MST Standard 3 Math:
Grade 3
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Through the integrated study of number sense and operations, algebra, geometry, measurement,
and statistics and probability, students will:
- understand the concepts of and become proficient with the skills of mathematics;
- communicate and reason mathematically;
- become problem solvers by using appropriate tools and strategies;
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Algebra
Students will perform algebraic procedures accurately.
Equations and Inequalities
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3.A.1 |
Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers and unit fractions (1/2, 1/3, 1/4, 1/5, 1/6, and 1/10)
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Algebra
Students will recognize, use, and represent algebraically patterns, relations, and functions.
Patterns, Relations, and Functions
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3.A.2 |
Describe and extend numeric (+, -) and geometric patterns
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Communication
Students will organize and consolidate their mathematical thinking through communication.
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3.CM.1 |
Understand and explain how to organize their thought process
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3.CM.2 |
Verbally explain their rationale for strategy selection
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3.CM.3 |
Provide reasoning both in written and verbal form
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Communication
Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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3.CM.4 |
Organize and accurately label work
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3.CM.5 |
Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form
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3.CM.6 |
Answer clarifying questions from others
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Communication
Students will analyze and evaluate the mathematical thinking and strategies of others.
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3.CM.7 |
Listen for understanding of mathematical solutions shared by other students
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3.CM.8 |
Consider strategies used and solutions found in relation to their own work
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Communication
Students will use the language of mathematics to express mathematical ideas precisely.
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3.CM.9 |
Increase their use of mathematical vocabulary and language when communicating with others
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3.CM.10 |
Describe objects, relationships, solutions and rationale using appropriate vocabulary
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3.CM.11 |
Decode and comprehend mathematical visuals and symbols to construct meaning
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Connections
Students will recognize and use connections among mathematical ideas.
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3.CN.2 |
Compare and contrast mathematical ideas
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3.CN.3 |
Connect and apply mathematical information to solve problems
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3.CN.1 |
Recognize, understand, and make connections in their everyday experiences to mathematical ideas
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Connections
Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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3.CN.4 |
Understand multiple representations and how they are related
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3.CN.5 |
Model situations with objects and representations and be able to make observations
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Connections
Students will recognize and apply mathematics in contexts outside of mathematics.
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3.CN.6 |
Recognize the presence of mathematics in their daily lives
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3.CN.7 |
Apply mathematics to solve problems that develop outside of mathematics
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3.CN.8 |
Recognize and apply mathematics to other disciplines
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Geometry
Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
Shapes
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3.G.3 |
Name, describe, compare, and sort three-dimensional shapes: cube, cylinder, sphere, prism, and cone
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3.G.4 |
Identify the faces on a three-dimensional shape as two-dimensional shapes
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3.G.1 |
Define and use correct terminology when referring to shapes (circle, triangle, square, rectangle, rhombus, trapezoid, and hexagon)
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3.G.2 |
Identify congruent and similar figures
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Geometry
Students will apply transformations and symmetry to analyze problem solving situations.
Transformational Geometry
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3.G.5 |
Identify and construct lines of symmetry
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Measurement
Students will determine what can be measured and how, using appropriate methods and formulas.
Units of Measurement
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3.M.5 |
Compare capacities (e.g., Which contains more? Which contains less?)
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3.M.6 |
Measure capacity, using cups, pints, quarts, and gallons
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3.M.4 |
Recognize capacity as an attribute that can be measured
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3.M.1 |
Select tools and units (customary) appropriate for the length measured
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3.M.2 |
Use a ruler/yardstick to measure to the nearest standard unit (whole and ½ inches, whole feet, and whole yards)
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3.M.3 |
Measure objects, using ounces and pounds
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Measurement
Students will use units to give meaning to measurements.
Units
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3.M.8 |
Relate unit fractions to the face of the clock:Whole = 60 minutes½ = 30 minutes¼ = 15 minutes
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3.M.7 |
Count and represent combined coins and dollars, using currency symbols ($0.00)
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Measurement
Students will develop strategies for estimating measurements.
Estimation
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3.M.10 |
Select and use standard (customary) and non-standard units to estimate measurements
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3.M.9 |
Tell time to the minute, using digital and analog clocks
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Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Systems
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3.N.3 |
Compare and order numbers to 1,000
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3.N.4 |
Understand the place value structure of the base ten number system: 10 ones = 1 ten 10 tens = 1 hundred 10 hundreds = 1 thousand
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3.N.5 |
Use a variety of strategies to compose and decompose three-digit numbers
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3.N.6 |
Use and explain the commutative property of addition and multiplication
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3.N.7 |
Use 1 as the identity element for multiplication
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3.N.8 |
Use the zero property of multiplication
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3.N.9 |
Understand and use the associative property of addition
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3.N.10 |
Develop an understanding of fractions as part of a whole unit and as parts of a collection
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3.N.15 |
Compare and order unit fractions (½, ⅓, ¼) and find their approximate locations on a number line
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3.N.14 |
Explore equivalent fractions (½, ⅓, ¼)
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3.N.13 |
Recognize fractional numbers as equal parts of a whole
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3.N.1 |
Skip count by 25's, 50's, 100's to 1,000
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3.N.2 |
Read and write whole numbers to 1,000
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3.N.12 |
Understand and recognize the meaning of numerator and denominator in the symbolic form of a fraction
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3.N.11 |
Use manipulatives, visual models, and illustrations to name and represent unit fractions (1/2, 1/3, 1/4, 1/5, 1/6, and 1/10) as part of a whole or a set of objects
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Number Sense and Operations
Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
Number Theory
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3.N.17 |
Develop an understanding of the properties of odd/even numbers as a result of addition or subtraction
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3.N.16 |
Identify odd and even numbers
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Number Sense and Operations
Students will understand meanings of operations and procedures, and how they relate to one another.
