# Mathematics

## General  Math Goals

The student will:

• compute efficiently and accurately (add, subtract, multiply, and divide).
• recognize and accurately use various units of time, money, and measurement.
• communicate mathematical concepts in verbal and written form.
• develop skills in estimation.
• logically interpret and solve word problems using various strategies while developing higher level thinking skills.
• demonstrate proficiency in reading, writing, and interpreting graphs and tables.
• identify and measure geometric figures.
• recognize, write, and solve simple and complex expressions and equations.
• demonstrate proficiency in recognizing and utilizing algebraic concepts, structure and method.

Kindergarten

The student will:

•  understand and apply the meaning of numbers.
• count by 1’s to 100; count by 5’s to 50; and count by 10’s to 100
• recognize the value of numbers to 100 (matches the number of objects in a group to the correct numeral
• write numbers to 100
• demonstrate how many objects are left when part of the group is taken away
• model situations that involve whole numbers using pictures, objects, or symbols
• apply geometric terms, spatial relationships, and measurement
• identify, draw, sort, and classify two-dimensional shapes (circle, square, triangle, rectangle)
• identify three-dimensional shapes (cone, cylinder, cube, sphere)
• compare the length of two objects
• measure with multiple copies of a unit of the same size
• identify time to the nearest hour and half hour on the clock
• identify whole and half
• collect, display, and interpret data
• interpret simple graphs
• organize data in graphs
• represent data using physical objects
• recognize and create patterns
• recognize and explain a pattern
• extend a pattern
• create a pattern
• express numbers in different forms
• identify and know the value of a penny, nickel, dime, and quarter
• count, order, compare, and organize objects and numbers
• explain the meaning of positional words: inside, outside, over, under, on, behind, and beside
• determine the top, middle, bottom, left, and right of an object
• explain the meaning of same and different
• compare sets to determine more, less, or equal
• determine ordinal position of an object (first through tenth)
• arrange objects by size
• sort and classify objects by various attributes
• identify own sorting rule
• sequence pictures of events correctly

The student will:

•  Recognize and solve problems using a variety of strategies (Problem Solving)
• Restate a problem in own words
• Devise own plan to solve a problem
• Justify or explain own solution
• Solves one step word problems
• Communicate mathematical ideas orally, in writing, with pictures, and with objects (Communication)
• Use mathematical reasoning to draw conclusions and to explain and justify solutions (Reasoning)
• Use mathematics in other subject areas and in real world situations (Connections)
• Understand and apply the meaning of numbers (Number Sense)
• Count by ones to 400
• Count by twos to 100
• Count by fives to 100
• Count by tens to 400
• Touch count to 50
• Match the number of objects or pictures
• Illustrate addition facts (through sums of 20) using objects or pictures
• Know addition facts (through sums of 20)
• Write number sentences for addition facts
• Illustrate subtraction facts (through differences of 20) using objects or pictures
• Know subtraction facts (through differences of 20)
• Write number sentences for subtraction facts
• Organize objects into groups of tens and ones (place value)
• Write the numeral for a two-digit number
• Add two-digit numerals without regrouping
• Be introduced to regrouping
• Count money up to a value of 50c
• Record quantities of money using proper notation up to 50c
• Determine appropriate estimates for quantities and computations
• Be introduced to multiplication by visual representation
•  Apply geometric terms, spatial relationships, and measurement (Geometric and Spatial Sense)
• Identify three dimensional shapes: sphere, cube, cone, cylinder, and rectangular prism
• Identify two dimensional shapes:  circle, square, rectangle, triangle, and trapezoid
• Draw two dimensional shapes: circle, square, rectangle, and triangle
• Describe attributes of each three dimensional and two dimensional shapes
• Compare the lengths of two objects
• Measure length with nonstandard units
• Measure length to the nearest centimeter
• Measure length to the nearest inch
• Compare the mass of two objects
• Measure weight using pounds
• Compare the capacity of two containers
• Measure temperature with a thermometer
• Indicate time to the hour and half-hour:  face clock and digital
• Identify visual representations of: one whole, ½, 1/3, and ¼
• Collect, display, and interpret data (Data Analysis, Probability, and Statistics)
• Identify the information contained in a bar graph, pictograph, or chart
• Interpret and explain the information in a bar graph, pictograph, or chart
• Collect data
• Understand and use tally marks to represent data collected
• Organizes data into either a bar graph, pictograph, or chart
• Use data to make and check predictions
• Predict the more likely of two events
• Predict an event based on how often it has happened in the past
• Recognize, create, and analyze patterns (Patterns and Relationships)
• Recognize and explain a pattern
• Extend a pattern
• Create a pattern
• Group objects by fives to 100
• Group objects by tens to 100
• Express numbers in different forms (Mathematical Systems and Number Theory)
• Write all the addition and subtraction number sentences of a fact family
• Identify a number as even or odd
• Identify coins:  penny, nickel, dime, and quarter
• Identify value of penny, nickel, dime, and quarter
• Add and subtract pennies, nickels, and dimes
• Count, order, compare, and organize objects and numbers (Discrete Mathematics)
• Understand and utilize calendar
• Say the days of the week and months of the year in order
• Explain the meaning of yesterday, today, and tomorrow
• Use one-to-one correspondence to compare sets of objects
• Compare with objects and numbers to determine more, most, few, fewer
• Compare numerals to determine less than (<), greater than (>), or equal to (=)
• Determine ordinal position of an object (first through tenth)
• Arrange objects by size
• Sort and classify objects by various attributes
• Identify own sorting rule (basic for organization)

