Arithmetic Curriculum

Mathematics

A structured, level-by-level path through Arithmetic. Start with Foundations of Place value and Core methods in Addition & subtraction at the Intermediate level, then build toward advanced practice and expert-level mastery — with hands-on projects and quizzes at every stage.

3 levels 9 modules 27 topics 6 weeks · about 24 hours · 8 weeks · about 32 hours · 10 weeks · about 40 hours
Intermediate

Intermediate Arithmetic

6 weeks · about 24 hours

3 modules

Advanced

Advanced Arithmetic

8 weeks · about 32 hours

3 modules

Expert

Expert Arithmetic

10 weeks · about 40 hours

3 modules

Arithmetic Course Curriculum

9 modules across 3 levels.

Intermediate

Intermediate Arithmetic

Start with Place value, Addition & subtraction and Multiplication & division. Each module explains the idea, shows a worked example and ends with a short project, so Arithmetic becomes something you can do rather than something you have only read about.

6 weeks · about 24 hours 3 modules

Topics

Project

Write a one-page explanation of Place value in your own words, with an example you chose yourself, and test it against the module checklist.

Learning Path

1

Foundations of Place value

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

2

Core methods in Addition & subtraction

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Foundations of Place value

3

Applying Multiplication & division

Work through the three topics in this module, complete the project, then answer the self-check questions before moving on.

Prerequisites: Core methods in Addition & subtraction

Practice Problems

EasyExplain Place value to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines place value precisely, gives one concrete example, and names the limitation it runs into.
MediumExplain Addition & subtraction to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines addition & subtraction precisely, gives one concrete example, and names the limitation it runs into.
HardExplain Multiplication & division to someone who has never studied the subject, using one worked example.
Solution: A strong answer defines multiplication & division precisely, gives one concrete example, and names the limitation it runs into.

Glossary

Place value

A central idea in the intermediate Arithmetic path, covered in the module of the same name.

Example: apply Place value to a small, familiar case step by step, then check your reasoning against the walkthrough.

Addition & subtraction

A central idea in the intermediate Arithmetic path, covered in the module of the same name.

Example: apply Addition & subtraction to a small, familiar case step by step, then check your reasoning against the walkthrough.

Multiplication & division

A central idea in the intermediate Arithmetic path, covered in the module of the same name.

Example: apply Multiplication & division to a small, familiar case step by step, then check your reasoning against the walkthrough.

About the Arithmetic curriculum

The Arithmetic curriculum is a complete, self-paced course in mathematics, organised into 3 progressive levels and 9 modules. It opens with Foundations of Place value and Core methods in Addition & subtraction, moves through Applying Multiplication & division and finishes with expert-level work on Leading practice in Mental maths strategies and Mastering Word problems.

Across the whole path you work through 27 individual topics — from Place value and Putting place value to work at the start to Putting word problems to work and Checking your understanding of word problems by the end. The levels are estimated at 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Each level assumes the one before it, so you can work straight through from Intermediate to Expert, or start at the level that matches what you already know.

It suits analysts, researchers and students who need to reason with numbers and defend a conclusion, not just run a tool. The emphasis is on interpretation: every technique is introduced with the question it answers, the assumption it needs and the way it fails, so you can apply it to unfamiliar data.

Every module pairs a written summary with a worked example, a short quiz to check the idea landed, and a project brief drawn from real practice. You are never asked to take a concept on trust: the reasoning, the common mistakes and the situations where the approach stops working are all laid out, so you finish a module able to explain the idea rather than only recognise it.

What you’ll be able to do

By the end of the Arithmetic path you should be able to work confidently with:

Place value

Putting place value to work

Checking your understanding of place value

Addition & subtraction

Hands-on: addition & subtraction

Checking your understanding of addition & subtraction

Multiplication & division

Putting multiplication & division to work

How the Arithmetic curriculum is structured

Intermediate 6 weeks · about 24 hours 3 modules 9 topics

Intermediate Arithmetic

Start with Place value, Addition & subtraction and Multiplication & division. Each module explains the idea, shows a worked example and ends with a short project, so Arithmetic becomes something you can do rather than something you have only read about.

Modules: Foundations of Place value · Core methods in Addition & subtraction · Applying Multiplication & division

  • Place value: This module treats Place value as a tool: the question it answers, what it assumes, and what a correct use of it looks like in Arithmetic.
  • Putting place value to work: Place value is introduced from first principles, with the few terms you actually need and an example that shows how the idea behaves in practice.
  • Checking your understanding of place value: This module treats Place value as a tool: the question it answers, what it assumes, and what a correct use of it looks like in Arithmetic.

