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Mathematical reasoning
| Students use mathematical reasoning to analyze mathematical
situations, make conjectures, gather evidence, and construct an argument. |
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Problem Solving
The learner will be able to explore problem solving strategies using
manipulatives. |
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The learner will be able to apply basic computational skills to problems from other subject areas and real-world situations.
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The learner will be able to write and solve open sentences while working with word problems.
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The learner will be able to construct physical representations for complex problems.
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Constructing an Argument
The learner will be able to predict the effects of changing
the parameters of a problem statement. |
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The learner will be able to participate in record keeping projects involving data gathering. |
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The learner will be able to demonstrate and explain at least one method of solution. Ex: words, numbers, symbols,
pictures, charts, graphs, tables, diagrams, and models. |
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The learner will be able to develop strategies and use computation skills in games. Ex: Nim, Multiplication War,
Mind Trap, Mancala.
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Logic
The learner will be able to brainstorm to find strategies to solve problems and
discuss the advantages and disadvantages of the chosen process and subsequent solutions. |
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The learner will be able to create and explain algebraic sentences to illustrate general solutions with one variable.
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Drawing Conclusions
The learner will be able to define simple and compound numerical
statements using and/or connectors. |
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The learner will be able to use number lines to demonstrate an understanding of negative and positive numbers.
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| Students use number sense and numeration to develop an understanding
of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers
in the development of mathematical ideas. |
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Number Order
The learner will be able to recognize negative numbers. |
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The learner will be able to order decimals to thousandths.
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Number Theory
The learner will be able to develop relationships between hundredths and
percents using concrete materials. |
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The learner will be able to relate and integrate the study of fractions, ratio, and probability as it relates to
the study of geometric shapes and the areas of those shapes.
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The learner will be able to illustrate positive and negative numbers on a number line. |
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The learner will be able to explain the concept of prime and composite numbers. |
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The learner will be able to use factoring techniques to determine common denominators. |
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The learner will be able to factor numbers using rules of divisibility for 2,5,10.
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Numeration
The learner will be able to read and write numerals to one billion. |
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The learner will be able to use place value concepts to thousandths. |
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The learner will be able to identify proper and improper fractions. |
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The learner will be able to use the number line to model a variety of numbers. |
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The learner will be able to recognize the basic role of place value in decimal fractions (1/10,1/100,1/1000).
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Ratio
The learner will be able to demonstrate the concept of ratio using "to", ":" and
fraction format. |
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The learner will be able to use ratios in real situations such as unit pricing, interpretation of data and probability.
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| Students use mathematical operations and relationships among
them to understand mathematics. |
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Math Facts
The learner will be able to recall basic addition, subtraction, multiplication,
and division facts without any addition.
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Computation
The learner will be able to add, subtract, and multiply proper/improper
fractions and mixed numbers, with like and unlike denominators. |
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The learner will be able to understand, use, and apply addition, subtraction, multiplication, and division of decimals.
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The learner will be able to use grouping symbols (parentheses) to clarify the intended order of operations (i.e.
(3 + 5) - 6 = 2).
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The learner will be able to understand, use and apply the order of operation, (i.e. parentheses,
multiplication and division, addition and subtraction).
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The learner will be able to simplify fractions.
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The learner will be able to change mixed numbers to improper fractions and improper fractions
to mixed numbers.
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The learner will be able to calculate LCD for fractions and GCF and LCM for sets of numbers.
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Properties
The learner will be able to understand, use, and apply Associative, Commutative,
Inverse, and Identity Properties.
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Problem Solving
The learner will be able to understand, use, and apply grade appropriate
strategies (i.e. making a list of data; using patterns; using open sentences; solving a simpler problem; breaking a problem
into parts; using associative and commutative properties; using diagrams, charts, and tables; drawing pictures; using manipulatives;
restating a problem, guess and check, logical reasoning chart) for selecting a correct computational and operational method
to solve a problem with an explanation.
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| Models and Multiple Representation |
| Students use mathematical modeling/multiple representation to
provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.
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Charts and Graphs
The learner will be able to create, read and interpret circle and
line graphs. |
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The learner will be able to create a bar graph from independently gathered information.
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The learner will be able to read, interpret, and create bar graphs independently. |
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The learner will be able to use bar graphs for comparing and contrasting.
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Geometric Representation
The learner will be able to identify and construct regular
and irregular polygons based on knowledge of angles and sides. |
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The learner will be able to explore and measure acute, obtuse, and right angles. |
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The learner will be able to build symmetrical and congruent shapes and use transformations to create tessellations.
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The learner will be able to manipulate a protractor and compass. |
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The learner will be able to describe and identify lines, rays, points, line segments and intersecting lines.
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The learner will be able to apply knowledge of Cartesian plane (x,y axis)/coordinate plane.
