5th Grade Math
Number and Operations
The student will develop number and operation sense needed to represent numbers and number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable estimates in problem solving.
Understanding numbers/Representing Numbers/Relationships Among Numbers/Number Systems
⎯read and write numbers from millions to thousandths (5-M[HM/Ch 1]A/IT)
⎯identify and name the place value of a given digit from millions to thousandths (5-M[HM/Ch 1]A/IT)
⎯order and compare (<, >, or =) whole numbers, fractions, mixed numbers, and decimals using models (e.g., number lines, base ten blocks, Venn diagrams, and hundreds boards) (5-M[HM/Ch 1]D/IT)
⎯demonstrate and communicate knowledge and understanding of grade level mathematical terms and symbols (5-M[HM/ALL]D/IT)
⎯represent proper fractions, improper fractions, and mixed numbers using concrete objects, pictures, and the number line (5-M[HM/Ch 9&12]D/IT)
⎯Identify and change improper fractions to mixed numbers and vice versa (5-M[HM/Ch 9&12]D/IT)
⎯generate equivalent forms of commonly used fractions, decimals, and percents (e.g., 1/10, 1/4, 1/2, .75, 50%) (5-M[HM/Ch 9,10,&11]A/IT)
⎯recognize relationships among commonly used fractions and decimals (5-M[HM/Ch 9,10,&11]A/IT)
Understand meanings of operations and how they relate to one another
⎯use commutative, associative, and identity properties (5-M[HM/Ch 2, 3, &5]D/IT)
⎯ explain and demonstrate the inverse nature of addition and subtraction (5-M[HM/Ch 2]D/IT)
⎯explain and demonstrate the inverse nature of multiplication and division (5-M[HM/Ch 3, 4, &5]D/IT)
⎯explain how addition, subtraction, multiplication, and division affect the size and order of numbers (5-M[HM/Ch 2, 3, &5]D/IT)
Solve problems, compute fluently, and make reasonable estimates
⎯select appropriate methods and tools for computations (e.g., mental computation, estimation, calculators, paper and pencil) (5-M[HM/ALL]D/IT)
⎯explain why one form of a number might be more useful for computation than another form (5-M[HM/ALL]I/IT)
⎯recognize reasonable estimates for operations (5-M[HM/ALL]D/IT)
⎯add, subtract, multiply, and divide whole numbers and decimals (5-M[HM/Ch 2, 3, 4,5,11, 12 &14]D/IT)
⎯use models, benchmarks, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators (5-M[HM/Ch 10]D/IT)
⎯identify missing information and/or too much information in real-world problems (5-M[HM/ALL]D/IT)
⎯solve one- or two-step real-world problems involving addition, subtraction, and/or multiplication of whole numbers and decimals (5-M[HM/Ch 2,3,4,5,11, 13,&14]A/IT)
⎯solve real-world problems using decimals (including money), fractions, and percents (5-M[HM/Ch 10-14 & 19]D/IT)
⎯represent whole numbers and two-place decimals in expanded form (5-M[HM/Ch 1]A/IT)
⎯represent, compare, and order whole numbers and decimals to thousandths (5-M[HM/Ch 1]A/IT)
⎯compare and order fractions using the appropriate symbol (<, >, and =) (5-M[HM/Ch 1]A/IT)
⎯connect symbolic representations of proper and improper fractions to models of proper and improper fractions (5-M[HM/Ch 9,10,12]A/IT)
⎯represent numbers as both improper fractions and mixed numbers (5-M[HM/Ch 9,10]A/IT)
⎯use estimation to determine a reasonable solution to a whole number computation (5-M[HM/ALL]A/IT)
⎯use math journals as a means of understanding math concepts and terms (5-M[HM/ALL]M/IT)
Algebra
The student will understand and generalize patterns as they represent and analyze quantitative relationships and change in a variety of contexts and problems using graphs, tables, and equations.
Represent and analyze patterns, relations, and functions
⎯generalize and extend numerical and geometric patterns using a variable (5-M[HM/Ch 15,21]A/IT)
⎯represent and analyze patterns and functions using words, tables, and graphs (5-M[HM/All]D/IT)
⎯apply basic function rules (5-M[HM/Ch 1, 21]D/IT)
Represent and analyze patterns, relations, and functions
⎯demonstrate understanding that an equation is a number sentence stating two quantities are equal (5-M[HM/All]M/IT)
⎯solve open sentences using informal methods and knowledge of operations (5-M[HM/All]M/IT)
⎯express mathematical relationships using equations (5-M[HM/All]M/IT)
⎯represent the idea of a variable as an unknown quantity using a letter or a symbol (5-M[HM/Ch 21]D/IT)
Illustrate general properties of operations
⎯apply commutative, associative, zero, distributive, and identity properties (5-M[HM/Ch 2, 3, &5]M/IT)
⎯show that division is not commutative (5-M[HM/Ch 4,5,12&14]M/IT)
Analyze change in various contexts
⎯investigate how a change in one variable relates to a change in a second variable (5-M[HM/CH 21]D/IT)
⎯use a variety of methods to compare and describe situations involving constant and/or varying rates of change (5-M[HM/Ch 21]D/IT)
⎯extend numerical patterns (5-M[HM/All]A/IT)
⎯extend geometric patterns (5-M[HM/Ch 15]A/IT)
⎯solve open sentences involving addition, subtraction, multiplication, and division (5-M[HM/Ch2-5,11-14]A/IT)
⎯connect open sentences to real-world situations (5-M[HM/All]A/IT)
⎯select an equation that represents a given mathematical relationship (5-M[HM/All]A/IT)
⎯locate and specify a point in Quadrant I of a coordinate system (5-M[HM/Ch22]A/IT)
⎯make predictions based on data (5-M[HM/Ch7-8]A/IT)
⎯generalize and extend or complete patterns involving geometric figures or numbers (5-M[HM/Ch1-4& 15]D/IT)
⎯determine or apply a function rule (5-M[HM/Ch 21]D/IT)
Geometry
The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.
