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Dallas School District
K-12 Curriculum
Elementary Mathematics - Kindergarten
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The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties.
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Number Sentence: Solve
The learner will be able to
apply physical objects and trial and error to obtain solutions to number sentences and to confirm that solutions are reasonable and accurate.
| Strand |
Source |
| Number Sentence |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.B (Back Mapped) |
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Operations: Show Understanding
The learner will be able to
show an understanding of the basic facts of the four operations.
| Strand |
Source |
| Operations |
PA: Academic Standards, January 16, 1999, Grade 3, p.3,2.1.3.L (Back Mapped) |
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Algebraic Concepts: Symbols/Objects
The learner will be able to
apply physical objects and symbols to illustrate the concepts of variables, expressions, equations, and inequalities.
| Strand |
Source |
| Algebraic Concepts |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.E (back mapped) |
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Solution Methods: Choose/Apply
The learner will be able to
choose and apply an appropriate strategy and materials to obtain solutions to problems, including mental math, paper and pencil, and physical objects.
| Strand |
Source |
| Solution Methods |
PA: Academic Standards, January 16, 1999, Grade 3, p.8,2.5.3.C (back mapped) |
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Table/Chart: Collect/Display
The learner will be able to
collect data and display it in a table or chart.
| Strand |
Source |
| Tables/Charts |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.G |
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Algebraic Symbols/Solutions
The learner will be able to
describe the meaning of solutions and symbols.
| Strand |
Source |
| Identify Sentence |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.F (back mapped) |
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Missing Addend
The learner will be able to
substitute a missing addend in a number sentence.
| Strand |
Source |
| Missing Information |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.C (back mapped) |
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Operations: Addition/Subtraction
The learner will be able to
use physical objects in applying addition and subtraction in everyday scenarios.
| Strand |
Source |
| Operations |
PA: Academic Standards, January 16, 1999, Grade 3, p.4,2.2.3.A (back mapped) |
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Computation: Reasonableness
The learner will be able to
determine the reasonableness of calculations.
| Strand |
Source |
| Computation |
PA: Academic Standards, January 16, 1999, Grade 3, p.4,2.2.3.F (back mapped) |
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Computation
The learner will be able to
apply an understanding of basic facts and algorithms, determine situations in which to use specific computation techniques, and evaluate the reasonableness of given computations.
| Strand |
Source |
| Computation |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Sense: Manipulatives
The learner will be able to
use manipulatives to demonstrate the following algebraic concepts: sets, elements of sets (a different shaped or colored manipulative can be used to represent a set of manipulatives), equal sets, variables representing unequal values (specific manipulatives can be used to equal five of another kind of manipulative), the symbolic nature of algebra, patterns in algebra, and the connection between manipulatives and the written expressions they represent.
| Strand |
Source |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Operations: Analyzing
The learner will be able to
analyze the functions and effects of addition, subtraction, multiplication, and division by discussing these operations formally and informally using mathematics language and symbols, and recognize the variety of mathematical scenarios which can be solved through one or more of these operations.
| Strand |
Source |
| Operations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Translate Problems
The learner will be able to
listen to a given scenario, consider the elements of the scenario, determine the missing factor, and write a number sentence which represents the scenario.
| Strand |
Source |
| Relating Number Sentences/Problems |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. The Data Interpretation Unit includes data collection and classification, organization and display of data, logical reasoning and problem solving.
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Data Collection: Organize/Illustrate
The learner will be able to
collect, organize, and illustrate data using pictures, tallies, charts, bar graphs, and pictographs.
| Strand |
Source |
| Graphing |
PA: Academic Standards, January 16, 1999, Grade 3, p.9,2.6.3.A |
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Data Collection: Analysis
The learner will be able to
gather and/or study data by applying the notions of largest, smallest, most frequent, less frequent, and/or middle.
| Strand |
Source |
| Data Collection and Classification |
PA: Academic Standards, January 16, 1999, Grade 3, p.11,2.7.3.D (back mapped) |
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Bar Graphs: Recognize Values
The learner will be able to
recognize least and greatest values illustrated in bar graphs and pictographs.
| Strand |
Source |
| Bar Graphs |
PA: Academic Standards, January 16, 1999, Grade 3, p.19,2.11.3.B |
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Tables/Charts: Explain
The learner will be able to
explain information shown in tables and charts.