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Variables and Visual Reproductions
The learner will be able to use variables in area
and perimeter formulas involving squares or rectangles. |
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The learner will be able to explore and explain one or two unknown quantities in math sentences involving the four
operations (addition, subtraction, multiplication and division). |
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The learner will be able to create and explain variables through line graphs.
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| Students use ideas of uncertainty to illustrate that mathematics
involves more than exactness when dealing with everyday with everyday situations. |
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Estimation
The learner will be able to round whole numbers to the nearest ten thousand.
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The learner will be able to estimate the outcomes of problems and experiments, complete the task, and do a comparison.
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The learner will be able to identify changes in the solution (size and order) based on the effects of addition,
subtraction, subtraction and division. |
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The learner will be able to round fractions and decimals in computation. |
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The learner will be able to round decimals to the nearest hundredth.
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Reasonableness
The learner will be able to justify and explain the answer to determine
if results are reasonable. |
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Probability
The learner will be able to predict the outcomes of an experiment, conduct
the experiment, then compare the results with the prediction. |
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The learner will be able to draw conclusions and explain the outcome of experiments expressing the outcome
as fractions, ratio, and words , i.e. roll dice, spinner, random choices. |
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The learner will be able to demonstrate and apply the concept of problems that involve systematic identification
of ordered arrangements, i.e. combinations. |
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The learner will be able to estimate the probability of events using a simulation.
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The learner will be able to determine the probability of independent events using dice, coins, cards, spinners,
etc. and express the outcome (ex. tree diagrams, sample spaces). |
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The learner will be able to construct and explore models that do and do not rely on chance.
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The learner will be able to describe and explain mutually exclusive events (i.e. counting principle). |
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The learner will be able to describe and explain events with replacement. |
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The learner will be able to explore and discuss arrangements and combinations.
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| Students use patterns and functions to develop mathematical
power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
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Exploring Patterns
The learner will be able to extend computation skills by describing
and extending number patterns and sequences i.e. (1, 4, 7, 10).
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The learner will be able to extend and/or complete a simple pattern of numbers i.e. (1,4,7, ...,13).
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The learner will be able to solve problems based on Math sentences using manipulatives to represent patterns.
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Graphic Patterns
The learner will be able to identify patterns using tables and graphs.
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The learner will be able to create patterns using tables and graphs.
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Functions
The learner will be able to determine the missing value in a whole number
proportion in which three of the numbers are known.
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Variables
The learner will be able to solve one-step linear equations with one variable.
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The learner will be able to explore functions and relationships such as 1/8 = x/24. |
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The learner will be able to analyze graphs and determine how the values of one variable is related to the values
of another variable.
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Geometric Patterns
The learner will be able to use concrete models to explain similarity
and congruence in plane geometric figures i.e. (rectangles, triangles, symmetry, geometric.
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The learner will be able to classify polygons by properties. |
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The learner will be able to develop definitions of basic polygons i.e. triangles, rectangles, square, rhombus,
trapezoid, parallelogram. |
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The learner will be able to define symbols for parallel, perpendicular, similar and congruent.
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The learner will be able to distinguish the similarities and differences among trapezoids, rhombi and quadrilaterals.
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The learner will be able to explore the basic characteristics of angles, lines, line segments and rays. |
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The learner will be able to define right triangle. |
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The learner will be able to model the concept of similarity among triangles. |
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The learner will be able to solve verbal problems that utilize area and perimeter formulas.
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| Students use measurement in both metric and English measure
to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects
and data. |
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Approximation
The learner will be able to determine if estimates in measurements are
reasonable.
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Data
The learner will be able to display data (pictographs, bar graphs, line graphs,
stem-and-leaf plots, double line graphs, double bar graphs, venn diagrams, models, pictures, lists, etc.).
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Data Analysis
The learner will be able to find and compare mean, mode, median, and range.
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The learner will be able to observe data to evaluate distribution around the middle (gaps, clusters, extremes).
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The learner will be able to use graphic representations to model problems.
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Geometric Measurement
The learner will be able to perform operations between Metric
or English units of measure (time, temperature, weight, length, capacity/volume, area) i.e. (3 ft. 2 in. + 1ft. 11 in.).
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The learner will be able to understand and use prefixes (i.e. centi, milli, kilo) and symbols (i.e. cm, mL, km)
in measurement.
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The learner will be able to determine length, weight/mass, and liquid volume/capacity using standard (Metric and English)
and non-standard measurement tools.
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The learner will be able to identify types of angles and explore their measurements using a protractor.
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The learner will be able to use manipulatives to demonstrate the concepts of units, square units, and cubic units.
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Tools
The learner will be able to make effective use of rulers, thermometers and scale
for making measurements. |
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