## Grade 6 Skills and concepts

## Curriculum in a nutshell

Problem Solving (evidence-claim-reasoning)

Number theory (factors, multiples, primes, LCM, GCF)

Expressions (evaluating both numerical and variable expressions -- order of operations, simplifying, combining like terms, distributive property, associative property, commutative property)

Fractions (review of comparing ordering and equivalence, fraction operations - all)

Decimals (fraction equivalents, review of comparing ordering and equivalence, fraction operations - all, includes long division refresher)

Percentage (includes percent proportions)

Ratio, rates and proportions (unit rate, solving proportions, proportional reasoning, interpreting graphs)

Two-dimensional geometry (area and perimeter - includes circles) and three-dimensional geometry (surface area and volume - prisms, and pyramids)

Statistics (measures of center and variation - range IQR, MAD; displays: box plots, line plots, histograms, pie charts)

Equations and inequalities (solving equations and graphing basic inequality on the number line)

Number theory (factors, multiples, primes, LCM, GCF)

Expressions (evaluating both numerical and variable expressions -- order of operations, simplifying, combining like terms, distributive property, associative property, commutative property)

Fractions (review of comparing ordering and equivalence, fraction operations - all)

Decimals (fraction equivalents, review of comparing ordering and equivalence, fraction operations - all, includes long division refresher)

Percentage (includes percent proportions)

Ratio, rates and proportions (unit rate, solving proportions, proportional reasoning, interpreting graphs)

Two-dimensional geometry (area and perimeter - includes circles) and three-dimensional geometry (surface area and volume - prisms, and pyramids)

Statistics (measures of center and variation - range IQR, MAD; displays: box plots, line plots, histograms, pie charts)

Equations and inequalities (solving equations and graphing basic inequality on the number line)

## Specific skills and concepts

On this page you will find a list of skills and concepts that you will learn during sixth grade. The skills shown in regular text are skills you should know. The skills listed below in gray show where we are headed. New skills will also be added as the year progresses.

## Skills and Concepts From Grade 5

To start the year, there are certain skills and concepts that you should have mastered in fifth grade.

Among other skills, you should be able to:

Among other skills, you should be able to:

- Add and subtract whole numbers
- Multiply whole numbers using any method, including the "traditional" algorithm
- Divide whole numbers using any method (if you haven't learned it yet, you will learn long division in sixth grade)
- Automatically recall addition, subtraction, multiplication, and division facts (1-12).
- Find factors and multiples, and prime factorization
- Compare and order fractions and decimals
- Make equivalent fractions, and simplify fractions
- Add and subtract fractions, mixed numbers and decimals

## skills and concepts

As of

**September 21, 2015,**skills and concepts you should be striving to master are shown in black

**.**The skills listed below in gray show where we are headed. New skills will also be added as the year progresses.

**Unit 1: Problem Solving**

Understand and execute the evidence-claim-reasoning format in problem solving.

**Unit 2: Number Theory**

List multiples

Use divisibility rules

Use factorization for determining divisibility

Find all factors of a number

Recognize prime numbers

Determine prime numbers greater than 100

Find prime factorization

Find GCF of numbers greater than 100

Find LCM of numbers greater than 100

Understands basic, squares, square roots, exponents

Using prime factorization to find squares and square roots

**Unit 3: Expressions**

Applies commutative and associative properties

Applies distributive property

Can identify equivalent algebraic expressions

Evaluates basic expressions

Evaluates expression with parens and exponents

Evaluates expressions - advanced

Translates words into expressions, and expressions into words

Understands exponential notation

**Unit 4: Fractions**

Compare fractions using benchmarks

Compare fractions using common denominator

Compare fractions using common numerator

Find equivalent fractions/simplify fractions

Find equivalent improper fractions and mixed numbers

Identify/place fractions on a number line

Name a fraction between consecutive unit fractions (optional)

Addition and subtraction with common fractions

Mixed number addition and subtraction

Mixed number subtraction including regrouping

Estimate fraction addition

Finds part of whole number (what is 3/4 of 16?).

Finds whole when given part (3/4 of what number is 6?)