| Strand |
Source |
| Tables/Charts |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.H (back mapped) |
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Table/Chart: Interpret
The learner will be able to
interpret information presented in tables and charts.
| Strand |
Source |
| Tables/Charts |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.H (back mapped) |
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Logical Reasoning: Questions
The learner will be able to
formulate and answer questions based on data displayed on graphs.
| Strand |
Source |
| Logical Reasoning |
PA: Academic Standards, January 16, 1999, Grade 3, p.9,2.6.3.B (back mapped) |
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Analyzing: Graphical Forms
The learner will be able to
demonstrate the ability to interpret graphical forms of data by explaining data presented in different graphical forms (tables, charts, graphs, diagrams, etc.) orally or in writing.
| Strand |
Source |
| Analyzing/Evaluating Graphical Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Analyzing: Graphical Forms
The learner will be able to
demonstrate the ability to interpret graphical forms (tables, charts, graphs, diagrams, etc.) of data by transferring information from one graphical form to another.
| Strand |
Source |
| Analyzing/Evaluating Graphical Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Analyzing: Graphical Forms
The learner will be able to
demonstrate the ability to interpret graphical forms of data (tables, charts, graphs, diagrams, etc.) by making decisions about a topic based on information presented in graphical form.
| Strand |
Source |
| Analyzing/Evaluating Graphical Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. The Fractions Unit includes comparison, ordering, fractions parts, estimation, reasoning and problem solving.
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Fraction Parts: Part of a Whole
The learner will be able to
demonstrate the idea of fraction as part of a whole using drawings, diagrams, or models.
| Strand |
Source |
| Fraction Parts |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.D (back mapped) |
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Number Sense: Using Bar Graphs
The learner will be able to
demonstrate an understanding of the relationships among fractions (simple, mixed, improper) by creating a bar graph which accurately represents a given series of simple, mixed, and improper fractions.
| Strand |
Source |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Sense: Using Fractions
The learner will be able to
explore fractions and use an intuitive sense of fractions as proportions and/or ratios to evaluate the reasonableness of a given problem and solution.
| Strand |
Source |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving
The learner will be able to
evaluate a real-world scenario problem involving fractions to determine the appropriate operation (addition or subtraction), decide on relevant elements, set up an equation, and solve the equation.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Functions Unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions.
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Function: Illustrate/Rules
The learner will be able to
illustrate simple function rules.
| Strand |
Source |
| Functions |
PA: Academic Standards, January 16, 1999, Grade 3, p.14,2.8.3.I (back mapped) |
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The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. The Geometry Unit includes properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving.
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Figures: Name/Label
The learner will be able to
name plane and solid geometric figures.
| Strand |
Source |
| Figures: Identify |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.A (back mapped) |
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Figures: Form/Check/Confirm
The learner will be able to
formulate, check, and confirm predictions about the quantity, size and shape of objects and sets of objects.
| Strand |
Source |
| Figures |
PA: Academic Standards, January 16, 1999, Grade 3, p.7,2.4.3.A (back mapped) |
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Geometric Concepts: Identify
The learner will be able to
identify, observe and describe geometry in the environment and real-world situations.
| Strand |
Source |
| Geometric Concepts |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.D |
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Figures: Construct/Physical Object
The learner will be able to
construct geometric shapes using physical objects.
| Strand |
Source |
| Figures: Construct |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.B (back mapped) |
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Figures: Construct/Geoboard
The learner will be able to
construct rectangles, squares and triangles on the geoboard from specified criteria.
| Strand |
Source |
| Figures: Construct |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.C (back mapped) |
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Shapes: Draw
The learner will be able to
create drawings of two dimensional shapes.
| Strand |
Source |
| Two-Dimensional Shapes |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.C |
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Reflection: Fold Paper
The learner will be able to
illustrate reflections about a line by folding paper.
| Strand |
Source |
| Reflections |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.G (back mapped) |
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Symmetry: Recognize
The learner will be able to
recognize symmetry in nature.
| Strand |
Source |
| Symmetry |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.F (back mapped) |
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Symmetry: Symmetrical Lines
The learner will be able to
identify lines of symmetry in figures.
| Strand |
Source |
| Symmetry |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.E |
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Symmetry: Drawing Lines
The learner will be able to
draw lines of symmetry in figures.
