# Math

Math

### Kindergarten

#### General Math

• Explore math manipulatives
• Recognize and create simple patterns
• Begin to do simple story problems

#### Numbers and Numeration

• Understand 1-1 correspondence, relate number of objects to a numeral
• Count by rote and practice to 100
• Practice writing numbers to 30
• Use ordinal numbers to 10
• Recognize numbers to 50
• Recognize and name coins. Practice values of coins

#### Computation and Estimation

• Be introduced to subtraction
• Count by tens and fives to one hundred
• Begin to understand temperature

#### Measurement

• Begin to learn about time, calendar, seasons, weeks, days
• Measure using a variety of standard and non-standard units

#### Geometry

• Recognize basic 2-D and 3-D shapes
• Sort objects by attributes using concrete materials

#### Data Collection and Analysis

• Collect, organize, represent and interpret simple bar graphs

#### Numbers and Numeration

• Read and write symbols (=, +, -)
• Understand “add, subtract, sum, difference, total, more, less, pattern, equal, odd, and even”
• Count by 1’s, 2’s, 5’s, 10’s to 100
• Use ordinal numbers
• Match and write numerals for sets of tens and ones
• Compare non-equivalent sets by using “greater than” or “less than” and their signs < and >
• Arrange five numbers that are out of order, each less than 100, in proper sequence
• Develop an understanding of zero
• Identify fractional parts (halves, thirds, fourths) using manipulatives

#### Computation and Estimation

• Know sums and differences up to 10 with and without manipulatives
• Add and subtract numbers over 10 without regrouping
• Do mixed operations on a page with facts to 10
• Use concrete objects to show addition and subtraction equations to 18
• Create an oral story problem as an explanation of a numerical equation
• Decide whether it is reasonable to estimate and answer or necessary to do the precise calculation
• Estimate answers to computational problems, then complete the computation

#### Measurement

• Make simple comparisons of volume, length, weight, area • Apply measurement concepts in context of concrete problem solving situations
• Estimate and measure real objects using standard and non-standard units
• Compare size and weight of objects
• Use a balance
• Choose an appropriate measuring tool
• Name days of the week and seasons
• Use a calendar
• Recognize hours and half-hours on the clock
• Recognize penny, nickel, dime, quarter, dollar and match with value. Begin interchangeability

#### Geometry

• Recognize and name triangle, square, rectangle, circle, hexagon, rhombus, trapezoid, octagon, decagon
• Sort geometric shapes by attributes
• Explore the ways shapes combine into other figures
• Understand and demonstrate symmetry

#### Data Collection and Analysis

• Gather, organize and interpret simple data
• Know how to read and make bar graphs
• Explore probability through activities

#### Problem Solving, Reasoning, and Communication

• Use problem-solving approaches to investigate and understand mathematical content
• Evaluate the reasonableness of answers
• Develop and apply strategies to solve a variety of problems
• Recognize multiple solutions as well as strategies and approaches
• Classify and sort objects, using one or more attributes

#### Patterns, Functions, and Algebra

• Identify, verbalize, and extend a pattern in a sequence of objects
• Identify odd and even numbers
• Identify patterns on a number line

#### Numbers and Numeration

• Count, read, and write numbers by 1’s to 1000
• Skip count by 2’s, 5’s, and 10’s to 100
• Define and label odd and even numbers
• Recognize and repeat patterns
• Understand and use place value
• Review and expand knowledge of fractions

#### Computation and Estimation

• Recognize and use math symbols (+ , - , < , >)
• Add and subtract up to 3-digit numbers without regrouping
• Add two 3-digit numbers with regrouping
• Know math facts to 20 (+/-)
• Fill in missing numbers in equations
• Use computation skills to solve story problems
• Recognize, name, and identify value of coins
• Count money and make change

#### Measurement

• Measure using appropriate units (inches, feet, yards, centimeters, meters)
• Expand knowledge of money (value of coins, adding amounts up to \$1.00)
• Name days of week, months of year, and seasons
• Read a thermometer in Celsius and Fahrenheit
• Tell time to quarter-hour

#### Geometry

• Recognize and name common two and three- dimensional shapes
• Learn and apply geometric terms: open/closed, line, point, perpendicular, parallel, symmetrical, area, perimeter

#### Data Collection and Analysis

• Collect and organize data
• Make and read bar graphs, line graphs, pie graphs, and pictographs

