Mathematics - Grade 5.pdf

ISB Mathematics Grade 5
Mathematics
Grade 5
PYP Overall Expectations (Age Range 9-12 years)
Students will have the opportunity to identify and reflect upon “big ideas” by making connections between the questions asked and the concepts that drive the inquiry.
They will become aware of the relevance these concepts have to all of their learning.
Data Handling: Statistics and Probability
Students will collect, display and interpret data in a variety of ways. They will compare data displays, including how well they communicate information. They will
create and manipulate an electronic database and set up a spreadsheet using simple formulas to create graphs. They will find, describe and explain the range, mode, median
and mean in a set of data, use a numerical probability scale 0-1 or 0%-100%. They will determine the theoretical probability of an event and explain why this might be
different from the experimental probability.
Measurement
Students will estimate, measure, label and compare perimeter, area and volume using
formal methods and standard units of measurement. They will develop procedures for finding perimeter, area, and volume and recognize the relationship between them.
They will use the correct tool for any measurement with accuracy. They will measure and construct angles in degrees using a protractor. They will know that the
accuracy of measurement depends on the situation and the precision of the tools. They will use and construct 12-hour and 24-hour timetables and be able to determine
times worldwide.
Shape and Space
Students will use the mathematical vocabulary of 2-D and 3-D shapes and angles. They will classify, sort and label all types of triangle and quadrilateral. They will turn
ad 2-D net into a 3-D shape and vice versa. They will find and use scale and ratio to enlarge and reduce shapes. They will use the language and notation of bearing to
describe position, and be able to read and plot coordinates in four quadrants.
Pattern and Function
Students will understand and use the relationships between the four operations. They will model and explain number patterns and use real-life problems to create a
number pattern following a rule. They will develop, explain and model simple algebraic formulas. They will model exponents as repeated multiplication, and understand
and use exponents and roots as inverse functions.

ISB Mathematics Grade 5
Number
Students will read, write and model numbers to one million and beyond, extending the base 10 system to the millions and thousandths. They will automatically use
number facts. They will read, write, model, compare and order fractions (including improper fractions and mixed numbers), decimals (to any given place) and percentages.
They will interchange fractions, decimals and percentages. They will add and subtract fractions with related denominators, simplify fractions and explore fractions using a
calculator. They will add and subtract decimals to the thousandths and will model multiplication and division of decimals in the context of money. They will find and use
ratios; read, write and model addition and subtraction of integers; and use exponential notation. They will use and describe multiple strategies to create and solve more
complex problems, reasonably estimating the answers. They will select and defend the most appropriate and efficient method.

ISB Mathematics Grade 5
PYP
Understands the meaning, uses, and representation
of numbers
Reads and writes whole numbers through billions and
decimal through thousandths using standard base-10
place-value notation; identifies digits and expresses
their values in such numbers.
Uses and explains strategies (e.g., using equivalent
fractions) for solving problems involving percents and
discounts.
Curriculum Examples/Ideas
PYP Understands equivalent names and numbers Curriculum Examples/Ideas
Uses numerical expressions involving all four
operations, parentheses, and exponents to represent
equivalent names for whole numbers, fractions, and
decimals; uses and explains multiplication and division
rules to find equivalent fractions and fractions in
simplest form; converts between fractions and mixed
numbers; converts between fractions, decimals, and
percents; renames numbers written in exponential
notation as repeated-factor expressions (e.g., 2 ^ 3 = 2 * 2
* 2) and in standard notation (e.g., 2 ^ 3 = 8).

ISB Mathematics Grade 5
PYP Understands common numerical relations Curriculum Examples/Ideas
Orders whole numbers through billions, decimals
through thousandths, mixed sets of decimals and
fractions and signed numbers; uses and justifies
strategies for ordering fractions and mixed numbers such
as area models, benchmark comparisons, and analyses of
numerators and denominators.
Identifies prime and composite numbers; factor
numbers.

ISB Mathematics Grade 5
PYP Computes accurately Curriculum Examples/Ideas
Chooses, uses, and explains appropriate algorithms for
solving problems and number stories involving the
addition and subtraction of whole numbers, decimals,
and 1- and 2-digit signed numbers.
Knows and applies multiplication facts, related division
facts, and extended facts.
Chooses, uses, and explains appropriate algorithms
(mental and/or paper-and-pencil) for solving problems
and number stories involving the multiplication of
multi-digit whole numbers and decimals and the
division of multi-digit whole numbers (expressing the
remainder as a whole number or fraction as appropriate
to the context of the problem.) and decimals by whole
numbers.
Chooses, uses, and explains algorithms (mental and/or
paper-and-pencil) for solving problems and number
stories involving the addition and subtraction of
fractions and mixed numbers.
Uses and explains strategies (e.g., area model, paperand-pencil
algorithm) for solving problems and number
stories involving the multiplication of fractions and
mixed numbers; uses and explains strategies (e.g.,
diagrams or common-denominator method) for solving
problems and number stories involving the division of
fractions.

