a solution (ITBS) Substitutes a number in an expression containing a variable to find its value (ITBS)	Mystery Operations Stability in Numbers	AEA1 AEA9 AEA10 AEA16
b: Uses operation properties to simplify expressions	commutative property associative property distributive property parentheses	Recognizes like terms Knows rules to simplify expressions	Simplifies expressions using operation properties		AEA9 AEA16
Interval Benchmark 4: Uses models to represent mathematical problems
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Uses expressions and equations to represent problem situations   ITBS *	pictorial model manipulative graphical diagram list table chart	Recognizes the various ways a math situation can be represented and how to choose the one that fits the purpose Represents change using positive and negative integers	Chooses a correct operation for a situation (ITBS) Expresses the disadvantages and advantages of one form of representation compared with another Uses representations for building understanding, communicating information, and demonstrating reasoning Solves a math equation (ITBS) Solves word problems representing change using positive or negative integers (ITBS)	The Million $ Mission Virtual Manipulatives	AEA1 AEA9 AEA10 AEA16
b: Writes and solves an equation for a multiple-step problem involving whole numbers   ITBS ***	commutative property associative property distributive property parentheses expanded notation	Understands how to use expanded notation with numbers and compute in flexible ways	Uses the commutative, associative, and distributive properties to compute with whole numbers Solves multiple-step problems (ITBS)	Math Mysteries: Try a Problem	AEA1 AEA9 AEA10 AEA16
Interval Benchmark 5: Analyzes change in a variety of situations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Compares situations with constant or varying rates of change	constant rate of change variable change	Understands rates of change that increase or decrease Understands the steepness of the line shows how fast the change occurred	Describes how a change in one quantity affects the other in a functional relationship		AEA9 AEA16
Standard 7: Communicates and reasons mathematically
Interval Benchmark 1: Comprehends mathematical language
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Comprehends mathematical texts	graphic organizers	Knows strategies to help learn vocabulary Knows the text is set up to help vocabulary understanding	See Integrating Standards Website for Reading: http://integratingstandards.com/standards/reading/index.html Uses graphic organizers to understand mathematical terms		AEA9 AEA16
Interval Benchmark 2: Expresses ideas using mathematical terms and representations
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Conncects ideas to mathematical terms	grade level mathematical terms	Knows expressions represent rules and generalizations Knows strategies to organize ideas Knows the characteristics of a well-written solution	Organizes mathematical ideas for understanding by a third party Writes coherent solutions Uses correct mathematical terms, language, and drawings for grade level content Presents solutions using mathematical terms and representations		AEA9 AEA16
Interval Benchmark 3: Analyzes and evaluates mathematical thinking
Grade Level Benchmark	Vocabulary	Information	Skills	Classroom Resources (Additional resources)	AEA Resources
a: Reviews mathematical thinking	clarity reasons evidence solutions characteristics	Knows strategies to organize ideas Knows mathematicians defend solutions Knows the characteristics of a well-written solution	Organizes work and labels drawings to make meaning clear Checks for clarity in solutions and revises Gives reasons for decisions made while solving a problem Considers the solutions of others and learns from them Supports solutions with evidence Answers questions regarding solutions