Grade Three Mathematics Expectations

Mathematics Standard 1: Numbers and Operations

Students will demonstrate the ability to:

Whole numbers 0-999

  • Find equivalent representations for the same number
  • Use models, explanations, or other representations to represent place value to the thousands place
  • Order and compare numbers (ordinal and cardinal)
  • Compare whole numbers to landmark numbers (e.g., 100, 250, 500, 1,000)
  • Show the relationship between whole numbers
  • Compose and decompose (e.g., 34 = 17+17; 34 = 29+5; 34 = 30+4)
  • Connect number words and numerals to the quantities they represent

Fractional numbers

  • Represent common fractions, such as halves, thirds, fourths, sixths, and eighths
  • Represent a fraction as part of a whole (i.e., fraction of a set, fraction of an area)
  • Compare or identify equivalent positive fractional numbers (e.g., a/2, a/3, a/4 where a is a whole number greater than 0 and less than or equal to the denominator)
  • Use models, number lines, or explanations

Decimal numbers

  • Represent decimals as part of 100 (within the context of money)

Operations

  • Use addition or subtraction of positive fractional numbers with like denominators
  • Use addition or subtraction of decimals
  • Describe or illustrate the inverse relationship between addition and subtraction or multiplication and division
  • Describe the relationship between repeated addition and multiplication using models, number lines, or explanations
  • accurately solves problems involving addition and subtraction using algorithm as one method with regrouping

Computation Fluency and Estimation

  • Develop fluency in adding, subtracting, multiplying and dividing whole numbers
  • Develop and use strategies to estimate the results of whole number computations

Mathematics Standard 2: Algebra

Students will demonstrate the ability to:

Patterns, Relationships, and Functions

  • Identify specific cases of a variety of patterns both linear and non-numeric, represented in models, tables, words, graphs or sequences by extending the pattern to the next one, two, or three elements, or finding missing elements (geometric and numeric patterns

Algebraic Symbols

  • Show the equality between two expressions using models or different representations of the expressions or by finding the value that will make an open sentence true (e.g., 2 + _ = 7) using one operation with addition, subtraction or multiplication
  • solve mathematical problems to show relationships with equations

Mathematical Models

  • Model problem situations with objects and use graphs, tables, equations to draw conclusions

Analysis of Change

  • Introduce how a change in one variable relates to a change in a second variable
  • Identify, describe, and/or compare situations that represent constant rates of change

Mathematics Standard 3: Geometry

Students will demonstrate the ability to:

Geometric Shapes

  • Identify, compare, and analyze attributes or properties of angles (i.e., number of angles) or sides (i.e., number of sides or length of sides) of two and three-dimensional shapes
  • Develop vocabulary to describe attributes and define classes of shapes such as triangles and pyramids
  • Use composition or decomposition of shapes to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or circles demonstrate congruence and similarity of shapes

Spatial Relationships

  • Apply coordinate systems to specify locations and to describe paths
  • Find location on a coordinate grid using positional words or compass directions interpret and give directions from one location to another using positional words

Transformations and Symmetry

  • Predict and describe the results of sliding, flipping, and turning two-dimensional shapes
  • Determine if two-plane figures are congruent by matching
  • identify line (mirror) symmetry in two-dimensional models

Problem Solving

  • Build, compare, copy, and draw geometric objects such as triangles, squares, rectangles, rhombi, trapezoids, hexagons, and circles
  • Describe and create mental images of objects, patterns, and paths
  • Identify and build models of rectangular prisms from three-dimensional representations
  • Use geometric models to solve problems in other areas or disciplines

Mathematics Standard 4: Measurement

Students will demonstrate the ability to:

Units, Systems, and Processes of Measurement

  • Compute perimeter of polygons
  • Draw the area of rectangles on grids using a variety of models Express all measures using appropriate units
  • Measure length, weight, and volume and select an appropriate type of unit for measuring
  • Measure with standard units in the customary system
  • Carry out simple unit conversions when solving problems across content strands use units of measures appropriately and consistent

Determining Measurement

  • Estimate perimeters, area, and volumes of irregular shapes (benchmarks: quart to whole quart; kilogram to whole kilogram; gram to whole gram; pound to whole pound)
  • Apply appropriate standard units and tools to measure length, area, volume, time, and temperature (benchmarks: hour to 5 minute interval; day; year; 24 hours in 1 day 7 days in 1 week; 365 days in 1 year; C degrees and F degrees to 1 degree)
  • Use benchmarks to estimate measurements (benchmarks: inch to ½ inch; foot to whole inch; centimeter to whole centimeter; meter to whole centimeter)
  • Use formulas to find the area of a rectangle
  • analyze the parts of rectangular solids

Mathematics Standard 5: Data Analysis and Probability

Students will demonstrate the ability to:

Formulation of Questions

  • Interpret a given representation such as line plots, tally charts, tables, line graphs, or bar graphs to answer questions related to the data (Up and Down the Number Line, Inv. 2; Things That Come in Groups, Inv. 5)
  • Collect data using observations, surveys and experiments
  • Recognize the differences in representing categorical and numerical data
  • formulate a question and develop a plan to collect information to address the question
  • Answer questions related to the data

Analysis of Data

  • Analyze patterns, trends or distributions in data in a variety of contexts by determining or using most frequent (mode), least frequent, largest, or smallest
  • Identify or describe representations or elements of representations that best display a given set of data or situation using line plots, tally charts, tables or bar graphs
  • Compare different representations of the same data and evaluate how well each representation shows important aspects of the data

Inferences and Predictions

  • Make and justify predictions that are based on data
  • analyze data to formulate conclusions or to make predictions