Number Properties and Operations

Big Idea: Number Properties and Operations
Whole number sense and addition and subtraction are key concepts and skills developed in early
childhood. Students build on their number sense and counting sense to develop multiplication and
division. They move flexibly and fluently through basic number facts, operations and representations.
Their understanding of the base-10 number system expands to include decimals. They examine various
meanings and models of fractions. They explore data, perform measurements and examine patterns as
part of the development process for number and operations, using other mathematics strands to enrich
number. Elementary number encompasses computational fluency with whole numbers, relationships
between decimals and fractions and techniques for reasonable estimations.
Academic Expectations
2.7 Students understand number concepts and use numbers appropriately and accurately.
2.8 Students understand various mathematical procedures and use them appropriately and accurately.
Primary Enduring Knowledge – Understandings
Students will understand that
• numbers, ways of representing numbers, relationships between numbers and number systems
are means of representing real-world quantities.
• meanings of and relationships among operations provide tools necessary to solve realistic
problems encountered in everyday life.
• computing fluently and making reasonable estimates increases the ability to solve realistic
problems encountered in everyday life.
Primary Skills and Concepts – Number Sense
Students will
• read, write, count and model whole numbers 0-10,000, developing an understanding of place
value for ones, tens, hundreds, thousands and ten thousands
• apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines,
expanded form, symbols) to describe and compare whole numbers and fractions (e.g., halves,
thirds, fourths) in mathematical and real-world problems
• order groups of objects according to quantity
• order, compare and understand the relative magnitude of numbers from 0-10,000, using the
symbols <, >, =, including the use of physical and visual models for smaller numbers
• develop beginning fractional concepts (e.g., dividing an object into equal parts and naming the
equal parts [e.g., halves, thirds, fourths])
• expand fraction concepts (e.g., whole to part and part to whole; one-half is larger than one-fourth)
• be introduced to and use decimals to represent money
Kentucky Department of Education
Program of Studies – Mathematics – Primary 38
Big Idea: Number Properties and Operations – Continued
Primary Skills and Concepts – Estimation
Students will
• explore appropriate estimation procedures for different situations
• apply and describe appropriate strategies for estimating quantities of objects and computational
results
Primary Skills and Concepts – Number Operations
Students will
• develop an understanding of the concepts of addition and subtraction using physical objects and
concrete materials
• explore and develop an understanding of the concepts of multiplication and division using
physical models
• develop part-whole relations using numbers (e.g., 3+2=5, 1+4=5)
• explore and solve two-digit addition and subtraction problems through the use of manipulatives
• explore and develop factor-factor-product (e.g., 2x3=6) using manipulatives. (e.g., hundreds
charts, base-10 blocks, arrays)
• multiply whole numbers through 10 x 10
• relate division facts to multiplication facts (e.g., using factor-factor-product)
• solve multi-digit addition and subtraction problems that contain numerals and symbols
• add common fractions with like denominators using manipulatives
• add and subtract decimals using money
• use mental math, pencil-and-paper methods, calculators and/or computers to explore
mathematical concepts and to assist with computation in problem solving situations
Primary Skills and Concepts – Properties of Numbers and Operations
Students will
• explore, develop and use the concepts of multiples
• skip-count forwards and backwards by 2s, 5s, 10s and 100s, using manipulatives, mental math
and written and electronic means to communicate understanding
• explore, develop and use the concepts of odd and even numbers
• explore and use of properties of numbers for written and mental computation (e.g., 4+7+6 could
be mentally regrouped as 4+6+7 using the commutative property of addition)

Measurement

Students translate from measuring using nonstandard units to using standard units of measurement.
They identify measurable attributes of objects, estimate and measure weight, length, perimeter, area,
angles, temperature, time and money. They convert units within the same measurement system.
Academic Expectations
2.10 Students understand measurement concepts and use measurements appropriately and accurately.
2.11 Students understand mathematical change concepts and use them appropriately and accurately.
Primary Enduring Knowledge – Understandings
Students will understand that
• measurable attributes of objects and the units, systems and processes of measurement are
powerful tools for making sense of the world around them.
• measurements are determined by using appropriate techniques, tools and formulas.
• for each situation, there is an appropriate degree of accuracy in measurement.
Primary Skills and Concepts – Measuring Physical Attributes
Students will
• apply standard units to measure length (inches and centimeters), weight (pounds), time (hours,
half-hours, quarter-hours, five- and one-minute intervals), money (coins and bills) and
temperature (Fahrenheit and Celsius)
• use nonstandard units to measure and compare the length, weight, area or volume of familiar
objects
• use standard units of measurement to identify, describe and compare measurable attributes of
objects (e.g., length, weight, volume) and make estimates using appropriate units of
measurement
• choose and use appropriate tools for specific measurement tasks
• sort/classify or compare and order objects by shape, size and color (e.g., attribute blocks)
• estimate weight, length, perimeter, area, angle and time using appropriate units of measurement
• explore concepts of perimeter and area of rectangles using manipulatives
• identify, compare and order amounts of money using coins and bills and use correct symbols for
money
• combine coins and bills to make a given amount and make change up to a dollar
• relate time to daily activities, tell time to the hour, half-hour, quarter-hour, five minutes and one
minute and determine elapsed time
Primary Skills and Concepts – Systems of Measurement
Students will
• determine equivalent U.S. customary measurements
• describe, define, give examples of and use to solve real-world and/or mathematical problems
both nonstandard and standard (U.S. Customary, metric) units of measurement to include length,
time, money, temperature (Fahrenheit and Celsius) and weight

