Grade 5

NUMBER SENSE and NUMERATION including FRACTIONS Develop an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.

OPERATIONS and ALGEBRAIC THINKING Use basic and advanced procedures while performing the processes of computation and apply basic and advanced properties of functions and algebra.

MEASUREMENT and DATA Understand measurable attributes of objects and the units, systems, and processes of measurement

GEOMETRY Analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships.

STATISTICS, PROBABILITY, AND DATA ANALYSIS Design investigations, select, use and appropriate statistical methods to analyze data in order to make inferences and predictions based on data.

Understand the place-value structure of the base-ten number system and be able to represent and compare, order and round whole numbers and decimals.

Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Use models, benchmarks, and equivalent forms to judge the size of fractions

Recognize and generate equivalent forms of commonly used fractions, decimals, and percent

Describe classes of numbers according to characteristics such as the nature of their factors.

Explore numbers less than 0 by extending the number line and through familiar applications.

Understand meanings of operations and how they relate to one another (Computation)

Understand the general principles and properties of multiplication and division.

Understand the meaning of operations and develop fluency in adding, subtracting, multiplying, and dividing whole numbers

Develop and use strategies to estimate computations involving whole numbers, fractions and decimals in situations relevant to the learners’ experiences

Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.

Understand patterns, relations, and functions 

Represent and analyze mathematical situations and structures using algebraic symbols. (see OA.2.a) 

Express mathematical relationships using equations.

Use mathematical models to represent and understand quantitative relationships. 

Analyze change in various contexts.

Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute.

Estimate and measure in both customary and metric measurements of length, weight, capacity, temperature, time and money.

Select and apply appropriate standard units, techniques, tools, and formulas to determine measurements 

Apply simple unit conversions in customary measure and metric measure.

Develop strategies for estimating the perimeter, area, and volume of irregular shapes.

Select and use benchmarks to estimate measurements. 

Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms.

Develop strategies to determine the surface areas and volumes of rectangular solids.

Identify, compare, and analyze attributes of two and three-dimensional shapes and develop vocabulary to describe the attributes

2. Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids; 

Investigate, describe, make, test and reason about geometric properties and relationships.

Graph points on the coordinate plane to specify locations and describe special relationships to solve real-world and mathematical problems.

Apply transformations and use symmetry to analyze mathematical situations

Use visualization, spatial reasoning, geometric modeling and relate ideas in geometry to ideas in number and measurement to solve problems

Use geometric models to solve problems in other areas of mathematics

Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer the question.

Collect data using observations, surveys, and experiments

Represent data using tables and graphs such as line plots, pictographs, bar graphs, and line graphs.

Recognize the difference in representing categorical and numerical data

Describe the important features of a set of data and compare related data sets, with an emphasis on how the data are distributed

Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.

Compare different representations of the same data and evaluate how well each representation shows important aspects of the data

Develop and evaluate inferences and predictions that are based on data.

Understand and apply basic concepts of probability.

Order and compare whole numbers and decimals up to the 10 billions and thousandths.

Round whole numbers to ten billions and decimals to the thousandths.

Convert between numbers in standard, word and expanded form for numbers up to billions and decimals to thousandths.

Introduce expanded form with exponents.

Explain different interpretations of fractions: as parts of a whole, parts of a set, and division of whole numbers by whole numbers.

Identify, on a number line, the relative position of simple positive fractions, positive mixed numbers and positive decimals.

Write mixed numbers as improper fractions, and proper as improper based on objects or pictures.

Write equivalent fractions in simplest form.

Represent tenths and hundredths in decimal, percent, and fraction notation (half, fourth, third)

Describe and identify prime and composite numbers for numbers up to 20

Describe and identify prime factorization, GCF and LCM of numbers

Identify negative numbers on a number line

Identify negative number in real life authentic situations.

Use a standard algorithm to multiply numbers using relevant

Use a standard algorithm to divide numbers without remainders, using relevant properties of the number system

Use the distributive property in numerical equations and expressions.

Fluently recall multiplication and division facts 0-12 

Compute with basic multiplication facts using 11’s and 12’s

Identify, select and use the most appropriate method of computation for all operations.

Identify patterns in multiples of 10. Divide by multiples of 10, 100, 1000.

Use rules of divisibility (2,3,5,6,9 and 10) to compute fluently and make reasonable estimates. 

Divide whole numbers with up to 4 –digit quotients with a remainder

Divide whole numbers with a 2- digit divisor

Solve problems involving multiplication and division of any whole numbers.

Add and subtract decimals and verify the reasonableness of the results

Use mental arithmetic to add or subtract simple decimals.

Understand methods to multiply fractions.

Understand methods to divide fractions.

Use models to demonstrate understanding of multiplication of fractions.

Divide fractions.

Add and subtract fractions, including mixed numbers, with different denominators.

Use function tables for addition, subtraction and multiplication to represent and analyze patterns and functions.

Use the commutative, associative, identity, zero, and distributive properties in numerical equations and expressions.

