Download The following are systemwide content expectations. These

Upper School Mathematics Sequence
The SCIS-HIS Mathematics Framework
US5000y Mathematics 6
Aims
The aims of the Mathematics Program are to help students acquire and apply mathematical concepts, skills and processes and to increase
independent learning capacity through a mathematical approach to problem solving and to data processes.
US5006y Mathematics 7
Structure
Mathematics is a core subject offered in continuum. Mathematics courses are an integrated part of the nursery and preschool curriculum,
provide transition during prekindergarten, and have a separate subject identity beginning in kindergarten. The core teacher provides
mathematics instruction throughout lower school. Teachers specifically assigned mathematics teach the stand-alone courses in the upper
school.
US5016y Mathematics 8
Mathematics and ESOL
US5020y Mathematics 9
US5022y Mathematics 10
Students at the beginning stages of English language learning might find some comfort in the familiarity of numbers and mathematical
symbols. Teachers use this familiarity to support conceptual understanding while the student gains the necessary vocabulary to discuss about
and to learn mathematics in an English medium environment. It is little surprise that students struggle most with context that requires highlevel conceptual language.
US5023y Mathematics 10A
Placement
Students are placed according to grade-level. Generally, differentiation is sufficient to address the wide range of prior mathematical
knowledge of our students. Students with a keen interest and aptitude are stretched to appreciate the abstract nature and power of
mathematics. Teachers support all students in building confidence and interest in mathematics and mathematical ways of thinking.
Occasionally a student may be placed in a class other than that of his or her peers to better accommodate his or her mathematical abilities.
Content Standards
*UAPCA
AP Calculus
*UAPST
AP Statistics
The SCIS-HIS content standards for mathematics are based on the standards from the United States, Singapore, Australia, the UK and New
Zealand and are aligned with the Expected Schoolwide Learning Results. The content standards include competencies in data and data
processes, measurement, probability and statistics, algebra and algebraic thinking, functions, calculus, geometry, trigonometry, number and
number systems, and computation.
Course Materials
US5040y & US5045y
IB Mathematical Studies
Standard Level
US5050y & US5055y
IB Mathematics
Standard Level
US5060y & US5065y
IB Mathematics
Higher Level
Course materials are two fold, those used for isolated skill development, such as arithmetic computations and solving algebraic equations, and
those used for mathematical process and thinking development. Drill and flexibility exercises provide the text for the former, whereas
authentic and multifaceted problems and explorations provide the text for the later.
Pedagogy
Teachers use a gradual release of responsibility method for teaching isolated skills and concepts, providing strong support and structure in the
early stages of the learning process, followed by guided practice, and leading to students’ independent use of the strategies, skills, and
knowledge. Teachers use authentic and multifaceted contexts and scaffolding to support learning of mathematical processes and problem
solving. Teachers target growth in student learning by helping them to build confidence and capacity in mathematics and mathematical ways
of thinking. Students with a keen interest and aptitude are stretched to appreciate the abstract nature and power of mathematics.
*Select offerings. Check with upper school counselor or IB Coordinator to determine availability.
Assessment
Teachers provide assessment supporting individual student learning and reporting on individual student progress. Internally, systemwide data
is collected four times per year, (1) October, skill and knowledge, (2) December, problem solving, (3) March, skill and knowledge, and (4) May
problem solving. External data in the form of the NWEA-MAP testing is also conducted in September and May for Students in grades two
through nine and through the PSAT for grade 10. Systemwide data and the externally collected data provide teachers with additional data
points for assessing individual students as well as prove teachers and administrators data used to moderate consistency and rigor of program.
SCIS-HIS Office of Curriculum
Learning Opportunities that
Nurture
Content Standards aligned to
Expected Schoolwide Learning Results
We nurture the following attributes through providing the
following types of learning opportunities.
We expect all students to demonstrate progress towards meeting the following Mathematics
standards.
Curiosity and Inquiry
Standards for Mathematics competencies contributing to a:

Making personal connection while playing with mathematical skills,
processes and concepts
Planning, designing and conducting mathematical explorations

