What is a function machine in maths?

A function machine takes an input number, applies a rule (like multiply by 2 and add 3), and produces an output. For example, with the rule 2x + 3, an input of 5 gives output 13. Function machines help you understand how algebraic expressions work.

How do you solve a one-step equation?

Use the inverse operation. For x + 7 = 15, subtract 7 from both sides to get x = 8. For 3x = 18, divide both sides by 3 to get x = 6. Always check your answer by substituting back into the original equation.

What is the difference between an expression and an equation?

An expression is a combination of numbers, variables, and operations without an equals sign (e.g., 3x + 5). An equation has an equals sign and states that two things are equal (e.g., 3x + 5 = 20). You simplify or evaluate expressions, but you solve equations.

Worksheets

Algebraic Thinking Class 6 IB Worksheet Free PDF Download with Answers

Think like a mathematician. 60 questions on variables, expressions, equations, function machines, and algebraic reasoning.

IBClass 6

SparkEd Team · Reviewed by Vivek Verma15 April 20267 min read

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45 practice questions across 3 difficulty levels with complete answer keys. Printable A4 format, perfect for revision!

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Class 6 Maths Worksheet — Free PDF with Answers

This is your one-stop class 6 maths worksheet collection — every topic, every chapter, completely free with step-by-step answers. Whether you searched for a maths class 6 worksheet or a worksheet math class 6 resource, you have landed in the right place. SparkEd's Class 6 maths practice covers the full IB MYP syllabus with 60 questions per topic, and each worksheet comes as a printable PDF.

Parents and teachers often look for a class 6 maths chapter 7 worksheet with answers or a class 6 maths chapter 3 worksheet with answers — here you will find those and every other chapter too. Every class 6th maths worksheet is aligned to the latest IB MYP pattern, so the maths worksheets of class 6 you download match exactly what is taught in school. Need a quick class 6th mathematics solution or a handy class 6th math formula sheet? Check out the Class 6 All Formulas guide.

Each maths worksheet for class 6 includes a mix of short-answer, long-answer, and maths questions and answers for class 6 in MCQ format. You get a complete maths worksheet for class 6 with answers, making self-study easy. The content is suitable as a maths worksheet for class 6 cbse as well as a maths worksheet for class 6 ncert resource — both boards follow the same core syllabus. Looking for a simpler label? It is the same math worksheet for class 6 you need.

For revision before exams, try the maths worksheet for class 6th with answers alongside our maths mcq for class 6 with answers sets. Teachers can use the class 6 maths mcq question paper bank for quick classroom tests. Browse all class 6 maths worksheets cbse topics on the All Class 6 worksheets page, or start with the popular Number Play worksheet. Ready to practise? Head to SparkEd home and pick your chapter.

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IB MYP Maths Worksheet — Free PDF with Answers

SparkEd's IB MYP Year 1 maths worksheets are designed for students in the International Baccalaureate Middle Years Programme. Each worksheet has 60 questions across three difficulty levels, with complete step-by-step answers. The questions align with the IB MYP mathematics framework, emphasising conceptual understanding and inquiry-based learning.

Whether you are preparing for a criterion-based assessment or want extra practice, these worksheets are free to download as printable PDFs.

Want to practise Algebraic Thinking digitally? Try free online practice on SparkEd — instant grading, visual solutions, and an AI coach to help when you are stuck.

Algebraic Thinking — From Arithmetic to Algebra

In the IB MYP framework, algebra is not just about solving for $x$ . It is about thinking in general terms, spotting patterns, and expressing relationships. Algebraic thinking means moving from specific numbers to general rules.

For example, instead of saying "I added 5 to 3 and got 8", you learn to say "When I add 5 to any number $n$ , I get $n + 5$ ." This shift from specific to general is the heart of algebra.

This worksheet builds algebraic thinking through function machines, pattern rules, and real-world contexts that make variables meaningful.

What Does This Worksheet Cover?

Aligned with the IB MYP Year 1 mathematics framework:

- Variables — using letters to represent unknown or changing quantities
- Algebraic expressions — writing and simplifying expressions
- Substitution — finding the value of an expression for given values
- Function machines — input-output tables and rules
- Forming equations — from word problems and patterns
- Solving simple equations — using inverse operations
- Inequalities — introduction to greater-than and less-than relationships

| Level | Focus | Count |
|-------|-------|-------|
| Level 1 | Identify variables, write expressions, basic substitution | 20 |
| Level 2 | Function machines, form equations, solve one-step equations | 20 |
| Level 3 | Two-step equations, pattern rules as expressions, inequalities | 20 |

Sample Questions

Level 1 — Warm Up

Write an algebraic expression for: " $8$ less than a number $m$ ."
If $a = 5$ , find the value of $3a + 7$ .
A function machine multiplies the input by $4$ and then subtracts $1$ . Find the output when the input is $6$ .

Level 2 — Build Confidence

Complete the function table:
| Input ( $x$ ) | Output ( $y = 2x + 3$ ) |
|---|---|
| 1 | ? |
| 4 | ? |
| 7 | ? |
Form an equation: "Three times a number, decreased by $4$ , equals $17$ ."
Solve: $5n + 3 = 28$ .

Level 3 — Push Yourself

The $n$ th term of a pattern is $4n - 1$ . Find the first 5 terms. What is the 20th term?
Solve: $\frac{x}{3} + 5 = 9$ .
Find all whole numbers $x$ that satisfy: $2x + 1 < 15$ .