As your sixth-grader starts middle school, he or she will find math is becoming more complicated and abstract. Your student will connect multiplication and division to ratios and rates and will solve equations with variables. Here are several examples of the standards for sixth-grade mathematics, along with questions to ask your son or daughter’s teacher and ways you can reinforce learning at home.

### Ratios and Proportional Relationships

1. Understand the concept of ratios and unit rates; use correct language to describe the meanings.
Q: Students preferred milkshakes over water 4:1.
A: For every student who preferred water, there were four students who preferred milkshakes.
Q: We paid \$20 for four necklaces.
A: This is a rate of \$5 per necklace.

### Number System

1. Build upon previous understanding of multiplication/division to divide fractions by fractions.
Q: Timmy brought 5¼ pounds of chocolate to share with the class. He wants to portion the chocolate into bags that are ¼ pounds each. How many bags will he have?
Alternative: Apply knowledge of fractions and use visual depictions to show there are 21 quarters in 5¼ pounds, so there will be 21 bags of chocolate.
2. Multiply and divide numbers with multiple digits.
3. Use positive and negative numbers to describe real-world situations, and explain what 0 means in each scenario.
The Denver Broncos football stadium is 5,280 feet above sea level (5,280 ft. elevation), whereas the Death Valley desert is 282 feet below sea level (-282 ft. elevation).
4. Interpret ordering and absolute values of rational numbers in real-world situations.
-12°F > -20°F means that -12°F is warmer than -20°F

### Expressions and Equations

1. Evaluate expressions where words and letters stand for numbers and mathematical terms.
Q: Divide the sum of y and 4 by z
A: (y + 4) ÷ z
2. Apply properties of operations to indicate equivalent mathematical expressions.
6(5 + x) = 30 + 6x
y + y + y + y = 4y
3. Identify and assess relationships between independent and dependent variables.
Q: If a car is moving at 60 mph, how many miles will the car travel in two hours?
A: Independent variable = time (t); dependent variable = distance (d)
d = 60t

### Geometry

1. Solve problems that involve area, surface area, and volume.

### Statistics and Probability

1. Develop knowledge of “statistical variability”: a statistical question anticipates differences in the data, and the answers account for these differences as well.
Q: Students just completed a multiple choice exam for their modern history class. Which of the following is a statistical question?
How many students earned an A?
How did the students score on the test?
A: The second question is a statistical question. There are multiple responses to the question, and both the question and answer account for the variability. The first question is not statistical because there is only one definitive answer, with no variability in the answers.
2. Summarize and describe “distributions”: the arrangement of values in a data set, often described by using center (mean, median, mode) and spread (range of data points).