# 6th Grade Skills in Math

The 6th Grade Skills below are based on the Common Core Standards For Mathematics. You can find out more about the Common Core Standards here.

You will also find a listing of related math resources (worksheets, charts, etc.) here.

Note: Math standards and curricula can vary by location or school. Check with your child’s school to determine what 6th grade math skills are expected in your location.

## Ratios & Proportional Relationships

Using the concept of ratio to show the relationship between two quantities. e.g. the ratio of boys to girls was 15:17

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Using ratios to determine unit rates. e.g. if paint is to be mixed in a ratio of 2:3 parts red to blue, there will be 2/3 tins of red paint for each tin of blue.

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Solving real world problems using ratio and rate including by the use of equivalent ratios and by understanding and using the concept of percentages.

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## The Number System

Dividing fractions by fractions to solve word problems.

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Dividing multi-digit numbers with fluency.

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Using the four operations fluently with multi-digit decimals.

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Finding greatest common factors ( up to 100) and least common multiples (for numbers to 12) and using distributive property to rewrite expressions. e.g. 48 + 40 as 8(6 + 5)

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Recognizing how negative and positive numbers can be used to indicate quantities in opposite directions. e.g. money saved and money owed, temperature above and below zero.

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Identifying and showing negative values graphically. e.g. on number lines and on all 4 quadrants of the coordinate system.

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Understanding the absolute value of rational numbers. e.g. recognizing that - 8 is to the left of -4 on a horizontal number line and that -4 degrees is warmer than -8 degrees, recognizing that a rational number's absolute value is its distance from zero on a number line.

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Graphing ordered pairs on the 4 quadrants of the coordinate system and using absolute values to find the distance between points (horizontally or vertically - no Pythagoras required)

## Expressions & Equations

Evaluating numeric expressions that include exponents. e.g. 42 + 53

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Reading, writing, and evaluating expressions that include numbers and letters

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Generating equivalent expressions by using the properties of operations. e.g. 5(2x + 3) = 10x + 15 and 12b + 18c = 6(2b + 3c)

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Recognize two equivalent expressions.

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Recognizing that equations and inequalities can solved by finding the value or set or values that make them true.

Writing expressions to solve real-world problems using variables in place of unknown numbers.

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Writing and solving equations to solve real-world problems.
e.g. a + b = c and xy = z

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Writing inequalities given specified conditions in real-world problems.

Writing equations that include both dependent and independent variables and examining the relationship between these two variables using graphs and tables. e.g. for a car traveling at a constant speed of 85 km/ h, the distance traveled ('d') can be shown as d = 85t where 't' represents time in hours.

## Geometry

Finding the area of triangles and other polygons and doing so to solve real-world problems.

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Finding the volume of a rectangular cuboids.

Drawing polygons by plotting their vertices on the coordinate system and determining the length of horizontal and vertical sides.

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Finding the surface area of 3-D shapes using nets of rectangles and triangles.

## Statistics & Probability

Distinguishing questions that are statistical from those that are not based on whether they anticipate variability. e.g. What age is my teacher? is not statistical whereas What ages are my teachers? is.

Recognizing that data gathered in response to a statistical question can be described by its center, its range, and it's shape.

Understanding that, for numeric data, a measure of center is a single number that is a summary of all values unlike a measure of variation which is a single number that describes how the values vary.

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Displaying numeric data on histograms, dot plots, and box plots.

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Summarizing sets of numeric data including the numbers, nature, units of measurement, appropriate measures of center (mean/ median, mode) and of variability.

Browse for skills and worksheets at other grade levels by clicking in the table below.

 Grade K 1 2 3 4 5 6 7 8 Skills Worksheets

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