The student will:

•  demonstrate an understanding of money, know how to make change and how money is used throughout the world.
• recognize, interpret, write and solve double and triple digit addition and subtraction problems.
• demonstrate an understanding of time and the ability to interpret how long events last.
• demonstrate the ability to collect, graph, interpret and recognize various kinds of data and read data in tables, charts and graphs of various kinds.
• accurately identify and use units of measure in standard and metric form.
• identify and measure geometric figures
• correctly identify fractions and predict probability.
• demonstrate an accurate understanding of place value to 1,000.
• demonstrate proficiency in number patterns, comparing and ordering numbers and number operations.
• be introduced to multiplication and division concepts.

Students will:

• review and improve whole number operation skills: adding, subtracting, multiplying, and dividing.
• be introduced to division with remainders.
• identify and work with numerals in various place-values up to hundred-thousands.
• read and interpret pictographs, bar graphs and line graphs and use these in solving word problems.
• organize and compute using both money and time.
• understand the concept of fractional parts and decimals and do basic computation using fractions.
• demonstrate an ability to measure items using the metric system.
• identify and classify geometric figures
• be introduced to points on a line.
• improve proficiency in rounding and estimating numbers to the tens and hundreds place.

The student will:

•  have an understanding of place value and patterns, read and write numbers up to millions, and correctly round to the nearest ten through the nearest thousand.  Students will solve problems through estimation and rounding.
• demonstrate the ability to add two digit, three digits, and greater numbers and column addition.  Students will be introduced to properties of addition.
• accurately subtract two digit, three digit, and greater numbers and students will regroup to solve subtraction problems.
• know multiplication facts from zero through twelve and be able to multiply one digit, two digit, three digit, and four digit numbers by one and two digit numbers.
• accurately divide one and two digit numbers with and without remainders; they will be able to divide three and four digit numbers with remainders using long division.
• add, subtract, multiply, and divide money using a dollar sign and decimal point and be able to use these skills in solving word problems.
• recognize rays, lines, and segments, identify and name angles and pairs of lines.
• identify polygons, their number of sides, and vertices, describe circles, diameters, and radii, and know congruent figures and lines of symmetry.
• identify fractional parts of a region and parts of a group by comprehending numerators and denominators, find parts of a group by understanding the fraction of a group or a whole number, and recognize and name mixed numbers.

