Sixth grade math checklist

What follows is a comprehensive, cumulative checklist of the key math topics and skills a student should have mastered by the end of sixth grade. This list reflects a mastery level - students should be comfortable and fluent with each topic by the end of Grade 6.

1) Number Sense & Place Value

• Understanding place value to the millions and to the thousandths
• Reading, writing, and comparing whole numbers, decimals, and fractions
• Rounding and estimating with whole numbers and decimals

2) Operations with Whole Numbers

• Addition, subtraction, multiplication, and division of multi-digit numbers
• Order of operations (including parentheses, exponents, multiplication/division, addition/subtraction - PEMDAS)
• Prime and composite numbers; least common multiple (LCM) and greatest common factor (GCF)
• Divisibility rules (2, 3, 5, 9, 10)

3) Fractions & Mixed Numbers

• Representing fractions on number lines
• Equivalent fractions and simplest form
• Comparing and ordering fractions
• Addition and subtraction of like and unlike fractions and mixed numbers
• Multiplication of a fraction by a whole number

4) Decimals

• Writing fractions as decimals and vice versa
• Comparing and ordering decimals (to at least thousandths)
• Addition and subtraction of decimals
• Multiplication of a decimal by a whole number

5) Rational Number Operations

• Addition and subtraction of positive and negative integers
• Understanding the number line for integers and decimals
• Introduction to multiplication and division of positive and negative integers

6) Ratios, Rates & Proportional Reasoning

• Ratio concepts and notation (a:b, “a to b”)
• Unit rates (e.g., miles per hour)
• Solving ratio and rate problems (including scaling up and down)
• Understanding and solving simple proportion equations

7) Percents

• Converting between fractions, decimals, and percents
• Finding a percent of a quantity (e.g., 25% of 80)
• Solving basic percent-increase and percent-decrease problems

8) Algebraic Thinking & Expressions

• Understanding variables and algebraic expressions
• Writing expressions for real-world situations (e.g., “n × 5” for “five times a number n”)
• Evaluating expressions by substituting values for variables
• Using the distributive property

9) Equations & Inequalities

• Writing and solving one-step equations (addition/subtraction, multiplication/division)
• Writing and solving two-step equations
• Understanding and graphing simple inequalities on a number line

10) Geometry: Area, Perimeter & Volume

• Perimeter and area of rectangles, squares, triangles, parallelograms, and compound shapes
• Surface area and volume of right rectangular prisms
• Finding missing dimensions given area or volume

11) Geometry: Properties of 2D Shapes

• Classifying triangles (by side: equilateral, isosceles, scalene; by angle: acute, right, obtuse)
• Classifying quadrilaterals (parallelogram, rectangle, square, trapezoid)
• Understanding angles: measure, sum of interior angles, supplementary and complementary

12) Coordinate Plane

• Plotting and identifying points (x,y)(x,y) in all four quadrants
• Understanding horizontal and vertical distances

13) Measurement & Units

• Converting within measurement systems (e.g., mm↔cm↔m, in↔ft↔yd)
• Understanding and using customary units (inch, foot, yard, mile; ounce, pound; cup, pint, quart, gallon)
• Time (reading clocks, elapsed time calculations)
• Perimeter and area units vs. volume units

14) Data Analysis & Statistics

• Collecting data and organizing into tables
• Displaying data: bar graphs, line plots, histograms, and circle graphs (pie charts)
• Calculating measures of central tendency: mean, median, mode, and range
• Interpreting data sets and drawing conclusions

15) Probability (Introduction)

• Simple probability models (e.g., rolling a die, drawing colored counters)
• Expressing probability as a fraction, decimal, or percent
• Experimental vs. theoretical probability

16) Exponents & Powers

• Understanding exponents as repeated multiplication
• Evaluating expressions with whole-number exponents

17) Mathematical Practices

• Problem-solving strategies (draw a picture, make a table, guess and check)
• Reasoning and proof (explaining why an answer makes sense)
• Precision in calculation and terminology
• Looking for and making use of structure (patterns, relationships)
• Using tools (ruler, protractor, calculator) appropriately

Rules of exponents in math operations

Rules of exponents explained for 6th and 7th graders

Exponents are a way to show that a number is multiplied by itself several times. Instead of writing out the same number again and again, we use exponents to make it easier. For example, instead of writing 2 × 2 × 2, we can write 2³.

Here are the key rules of exponents you need to know, explained step by step:

1. The Product Rule (Multiplying with the Same Base)
When multiplying two numbers with the same base, add the exponents.

Rule:
aᵐ × aⁿ = aᵐ⁺ⁿ

• Base: The number that is being multiplied.
• Exponent: The small number that tells how many times the base is multiplied by itself.

Example:
2³ × 2⁴ = 2³⁺⁴ = 2⁷ = 128

2. The Quotient Rule (Dividing with the Same Base)
When dividing two numbers with the same base, subtract the exponents.

Rule:
aᵐ ÷ aⁿ = aᵐ⁻ⁿ (as long as m > n)

Example:
5⁶ ÷ 5² = 5⁶⁻² = 5⁴ = 625

3. The Power of a Power Rule
When raising a power to another power, multiply the exponents.

Rule:
(aᵐ)ⁿ = aᵐ × ⁿ

Example:
(3²)⁴ = 3² × ⁴ = 3⁸ = 6,561

4. The Power of a Product Rule
When you raise a product to a power, raise each factor in the product to that power.

Rule:
(ab)ᵐ = aᵐ × bᵐ

Example:
(2 × 3)⁴ = 2⁴ × 3⁴ = 16 × 81 = 1,296

5. The Power of a Quotient Rule
When raising a fraction to a power, raise both the numerator and the denominator to the power.

Rule:
(a/b)ᵐ = aᵐ / bᵐ

Example:
(3/4)² = 3² / 4² = 9/16

6. The Zero Exponent Rule
Any number raised to the power of zero is always 1 (as long as the base is not zero).

Rule:
a⁰ = 1

Example:
7⁰ = 1

This rule works for any number except zero, because 0⁰ is undefined.

7. The Negative Exponent Rule
A negative exponent means you take the reciprocal (flip the fraction) of the base and change the exponent to positive.

Rule:
a⁻ᵐ = 1/aᵐ

Example:
2⁻³ = 1/2³ = 1/8

8. The Identity Exponent Rule
Any number raised to the power of 1 is just the number itself.

Rule:
a¹ = a

Example:
9¹ = 9

Summary of Rules:

• Product Rule: Add the exponents when multiplying.
• Quotient Rule: Subtract the exponents when dividing.
• Power of a Power: Multiply the exponents.
• Power of a Product: Distribute the exponent to all factors.
• Power of a Quotient: Apply the exponent to both numerator and denominator.
• Zero Exponent: Any base to the power of zero equals 1.
• Negative Exponent: Flip the base and make the exponent positive.
• Identity Exponent: Any number raised to the power of 1 is itself.

These rules help simplify expressions with exponents and make it easier to calculate large powers. With these examples and rules, you can solve any exponent problem!