#### Problem Solving, Reasoning, and Communication

• Approach problem solving systematically and creatively
• Apply problem solving strategies to more complex problems
• Practice spatial problem solving

#### Patterns, Functions, and Algebra

• Represent a concrete model of a pattern symbolically
• Classify, sort and order objects

#### Numbers and Numeration

• Recall addition, subtraction, and multiplication facts
• Read and write ordinal numbers, whole numbers, decimals for money, and simple fractions
• Use <, >, =, +, -, x, /
• Identify place value to 10,000
• Round to nearest 10 and 100
• Use expanded notation under 1,000
• Recognize odd and even numbers
• Recognize value of one or more coins up to \$1.00
• Make change up to five dollars
• Understand commutative and associative properties with addition

#### Computation and Estimation

• Add and subtract up to 3-digit numbers with regrouping
• Subtract two 3-digit numbers with zeros
• Multiply a 2-digit number by a 1-digit number with regrouping
• Estimate, then divide a 2-digit number by a 1-digit number
• Add money using decimal notation
• Add and subtract fractions with common denominators

#### Measurement

• Use a calendar
• Know months, weeks, and days
• Begin to understand volume
• Estimate and measure length, perimeter, area, volume, and weight
• Read, write and tell time to the hour, half-hour, quarter-hour, and minute
• Use a thermometer (Cº and Fº)
• Calculate elapsed time

#### Geometry

• Classify angles
• Identify, name and draw polygons
• Recognize congruent and similar shapes and symmetry
• Identify intersecting, parallel, and perpendicular lines
• Identify characteristics of polyhedra

#### Data Collection and Analysis

• Collect, organize, represent, and interpret data from surveys and experiments using lists, tables, and graphs
• Explore and pre

#### Problem Solving, Reasoning, and Communication

• Create and use a variety of strategies and approaches to solve problems
• Make sensible and reasonable estimates

#### Patterns, Functions, and Algebra

• Identify, describe and extend a pattern
• Determine a location on a grid using ordered pairs
• Classify, sort and order objects
• Distinguish between the intersection and the union of two sets

#### Numbers and Numeration

• Define and use: +, -, x, / , =, <, >
• Introduce sum, difference, product, quotient, fraction
• Read and write numbers to 1,000,000
• Know place value to 1,000,000
• Compare place values and decide the relation symbol (<,>,=) between numerals
• Round to nearest 10, 100, 1000
• Use expanded notation to show regrouping of tens, hundreds, etc.
• Understand the inverse relationship of addition and subtraction, multiplication and division
• Recognize odd, even and prime numbers

#### Computation and Estimation

• Know addition, subtraction, multiplication and division facts (up to 10's)
• Add and subtract with regrouping
• Subtract with regrouping with zeros
• Multiply with regrouping, 2-digit by 2-digit numbers
• Divide 4-digit numbers by 2-digit numbers, with remainders
• Use the commutative, associative, distributive and identity properties
• Write, order, add, and subtract fractions with like and unlike denominators
• Find the least common factor and the least common multiple of numbers
• Find a common denominator of fractions
• Add money and decimals up to the thousandths
• Use strategies for mental math

#### Measurement

• Use standard and metric measurement for length, mass and temperature
• Apply knowledge of seconds, minutes, hours, weeks, months and years in solving problems
• Understand coin values, make change and solve money problems
• Calculate area, perimeter, and volume

#### Geometry

• Review point, line, line segment, ray, angle, parallel, perpendicular, circle, square, rectangle, triangle
• Classify angles
• Identify and construct polygons
• Identify three-dimensional shapes
• Explore congruency and symmetry of shapes
• Use protractor and compass

#### Data Collection and Analysis

• Collect, organize, represent, and interpret data using lists, tables, bar graphs and line graphs
• Interpret data using the mean, median, mode and range
• Predict, perform, and record simple probability experiments

#### Problem Solving, Reasoning, and Communication

• Translate word problems into number sentences
• Learn to recognize key words and phrases
• Write word problems
• Understand and apply appropriate strategies to solving problems

#### Patterns, Functions, and Algebra

• Identify, describe and extend patterns
• Classify and sort objects using attributes
• Identify and graph points in the coordinate plane
• Use order of operations to solve equations

