Grade 6 Mathematics Content

Whole Number Applications

Addition, subtraction, multiplication, division

Basic facts

Properties: associative, commutative, distributive, identity, inverse and zero

Estimation of sums, differences, products, quotients

Addition with regrouping

Subtraction across zeroes

Division with and without remainders

Order of operations

Rounding

Exponential notation

Evaluate expressions with exponents

Estimating

Place value to trillions

Decimals

Order and compare decimals

Estimating decimals

Rounding decimals

Addition, subtraction, multiplication and division of decimals

Place value

Decimal expressions and equations

Interpreting the remainder

Fraction Concepts and Operations

Divisibility rules

Prime factors

Least common multiple

Greatest common factor

Equivalent fractions and simplest form

Mixed numbers and fractions

Compare and order fractions

Change improper fractions to mixed numbers

Change fractions to decimals and percents

Multiplicative inverse (reciprocals)

Addition, subtraction, multiplication and division of fractions and mixed numbers

Estimate sums, differences, products and quotients

Percent

Change a decimal to a percent

Change a fraction to a percent

Find the percent of a number

Estimate a percent of a quantity

Algebra and Functions

Identify, write and evaluate algebraic expressions with a variable

Number patterns and functions

Absolute value

Rational Numbers

Translate 2 step verbal expressions into algebraic expressions

Use substitution to evaluate an expression

Solve 2 step equations

Measurement

Customary and metric units of measure

Perimeter and circumference

Area of a triangle, rectangle, square, circle, and irregular polygons

Capacity and volume of a rectangular prism

Identify customary and metric units of capacity Identify equivalent units

Estimate volume, area and circumference

Statistics and Probability

Collect, organize and display data

Determine and justify the most appropriate graph to display a set of data (pictograph, bar graph, line graph, histogram, or circle graph)

Find the range, mean, median and mode

Construct Venn Diagrams

Read and interpret graphs

List possible outcomes for compound events

Determine the probability of dependent events

Use the Fundamental Counting Principle

Geometry

Calculate the length of corresponding sides of similar triangles using proportions

Recognize similarity and congruence

Classify polygons

Recognize geometric figures

Find the area of triangles and quadrilaterals

Use strategies to find the area of regular and irregular polygons

Find the volume of rectangular prisms

Identify radius, diameter, chords and central angles of a circle

Understand diameter and radius and circumference

Find the area and circumference of a circle

Find the area of a sector of a circle

Identify and plot points in all four quadrants

Calculate the area of basic polygons on a coordinate plane

Ratio and Proportion

Venn Diagrams

Describe and compare 2 sets of data using ratios

Write ratios and proportions

Sample space

Solve a proportion

Identify the probability of certain events

Conduct and predict outcomes of experiments

Rate

Solve proportions using equivalent fractions

Integers

Understand integers and rational numbers

Compare and order rational numbers

Additive inverse

Addition and subtraction of integers on a number line

Problem Solving(Strategies used in all units)

Make a table, model, graph, or organized list

Estimate or find exact answers

Draw conclusions, sequence information

Choose the correct operation(s),

Find a pattern

Write an equation

Draw a diagram

New York State Education Department Learning Standard for Mathematics

Students will understand the concepts of and become proficient with the skills of mathematics; communicate and reason mathematically; become problem solvers by using appropriate tools and strategies through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.

Content Strands / Definition / Example
Strand 1:

Number Sense and Operations

/ Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems; understand meanings of operations and procedures, and how they relate to one another; compute accurately and make reasonable estimates. /
  1. Verbally count by 1’s to 20.
  2. Solve proportions using equivalent fractions.

Strand 2:
Algebra / Students will represent and analyze algebraically a wide variety of problem solving situations; perform algebraic procedures accurately; recognize, use, and represent patterns, relations, and functions algebraically. /
  1. Use a variety of manipulative materials to create patterns using attributes of color, size, or shape.
  2. Solve simple one-step equations using basic whole number facts.

Strand 3:
Geometry / Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes; identify and justify geometric relationships, formally and informally; apply transformations and symmetry to analyze problem solving situations; apply coordinate geometry to analyze problem solving situations. /
  1. Identify and appropriately name two-dimensional shapes: circle, square, rectangle, and triangle (both regular and irregular).
  2. Classify angles as acute, obtuse, right and straight.

Strand 4:
Measurement / Students will determine what can be measured and how, using appropriate methods and formulas; use units to give meaning to measurements; understand that all measurement contains error and be able to determine its significance; develop strategies for estimating measurements. /
  1. Compare the length of two objects by representing each length with string or a paper strip.
  2. Identify radius, diameter, chords, and central angles of a circle.

Strand 5:
Statistics
and Probability / Students will collect, organize, display, and analyze data; make predictions that are based upon data analysis; understand and apply concepts of probability. /
  1. Display data in bar graphs using concrete objects with intervals of one.
  2. Calculate the mean for a given set of data and use it to describe a set of data.

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