## 6th Grade Math Skills

In 6th Grade, students focus on connecting their understanding of multiplication and division to ratios and rates, developing an understanding of rational numbers and the relationships between independent and dependent variables, and writing and solving equations with letters that stand for numbers (variables).

##### Understanding Ratios

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

Ratio of red stars to green stars is 3 to 1 (written as 3:1) ##### Writing Ratios

Write and describe a relationship as a ratio.

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.

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

• 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.
##### Dividing by Fractions

Use fraction bars, diagrams, drawings, and/or modeling with materials to understand division of fractions by fractions. Tip: Cooking With Fractions
Cooking and baking remain a great way for your child to practice working with fractions. Ask him to scale recipes for your family. Have him start by halving or doubling a recipe. When he feels comfortable doing this, ask him to convert it by 1 ½, allowing a recipe that is supposed to feed a family of 4 to work for a family of 6.

##### Solving Word Problems

Solve word problems involving division of fractions by fractions.

• Daniel and his dad are baking cupcakes. They have 34 of a cup of cocoa powder. They need 18 of a cup for each batch of cupcakes they bake. How many batches can they make? 34 ÷ 18 = ? Illustrate or explain your reasoning.
• How many 13 cup servings are in 34 of a cup of yogurt? 34 ÷ 13 = ? Illustrate or explain your reasoning.
##### 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).

Explain why -13 is less than 3. ##### 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  ##### Four-Quadrant Graph

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

• 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).

• 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. For example: 13 + 42 = 13 + 16 = 29.

##### 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).

Before the lab researcher can place an order for materials, she needs to know: how many 2” x 2” x 1” frozen samples will fit in her 16” x 8” x 12” specimen freezer? ##### Graphing Polygons

Graph polygons (figures with three or more sides); find side lengths by subtracting coordinates. ##### 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 Using the data in this bar graph, find the mean (or average) height and median height of these trees, and the range in tree height. How do these measurements change if you add to the data set a fourth tree that is 1 meter tall? Explain your reasoning.

Tip: Chance of Rain?
Use the weather report to talk about probability with your child. If there’s an 80% chance of rain will he need to bring an umbrella and wear his rainboots?

#### Academics

Understanding the concepts your children are learning in school can help you support them at home. Find ways to support them from Pre-K all the way through high school.