Ingenuity and Productivity


Mastering skills and processes for making sense of problems
Producing explicit communication, reliable outcomes, and valid
results
Engaging in the problem-solving process

Resourcefulness and Flexibility

Exploring broad and varied applications and problems and through
strategic play with data, data representation and mathematically
supported decision-making
Imagination and Expression

Experimenting with mathematical modeling, data representation
and mathematical language in a wide range of contexts and
relationships involving the simple, well-defined and concrete as well
as the complex, ambiguous, and abstract
Thoughtfulness and Consideration

Using mathematical processes to reason abstractly and to move
between de-contextualization and contextualization while applying
mathematical processes in a wide range of contexts both theoretical
and practical
Connectivity and Influence

Engaging in decision-making supported by mathematical thinking,
such as finding patterns, using structures, recognizing regularity,
constructing reasoned arguments, critiquing the arguments and
assumptions of others, making sense of problems, and informing
solutions
Demonstration of
Learning Products
We expect students to become well versed in a wide-range of mathematics,
including the following strands. Many strands of mathematics overlap.
Inclusion in one strand is not an indication of exclusion from another.
Data processes (i.e. collection, organization, synthesis, analysis, and
representation) and tools for processing data/information
Solid Foundation of Knowledge
MT1
The student recognizes and is able to use the concepts and tools of data processes, including algorithmic processing
in theoretical and practical contexts.
MT2
The student recognizes and applies the concepts of geometry in theoretical and practical contexts.
MT3
The student recognizes and applies the properties and operations of the complex number system and all related
subsets (e.g. whole numbers, ratios, integers, irrational numbers).
MT4
The student knows and is able to apply a range of problem-solving strategies, such as working backwards, solving a
simpler problem.








Geometry
Positive Learning Attitudes and Behaviors
MT5
The student uses a wide variety of methods, tools, and technologies to support problem solving and data processing,
to validate mathematical results, and to obtain the necessary degree of accuracy, reliability, precision and validity.
MT6
The student counts, computes, and uses algorithms and mathematical vocabulary with appropriate fluency, precision
and accuracy.
Effective Communication




The student uses and creates mathematical models.
MT8
The student recognizes and represents mathematical information visually (e.g. drawings, charts, graphs, plots, and
diagrams), symbolically (e.g. numerals, equations, algebraic expressions, summation, exponentials, integrals, etc.)
and using mathematical vocabulary.
Spatial reasoning
Euclidean geometry
Coordinate geometry
Right triangle trigonometry
Number and Number Systems

MT7

Complex number system and all related subsets of the complex number system, i.e.
counting numbers, whole numbers, integers, rational numbers, irrational numbers, real
numbers, and imaginary numbers
Computation and estimation
Problem Solving Strategies










High Level Thinking
MT9
Measurement
Graphs, charts, plots, diagrams
Statistical methods and probability
Mathematical modeling
Patterns and structures
Functions and relations
Algebra
Calculus
The student chooses strategies, tools, and techniques for making sense of and for solving problems.
MT10 The student constructs viable arguments and critiques the reasoning of others through the strategic and accurate use
of mathematical reasoning.
Global and Community Appreciation
MT11 The student uses mathematical tools to assess risk, make sense of information, and to make reasoned decisions,
opinions and predictions.
Guess and check
Looking for a pattern
Making an organized/systematic list, table, diagram
Using logical reasoning
Working backwards
Solving a simplified version of the problem
Creating/drawing a model, visual representation
Using algebraic representation and application of properties of equality and inequality
Using statistical analysis
Using calculus representation and application of differentials and/or integrals
Sequence of Development
Nursery – Prekindergarten
Acquiring language for describing the physical
world mathematically and beginning problemsolving strategies




Sorting, patterns
Size, shape, capacity
Spatial orientation
Numbers and counting
Kindergarten – Grade 2
Developing foundational skills of numeracy,
problem solving, and mathematical
representations






Visual representation of data, e.g.
graphs, charts, diagrams
Properties of two and three
dimensional shape
Geometric transformations, i.e. slide,
turn, flip
Measurement
Place-value, whole numbers
Addition and Subtraction
Grades 3 – 5
Consolidating knowledge and skills related to
place-value, whole number operations,
composition and de-composition of whole
numbers, measurement and estimation