| Strand |
Source |
| Symmetry |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.E (back mapped) |
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Combine/Partition: Predict
The learner will be able to
forecast the outcome of combining or partitioning geometric figures.
| Strand |
Source |
| Combine/Partition/Transform |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.I (back mapped) |
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Angles: Right
The learner will be able to
study right angle concepts, create right angles, and find right angles within the classroom and at home, including folding paper to make square corners, identifying the square corners as right angles, transferring this observation to another medium by drawing square corners or right angles, and discussing angles which are greater than or less than right angles.
| Strand |
Source |
| Lines/Angles/Polygons |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Exploring: Outlines
The learner will be able to
walk along, touch, and discuss a plane figure outlined on the floor in tape, and then help duplicate the figure using a different medium, or with smaller proportions.
| Strand |
Source |
| Exploring Spatial Concepts |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Figures
The learner will be able to
extend recognition of whole figures to the ability to analyze parts of figures, and classify figures by the similarities and differences of their parts.
| Strand |
Source |
| Figures |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Patterns: Analyzing Visual
The learner will be able to
analyze visual patterns in geometric figures by exploring how placing different figures on different sized backgrounds in rows creates different combinations of figures within each row.
| Strand |
Source |
| Geometric Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Patterns: Problem Solving
The learner will be able to
solve problems involving geometry by applying the ability to study, recognize, and extend pictorial, concrete, and numerical patterns.
| Strand |
Source |
| Geometric Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking
The learner will be able to
develop spatial sense by drawing, modeling, describing, and classifying shapes.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking: Familiar Figures
The learner will be able to
identify, describe, compare, and classify two and three dimensional figures found in his/her immediate environment.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking: Geometric Figures
The learner will be able to
develop perception in spatial relationships by studying geometric figures in different sizes and positions, and by performing "mental flips" of the figures before holding them.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking: Manipulatives
The learner will be able to
practice modeling, drawing, and explaining shapes and their properties using manipulatives and exploring the shapes in a real-world context.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking: Perspective
The learner will be able to
have an intuitive sense of physical objects in the world, how they compare in size and shape, and the concepts of perspective and direction.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking: Visual Discrimination
The learner will be able to
demonstrate visual discrimination skills by sorting plane and solid figures by a given set of criteria and accounting for perspective and orientation.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Spatial Thinking: Visual Memory
The learner will be able to
duplicate a three dimensional model (of linking cubes) one cube high with up to five cubes attached, draw or construct the model using visual memory and spatial thinking, and evaluate the model.
| Strand |
Source |
| Spatial Thinking |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Transformations: Predicting
The learner will be able to
demonstrate visualization skills by predicting the results of transformations two to four steps in advance.
| Strand |
Source |
| Transformations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Transformations: Predicting
The learner will be able to
show the ability to visualize figures and their properties by predicting the results of transformations two to four steps in advance, and articulate how different figures are the same and/or different before and after transformations.
| Strand |
Source |
| Transformations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Mathematics Processes Unit focuses on mathematical connections, communication, modeling, concepts and procedures.
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Math as Reasoning
The learner will be able to
understand that mathematics is logical, and that solutions to mathematics problems, and mathematics patterns, relationships, and properties make sense, and apply their ability to reason, to analyze mathematical situations and to justify answers and solutions to problems.
| Strand |
Source |
| Reasoning |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Mathematical Connections
The learner will be able to
make connections among number relationships, systems, and forms, conceptual and procedural knowledge, and the written forms of numbers and their representative values.
| Strand |
Source |
| Connections |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Mathematical Connections
The learner will be able to
make mathematical connections among mathematics topics, across the curriculum, and in day to day life.
| Strand |
Source |
| Connections |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Mathematics as Communication
The learner will be able to
use communication skills to describe the way he/she is thinking about principles of mathematics, to clarify thinking and conceptualization of mathematics principles, and to provide informal and formal feedback to teachers of mathematics.
| Strand |
Source |
| Communication |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Mathematics as Communication
The learner will be able to
understand that language arts processes such as reading, writing, speaking, listening, and viewing are utilized in thinking about, learning, and articulating mathematics concepts.
| Strand |
Source |
| Communication |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Mathematics as Communication
The learner will be able to
use everyday language to discuss mathematics concepts (including number systems, relationships, and forms) both formally and informally using the symbols and the language of mathematics.
| Strand |
Source |
| Communication |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. The Measurement Unit includes concepts of length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns and problem solving.