Use a variable to represent an unknown number in simple expressions, equations, and inequalities. (new term)

Write simple algebraic expressions with one variable and evaluate them by substitution.

se a variety of models such as graphs, tables, and equations to represent and draw conclusions about a quantitative relationship.

Identify and graph ordered pairs including positive and negative numbers.

Use function tables to evaluate expressions.

Use function tables and expressions to describe and extend patterns

Use information from a graph or equation to answer questions about a problem or situation.

Identify the measurable attributes of an object (length, area, weight, volume, size) of an angle

Name units to measure length, area, weight, volume (capacity) and angles.

Identify units of measure in length (inch, 1⁄2 inch, 1⁄4 inch, foot, yard, mile, millimeter, centimeter, meter, decimeter, and kilometer) 

Identify units of measure in weight (ounce, pound, ton, gram, kilogram)

Identify units of volume (fluid ounce, cup, quart, pint, gallon, milliliter, liter)

Identify the unit of measure in angles – (degree)

Money - Count coins and bills to make change from a given amount.

Calculate elapsed time to the nearest second.

Use thermometers to measure temperature using Celsius and Fahrenheit in positive and negative degrees

Select and use an appropriate instrument to measure length to the nearest quarter-inch, eighth- inch, millimeter, centimeter for a given situation 

Select and use an appropriate scale to measure weight in ounces, pounds, grams and kilograms for a given situation

Select and use appropriate units of volume, pint, quart, gallon, liter for a given situation. Determine the volume of a rectangular solid in cubic units

Measure area to the nearest Measure area to the nearest

Use a protractor to measure angles.

Convert basic units of length • Inch, foot, yard, mile • Millimeter, centimeter, decimeter, meter, kilometer 

Convert basic units of volume (capacity) • Fluid ounce, cup, pint, quart, gallon • Milliliter, liter

Convert basic units of weight/mass • Ounce, pound, ton • Gram, kilogram

Convert basic units of time • Hour, minute, second, day, week, month, year, decade, century

Determine how the area and perimeter of a parallelogram change when the shape is changed

Estimate area and volume of irregular shapes using square or cubic units

Length: estimate length to the nearest quarter-inch, eighth-inch, centimeter, millimeter, and meter

Capacity: estimate capacity using cup, pint, quart, gallon, and liter and millimeter

Volume: estimate volume using cubic units.

Weight/Mass: estimate weight using ounce, pound, ton, gram, milligram and kilogram

Area: estimate length to the nearest square unit.

State and use formulas for finding the perimeter of rectangles, squares, and triangles

State and use formulas for finding the area of rectangles, squares, and triangles

Determine the volume of a rectangular solid.

Determine the surface area of a rectangular solid.

Identify and compare triangular prism, square pyramid, triangular pyramid.

Identify and classify polygons and define according to their properties. Triangles (equilateral, isosceles, right, scalene, acute, obtuse) • Quadrilateral (rectangle, parallelogram, square, trapezoid, rhombus) • Pentagon • Hexagon • Octagon

Classify three-dimensional shapes according to their attributes.

Develop logical arguments to justify conclusions relating to symmetry and congruency

Define and identify the terms quadrant, origin, x-axis, y-axis

Plot points on a four-quadrant grid given ordered pairs. 

Name the ordered pair for a point on a four-quadrant grid.

Find the distance/change between two points on either the vertical or horizontal line within the first quadrant.

Identify rotational and line symmetry in polygons

Identify shapes that have rotational symmetry. 

Describe and predict the changes in direction and position that occur in a figure as a result of a transformation: translation (slide), reflection (flip), or rotation (turn).

Describe tessellation.

Draw circles and polygons • Triangles (equilateral, isosceles, right, scalene acute, obtuse) • Quadrilateral (rectangle, parallelogram, square, trapezoid, rhombus ) • Pentagon • Hexagon • Octagon

Describe an object using geometric shapes to solve problems.

Continue a pattern of geometric shapes to solve a problem

Determine perimeter, area, and volume using geometric models

Examine geometric connections in other disciplines and everyday life.

Design an investigation to answer a question

Choose a data collection method

Analyze the effectiveness of the data collection method.

Use Observations, surveys, or experiments to collect data.

Represent data on graphs such as line, bar, double bar, pictograph, and line plot.

Represent data in tables, including frequency table

Use graphs to display different types of data.

Choose an appropriate graph and identify graphs that are misleading

Read and make stem and leaf plots

Find the mean of a data set

Determine the mode, range, median, and mean in a set of data.

Describe what mode, range, median, and mean tell about a data set

Choose an appropriate graph given a set of data.

Evaluate how well the mean, median and mode represent the data set and choose the appropriate measure

Use data to predict outcomes of probability experiments.

Express outcomes of experimental probability situations verbally and numerically (e.g. 3 out of 4)

Describe the probability that an outcome will happen using the vocabulary likely or unlikely to the degree of certain, impossible, equally likely. 

Interpret data graphs to answer questions about the degree of likelihood of a situation.

Predict and test the possible outcomes for a simple probability experiment

Determine the probability with a value between 0 and 1 (events that are not going to have a probability of 0, events certain to occur have probability 1)