Basic probability and measures of
central tendency
Estimation of quantity,
length/distance, capacity,
mass/weight, area, time
Points, lines, planes, angles
Properties of quadrilaterals
Multiplication, division
Friendly fractions, decimals
Grades 6 – 8
Consolidating technical skills in problem-solving
techniques, expanding computation to include
rational numbers





Ratios, proportions, operations with
rational numbers, e.g. fractions,
decimals, percentages, negative
numbers, etc.
Algebra - fundamentals, linear and
quadratic equations
Coordinate geometry
Reliability and precision
Probability of compound events
Grades 9 – 10
Approaching mathematics as a tool for advanced
academic study in areas such as pure
mathematics, science and economics






Sets
Right triangle trigonometry
Roots (surds) and indices
Functions and function notation
Euclidean geometry
Probability and binomial expansion
Grades 11 - 12
All options for grades 11 and 12 include the
following topics



Applications of Algebra
Applications of probability and
statistics, including normal distribution
Applications of Calculus
Systemwide Mathematics Content Topics
The following are systemwide content expectations. These expectations are primarily broad to provide each campus with flexibility while maintaining sufficient consistencies across the campuses. Curriculum at every grade-level includes opportunities to pursue problems for which the solution is not
immediately evident and that allow for multiple problem solving approaches. Curriculum at every grade-level includes patterning. Also at every grade-level is the use of models, situation acting out, and/or manipulatives to support conceptual understanding, problems solving and/or communication.
Kindergarten through Grade 5 emphasis is given to place value place value in the base-10 number system.
Data and Data Processing
Nursery - Preschool
Prekindergarten
Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5

Collecting and analyzing
data through exploring and
manipulating objects and
navigating spaces
Language associated with
measurable attributes such
as length, weight, capacity









Elapse time
Mean, median, mode
Survey

Networks, including
structure, traceability and
applications

Probability
Means to organize data
related to count e.g.
frequency charts, tree
diagrams
Coordinate locations
Acquiring conceptual
understanding and language
related to shape, size and
location

Properties of two and three
dimensional shapes
Compose and decompose
shapes based on attributes
Tessellation
Rotational and reflection
symmetry

Perimeter and area

Points, lines and planes,
including relationships of
parallel and perpendicular
Unit conversion, e.g.
minutes/seconds,
millimeters/centimeters,
kilograms/grams


Static and rotational angles
Volume in terms of cubic
units
Addition and subtraction
requiring regrouping
Place value associated with
regrouping
Inequality (i.e. less than, <,
and greater than,>)
Odd and even
Fractions to show parts to
whole, denominators of 2,3,
4,6, and 8)

Adding and subtracting
fractions, including mixed
numbers, with common
denominators
Moving between decimals
and fractions with powers of
10 denominators
Addition and subtraction of
decimal numbers

All operations with decimal
numbers
Composing and
decomposing numbers, e.g.
factors, multiples, prime
factorization, whole and
fractional parts
Operations on friendly
fractions, those with
denominators 12 or less
Estimating fractions with
denominators more than 10,
using an estimate with
denominator of 10 or less

Geometry

Graphic displays of data
such as pictographs


Shapes and variations of
shape, including circle,
triangle, rectangle, square



Number and Number
Systems


Acquiring conceptual
understanding and language
related to quantity
Combining and separating
Describing and comparing
measurable attributes


Recites numbers in order
One-to-one correspondence





Transformations, i.e. slide,
turn, flip, reflect,
enlarge/reduce
Relative location, e.g. in,
under, beside
Distinguish between two and
three dimensional shapes

Count to 100
Written numerals 0-20
Cardinality
Adding and subtracting
within 10
Place value 11-19





Measurement using
conventional tools such as
scales and rulers
Write and tell time


Defining attributes (e.g.
closed, number of sides)
versus non defining
attributes (e.g. color,
orientation, overall size)

