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# 6th grade math skills: Find out what you need to know for your student

In sixth grade, students focus on connecting their understanding of multiplication and division to ratios and rates.

Want to help your sixth-grader master math? Here are some of the skills your sixth-grader will be learning in the classroom.

## Ratios & unit rates

Understanding ratios

Understand ratio as a comparison of (exactly) two numbers or quantities.

Writing ratios

Write and describe a relationship as a ratio.

Example:

In a herd of horses, the ratio of legs to tails is 4 to 1 (or 4:1) because for every 4 legs there is 1 tail.

Understanding unit rates

Understand the concept of unit rates: or representing a measurement as a ratio of x to a single unit, or 1.

Example:

There are 18 chairs and 3 tables. Find the unit rate for chairs per table (how many chairs per 1 table).

Solving unit rate & rate problems

Use tables, diagrams, and/or equations to solve unit rate and rate problems.

Example:

• Unit pricing: An 8-ounce can of beans costs \$1.36. What is the unit price (dollars per ounce)? Illustrate or explain your reasoning.
• Conversions from one unit to another: A half-gallon of milk costs \$2.48. How much does a cup of milk cost? Illustrate or explain your reasoning.
• Constant speed: If it took 7 hours to mow 4 lawns, at what rate were lawns being mowed? At that rate, how many lawns could be mowed in 35 hours? Illustrate or explain your reasoning.
• Percents: During the school year, a student uses 25 pages, or 50 percent of the pages in a lab workbook. What is the total number of pages in the workbook?
• Consumer math problems: New sneakers cost \$50. Which coupon is the better deal: TAKE \$20 OFF ANY ITEM or 30% OFF ANY PURCHASE? Illustrate and explain your reasoning.

## Fractions

Dividing by fractions

Use fraction bars, diagrams, drawings, and/or modeling with materials to understand division of fractions by fractions.

Solving word problems

Solve word problems involving division of fractions by fractions.

Example:

• Daniel and his dad are baking cupcakes. They have 3⁄4 of a cup of cocoa powder. They need 1⁄8 of a cup for each batch of cupcakes they bake. How many batches can they make? 3⁄4 ÷ 1⁄8 = ? Illustrate or explain your reasoning.
• How many 1⁄3 cup servings are in 3⁄4 of a cup of yogurt? 3⁄4 ÷ 1⁄3 = ? Illustrate or explain your reasoning.

## Numbers

Recognizing negative numbers

Recognize a minus ( - ) directly in front of a number as indicating the number is a negative number (a number less than zero). Understand that on a number line, positive and negative numbers are on opposite sides of 0 (zero).

Real-world examples

Find real-world examples of negative numbers, including temperature above and below zero, elevation above and below sea level, or credits and debits in a checking account.

Use understanding of negative numbers to plot points in all four quadrants of a four-quadrant graph.

## Independent & dependent variables

Algebraic expressions

Write, read and understand algebraic expressions (mathematical statements) in which letters stand for numbers. Understand that solving an equation such as 2 + x = 12 means “2 plus what number equals 12”?

Example:

• Solve one-step equations with whole numbers, for example: b + 26 = 42.
• Solve one-step equations with fractions, for example: c + 1/3 = 6.

Equations vs. expressions

Understand the difference between a mathematical equation (like a complete sentence) and a mathematical expression (like a phrase in a sentence).

Example:

• 10 = x – 3 is an equation: has an unknown variable (symbol for an unknown number), an “equals” sign ( = ), and can be solved.
• 4x + 28 is an expression: has an unknown variable, does not have an “equals” sign ( = ), and cannot be solved.

Writing expressions

Identify and write equivalent (equal) mathematical expressions in more than one way – for example, 2 (3 + x) is the same as 6 + 2x.

Whole number exponents

Write and determine the value of expressions with whole number exponents.

## Geometry

Area, surface area, & volume

Solve real-world and mathematical problems involving area, surface area, and volume of non-circular figures, including cubes, rectangles and rectangular prisms (three-dimensional objects with 6 rectangular faces; see example below).

Graphing polygons

Graph polygons (figures with three or more sides); find side lengths by subtracting coordinates.

## Statistics & probability

Mean, median, & range

Understand the meaning of mean and median as different measures of center and range. Learn how to find mean, median, and range:

• mean– the average: add data values together; divide by number of values or sample size
• median– the middle value (half the values are less than the median, and half the values are more than the median): rank data in order from lowest to highest; find the number in the middle
• range– difference between the largest and smallest values: subtract the lowest value from the highest value. To find mid-range, add the lowest and highest values together, and divide by 2

For tips to help your sixth-grader in math class, check out our sixth grade math tips page.

Parent Toolkit resources were developed by NBC News Learn with the help of subject-matter experts, and align with the Common Core State Standards.