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Money: Count/Compare/Change
The learner will be able to
count, compare, and make change from a group of coins and one-dollar bills.
| Strand |
Source |
| Money |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.E (back mapped) |
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Estimation: Standard/Non-Standard Units
The learner will be able to
make approximations and/or actual measurements through the use of standard and/or non-standard units of measure.
| Strand |
Source |
| Measurement: Estimation |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.B (back mapped) |
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Measurement Concepts: Varied Attributes
The learner will be able to
illustrate that one object has various properties that can be measured in various ways.
| Strand |
Source |
| Measurement Concepts |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.G (back mapped) |
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Units: Choose Appropriate
The learner will be able to
choose suitable units of measure.
| Strand |
Source |
| Units |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.E (back mapped) |
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Time: Compare
The learner will be able to
compare lengths of time.
| Strand |
Source |
| Time |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.C |
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Time: Hour
The learner will be able to
tell time to the hour using both digital and analog clocks.
| Strand |
Source |
| Time |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.D |
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Perimeter/Area: Find
The learner will be able to
find area.
| Strand |
Source |
| Perimeter/Area/Volume |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.F (back mapped) |
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Measurement: Compare
The learner will be able to
make comparisons of the measurable attributes of various objects on the same dimension.
| Strand |
Source |
| Measurement: Exploring |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.A (back mapped) |
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Measurement: Apply/Real World
The learner will be able to
use measurement in many different real-world scenarios.
| Strand |
Source |
| Measurement: Application |
PA: Academic Standards, January 16, 1999, Grade 3, p.7,2.4.3.B (back mapped) |
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Measurement: Estimation
The learner will be able to
make measurement estimations.
| Strand |
Source |
| Measurement: Estimation |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.G (back mapped) |
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Estimate Measurements: Verify
The learner will be able to
verify measurement.
| Strand |
Source |
| Measurement: Estimation |
PA: Academic Standards, January 16, 1999, Grade 3, p.6,2.3.3.G (back mapped) |
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Applying: Decimals/Fractions
The learner will be able to
demonstrate the ability to apply measurement, fraction, and decimal concepts to real-world scenarios by identifying and expressing measurement problems using fractions and decimals.
| Strand |
Source |
| Measurement: Application |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Applying: Estimation/Measurement Units
The learner will be able to
apply an understanding of units of measurement to make and use measurements and estimations in real-world scenarios.
| Strand |
Source |
| Measurement: Application |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Applying: Measurement Concepts
The learner will be able to
apply an understanding of length, capacity, weight, mass, area, volume, time, and angle attributes, distinguish between situations which require exact measurement and those which require estimations, and utilize measurement concepts to solve real-world problems.
| Strand |
Source |
| Measurement: Application |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Communicating: Comparison Terms
The learner will be able to
use measurement terms to describe and compare objects by weight, length, time and temperature using the appropriate tools.
| Strand |
Source |
| Communicating Measurement Concepts |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Communicating: Measurement Concepts
The learner will be able to
use measurement terms, articulate how and when measurement is used in real-world situations, and give examples of situations which call for either estimation or exact measurement.
| Strand |
Source |
| Communicating Measurement Concepts |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Communicating: Measurement Concepts
The learner will be able to
use measurement terms, articulate how measurement terms relate to real-world objects, proportions, and amounts, justify why a particular form of measurement should be used, and distinguish between situations which call for estimation and those which call for exact measurement.
| Strand |
Source |
| Communicating Measurement Concepts |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Number Sense/Measurement Units
The learner will be able to
develop a sense of how numbers are manipulated in measurement scenarios, focusing on the study of the patterns inherent in units of measurement and formulas.
| Strand |
Source |
| Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Manipulatives
The learner will be able to
listen to or read a given scenario involving measurement, and articulate how the problem can be solved using manipulatives.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Manipulatives
The learner will be able to
use manipulatives to solve a given real-world situation, show how measurement can be used to solve mathematical problems, evaluate a situation to determine the nature of the problem and relevant elements, and select the appropriate measurement tools (without being told the specific unit of measurement which should be used).