Beginning place value
Counting to 120
Addition and subtraction
within 20
Equality
Conceptual understanding of
distribution








Estimation of quantity,
length, weight, temperature,
etc.
Time and money
Bar graphs



Multiplication and division
through products of 100
Remainders in practical
context
Rounding






General
Every grade includes
developing the following
strategies.
 Looking for a pattern
 Acting out/using
concrete materials


Sorting, arranging, and
comparing
Recognizing simple visual
patterns

Duplicating and creating
visual patterns

Using manipulatives to aid
problem solving




Considering a simpler case
Acting out the problem
Parts to whole relationships
(e.g. halves, one side of the
cube, a rectangle can be
made of two triangles)
Number patterns



Using estimation in problem
solving
Moving between forms of
information, e.g. words,
visual/graphic display,
objects, numbers and
equation, organized lists
Drawing diagrams as a
problem solving strategy


Drawing tables as a problem
solving strategy
Using guess and check as a
problem solving strategy




Ensuring that solutions
account for the conditions of
the problem
Defining likeness criterion
when using addition or
subtraction
Using working backwards as
a problem solving strategy
Drawing tree diagrams



Using simpler numbers as a
problem solving strategy
Using logical reasoning as a
problem solving strategy
Annotating mathematical
works during problem
solving
3
SCIS-HIS Office of Curriculum
Systemwide Math Content Topics
The following are systemwide content expectations. These expectations are primarily broad to provide each campus with flexibility while maintaining sufficient consistencies across the campuses.
Data and Data
Processing
Grade 6
Grade 7
Grade 8
Grade 9
Grade 10
Grades 11 and 12


Distortion in data representation
Moving between representation on
number, e.g. fractions, decimals,
percentages, to process and describe
data
Probability
Line graphs representing continuous
data







Quadratic Basics
Exponential and rational functions
Proportional growth and decay
Probability and Statistics continued from
grade 8
Transformational Geometry
Grade 10 is differentiated by focus. One
focus has more emphasis on discrete math,
e.g. networks, probability and statistics
leading to advanced application; and one
has more focus on continuous math, e.g.
concepts leading to calculus and advanced
applications of algebra and calculus. Both
foci included the study of the following.
 Bivariate Statistics
 Standard deviation and normal
distribution
 Quadratic equations
 Functions
 Combinations and permutations
 Binomial expansion
 Series and sequences


Using deductive reasoning (e.g. general
rules applied to reach conclusions about
specific example)
Using inductive reasoning (e.g. specific
examples studied to reach
generalization)





Quantifying qualitative data
Algebraic representation and operations
on algebraic expressions, i.e. addition,
subtraction and multiplication and
division of an algebraic term by a scalar
value
Substitution property of equality


Moving between representations of data,
such as charts, graphs and equations
Modeling situations using inequalities
and systems of inequalities
Using scatter plots and basic curve
fitting to represent relationships and to
make predictions
Statistics
Probability


Geometry

Applications of scale, congruence,
similarity and distortion


Transformations
Circles


Coordinate geometry
Right triangle trigonometry
Number and Number
Systems

Ratios, proportions, percentages,
operations with non-negative rational
numbers, including fractions and of any
denominator value and decimal numbers
Integer basics

Computation with any rational number
through symbol manipulation
Application of the distributive property
on algebraic expressions

Applying properties of equality and
inequality
Applications of radicals (surds)
Recognize flaws in proportional thinking
Check precision and accuracy of both
process and solution

Representing relationships in spatial and
number patterns using tables, graphs,
equations for linear relationships and
recursive rules for non-linear
relationships
Recognizing, in practical settings,
applications for and limitations of various
number sets



General





Creating mathematical models
Using algebraic equations and systems
of equations to represent and solve
problems



Determining a suitable model for a set of
data or a given situation


Applications of Algebra
Applications of probability and statistics,
including normal distribution
Applications of Calculus
Communicating exploration in a
coherent, well-organized, concise and
complete manner.
Conduct mathematical arguments
through use of precise statements,
logical deduction and inference, and by
the manipulation of mathematical
expressions.
4
SCIS-HIS Office of Curriculum