Finds whole and part with improper fractions

Multiplies fraction by whole number

Multiplies common fractions

Multiplies mixed numbers

Estimates fraction multiplication

Estimates fraction division

Finds reciprocals including mixed numbers

Divides common fractions

Divides mixed numbers

Simplifies complex fractions

Understands multiple models for fraction division

Evaluating expressions with fractions and decimals basic

Evaluating expressions with fractions and decimals, advanced

Problem solving with bar diagrams basic

Problem solving with bar diagrams advanced

Word problems with fraction/decimal division and multiplication

Reasons algebraically with fractions and decimal numbers

**Unit 5: Decimals**

Adds and subtracts decimals

Compares and orders decimals (and fractions/percents)

Divides decimals by powers of ten

Divides with decimal dividend (long division)

Divides with decimal divisor (long division)

Divides division with decimal quotient

Estimates decimal multiplication and division

Estimates decimals addition and subtraction

Finds fraction decimal equivalents

Fluency with fraction-decimal equivalents

Multiplies decimals

Multiplies decimals by powers of ten

Problem solving with decimal numbers

Recognizes/places decimals on the number line

Rounds decimals

Understands place value of decimal numbers

Understands terminating, repeating, and irrational decimal numbers

Reasons algebraically with fractions and decimal numbers

Word problems with fraction/decimal division and multiplication

Evaluating expressions with fractions and decimals basic

Evaluating expressions with fractions and decimals, advanced

**Unit 6: Percent**

Finds percent-decimal-fraction equivalents - advanced

Finds percent-decimal-fraction equivalents - basic

Finds percent of a quantity

Find missing whole 24% of ___ = 48

Finds missing percent

Percents problem solving

Identifies proportionality

**Unit 7: Ratio, Rate and Proportion**

Identifies/finds unit rates

Can make and identify ratio tables

Similar figures

Solve proportions (non-whole scale factor)

Solve proportions (whole number scale factor)

Understands how to compare ratios and determine equivalent ratios

Understands ratio basics

Uses proportional reasoning in problem solving

Writes proportions in standard format

**Unit 8: 2D Geometry (including coordinate geometry)**

Finds area and circumference of circles

Finds area of parallelogram

Finds area of triangle

Problem solving with geometry

Unit 8 part 2: 3D Geometry

Finds surface area of pyramids

Finds surface area of rectangular prisms

Finds volume of combined block structures

Finds volume of rectangular prism

Identifies prisms and pyramids

**Unit 9: Statistics**

Recognizes a statistical question

Constructs line plots/dot plots from raw data

Constructs a simple frequency table

Constructs a frequency table with data ranges

Constructs a bar graph from simple frequency table

Constructs a histogram from a frequency table

Finds the mean of a data set (raw data)

Finds the mean of a data set from a frequency table

Finds the median of a data set (raw data)

Finds the median of a data set from a frequency table

Finds the mode of a data set

Selects appropriate measure of center based on context

Finds the minimum and maximum of a data set

Constructs data sets that fit with measures of center and spread

Finds the lower and upper quartiles of a data set

Constructs a box plot based on the five number summary

Describes data distributions in terms of center and spread

Describes data distributions in terms of shape, outliers, clusters and gaps

Interprets basic displays of data such as line plots, frequency tables, bar charts, and identifies number of data points

Interprets all displays of data including histograms, box plots, and circle graphs

Finds the mean absolute deviation of a data set

Interprets mean absolute deviation

Solves missing value mean problems

Solves problems involving measures of center

Solves problems involving measures of spread

Solves problems involving statistics - advanced

**Unit 10: Equations and Inequalities**

Evaluates variable expressions for a given value

Factors expressions ("undistributes")

Finds 2-step basic rule for in/out table

Finds input values from rule and output value

Finds output value when given rule

Finds rule from visual pattern

Finds two-step rule with fraction, division or exponent

Graphs equations

Matches equation with in/out table

Solves basic equations algebraically

Solves equations using backtracking

Translates words into equations

Can use systematic reasoning to find a rule

Distinguishes independent and dependent variables

Graphs inequalities

Solves basic inequalities