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Measurement Concepts
The learner will be able to
demonstrate how principles of measurement can be used to solve real-world mathematical problems, evaluate a situation to determine the nature of the problem and relevant elements, and select the appropriate measurement tools (without being told the specific unit of measurement which should be found) to solve the problem.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Units: Reasoning
The learner will be able to
choose a specific unit of measurement to solve a problem and justify the choice, and focus on the reasons behind choosing the specific unit of measurement.
| Strand |
Source |
| Units |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Number Theory Unit focuses on manipulating number forms and classifications. Students make connections between number forms and their real-world applications.
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Equivalent Forms: Represent/Use
The learner will be able to
illustrate and/or apply equivalent forms of numbers by applying concrete models, drawings, word names, and/or symbols.
| Strand |
Source |
| Equivalent Forms |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.C (back mapped) |
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One-to-one Correspondence: Understanding
The learner will be able to
show an understanding of one-to-one correspondence.
| Strand |
Source |
| One-to-one Correspondence |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.H |
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Rounding: Appropriate
The learner will be able to
round when appropriate.
| Strand |
Source |
| Rounding |
PA: Academic Standards, January 16, 1999, Grade 3, p.3,2.1.3.J (back mapped) |
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Conceptualizing: Decimals/Fractions
The learner will be able to
demonstrate a sense of fractions and decimals, the functions of each of these number forms, and how these number forms relate to each other by creating models of equivalent fractions and decimals and by solving problems involving fractions and decimals.
| Strand |
Source |
| Conceptualizing Number Meanings |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Connecting: Forms/Operations/Systems
The learner will be able to
make connections between number forms, operations, and systems, and understand their real-world applications.
| Strand |
Source |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Connecting: Whole Numbers/Fractions
The learner will be able to
explain whole numbers and fractions in terms of how they relate to each other, what they express, and the contextual bases for each, articulate these in writing and incorporate the properties of each of these number forms focusing on the representational value of these numbers, not on how the numbers can be computed in isolated form.
| Strand |
Source |
| Connecting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Justifying Forms
The learner will be able to
articulate what decimals and fractions are, how they relate to whole numbers, and when and how they are used to solve problems, and read and/or listen to a given real-world scenario and make judgments about the best format for describing the scenario (using decimals, fractions, whole numbers).
| Strand |
Source |
| Justifying Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Math Structures: Forms/Operations/System
The learner will be able to
demonstrate an intuitive sense of number forms, operations, and systems, and their real-world applications.
| Strand |
Source |
| Math Structures |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Math Structures: Number Sense
The learner will be able to
develop an intuitive sense of number relationships, systems, and forms and their multiple applications in real-world scenarios.
| Strand |
Source |
| Math Structures |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Forms: Nature of Different Forms
The learner will be able to
investigate numbers by engaging in activities which address the nature of different number forms, how different operations (addition, subtraction, multiplication, division) manipulate numbers, and which require the student to formulate analysis level questions.
| Strand |
Source |
| Number Forms |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Sense: Applying
The learner will be able to
apply knowledge of number values and counting to "non-mathematical" activities (such as making a calendar), and understand mathematical principles in terms of their real-world applications (and not as an isolated school subject).
| Strand |
Source |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Sense: Classification
The learner will be able to
understand and use numbers found in newspapers, magazines, menus, and cereal boxes, and classify numbers found in his/her world based on a specific set of criteria.
| Strand |
Source |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Sense: Decimals
The learner will be able to
demonstrate an intuitive sense of decimal number properties by converting decimals to fractions and percents, use models to express both the conversions and the proportions the decimals, fractions, and percents describe, and create number lines, graphs, models, and partially shaded figures which represent numbers in each of these forms.
| Strand |
Source |
| Number Sense |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Odd/Even: Exploring
The learner will be able to
study the patterns of odd and even numbers (avoiding memorization techniques).
| Strand |
Source |
| Odd/Even |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Numeration Unit focuses on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships.
