Welcome to the Essential Guide for teaching the Problem Solving Strategies: Vertical Sums block.
Whether you are new to Waldorf education or deep into Grade 3, this guide gives you the philosophy, goals, and daily rhythm you need to teach strong, reliable written maths strategies, including the standard vertical algorithms, with real understanding.
The Philosophy: Multiple Paths, Then a Shortcut
In a traditional classroom, children are taught the vertical algorithm as the one correct way to add, subtract, or multiply. Line up the digits, carry the one, borrow across. The child memorises the moves without necessarily understanding why any of them work.
The Waldorf approach teaches multiple strategies first. Your child learns the split strategy (breaking numbers into tens and ones), the compensation strategy (adjusting numbers to make them easier), and only then the stacking strategy (the traditional vertical algorithm). By the time your child lines up the digits in a column, they already know exactly what those digits are doing, because they have added them a dozen different ways already.
This changes the vertical algorithm from a magic trick into a tidy shortcut. Carrying the one is no longer a mysterious move; it is what happens when the ones column adds up to more than ten, and the child has already felt that, in their hands, with split-strategy work.
By teaching strategies this way, your child achieves several things at once:
True understanding: they know why vertical addition works, not just how to do it.
Flexible thinking: they choose the strategy that fits the problem.
Confident vertical algorithms: when they do stack numbers, they do it with meaning.
Self-checking: they estimate before solving and compare two strategies to check their own work.
The Curriculum: What You Will Teach
This block is designed to take 20 instructional days. It moves through addition, subtraction, and multiplication using increasingly efficient strategies.
The Strategy Progression:
Split Strategy: breaking numbers into tens and ones.
Compensation Strategy: adjusting numbers to make them easier.
Stacking (Vertical Addition): lining numbers up in columns, with and without carrying.
Vertical Subtraction: with and without borrowing.
Vertical Multiplication: building toward the standard algorithm for larger numbers.
Word Problem Application: using each strategy inside real contexts.
Your Learning Intentions:
By the end of the 20 days, your child should be able to:
Solve addition and subtraction problems using at least three different strategies.
Use the vertical algorithm for addition, subtraction, and simple multiplication with understanding.
Explain why carrying and borrowing work.
Choose the most efficient strategy for a given problem.
Record working and answers neatly in the Main Lesson book.
Practical Guidance: How to Set Up Your Space
Materials Needed:
Main Lesson Book and Lined Exercise Book: For daily working and skills practice.
Block and Stick Crayons, Coloured Pencils, Graphite Pencil: Chunky or triangular grip.
Counters: For modelling carrying and borrowing with concrete quantities.
Scrap Paper or a Small Whiteboard: For modelling strategies before committing to the book.
💡 Teacher Tip: The Vertical Algorithm Is a Shortcut, Not a Truth
When you introduce stacking on Day 1, present it as the third strategy, not the most important. Say: “Here is another way to write what we have been doing. Some mathematicians find this tidier.” Your child has already added 34 + 25 using split and compensation. Now they write it stacked. The answer is the same. The mathematics is the same. The stacking is just a way of showing the work on a small piece of paper. When carrying comes in later, the child will see it as what happens when the ones add up to more than ten, not as a new mystery.
The Waldorf Method: How to Structure a Daily Lesson
Each day follows a steady rhythm: Review, New Learning, Modelled Problems, Independent Practice. Here is how it looks on Day 1: Three Strategies for Addition.
Step 1: Review Addition
Warm up orally: “What is 20 + 30? What is 40 + 5? What is 60 + 20?” Remind your child that addition means putting quantities together.
Step 2: New Learning (Three Strategies)
Model each strategy for 34 + 25:
Split: 30 + 20 = 50; 4 + 5 = 9; total 59.
Compensation: find a tidy number nearby. (Not always useful for this problem, but introduce the idea for 39 + 21: move 1 from 21 to 39, now it’s 40 + 20 = 60.)
Stacking: line the numbers up under each other, add the ones first, then the tens. Same answer: 59.
Step 3: Modelled Problems
Display six problems (three easier, three harder). For each, your child says which strategy they will use before solving. Examples: 23 + 14, 40 + 28, 36 + 13, then 47 + 32, 58 + 21, 64 + 15.
Step 4: Independent Practice
Your child works through 6 to 8 problems in the Main Lesson book or a maths book, choosing whichever strategy makes the most sense. Remind them to line up numbers carefully if stacking, and to estimate first to check reasonableness. Include two word problems at the end.
Build It Yourself vs. The Guided Curriculum
You now have the method and the first day. If you have the time, you can plan the 20-day progression, sequence the strategies carefully, design examples that build toward carrying and borrowing, and prepare the bookwork pages.
For many homeschooling families, four weeks of carefully paced written maths strategies is more than a busy week allows. If you would rather spend your mornings solving with your child than writing problems late at night, the complete Vertical Sums block is ready for you.
What’s Inside the Complete Block?
20 Complete Daily Lesson Plans: Step by step from split strategy through the standard vertical algorithms.
Worked Examples for Every Strategy: With commentary on when each strategy fits best.
Carefully Paced Problem Sets: Easy and harder problems for each day, plus challenge problems.
Word Problem Integration: Real-world applications of every strategy.
Main Lesson Book Artwork: Reference pages for every day.
Daily Skills Practice: Basic facts, time reading, cursive, spelling.
Teacher Tips Throughout: So you always know when to prompt a different strategy and when to let your child stack the numbers.
Everything is carefully structured to give you the confidence of an experienced Waldorf teacher, right through to the last carried one.