Download Competencies w backmapping 03-24

SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 1
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics
Prerequisite
Grade Kindergarten
Skills
Represent, compare, and order whole numbers, and
join and separate small sets of numbers or objects.
Order objects by measurable attributes, such as
length and weight, and indirectly compare lengths to
a third object to solve problems.
Identify, name and describe a variety of two and
three dimensional shapes presented in different
sizes and orientations, as well as combining those
shapes to construct more complex shapes.
Identify, duplicate, and extend simple number,
sequential and growing patterns.
Sort and re-sort objects using one or more attributes
to solve problems.
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 2
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Grade 1
Represent, compare, and order whole numbers up
to 100, including using the number line and
grouping in tens and ones.
Use properties (commutative, associative) and a
variety of models to develop understanding of two
digit addition and subtraction, and the relationship
between them, as well as develop strategies for
basic addition facts and related subtraction facts.
Use standard and non-standard units of
measurement to find lengths and subsequently solve
problems.
Decompose, as well as compose, two- and threedimensional shapes, describing their properties in
order to build understanding of part-whole
relationships.
Apply, as well as identify and describe number
patterns and properties such as odd and even.
Represent measurements and discrete data in
picture and bar graphs involving counting and
comparing. These should provide meaningful
connections to number relationships.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 3
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Grade 2
Represent, compare, and order whole numbers up
to 1000, and their equivalents (e.g. 35 is 3 tens and
5 ones or two tens and 15 ones), including using the
number line and expanded notation, while grouping
in hundreds, tens and ones.
Develop extended understanding of multiple models,
and properties of addition and subtraction, leading
to fluency with efficient, accurate and generalizable
methods to add and subtract multi-digit whole
numbers and develop quick recall of addition and
related subtraction facts. Select and apply
appropriate methods to estimate sums and
differences or to calculate them mentally.
Extend concepts and procedures for estimating and
measuring length, area, volume, weight, time and
elapsed time.
Use processes (e.g. partitioning, transitivity, inverse
relationships) to estimate, measure, and compute
lengths to solve problems involving data, space and
movement, including standard measures such as
centimeter and inch.
Use number patterns to extend knowledge of
properties of numbers and operations (skip counting
as a foundation for understanding multiples)
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 4
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Grade 3
Develop an understanding of multiplication and
division of whole numbers by building on knowledge
of the base ten system/operations and through the
use of representations (e.g., equal-sized groups,
arrays, area models, equal “jumps” on number lines,
successive subtraction, partitioning, and sharing) in
order to describe relationships, make estimations,
and solve problems.
Develop an understanding of the size, meaning, and
uses of fractions to represent parts of a whole, parts
of a set, or points/distances on a number line, and
that fractions are used to represent numbers that
are equal to, less than, or greater than one.
Extend the concepts of measurement to include
perimeter as a measurable attribute and select
appropriate units, strategies, and tools to solve
problems involving perimeter.
Describe, analyze, compare, and classify two- and
three-dimensional shapes/figures using their
attributes. Use congruence and symmetry to
decompose, compose, and transform twodimensional figures.
Construct and analyze frequency tables, bar graphs,
picture graphs, and line plots and use them to
describe data and solve problems.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 5
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Grade 4
Apply increasingly sophisticated strategies to solve
multiplication and division problems that include and
go beyond basic facts and one-digit multiplier
problems, using properties of addition and
multiplication. Select and apply appropriate
strategies to estimate and/or solve a variety of
problems including problems involving addition and
subtraction of decimals and of fractions with like
denominators.
Read, represent, interpret the representation,
compare and order fractions in various forms (e.g.,
area model, fraction of a set, fraction notation).
Relate understandings of fractions to reading and
writing of decimals and understand decimal notation
as an extension of the base-ten system.
Understand area as a measurable attribute and
select appropriate units, strategies (e.g.,
decomposing) and tools to solve problems or make
estimations. Use properties of 2-dimensional shapes
to find the area of polygons, connect the area/array
model of multiplication to the area formula for
rectangles, and use this connection to justify the
formula.
Expand symmetry and congruence to describe basic
transformations, including reflections, rotations, and
translations (i.e., flips, turns, and slides). Use
transformations to design and analyze simple tilings
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 6
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Grade 4
and tessellations.
Identify a rule to describe and extend a sequence of
numbers, objects, and/or relationships observed in a
variety of contexts.
Continue to represent and analyze problems by
making frequency tables, bar and picture graphs,
and line plots; apply the concept of place value to
develop an understanding and use of stem-and-leaf
plots. Use plots to predict the likelihood of events.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 7
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics –Grade 5
Develop fluency with and an understanding of
efficient strategies for division (models, place value,
properties of operations, and the relationship
between multiplication and division) and use them to
solve problems.
Develop an understanding of and fluency with
addition and subtraction of fractions and decimals
(models, place value, properties of addition and
subtraction of decimals) to solve problems in a
variety of contexts, including measurement. Develop
understanding of negative integers using concrete
objects.
Extend informal understanding of volume of solids to
the measurement of capacity and weight or mass.
