# 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

- Begin simple addition
- 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

## Grade 1

#### 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
- Add coins to $1.00

#### 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

## Grade 2

#### 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

## Grade 3

#### 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
- Estimate answers
- 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
- Solve missing addend problems
- 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

## Grade 4

#### 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
- Estimate answers
- 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

## Grade 5

### 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

## Grade 6

#### 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

- mcs math