6th Grade Math Skills: Descriptions & Examples
Rewrite the numbers in order of least to greatest: 1/3, 0.22, | -5 |, -15
-15, 0.22, 1/3, | -5 | (Understand ordering and absolute value of rational numbers.)
We paid $75 for 15 hamburgers, which is a rate of $? per hamburger.
$5 per hamburger. (Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.)
Reflect (3,2) over both the x and y-axis.
(-3, -2) (Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.)
-(-3)=?
-(-3)=3 (Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, and that 0 is its own opposite.)
Compare -3 degrees C and -7 degrees C using an inequality.
-7 degrees Celsius < -3 degrees Celsius (Write, interpret, and explain statements of order for rational numbers in real-world contexts.)
Describe the expression 2 (8 + 7) as a sum of two factors
16 + 14 = 30 (Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.)
2.8 + 3.05 = ?, 2.8 - 1.05 = ?, 45.2 * 6.02 = ?, 6.8 ÷ 2.5 = ?
2.8 + 3.05 = 5.85, 2.8 - 1.05 = 1.75, 45.2 * 6.02 = 272.104, 6.8 ÷ 2.5 = 2.72 (Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.)
How wide is a rectangular strip of land with length 3/4 mile and area 1/2 square mile?
2/3 mile (Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.)
Evaluate 2x + 3x - 4 for x = 5
21 (Write, read, and evaluate expressions in which letters stand for numbers.)
414÷18=?
23 (Fluently divide multi-digit numbers using the standard algorithm.)
4^2 + 8 ÷ (2 - 1)
24 (Write and evaluate numerical expressions involving whole-number exponents.)
Express 36 + 8 as the GCF multiplied by the sum of two numbers. GCF (36, 64)=? LCM (8, 12)=?
4(9+2) GCF (36, 64)=4 LCM (8, 12)=24 (Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.)
Express the calculation "Subtract y from 5" as an algebraic expression.
5 - y (Write expressions that record operations with numbers and with letters standing for numbers.)
Find the GCF and apply the distributive property to rewrite 24x + 18y
6(4x + 3y) Apply the properties of operations to generate equivalent expressions.
If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Solve unit rate problems including those involving unit pricing and constant speed.
Use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.
V=1/8 cubic units, A=1/4 square units (Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). )
Are the expressions y + y + y and 3y equivalent?
Yes, because they name the same number regardless of which number y stands for. (Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). )