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Dallas School District
K-12 Curriculum
Elementary Mathematics - Grade 1
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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 |
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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 |
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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 |
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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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Algorithms: Describe/Add/Subtract
The learner will be able to
describe addition and subtraction algorithms with regrouping.
| Strand |
Source |
| Algorithms |
PA: Academic Standards, January 16, 1999, Grade 3, p.4,2.2.3.G (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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Inverse Operations: Add/Subtract
The learner will be able to
explain the inverse relationship that exists between addition and subtraction.
| Strand |
Source |
| Inverse Operations |
PA: Academic Standards, January 16, 1999, Grade 3, p.3,2.1.3.K |
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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 |
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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 geometric figures.
| Strand |
Source |
| Figures: Identify |
PA: Academic Standards, January 16, 1999, Grade 3, p.16,2.9.3.A |
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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 |
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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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Figures: Construct/Graph Paper
The learner will be able to
construct rectangles, squares and triangles on graph paper using 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.
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