ISB Mathematics Grade 5
PYP Makes reasonable estimates Curriculum Examples/Ideas
Chooses, uses, and explains strategies to estimate
reasonable solutions (ballpark and magnitude
estimates) for whole number and decimal addition,
subtraction, multiplication, and division problems and
fraction and mixed number addition and subtraction
problems.
PYP Understands patterns, relations, and functions Curriculum Examples/Ideas
Creates, describes and extends numerical patterns;
finds, describes, and records rules for patterns and uses
them to solve problems.
Finds and records rules for simple functions (e.g., rates)
involving all four operations; represents simple
functions using words, symbols, tables, and graphs; and
uses those representations or other strategies to solve
problems.

ISB Mathematics Grade 5
PYP
Represents and analyzes situations and structures
using algebraic symbols
Determines whether number sentences are true or false;
solves open number sentence and explains the solution
strategies used; uses a single variable to write an open
sentence to fit a number story.
Evaluates expressions containing parentheses and
nested parentheses; inserts parentheses and nested
parentheses to make number sentences true; uses and
explains the precedence of multiplication and division
over addition and subtraction.
Explains and applies the basic properties of addition and
multiplication (the Additive and Multiplicative
Identities, the Commutative and Associative Properties
of Addition and Multiplication, and the Distributive
Property of Multiplication over Addition).
Uses a pan-balance model to solve simple equations.
Uses scales to find distances and other measurements;
uses ratios expressed in a variety of ways (e.g., as
words, fractions, percents, and with colons); solves
simple ratio problems (e.g., problems involving ratios of
parts of a set to the whole set).
Curriculum Examples/Ideas

ISB Mathematics Grade 5
PYP
Understands the units, systems, and processes of
measurement; uses appropriate techniques, tools,
and formulas to determine measurement
Estimates the length of, measures objects, and draws
line segments to the nearest ⅛ inch and millimeter;
estimates the measure of an angle; uses a full-circle or
half-circle protractor to measure and draw angles.
Describes and uses strategies to calculate the perimeter
of a shape and the area of a circle; chooses and uses
appropriate formulas to calculate the areas of rectangles,
parallelograms, and triangles, and to calculate the
volume of a prism; derives pi as the ratio of the
circumference to the diameter of a circle.
Describes relationships among U.S. customary units of
length, among U.S. customary units of capacity, among
metric units of length; identifies equivalent measures of
length in each system and equivalent measures of
capacity in U.S. customary system.
Curriculum Examples/Ideas

ISB Mathematics Grade 5
PYP
Uses reference frames to locate numbers within a
given context
Uses ordered pairs of numbers to name, locate, and plot
points on the first quadrant of a coordinate grid.
Curriculum Examples/Ideas
PYP
Analyzes characteristics and properties of two- and
three-dimensional geometric shapes
Identifies, describes, compares, names, and draws right,
acute, obtuse, straight, and reflex angles; determines
angle measures by applying properties of sums of angle
measures in triangles and quadrangles.
Describes, compares, and classifies plane and solid
figures using appropriate geometric language; identifies
and models congruent figures and describes their
properties.
Curriculum Examples/Ideas
PYP
Applies transformations and uses symmetry to
analyze mathematical situations
Identifies, describes, and sketches instances of reflection
symmetry, translations, and rotations.
Curriculum Examples/Ideas

ISB Mathematics Grade 5
PYP
Selects, creates, and uses appropriate graphical
representations of collected or given data
Selects, creates (with reasonable titles, labels, keys,
intervals) and uses a graph (e.g., bar or line) for a given
set of grade-appropriate data.
Curriculum Examples/Ideas
PYP Analyzes and interprets data Curriculum Examples/Ideas
Uses data landmarks (maximum, minimum, range,
median, mode, and mean) and grade-appropriate data
representations to ask and answer questions, draw
conclusions, and make predictions.
PYP
Understands and applies basic concepts of
probability
Predicts the outcomes of simple experiments, tests the
predictions, summarizes the results (including a
comparison of predictions based on theoretical
probability with experimental results), and uses them to
predict future events.
Curriculum Examples/Ideas