Operations
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3.N.20 |
Use a variety of strategies to solve multiplication problems with factors up to 12 x 12
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3.N.21 |
Use the area model, tables, patterns, arrays, and doubling to provide meaning for multiplication
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3.N.22 |
Demonstrate fluency and apply single-digit division facts
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3.N.23 |
Use tables, patterns, halving, and manipulatives to provide meaning for division
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3.N.24 |
Develop strategies for selecting the appropriate computational and operational method in problem solving situations
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3.N.19 |
Develop fluency with single-digit multiplication facts
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3.N.18 |
Use a variety of strategies to add and subtract 3-digit numbers (with and without regrouping)
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Number Sense and Operations
Students will compute accurately and make reasonable estimates.
Estimation
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3.N.27 |
Check reasonableness of an answer by using estimation
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3.N.25 |
Estimate numbers up to 500
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3.N.26 |
Recognize real world situations in which an estimate (rounding) is more appropriate
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Problem Solving
Students will build new mathematical knowledge through problem solving.
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3.PS.3 |
Interpret information correctly, identify the problem, and generate possible solutions
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3.PS.2 |
Understand that some ways of representing a problem are more helpful than others
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3.PS.1 |
Explore, examine, and make observations about a social problem or mathematical situation
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Problem Solving
Students will solve problems that arise in mathematics and in other contexts.
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3.PS.8 |
Select an appropriate representation of a problem
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3.PS.7 |
Represent problem situations in oral, written, concrete, pictorial, and graphical forms
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3.PS.6 |
Translate from a picture/diagram to a numeric expression
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3.PS.5 |
Formulate problems and solutions from everyday situations
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3.PS.4 |
Act out or model with manipulatives activities involving mathematical content from literature
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Problem Solving
Students will apply and adapt a variety of appropriate strategies to solve problems.
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3.PS.11 |
Make pictures/diagrams of problems
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3.PS.12 |
Use physical objects to model problems
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3.PS.13 |
Work in collaboration with others to solve problems
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3.PS.14 |
Make organized lists to solve numerical problems
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3.PS.15 |
Make charts to solve numerical problems
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3.PS.16 |
Analyze problems by identifying relationships
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3.PS.17 |
Analyze problems by identifying relevant versus irrelevant information
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3.PS.18 |
Analyze problems by observing patterns
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3.PS.19 |
State a problem in their own words
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3.PS.10 |
Use process of elimination to solve problems
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3.PS.9 |
Use trial and error to solve problems
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Problem Solving
Students will monitor and reflect on the process of mathematical problem solving.
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3.PS.21 |
Discuss with peers to understand a problem situation
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3.PS.22 |
Discuss the efficiency of different representations of a problem
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3.PS.23 |
Verify results of a problem
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3.PS.24 |
Recognize invalid approaches
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3.PS.25 |
Determine whether a solution is reasonable in the context of the original problem
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3.PS.20 |
Determine what information is needed to solve a problem
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Reasoning and Proof
Students will recognize reasoning and proof as fundamental aspects of mathematics.
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3.RP.1 |
Use representations to support mathematical ideas
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3.RP.2 |
Determine whether a mathematical statement is true or false and explain why
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Reasoning and Proof
Students will make and investigate mathematical conjectures.
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3.RP.4 |
Make conjectures from a variety of representations
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3.RP.3 |
Investigate the use of knowledgeable guessing by generalizing mathematical ideas
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Reasoning and Proof
Students will develop and evaluate mathematical arguments and proofs.
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3.RP.5 |
Justify general claims or conjectures, using manipulatives, models, and expressions
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3.RP.6 |
Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms
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3.RP.7 |
Discuss, listen, and make comments that support or reject claims made by other students
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Reasoning and Proof
Students will select and use various types of reasoning and methods of proof.
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3.RP.8 |
Support an argument by trying many cases
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Representation
Students will create and use representations to organize, record, and communicate mathematical ideas.
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3.R.1 |
Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations
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3.R.2 |
Share mental images of mathematical ideas and understandings
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3.R.3 |
Recognize and use external mathematical representations
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3.R.4 |
Use standard and nonstandard representations with accuracy and detail
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Representation
Students will select, apply, and translate among mathematical representations to solve problems.
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3.R.7 |
Construct effective representations to solve problems
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3.R.5 |
Understand similarities and differences in representations
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3.R.6 |
Connect mathematical representations with problem solving
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Representation
Students will use representations to model and interpret physical, social, and mathematical phenomena.
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3.R.8 |
Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)
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3.R.9 |
Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip)
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3.R.10 |
Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)
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Statistics and Probability
Students will collect, organize, display, and analyze data.
Collection of Data
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3.S.2 |
Collect data using observation and surveys, and record appropriately
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3.S.1 |
Formulate questions about themselves and their surroundings
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Statistics and Probability
Students will collect, organize, display, and analyze data.
Organization and Display of Data
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3.S.6 |
State the relationships between pictographs and bar graphs
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3.S.5 |
Display data in pictographs and bar graphs
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3.S.4 |
Identify the parts of pictographs and bar graphs
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3.S.3 |
Construct a frequency table to represent a collection of data
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Statistics and Probability
Students will collect, organize, display, and analyze data.
Analysis of Data
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3.S.7 |
Read and interpret data in bar graphs and pictographs
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Statistics and Probability
Students will make predictions that are based upon data analysis.
Predictions from Data
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3.S.8 |
Formulate conclusions and make predictions from graphs
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