Understand volume as a measurable attribute and
select appropriate units, strategies and tools to solve
problems or make estimations.
Relate 2-dimensional shapes to 3-dimensional
figures and analyze polyhedra solids, describing
them by their attributes.
Use patterns, models, and relationships as contexts
for writing and solving simple equations and
inequalities, and graph simple equations
Construct and analyze double-bar and line graphs
and use ordered pairs on coordinate grids. Use basic
concepts of probability to predict the likelihood of
event occurring.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 8
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics –Grade 6
Expand the meaning of multiplication and division of
fractions and decimals and their inverse relationships
to compute fluently and solve real world problems.
Use a variety of models to represent percents.
Extend previous understandings of the
characteristics of 2-d and 3-d shapes including the
measures of area and volumes by exploring, solving
and interpreting real world problems.
Write mathematical expressions and equations that
correspond to given situations, evaluate expressions
and use expressions and formulas to solve problems.
Understand ratios as part to part and part to whole
comparisons, and as comparisons of two different
quantities (e.g., rates). Represent part to whole
comparisons in fraction, decimal and percent
formats.
Understand the concepts of the measures of central
tendency of a data set, calculate accurately the
measures of central tendency, and interpret these
measures in the context of the given situation.
Use elementary probability and proportions to make
appropriate predictions.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 9
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Grade 7
Extend computational fluency, estimation strategies
and problem solving to include problems involving
positive and negative rational numbers (including
integers).
Extend previous understandings of the
characteristics of 3d-shapes to develop an
understanding of and use formulas to determine
surface areas and volumes.
Apply a variety of strategies for proportional
reasoning and use them to solve real world
problems including problems dealing with similarity
and rates of change.
Recognize problem situations in which two or more
variables have a linear relationship to each other.
Understand the connections between linear
equations and the patterns in the tables and graphs
of those equations: rate of change, slope, and yintercept.
Answer questions regarding a data set using
measures of center and spread and interpreting the
graphical representation (including box-and-whisker
plots) of the data set.
Determine the sample space for one-stage
experiments and determine, when possible, the
theoretical probabilities for events defined in the
sample space.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 10
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Pre-Algebra
Extend understanding of numbers (rational and
irrational), and operations, equivalent forms,
(integers, fractions, decimals, percents, roots,
exponents and scientific notation) and be able to use
these understandings in problem solving situations.
Understand and apply the Pythagorean Theorem to
find distances between points in a coordinate plane
and to analyze polygons and polyhedra.
Use fundamental facts about distances and angles to
describe and analyze figures and situations in 2- and
3-dimensional spaces and to solve problems
including those with multiple steps.
Use linear functions, linear equations, and linear
inequalities to represent, analyze, and solve a
variety of problems.
Use the appropriate graphical data representation
and extend understanding of the influence of scale
in data interpretation.
Extend understanding of probability to make
comparisons of empirical probability and theoretical
probability for the experiment.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 11
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Algebra 1
Use algebraic properties and processes in
mathematical situations and apply them to solve real
world problems.
Represent functions (linear and non-linear) in
multiple ways, including tables, algebraic rules,
graphs and contextual situations, and make
connections among these representations. Choose
the appropriate functional representation to model a
real world situation and solve problems relating to
that situation.
Write, solve, graph, and interpret linear equations
and inequalities to model relationships between
quantities.
Write, solve and interpret systems of two linear
equations and inequalities using graphing and
algebraic techniques.
Display, analyze, and make predictions using
univariate and bivariate data.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 12
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics - Geometry
Define and describe types of geometrical reasoning
and proof, using them to verify valid conjectures as
they surface in the study of geometry; develop a
counterexample to refute an invalid conjecture.
Define, describe, and analyze 2- and 3-dimensional
figures, their properties and relationships, including
how a change in one measurement will affect other
measurements of that figure.
Use concepts of congruence and similarity to relate
and compare 2- and 3-dimensional figures, including
trigonometric ratios.
Use coordinates and algebraic techniques to
interpret, represent and verify geometric
relationships.
Apply geometric properties of length or area to
represent and calculate probabilities.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs
SAS-Math Competencies With Backmapping
What all students should be able to do at the end of this year or course…
Page 13
SAS-Math Core Team – Jim Bohan – [email protected]
Competencies – Mathematics – Algebra 2
Extend algebraic properties and processes to
quadratic, exponential, and polynomial expressions
and equations and to matrices, and apply them to
solve real world problems.
Represent exponential functions in multiple ways,
including tables, graphs, equations, and contextual
situations, and make connections among
representations; relate the growth/decay rate of the
associated exponential equation to each
representation.
Represent a quadratic function in multiple ways,
including tables, graphs, equations, and contextual
situations, and make connections among
representations; relate the solution of the associated
quadratic equation to each representation.
Represent a polynomial function in multiple ways,
including tables, graphs, equations, and contextual
situations, and make connections among
representations; relate the solution of the associated
polynomial equation to each representation.
Distinguish between independent and dependent
events in order to calculate compound probabilities
within real world situations.
Prerequisite
Skills
Resources Available
Resources Needed
Professional
Development Needs