Analyze characteristics and properties of two- and three-dimensional shapes
⎯identify, compare, and analyze attributes of two- and three-dimensional figures (5-M[HM/Ch 15-17]D/IT)
⎯use the attributes of geometric figures to develop definitions of the figures (5-M[HM/Ch 15-17]D/IT)
⎯identify and draw points, lines, line segments, rays, and angles (5-M[HM/Ch 15-17]D/IT)
⎯draw circles and label diameter, circumference, radius, and center ((5-M[HM/Ch 15-17]D/IT)
⎯use properties to classify geometric figures (5-M[HM/Ch 15-17]D/IT)
⎯investigate and describe the results of subdividing and combining geometric figures (5-M[HM/Ch 15-17]D/IT)
⎯recognize, name, compare, and contrast congruent and symmetrical geometric figures (5-M[HM/Ch 15-17]D/IT)
⎯describe the relationships between lines and the characteristics of angles (e.g., parallel, perpendicular, intersecting, right, acute, obtuse, and straight) (5-M[HM/Ch 15-17]D/IT)
⎯make and test hypothesis about geometric properties ((5-M[HM/Ch 15-17]D/IT)
⎯explore similarity and how the sides and angles of similar triangles are related (5-M[HM/Ch 15-17]D/IT)
⎯identify lines, line segments, rays, and angles (5-M[HM/Ch 15-17]A/IT)
⎯classify geometric figures using properties (5-M[HM/Ch 15-17]A/IT)
Specify locations and describe spatial relationships using coordinate geometry and other representational systems
⎯describe location and movement using appropriate mathematical language (5-M[HM/Ch 22]D/IT)
⎯find and specify points in Quadrant 1 of a coordinate system (5-M[HM/Ch 22]D/IT)
Apply transformations and use symmetry to analyze mathematical situations
⎯use spatial reasoning to predict the result of sliding, flipping, or turning a two-dimensional shape (5-M[HM/Ch 15,17]A/IT)
⎯describe and identify line and rotational symmetry in two-dimensional figures (5-M[HM/Ch 15 & 17]I/IT)
⎯describe a motion or a series of motions that will show that two shapes are congruent (5-M[HM/Ch 15 & 17]D/IT)
⎯identify lines of symmetry in two-dimensional geometric figures (5-M[HM/Ch 15 & 17]I/IT)
⎯identify two- or three- dimensional shapes given defining attributes (5-M[HM/Ch 15]D/IT)
⎯
Use visualization, spatial reasoning, and geometric modeling to solve problems
⎯construct and draw two- and three-dimensional geometric figures (5-M[HM/Ch 15]D/IT)
⎯recognize and build a 3-dimensional object from a 2-dimensional representation (5-M[HM/Ch 15]D/IT)
⎯use spatial reasoning to identify the three-dimensional figure created from a two-dimensional representation (net) of that object (e.g., cube, rectangle or cylinder, prism, pyramid, cone) (5-M[HM/Ch 15,17]A/IT)
⎯use visualization and spatial reasoning (e.g., geometric models) to solve problems (5-M[HM/ALL]D/IT)
⎯create and describe mental images of objects, patterns, and paths (5-M[HM/ALL]D/IT)
⎯identify, predict, and describe the results of transformations of two-dimensional figures (i.e., slides, flips, and turns) (5-M[HM/Ch 15 & 17]D/IT)
Measurement
The student will become familiar with the units and processes of measurement in order to use a variety of tools, techniques, and formulas to determine and to estimate measurements in mathematical and real-world problems.