The students will:

•  Compute efficiently and accurately (add, subtract, multiply and divide) three, four and five place numbers including decimals, fractions and percentages.
• Recognize and accurately use units of time (analog and digital), including military time; money, understanding the value thereof and being able to give correct change up to five-hundred dollars; measurement, applying both standard and metric to all operations.
• Communicate mathematical concepts in verbal and written form for all operations at grade level.
• Develop skills in estimation for addition, subtraction, multiplication and division of three, four and five place numbers and including fractions, decimals, percentages, time, money and measurement
• Logically interpret and solve three to four place word problems using various strategies while developing higher level thinking skills.
• Demonstrate proficiency in reading, writing and interpreting grade level graphs including line, bar circle and pictographs and tables.
• Identify and measure geometric figures up to ten sides.
• Recognize, write and solve simple and complex expressions and equations using up to three variables.
• Demonstrate proficiency in recognizing and utilizing grade level algebraic concepts, structures and methods.

The student will:

• utilize the basic properties to review and improve proficiency in basic computation skills (addition, subtraction, multiplication, and division) involving whole numbers, decimals, fractions, and mixed numbers.
• improve proficiency in estimation involving whole numbers and decimals, and be introduced to estimating techniques for fractions and mixed numbers.
• accurately write, compare, and order decimals, fractions, and mixed numbers.
• review and improve proficiency in number theory concepts including patterns, sequences, exponents, greatest common factor (GCF), and least common multiple (LCM); be introduced to prime factorization and scientific notation.
• be introduced to writing and evaluating expressions using order of operations, and solving one-step equations involving whole numbers, decimals, fractions, and mixed numbers; be introduced to two-step equations involving multiplication and addition/subtraction of whole numbers and decimals.
• classify, compare, and describe the following:  lines, angles, polygons, circles, three-dimensional figures, and geometric transformations.
• graph decimals, fractions, and mixed numbers on a number line.
• be introduced to integers, absolute value, and the ordering of integers.
• expand problem solving strategies to include:  alternate solutions, too little/too much information, finding patterns, multi-stage problems, guess and test, working backwards, and logic.

The students will:

• review and improve proficiency in basic computation skills (addition, subtraction, multiplication, and division) involving whole numbers, decimals, fractions, and mixed numbers.
• review and improve proficiency in basic computational skills (addition, subtraction, multiplication, and division) involving integers.
• improve proficiency in estimation involving whole numbers, decimal,  fractions and mixed numbers.
• accurately write, compare, and order decimals, fractions, and mixed numbers and rational numbers
• write and solve expressions and multiple-step equations involving integers and rational numbers
• improve accuracy in using powers of ten and  square root in solving expressions, equations and word problems.
• identify, classify and be able to solve problems involving lines, angles and polygons.
• be able to solve basic area, volume and right triangle geometry problems.
• develop skills in graphing ordered pairs on the coordinate plane, be introduced to the graphing of linear equations and the concept of the basic slope of a line.
• improve problem solving skills involving alternate solutions, too much or too little information, working backwards, guess and test methods, and logic.

The students will:

• demonstrate and improve proficiency in basic computation skills (addition, subtraction, multiplication, and division) involving whole numbers, decimals, integers and rational numbers.
• demonstrate proficiency in number theory concepts including greatest common factor (GFC), least common multiple (LCM) and prime factorization.
• develop skills in writing single and multi-step equations involving whole numbers, decimals, integers and rational numbers for various kinds of word problems.
• accurately solve single and multi-step equations involving whole numbers, decimals, integers and rational numbers in mathematical expressions and in word problems
• improve speed and efficiency in evaluating algebraic expressions, formulas and functions.
• be introduced to simplifying numerical and algebraic expressions using the four operations and various properties such as Commutative, Associative, Distributive and others.
• be introduced to monomials, binomials and polynomials including addition, subtraction and multiplication of polynomials.
• be introduced to graphing linear equations.
• use a variety of techniques to improve problem solving skills (guess and test, drawing a diagram, making a table, looking for patterns, using logical reasoning and working backwards).