Project: Write a one-page explanation of Place value in your own words, with an example you chose yourself, and test it against the module checklist.

Advanced 8 weeks · about 32 hours 3 modules 9 topics

Advanced Arithmetic

Build on the intermediate level through Fractions, Decimals & percentages and Order of operations. The emphasis shifts from knowing the ideas to choosing between them — trade-offs, failure modes and the reasoning behind each decision.

Modules: In depth Fractions · Patterns and trade-offs in Decimals & percentages · Scaling Order of operations

  • Fractions: Fractions is pushed past the textbook case: competing approaches, their trade-offs and the situations where each one breaks down.
  • Putting fractions to work: The module examines Fractions closely, including the assumptions beneath it and what changes when those assumptions stop holding.
  • Common pitfalls in fractions: Fractions is pushed past the textbook case: competing approaches, their trade-offs and the situations where each one breaks down.

Project: Produce a short case analysis in which Fractions drives the recommendation, including the alternatives you rejected and why.

Expert 10 weeks · about 40 hours 3 modules 9 topics

Expert Arithmetic

Work at the edge of Arithmetic through Ratios & proportion, Mental maths strategies and Word problems. The modules assume fluency and ask for judgement: designing, critiquing and defending work at a professional standard.

Modules: Frontiers of Ratios & proportion · Leading practice in Mental maths strategies · Mastering Word problems

  • Ratios & proportion: This module asks you to critique and extend Ratios & proportion rather than simply apply it, producing work another expert could review.
  • Putting ratios & proportion to work: At expert level Ratios & proportion is treated as a field of judgement: current practice, contested positions and the evidence behind each.
  • Checking your understanding of ratios & proportion: This module asks you to critique and extend Ratios & proportion rather than simply apply it, producing work another expert could review.

Project: Write a professional-standard brief on Ratios & proportion — argument, evidence, limitations — plus a plan for taking the work further.

How to study Arithmetic, phase by phase

  1. 1

    Phase 1 — Intermediate

    Set aside around 6 weeks · about 24 hours. Work through 3 modules, starting with Foundations of Place value and Core methods in Addition & subtraction. Finish the phase by completing the project brief: Write a one-page explanation of Place value in your own words, with an example you chose yourself, and test it against the module checklist.

  2. 2

    Phase 2 — Advanced

    Set aside around 8 weeks · about 32 hours. Work through 3 modules, starting with In depth Fractions and Patterns and trade-offs in Decimals & percentages. Finish the phase by completing the project brief: Produce a short case analysis in which Fractions drives the recommendation, including the alternatives you rejected and why.

  3. 3

    Phase 3 — Expert

    Set aside around 10 weeks · about 40 hours. Work through 3 modules, starting with Frontiers of Ratios & proportion and Leading practice in Mental maths strategies. Finish the phase by completing the project brief: Write a professional-standard brief on Ratios & proportion — argument, evidence, limitations — plus a plan for taking the work further.

  4. 4

    Phase 4 — Consolidate

    Return to the sections that felt weakest, redo their quizzes from memory, and rebuild the Write a one-page explanation of Place value in your own words, with an example you chose yourself, and test it against the module checklist. without following along. Explaining Arithmetic to someone else in plain language is the clearest signal that the Expert level has landed.

Once you have finished, the Arithmetic path is a reasonable foundation for analytics, data science, research and quantitative roles. Because the curriculum is generated and kept as a structured outline rather than fixed videos, you can revisit any module, regenerate the outline at a different depth, or save it to your library and work through it over weeks rather than in one sitting.

Arithmetic — Frequently Asked Questions

Common questions about studying Arithmetic on LearnAnyCourse.

What does the Arithmetic curriculum cover?

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The Arithmetic curriculum is organised into 3 levels (Intermediate, Advanced and Expert) and 9 modules, including Foundations of Place value, Core methods in Addition & subtraction, Applying Multiplication & division, In depth Fractions, Patterns and trade-offs in Decimals & percentages and Scaling Order of operations.

How long does it take to learn Arithmetic?

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Each level is designed to take about 6 weeks · about 24 hours, 8 weeks · about 32 hours and 10 weeks · about 40 hours. Most learners work through one level at a time at their own pace.

Is the Arithmetic curriculum free?

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Yes. Every Arithmetic curriculum on LearnAnyCourse is free to read and study — create an account only if you want to save curricula to your personal library.

Do I need prior experience to study Arithmetic?

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The curriculum starts at the intermediate level and builds upward, so you can begin with the fundamentals and progress to expert-level Arithmetic topics without jumping ahead.

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