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Counting: Order/Group
The learner will be able to
count, order, and group concrete objects.
| Strand |
Source |
| Counting |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.G |
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Numeration: Apply Place Value
The learner will be able to
apply the idea of place-value and numeration to counting, ordering, and grouping.
| Strand |
Source |
| Numeration |
PA: Academic Standards, January 16, 1999, Grade 3, p.3,2.1.3.I (back mapped) |
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Pattern: Identify/Describe/Continue
The learner will be able to
identify, describe, continue, and create and reproduce many different patterns including attribute, activity, number and geometric patterns.
| Strand |
Source |
| Patterns: Identify/Describe/Continue |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.A |
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Pattern: Apply
The learner will be able to
use number patterns including even and odd.
| Strand |
Source |
| Patterns: Number |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.F (back mapped) |
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Comparison: Numbers/Hundred Board
The learner will be able to
use the hundred board to compare values of numbers.
| Strand |
Source |
| Comparison |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.F (back mapped) |
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Skip Counting: 2,5,10
The learner will be able to
count up to 110 by 2's, 5's and 10's using whole numbers.
| Strand |
Source |
| Skip Counting |
PA: Academic Standards, January 16, 1999, Grade 3, p.2,2.1.3.A (back mapped) |
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Pattern: Extend
The learner will be able to
extend number or object patterns that can be infinitely continued.
| Strand |
Source |
| Patterns |
PA: Academic Standards, January 16, 1999, Grade 3, p.19,2.11.3.D (back mapped) |
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Estimation: Strategies
The learner will be able to
apply estimation strategies to arrive at conclusions.
| Strand |
Source |
| Estimation |
PA: Academic Standards, January 16, 1999, Grade 3, p.4,2.2.3.E (back mapped) |
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Counting: Number Sense
The learner will be able to
practice counting, skip counting, counting on, and back counting, to gain a strong sense of numbers and ordinality.
| Strand |
Source |
| Counting |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Estimating: Across the Curriculum
The learner will be able to
explore activities such as estimating the number of letters in the names of class members, organizing the estimated letters in groups of ones and tens, and comparing original estimates with the results.
| Strand |
Source |
| Estimation |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Estimating: Application
The learner will be able to
explore estimation strategies, determine situations in which estimation (as opposed to exact computation) is appropriate, evaluate the reasonableness of given estimations, and apply estimation strategies across the mathematics curriculum.
| Strand |
Source |
| Estimation |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Values: Applying
The learner will be able to
demonstrate an intuitive sense of numbers and their values by articulating the relationship between numbers (as elements of a given scenario) and the scenario itself.
| Strand |
Source |
| Number Values |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Values: Applying
The learner will be able to
describe how pictures, manipulatives, and diagrams relate to mathematical sentences, and use manipulatives and other aids to express the relative size of numbers.
| Strand |
Source |
| Number Values |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Values: Manipulatives
The learner will be able to
demonstrate a conceptualization of number values and how these values relate to each other by using manipulatives (articulating how adding or taking away specific manipulatives changes the quantity of the remaining manipulatives), and see numbers in terms of what they represent (in quantity, values, etc.) in context.
| Strand |
Source |
| Number Values |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Number Values: Number Sense
The learner will be able to
develop a sense of number values by drawing one to one correspondences, by sorting, classifying, and comparing numbers in science, games, and daily life, and by using language to describe number values (more, less, most, least, some, none, etc.).
| Strand |
Source |
| Number Values |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Numeration Systems
The learner will be able to
apply an understanding of the numeration system by making connections among counting, grouping, and place value concepts.
| Strand |
Source |
| Numeration |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Ordering/Values: Number Sense
The learner will be able to
demonstrate an intuitive sense of numbers, their values, and how they can logically be ordered by articulating the relationship between numbers (as elements of a given scenario) and the scenario itself, and by using manipulatives to describe the scenario.
| Strand |
Source |
| Comparing/Ordering |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Analyzing
The learner will be able to
create graphical forms to record and analyze patterns, including breaking patterns into terms, seeing each term as a part of the overall pattern, and organizing graphical forms to show patterns and terms effectively.
| Strand |
Source |
| Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Creating/Extending
The learner will be able to
create patterns, and extend patterns from one medium to another, in mathematics, language, science, and art.
| Strand |
Source |
| Patterns: Identify/Describe/Continue |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Exploring Relationships
The learner will be able to
analyze, describe, extend, and create patterns involving mathematical relationships.
| Strand |
Source |
| Patterns: Exploring |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Predicting
The learner will be able to
demonstrate an understanding of the repetitive nature of patterns by making predictions about events and shapes based on patterns.
| Strand |
Source |
| Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Predicting
The learner will be able to
recognize the repetitive nature of patterns and make predictions about events, shapes, and sets of numbers based on these repetitions.
