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