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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.

## 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
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