| Strand |
Source |
| Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Problem Solving
The learner will be able to
solve problems by recognizing and extending pictorial, concrete, and numerical patterns.
| Strand |
Source |
| Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Recognizing
The learner will be able to
demonstrate an understanding of the predictability and repetition inherent in patterns, such as colors in pictures, action in songs or rhymes (clapping, stomping, jumping), symbols, nature (the four seasons), daily life (the green, yellow, red of traffic lights), and human behavior.
| Strand |
Source |
| Patterns: Identify/Describe/Continue |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Recognizing
The learner will be able to
identify patterns in action songs such as "Old McDonald Had a Farm," discuss the patterns in the songs, transfer the patterns to a geometry related medium, and substitute a specific number of cubes for each element of a pattern.
| Strand |
Source |
| Patterns: Identify/Describe/Continue |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Rules
The learner will be able to
conjecture about rules applicable to sets of three numbers.
| Strand |
Source |
| Patterns: Determining Rules |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Pattern: Searching
The learner will be able to
search for possible patterns in an organized and systematic way.
| Strand |
Source |
| Patterns |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Probability/Statistics Unit focuses on data analysis and probability concepts. This unit includes collecting, analyzing, and making sense of real-world data (including overlapping data, inconclusive data, etc.).
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Chance: Predicting
The learner will be able to
make predictions regarding the outcomes of events by applying concepts of chance.
| Strand |
Source |
| Chance |
PA: Academic Standards, January 16, 1999, Grade 3, p.11,2.7.3.A (back mapped) |
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Experiments: Understanding Results
The learner will be able to
understand that the outcomes of experiments may not be the same as earlier predictions.
| Strand |
Source |
| Experiments |
PA: Academic Standards, January 16, 1999, Grade 3, p.11,2.7.3.A (back mapped) |
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Experiments: List/Graph
The learner will be able to
list or graph the possible outcomes of an experiment.
| Strand |
Source |
| Experiments |
PA: Academic Standards, January 16, 1999, Grade 3, p.11,2.7.3.C (back mapped) |
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Communicating: Complex Ideas
The learner will be able to
communicate complex ideas effectively by providing visual or condensed representation of an idea and explaining the mathematical concepts involved.
| Strand |
Source |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Communicating: Pictograms
The learner will be able to
create pictograms which convey information such as the following about the class: how much milk did the class drink in one week, how many hours were spent sleeping by the entire class in one week, etc.
| Strand |
Source |
| Communicating |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data Analysis: Conclusions
The learner will be able to
collect data, organize the collected data, and create a display which explains the data and conclusions which can be drawn from the data.
| Strand |
Source |
| Data Analysis |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data Analysis: Projects
The learner will be able to
demonstrate the ability to make sense of data by engaging in projects which include the following steps: deciding on topics of interest, developing research objectives, collecting and organizing data, and creating graphical forms to communicate findings to others.
| Strand |
Source |
| Data Analysis |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data Analysis: Solutions
The learner will be able to
listen to a given real-world scenario problem involving probability and statistics, describe the problem the scenario presents, formulate a hypothesis, collect the necessary data, create graphs to organize the collected data, and refer to the graphs to make predictions about how the problem can be solved.
| Strand |
Source |
| Data Analysis |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data Management: Categorizing Objects
The learner will be able to
categorize objects (e.g., books) by one criteria, such as size, and then use the same books to categorize them using another set of criteria, such as weight.
| Strand |
Source |
| Data Management |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data Management: Taking Inventory
The learner will be able to
take an inventory of desks, chairs, books, toys, tables, and/or chairs in the classroom, develop an organizational format for keeping track of the data, and count one or each of these categories (using a calculator if necessary), and report findings in some way.
| Strand |
Source |
| Data Management |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data: Comparing
The learner will be able to
describe how two objects (e.g., two books) are the same and are different, and (with the teacher's help) develop the criteria for difference and similarity.
| Strand |
Source |
| Data |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data: Overlapping
The learner will be able to
extend organizational skills to deal with overlapping data.
| Strand |
Source |
| Data |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data: Problem Analysis
The learner will be able to
listen to a given real-world scenario problem involving probability and statistics, describe the problem the scenario presents, collect or list the necessary data, and refer to the data to make predictions about how the problem can be solved.