Geometry

Students explore and find basic geometric elements and terms, two-dimensional shapes and threedimensional
objects. They find and use symmetry. They move two-dimensional figures in a plane and
explore congruent and similar figures.
Academic Expectation
2.8 Students understand various mathematical procedures and use them appropriately and accurately.
2.9 Students understand space and dimensionality concepts and use them appropriately and accurately.
Primary Enduring Knowledge – Understandings
Students will understand that
• characteristics and properties of two-dimensional figures and three-dimensional objects describe
the world and are used to develop mathematical arguments about geometric relationships and to
evaluate the arguments of others.
• representational systems, including coordinate geometry, are means for specifying locations and
describing spatial relationships and are organizers for making sense of the world around them.
• transformations and symmetry are used to analyze real-world situations (e.g., art, nature,
construction and scientific exploration).
• visualization, spatial reasoning and geometric relationships model real-world situations.
Primary Skills and Concepts – Shapes and Relationships
Students will
• identify, describe, model, draw, compare and classify two-dimensional figures and threedimensional
objects using elements, attributes and properties
• explore the relationships among two-dimensional figures and three-dimensional objects (e.g.,
using virtual manipulatives)
• identify and describe congruent figures in real-world and/or mathematical situations
• investigate and solve real-world problems using the elements, attributes and properties of basic
two-dimensional figures and three-dimensional objects
• identify, draw and represent line segments and angles
• determine if simple shapes are congruent
Primary Skills and Concepts – Transformations of Shapes
Students will
• determine lines of symmetry in simple shapes and identify and describe symmetrical twodimensional
figures
• examine examples of line symmetry in real-world situations and apply one line of symmetry to
construct simple geometric designs, using graphic, technological or concrete
models/manipulatives to communicate understanding
• explore flips, slides and turns with physical models
• identify images from flips (reflections), slides (translations) and turns (rotations) in a plane
Primary Skills and Concepts – Coordinate Geometry
Students will
• locate points and figures on a grid representing a positive coordinate system

Data Analysis and Probability

Students pose questions, plan and collect data, organize and display data and interpret displays of data.
They generate outcomes for simple probability activities, determine fairness of probability games and
explore likely and unlikely events.
Academic Expectations
2.7 Students understand number concepts and use numbers appropriately and accurately.
2.8 Students understand various mathematical procedures and use them appropriately and accurately.
2.13 Students understand and appropriately use statistics and probability.
Primary Enduring Knowledge – Understandings
Students will understand that
• quantitative literacy is a necessary tool to be an intelligent consumer and citizen.
• the collection, organization, interpretation and display of data can be used to answer questions.
• the choice of data display can affect the visual message communicated.
• inferences and predictions from data are used to make critical and informed decisions.
• probability can be used to make decisions or predictions or to draw conclusions.
Primary Skills and Concepts – Data Representations
Students will
• make a graph using concrete manipulatives and read data displayed on a concrete graph
• display, read and compare data on student-invented graphs
• read, display, compare and interpret student-collected data
• display, read and compare data on a pictograph and bar graph
• display data in line plots
• analyze and make inferences from data displays (drawings, tables/charts, tally tables,
pictographs, bar graphs, circle graphs, line plots, two-circle Venn diagrams)
• use technology to organize and display data collected from student investigations
Primary Skills and Concepts – Experiments and Samples
Students will
• pose questions to generate data
• use data from student investigations to make predictions or draw simple conclusions
• use tools (including technology when appropriate) to organize and display student-collected data
Primary Skills and Concepts – Probability
Students will
• explore chance through games and events
• compare likely and unlikely outcomes
• explore basic concepts of probability through simple experiments

Algebraic Thinking

Students explore and examine patterns and develop rules to go with patterns. They generate input-output
for functions and create tables to analyze functions. Students use number sentences with missing values.
Academic Expectations
2.8 Students understand various mathematical procedures and use them appropriately and accurately.
2.11 Students understand mathematical change concepts and use them appropriately and accurately.
2.12 Students understand mathematical structure concepts including the properties and logic of various
mathematical systems.
Primary Enduring Knowledge – Understandings
Students will understand that
• patterns, relations and functions are tools that help explain or predict real-world phenomena.
• numerical patterns can be written as rules that generate the pattern.
• algebra represents mathematical situations and structures for analysis and problem solving (e.g.,
finding the missing value in open sentences).
• real-world situations can be represented using mathematical models to analyze quantitative
relationships.
• functions are used to analyze change in various contexts and model real-world phenomena.
Primary Skills and Concepts – Patterns, Relations and Functions
Students will
• identify and describe patterns in real life and in numerical and geometric situations
• reproduce and extend patterns using manipulatives
• use pictures or words to create, reproduce, extend and explain patterns of shapes, objects,
movements, sounds and numbers
• recognize and extend simple number patterns
• explore input-output machines (e.g., function machines) and solve simple function machine tasks
• use calculators to explore how constant addition produces a pattern and can be expressed as a
rule for a pattern
Primary Skills and Concepts – Variables, Expressions and Operations
Students will
• explore unknowns and open sentences to express relationships
• create stories about mathematical sentences with missing values
Primary Skills and Concepts – Equations and Inequalities
Students will
• solve simple equations (e.g., 1 + 1 = [ ]; [ ] - 2 = 7)
• solve simple inequalities (e.g., [ ] < 6)
• solve for unknowns in simple open sentences
• read and create story problems to represent mathematical sentences with missing values
• use manipulatives, numbers and/or symbols to model real-world situations with simple number
sentences