### Numbers and Numeration

• Add, subtract, multiply and divide and demonstrate the inverse relationships between them
• Read, write, and compare whole numbers, fractions, and decimals using <,>,=
• Know place value to a million, decimals to hundredths
• Round whole numbers to 10,000, decimals to hundredths
• Use the distributive properties, and the identity properties of zero and one
• Recognize odd, even, prime, and composite numbers
• Use the divisibility rules for 2,3,5,9,10
• Understand the concept of factors and multiples
• Continue work with fractions (add, subtract, multiply, divide, improper fractions, mixed numbers)

#### Computation and Estimation

• Use appropriate method for computing (mental math, paper and pencil, calculator, computer)
• Use appropriate strategies to learn math facts
• Add and subtract 4-digit whole numbers and decimals with regrouping
• Multiply whole numbers and decimals with regrouping (3-digit by 2-digit)
• Divide 3-digit numbers by 2-digit numbers
• Solve one, two and three step word problems
• Use estimation and rounding when appropriate

#### Measurement

• Review, use and apply standard and metric measurements (length, weight, volume, temperature)
• Convert units within a system of measurement (in., ft., mm., cm., sec., min., etc.)
• Understand coin values and make change

#### Geometry

• Identify and understand various terms of geometry (point, line, parallel, perpendicular, arc, sphere, etc.)
• Classify angles
• Identify and classify polygons
• Identify the center, radius, diameter and circumference of a circle
• Understand area and perimeter
• Use a compass

#### Data Collection and Analysis

• Gather, organize, analyze data
• Interpret data using the mean, median, mode and range
• Read, interpret and construct bar and line graphs
• Predict, and perform simple probability experiments
• Use calculators and/or computers to process data

#### Problem Solving, Reasoning, and Communication

• Approach problem solving systematically and creatively
• Apply various strategies in the problem solving process
• Develop flexibility, confidence, perseverance, and persistence both independently and in groups
• Use concrete, informal and formal strategies to solve mathematical problems in real-world situations

#### Patterns, Functions, and Algebra

• Recognize and create a wide variety of patterns
• Translate simple English phrases into algebraic expressions
• Use order of operations to solve equations
• Understand the use of variables in equations

#### Numbers and Numeration

• Demonstrate the inverse relationship of addition and subtraction, multiplication and division
• Read, write, and compare whole numbers, fractions, decimals, integers and percents, ratios and proportions
• Know place value to a million, decimals to thousandths
• Round whole numbers to 1,000,000, decimals to hundred thousandths
• Use the commutative, associative and distributive properties, and the identity properties of zero and one
• Recognize odd, even, prime, composite, and square numbers
• Understand prime factors, greatest common factors, and least common multiples

#### Computation and Estimation

• Add and subtract 5-digit whole numbers and decimals • Multiply whole numbers and decimals with regrouping, with up to a 3-digit multiplier
• Divide 5-digit whole or decimal numbers by 2- digit whole or decimal numbers
• Add and subtract any three proper or mixed fractions
• Multiply any combination of fractions, mixed or whole numbers
• Divide fractions, mixed or whole numbers
• Introduce percent problems
• Solve one, two and three-step word problems
• Find equivalents of decimals, fractions, ratios and percents

#### Measurement

• Measure length, perimeter, area, volume, circumference, surface area, and time
• Convert units within a system of measurement
• Estimate and measure angle degrees

#### Geometry

• Classify angles
• Identify and classify polygons
• Identify the center, radius, diameter, and circumference of a circle
• Identify pyramids, spheres, cubes, cylinders, and rectangular prisms
• Use protractor and compass

#### Data Collection and Analysis

• Collect, organize, represent, and interpret data using lists, tables, graphs (bar, line and circle)
• Interpret data using the mean, median, mode and range
• Predict, perform, record and analyze simple probability experiments
• Use calculators and/or computers to process data

#### Problem Solving, Reasoning, and Communication

• Approach problem solving systematically and creatively
• Develop flexibility, confidence, perseverance, and persistence both independently and in groups
• Use concrete, informal and formal strategies to solve mathematical problems in real-world situations

#### Patterns, Functions, and Algebra

• Identify, describe and extend patterns
• Use order of operations to solve equations involving parentheses and exponents
• Use tables, graphs and verbal or symbolic rules
• Understand the use of variables in equations
• Solve simple algebraic equations
• Graph, describe and compare equations on a Cartesian grid
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