| Strand |
Source |
| Data |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Data: Unclear
The learner will be able to
deal with real-world problems which don't have clear cut answers, including adding outlying data to graphs or diagrams which represent conclusions.
| Strand |
Source |
| Data |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Experiments: Designing
The learner will be able to
create and carry out appropriate experiments to find the probability of a given event (when the event is given, but the details of how to develop and carry out an experiment which proves probability are not).
| Strand |
Source |
| Experiments |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Experiments: Designing
The learner will be able to
conduct an independent experiment which requires posing questions, collecting data, organizing the data, and reporting on findings.
| Strand |
Source |
| Experiments |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Making Sense of Data
The learner will be able to
apply an understanding of data as a set of information, and how to collect, organize, and describe data by formulating and solving problems.
| Strand |
Source |
| Data |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Application
The learner will be able to
listen to a given real-world scenario problem involving probability and statistics, describe the problem the scenario presents, formulate a hypothesis, collect the necessary data, create graphs to organize the collected data, refer to the graphs to make predictions about how the problem can be solved, and present solutions both in written paragraph form and in a graphical form.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Problem Solving Unit focuses on the problem solving effort. This unit includes analyzing problems, evaluating solutions, problem exploration, and strategies.
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Solution: Communicate Process
The learner will be able to
communicate the mathematical processes used to solve a problem.
| Strand |
Source |
| Solution |
PA: Academic Standards, January 16, 1999, Grade 3, p.8,2.5.3.B (back mapped) |
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Word Problem: Create
The learner will be able to
formulate a story to match a given combination of symbols and numbers.
| Strand |
Source |
| Word Problems |
PA: Academic Standards, January 16, 1999, Grade 3, p.13,2.8.3.D (back mapped) |
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Evaluating Solutions: Reasoning
The learner will be able to
develop the ability to use models, technology (computers, calculators), and knowledge of number forms, operations, and systems to justify solutions and/or methods for finding a solution, and view mathematical properties as ways of explaining real-world phenomena logically.
| Strand |
Source |
| Evaluating Solutions |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Mathematical Principles
The learner will be able to
use principles of mathematics to solve problems, to investigate, verify, and justify solutions to problems, to formulate problems for mathematical situations, and to develop the confidence required to apply principles of mathematics in real-world contexts.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Using Tools
The learner will be able to
use language, diagrams, and technology (computers, calculators) to solve basic problems.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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The Whole Numbers Unit includes performing operations with whole numbers, using manipulatives to demonstrate whole number concepts, and solving problems with whole numbers in real-world contexts.
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Division: Sharing
The learner will be able to
illustrate the idea of division as sharing.
| Strand |
Source |
| Divide Whole Numbers |
PA: Academic Standards, January 16, 1999, Grade 3, p.4,2.2.3.D (back mapped) |
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Whole Numbers: Quantities
The learner will be able to
determine whole number quantities and measurements from least to most and greatest value.
| Strand |
Source |
| Whole Numbers |
PA: Academic Standards, January 16, 1999, Grade 3, p.19,2.11.3.A |
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Operations: Addition/Subtraction Facts
The learner will be able to
use manipulatives to explore addition and subtraction.
| Strand |
Source |
| Operations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Operations: Analyzing
The learner will be able to
understand whole number operations (addition, subtraction, multiplication, and division) as methods for solving real-world problems, and use manipulatives to solve problems.
| Strand |
Source |
| Operations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Operations: Solution Methods
The learner will be able to
understand whole number operations as methods for solving real-world problems, and use manipulatives and calculators to solve problems.
| Strand |
Source |
| Operations |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Real-World Scenarios
The learner will be able to
solve problems presented in real-world scenarios, including identifying the problem, breaking down the elements of the problem, determining the operation (addition, subtraction, multiplication, and division), setting up the correct number sentence or set of manipulatives, and solving the problem.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Real-World Scenarios
The learner will be able to
solve real-world whole number problems by determining the operation required (addition, subtraction, multiplication, division), setting up the correct number sentence, solving the problem, and using inverse operations to check the solution.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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Problem Solving: Representation
The learner will be able to
focus on the values, proportions, and/or quantities which the whole numbers in real-world mathematical problems represent, without viewing numbers and operations in problems as isolated figures and steps.
| Strand |
Source |
| Problem Solving |
National Council of Teachers of Mathematics (NCTM), March, 1989, Fourth Grade |
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