Number & Operations

Algebraic Relationships

Geometric & Spatial

Measurement

Data & Probability

Kindergarten

• Count to 100 by ones and tens.
• Write numbers 0-20.
• Recognize numbers 0-20
• Explain and apply the meaning of greater than, less than, and equal to.
• Count objects to 20 and write the correct number to answer “how many”.
• Recognize quantities without counting
• Count on from any given number
• Count backwards from 10 to 1
• Recognize without counting the quantity of groups up to 5 objects arranged in common patterns (subitize)

·  Compose and decompose numbers 1-19

· Compose and decompose numbers using ones and tens.

· Add and subtract using numbers up to 10.

· Name and describe 2-D and 3-D shapes.

· Draw or build 2-D shapes and create larger shapes.

· Describe relative positions in space.

• Name the days of the week
• Name ways to measure time (calendar, clock, stopwatch, etc.)
• Recognize concepts of time (morning, afternoon, evening, yesterday, today, tomorrow)
• Recognize pennies, nickels, dimes, and quarters

• Describe and compare two objects.
• Sort a set of objects

1^st Grade

• Count to 120 by 1s, 5s, and 10s.
• Count backward 20-1
• Read and write numerals and represent a number of objects with a written numeral
• Understand that 10 can be thought of as a bundle of ten ones called a “ten” and understand that 2-digit numbers are composed of tens and ones.
• Compare 2 two-digit numbers using the symbols <, >, =
• Add within 100
• Calculate 10 more and 10 less without counting and add or subtract a multiple of 10 from another 2-digit number

·  Use addition and subtraction to solve problems that call for addition of two and three whole numbers whose sum is within 20

·  Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false

·  Use properties as strategies to add and subtract

·  Demonstrate that subtraction can be solved as an unknown addend problem

·  Demonstrate fluency with addition and subtraction within 10

·  Draw or build shapes that possess defining attributes and understand the difference in defining vs. nondefining attributes

·  Compose and decompose two- and three-dimensional shapes to build an understanding of part-whole relationships and the properties of the original and composite shapes

·  Recognize two- and three-dimensional shapes from different perspectives and orientations

·  Partition circles and rectangles into two or four equal shares and describe the shares and the whole verbally

·  Read and write numerals and represent a number of objects with a written numeral

·  Order three or more objects by length

·  Demonstrate the ability to measure length or distance using objects and compare the lengths of two objects indirectly by using a third object

·  Tell and write time in hours and half hours using analog and digital clocks

·  Know the value of penny, nickel, dime, and quarter

·  Collect, organize, and represent data with up to three categories and draw conclusions from object graphs, picture graphs, T charts, AND tallies

2^nd Grade

*Understand place value of three digit numbers

*Understand three digit are composed of hundreds, ten, and ones

*Understand that 100 can be thought of as 10 tens called “a hundred”

*Count within 1000 by 1s, 10s, and 100s starting with any number

*Read and write numbers to 1000 using number names, base-ten numerals and expanded form

*Compare two three-digit numbers using the symbols <,>, =

*Demonstrate fluency with addition and subtraction within 100

*Add up to four two-digit numbers

*Add or subtract within 1000 and justify the solution

*Illustrate the relationship between addition and subtraction to solve problems

*Add or subtract mentally 10 or 100 to or from a given number within 1000

*Write and solve problems involving addition and subtraction within 100

*Demonstrate fluently with addition and subtraction within 20

*Develop foundations for multiplication and division

*Determine if a set of objects has an odd or even number of members

*Count by 2’s to 100 starting with any even number

*Express even numbers as pairings/groups of 2, and write an expression as repeated addition

*Show even numbers as being composed of equal groups and write an expression to represent the number with 2 equal addends.

*Find the total numbers of objects arranged in a rectangular array with up to 5 rows and 5 columns, and write an equation to represent the total as a sum of equal addends

*Reason with shapes and attirbutes

*Recognize and draw shapes having specific attributes, such as a given number of angles or sides

*Identify triangles, quadrilaterals, pentagons, hexagons, circles, and cubes

*Identify the faces of three-dimensional objects

*Partition a rectangle into rows and columns of same-sized squares and count to find the total number of squares.

*Partition circles and rectangles into two, three or four equal shares and describe the shares and the whole

*Demonstrate that equal shares of identical wholes need not have the same shape

*Work with time and money

*Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m

*Describe a time shown on a digital clock as representing hours and minutes, and relate a time shown on a digital clock to the same time on a an analog clock

*Find the value of combinations of dollar bills, quarters, dimes, nickels and pennies, using $ and c appropriately

*Find combination of coins that equal a given amount

*Measure and estimate length in standard units

*Measure the length of an object by selecting and using appropriate tools

*Analyze the results of measuring the same object with different units

*Estimate lengths using units of inches, feet, yards, centimeters, and meters

*Measure to determine how much longer one object is than another

*Relate addition and subtraction to length

*Use addition and subtraction within 100 to solve problems involving lengths that are given in the same units

*Represent whole numbers as lengths on a number line, and represent whole-number sums and differences within 100 on a number line

*Represent and interpret data

*Create a line plot to represent a set of numeric data, given a horizontal scale marked in whole numbers

*Generate measurement data to the nearest whole unit, and display the data in a line plot

*Draw a picture graph or a bar graph to represent a data set with up to four categories

*Solve problems using information presented in line plots, picture graphs and bar graphs

*Draw conclusions from line plots, picture graphs, and bar graphs

3^rd Grade

4^th Grade

*Use place value understanding and properties of operations to perform multi-digit arithmetic with numbers up to one million.

