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§ Expressions & Algebra·Grade 6

Formulas Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable formulas worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from substitute into speed = distance / time at the easy level through to rearrange formula then substitute at the advanced level.

CCSS.6.EECCSS.HSA.CED

What is formulas?

A formula is a mathematical equation that expresses a relationship between different variables using letters and symbols. In the formula A = πr², the area of a circle equals π times the radius squared, where A represents area and r represents radius. Formulas appear throughout mathematics and science, from simple area calculations to complex physics equations.

Why it matters

Formulas serve as mathematical shortcuts for solving real-world problems efficiently. Engineers use the formula v = u + at to calculate how fast a rocket accelerates, substituting initial velocity (u = 0), acceleration (a = 9.8 m/s²), and time (t = 10 seconds) to find final velocity (v = 98 m/s²). In construction, architects apply A = l × w to determine flooring needs, calculating that a 12-foot by 15-foot room requires 180 square feet of material. Financial planners use compound interest formulas to project investment growth over decades. Medical professionals rely on dosage formulas to ensure patient safety. CCSS 6.EE standards introduce formula substitution as a bridge to algebraic thinking, while CCSS HSA.CED extends this to function composition and complex relationships that appear in advanced mathematics and scientific modeling.

Common mistakes to watch for

  • ✗Forgetting order of operations leads to incorrect calculations, such as computing v = 5 + 10 × 2 as 30 instead of 25 by adding first rather than multiplying
  • ✗Mixing up variable assignments produces wrong substitutions, like using distance = 50 and time = 100 in speed = distance ÷ time to get 0.5 instead of reversing the values for the correct answer of 2
  • ✗Dropping units from final answers creates incomplete solutions, writing A = 36 instead of A = 36 square meters when calculating area

Questions teachers ask

What is the difference between a formula and an equation?+
A formula shows a general relationship between variables (like A = πr²), while an equation includes specific numerical values (like A = π × 4² = 50.3). Formulas are templates; equations are complete mathematical statements with solutions.
How do you know which variable to solve for in a formula?+
The problem statement typically indicates the unknown variable. If asked to 'find the area' in A = l × w, solve for A. The variable standing alone (isolated) on one side is usually what needs to be calculated.
Why do some formulas require rearranging before substituting?+
Rearranging isolates the unknown variable. If finding time in v = u + at, first rearrange to t = (v - u)/a, then substitute values. This ensures the desired variable appears alone on one side of the equation.
What happens if you substitute negative numbers into formulas?+
Negative numbers follow normal arithmetic rules. In v = u + at with u = -10, a = 5, and t = 3, the result is v = -10 + 15 = 5. Pay attention to signs during calculations to avoid errors.
How do you check if your formula substitution is correct?+
Verify by working backwards or using dimensional analysis. If speed = 50 km/h from distance ÷ time, multiply 50 × 2 hours to confirm distance = 100 km. Check that units make sense in the final answer.
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Pick a difficulty

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Beginner

Generate →
Concepts
Substitute into speed = distance / time
Range
multiples of 5, time 2–5
Steps
2 steps
Example
d = 150 km, t = 3 h, find speed

Easy

Generate →
Concepts
Substitute into area = l × w
Range
l: 3–12, w: 2–10
Steps
2 steps
Example
A = l × w, l = 8, w = 5

Medium

Generate →
Concepts
Substitute into v = u + at (3 values)
Range
u: 0–15, a: 2–10, t: 2–6
Steps
3 steps
Example
v = u + at, u = 10, a = 5, t = 3

Hard

Generate →
Concepts
Rearrange formula then substitute
Range
v, u: 0–20, a: 5 or 10, t: 2–6
Steps
4 steps
Example
Rearrange v = u + at for t, then solve

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