Understand measurable attributes of objects and the units, systems, and processes of measurement
⎯demonstrate understanding of the concepts of length, perimeter, circumference, area, weight, capacity, volume, elapsed time, and angle measure (5-M[HM/Ch 6, 16]D/IT)
⎯demonstrate understanding that measurements are approximations (5-M[HM/Ch 6, 16]D/IT)
⎯demonstrate understanding of the relationships among the units within both customary and metric systems of measurement (5-M[HM/Ch 6, 16]D/IT)
⎯understand how differences in units affect precision of measurements (5-M[HM/Ch 6, 16]I/IT)
⎯explore what happens to measurements of a two-dimensional shape when the shape is changed in some way (e.g., perimeter, area) (5-M[HM/Ch 6, 16]D/IT)
Apply appropriate techniques, tools, and formulas to determine measurements
⎯select and use appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles (5-M[HM/Ch 6, 16]D/IT)
⎯use estimation to determine if a length or volume measurement is reasonable (5-M[HM/Ch 6, 16]A/IT)
⎯select and use appropriate tools for measuring in real-world situations (5-M[HM/Ch 6]D/IT)
⎯solve real-world problems involving elapsed time (5-M[HM/Ch 6]A/IT)
⎯read temperatures on a thermometer using Fahrenheit and Celsius scales (5-M[HM/Ch 6]A/IT)
⎯apply formulas to find the area of parallelograms and triangles (5-M[HM/Ch 16]A/IT)
⎯explain and demonstrate how scale in maps and drawings shows relative size and distance (5-M[HM/Ch 16]D/IT)
⎯develop informal strategies to determine the surface area and volume of rectangular solids (5-M[HM/Ch 16]I/IT)
⎯connect simple units of measurement within the same system of measurement (5-M[HM/Ch 6, 16]AD/IT)
⎯select appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles (5-M[HM/Ch 6, 16]A/IT)
⎯use strategies to estimate perimeter and area of rectangles (5-M[HM/Ch16]D/IT)
⎯use a ruler to measure to the nearest centimeter and 1⁄4 inch (5-M[HM/Ch 6]D/IT)
Data Analysis and Probability
The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions
⎯collect data using observations, surveys, and experiments (5-M[HM/Ch 7-8]D/IT)
⎯understand how data-collection methods could affect the results (5-M[HM/Ch 7-8]D/IT)
⎯represent data using pictographs, bar graphs, tables, circle graphs, and line graphs (5-M[HM/Ch 7-8]D/IT)
⎯interpret data displayed in pictographs, bar graphs, tables, circle graphs, and line graphs (5-M[HM/Ch 7-8]D/IT)
Select and use appropriate statistical methods to analyze data
⎯use measures of central tendency (i.e., mean, median, and mode) (5-M[HM/Ch 7-8]D/IT)
⎯find the range of a data set (5-M[HM/Ch 7-8]D/IT)
⎯determine the mean, median, and mode of a data set (5-M[HM/Ch 7-8]A/IT)
Develop and evaluate inferences and predictions that are based on data
⎯make predictions and justify conclusions based on data (5-M[HM/Ch 7-8]D/IT)
⎯design investigations to address a question (5-M[HM/Ch 7-8]D/IT)
⎯examine various graphical representations of data to evaluate how accurately the data is depicted (5-M[HM/Ch 7-8]D/IT)
⎯explain the importance of sample size in investigations (5-M[HM/Ch 7-8]I/IT)
Understand and apply basic concepts of probability
⎯describe the likelihood or chance of events as likely, unlikely, certain, equally likely, or impossible (5-M[HM/Ch 20]D/IT)
⎯use a sample space to predict the probability of an event (5-M[HM/Ch 20]D/IT)
⎯represent the likelihood of an event using a fractional number from zero to one (5-M[HM/Ch 20]A/IT)
⎯represent and interpret data in bar graphs and pictographs (5-M[HM/Ch 7-8]D/IT)
⎯determine the most likely, least likely, or equally likely outcomes in simple experiments(5-M[HM/Ch 20]D/IT)
Computation
The student will learn to compute using concrete objects.
Counting/Identifying/Matching/Ordering Numbers
⎯multiply a fraction by a multiple of its denominator (denominator less than or equal to 10) (5-M[HM/Ch 12]a/IT)
⎯add, subtract, multiply, and divide whole numbers (multipliers and divisors no more than two-digits) (5-M[HM/Ch 23-5]a/IT)
⎯add, subtract, and multiply decimals (5-M[HM/Ch 11,13,14]A/IT)
⎯add and subtract commonly used fractions (5-M[HM/Ch 10 & 12]A/IT)
⎯use commutative, associative, and identity properties (5-M[HM/2,3,4,5]M/IT)
⎯select appropriate methods and tools for computations (e.g., mental computation, estimation, calculators, and paper and pencil) (5-M[HM/ALL]D/IT)
Real World Problem Solving
The student will gather information to compute and solve real world problems.
Story Problems
⎯make predictions based on data (5-M[HM/Ch 7-8]A/IT)
⎯solve real-world problems involving addition and subtraction of measurements (5-M[HM/CH 6]A/IT)
⎯solve real-world problems involving perimeter and area of rectangles (5-M[HM/Ch 16]A/IT)
⎯solve real-world problems using decimals (including money), fractions, and percents (5-M[HM/Ch 9,10 11,12,13,14]D/IT)
⎯use methods to compare and describe situations involving constant and/or varying rates of change and to solve real- world problems (e.g., extending rate charts) (5-M[HM/ALL]D/IT)
Graphs and Graphing
The student will make simple graphs using concrete objects and pictures.
Graphing
⎯Make predictions based on data (5-M[HM/Ch 7-8]D/IT)
⎯Interpret data displayed in pictographs, bar graphs, tables, circle graphs, and line graphs (5-M[HM/Ch 7-8]D/IT)