*Extend understanding of fraction equivalence and ordering. (Limit denominators to 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

*Extend understanding of operations on whole numbers fractions operations.

*Understand decimal notation for fractions and compare decimal fractions. (Denominators of 10 or 100)

*Use the four operations with whole numbers to solve problems.

*Work with factors and multiples.

*Generate and analyze data.

*Classify 2-dimensional shapes by properties of their lines and angles.  

*Draw and identify points, lines, line segments, rays, angles, perpendicular lines and parallel lines.  

*Construct lines of symmetry for two-dimensional figure.

*Understand the concepts of angles and measure angles.

*Solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit.

*Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

*Represent and analyze data

*Analyze data in a frequency table, line plot, bar graph, or picture graph.

5^th Grade

• Perform operations with multi-digit whole numbers to billions and decimals to thousandths
• Understand relationship between fractions & decimals (denominators are factors of 100)
• Perform operations & solve problems with fractions and decimals

• Generate two numeric patterns given two rules
• Translate numeric patterns into ordered pairs
• Write & interpret numerical expressions using order of operations
• Use the four operations to represent & solve problems

• Classify two- & three- dimensional geometric shapes
• Compute volume
• Graph points within first quadrant

·  Convert measurements of capacity, length, & weight within a measurement system

·  Solve multi-step problems including measurement conversions

·  Create a line graph to represent a data set

·  Create a line plot to represent data set & answer problems

·  Generate the median

6^th Grade

*Apply concepts to divide fractions by fractions using common factors and multiples. Compute non-negative multi-digit numbers.

*Apply concepts of rational numbers system.

*Interpret and use ratios to solve problems and compare two quantities.

*Apply math operations to algebraic expressions.

*Apply concepts of math operations to solve one-variable, one-step, non-negative linear equations and inequalities.

*Solve area, surface area, and volume problems.

*Convert measurements between systems of units.

*Draw conclusions of statistical variability, summarizing distributions.

7^th Grade

• Analyze proportional relationships and use them to solve real-world and mathematical problems.
• Apply and extend previous understands of operations with fractions to add, subtract, multiply and divide rational numbers.

· Use properties of operations to generate equivalent expressions.

*Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

· Draw, construct and describe geometrical figures and describe the relationships between them.  

· Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.  

·Use random sampling to draw inferences about a population.

*Draw informal comparative inferences about two populations.

*Investigate chance processes and develop, use and evaluate probability models. 

8^th Grade

• Know that there are numbers that are not rational, and approximate them by rational numbers.

• Work with radicals and integer exponents.
• Understand the connections between proportional relationships, lines and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.
• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.

• Understand congruence and similarity using physical models, transparencies or geometry software.
• Understand and apply the Pythagoreon Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, pyramids, and spheres.

• Understand congruence and similarity using physical models, transparencies or geometry software.
• Understand and apply the Pythagoreon Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, pyramids, and spheres.

·  Investigate patterns of associations in bivariate data.

Principles of Math

o Communicate mathematically

o   Review basic arithmetic

o    Solve linear equations in one variable

o    Investigate coordinate plane

o    Basic geometric shapes and spatial reasoning

Principles of Geometry

o   Communicate mathematically

o    Graph and analyze linear functions

o Transformational geometry

o Congruency

Principles of Algebra

o   Communicate mathematically

o   Review basic arithmetic and basic algebra

o    Manipulate radicals and polynomials

o    Solve and analyze linear inequalities, linear systems, quadratic, exponential and absolute value functions

o Investigate Euclidean properties

o  Review concepts of data analysis

Math Support

o   Communicate mathematically

o   Review basic arithmetic and basic algebra

HS Algebra I

o   Communicate mathematically

o   Simplify & use real #’s, powers, roots & radicals

o   Simplify polynomials

o    Solve & graph linear equations and inequalities and quadratic functions

Geometry

o    Reason deductively & inductively

o    Apply congruence & similarity to ratios & proportions

o   Use formulas to find area & volume

o   Explore transformations and coordinate geometry

o   Find trig values using right triangles

o    Use properties of lines, circles, angles & polygons

o    Review concepts of data analysis

Algebra II/

Algebra II (Honors)

o   Simplify & use real #’s, powers, roots & radicals

o   Simplify polynomials

o   Simplify functions

o   Simplify matrices & complex numbers

o   Solve linear, absolute value, quadratic, rational, irrational, exponential polynomial & logarithmic equations.

o   Solve systems & inequalities

o   Graph linear, quadratic, and exponential functions

o   Analytic geometry- Conic sections

o   Compare & contrast sequences & series

o    Concepts of statistics and probability

DC College Algebra

o   Simplify & use real #’s, powers, roots & radicals

o   Simplify polynomials

o   Simplify functions

o   Simplify matrices & complex numbers

o   Solve & graph linear, absolute value, quadratic, rational, irrational, exponential polynomial & logarithmic functions

o   Solve systems & inequalities

o   Analytic geometry- Conic sections

o   Compare & contrast sequences & series

DC Trignometry

o    Convert degrees & radian

o    Simplify trig identities

o    Find trig values using right triangles

o    Graph trig functions

Math Analysis

o   Simplify & use real #’s, powers, roots & radicals

o   Simplify polynomials

o   Simplify functions

o   Simplify matrices & complex numbers

o   Solve & graph linear, absolute value, quadratic, rational, irrational, exponential polynomial & logarithmic functions

o   Solve systems & inequalities

o   Analytic geometry- Conic sections

o   Compare & contrast sequences & series

DC Calculus

o   Explore pre-calculus concepts

o    Find limits of functions

o    Find derivatives and use them to analyze graphs

o    Find integrals and use them to solve application problems