Making Subtraction Simple: Strategies for Young Learners

When young learners first encounter subtraction, it often seems like a mysterious operation that’s harder to grasp than addition. Unlike adding, which feels natural when combining objects, subtraction requires children to think about what’s missing or what’s being taken away. But here’s the good news: when we introduce subtraction through meaningful experiences, concrete materials, and multiple models, children can develop a deep and lasting understanding of this essential mathematical operation.

Understanding subtraction as taking away 🔗

The journey into subtraction typically begins with the most intuitive model: the take-away approach. This is where children physically remove objects from a group and count what remains. Imagine a child with ten colorful blocks on the table. When you ask them to take away three blocks, they can see and feel the action happening right before their eyes.

Students first experience subtraction through the use of models like cubes, counting bears, buttons, and counters, which help them understand the action happening in early subtraction problems. The beauty of this concrete approach is that it transforms an abstract mathematical concept into something tangible and real.

Start with everyday situations that children naturally encounter. If there are five cookies on a plate and someone eats two, how many are left? This simple scenario becomes a powerful learning moment when children can actually manipulate objects to find the answer. Using manipulatives allows students to visualize the regrouping process so that when they later learn more abstract methods, they truly understand what they’re doing.

Four powerful models of subtraction 🔗

While taking away is the most common introduction to subtraction, it’s just one piece of the puzzle. Research shows that children benefit enormously from exploring multiple models of subtraction, each offering a different lens through which to understand this operation.

Partitioning: separating the whole 🔗

The partitioning model, also called the part-part-whole model, helps children see subtraction as breaking a whole into parts. Think of it this way: you have twelve crayons in total, and you know that seven are blue. How many crayons are not blue? This isn’t about taking anything away; it’s about recognizing that the whole can be separated into different categories or groups.

Part-part-whole diagrams are essentially bar models that represent the different parts and wholes in a number equation, making them excellent for helping young students see the connection between addition and subtraction. When children work with this model, they begin to understand that subtraction and addition are closely related operations.

Reduction: decreasing quantities 🔗

The reduction model focuses on how quantities decrease over time or through actions. Unlike the simple take-away model where we remove objects all at once, reduction emphasizes the process of getting smaller. If a child has fifteen stickers and gives away some to friends throughout the day, the collection reduces gradually.

This model connects beautifully to real-world scenarios. When you’re tracking how much juice is left in a pitcher after pouring several glasses, or how many pages remain in a book as you read, you’re using the reduction model of subtraction.

Comparison: finding the difference 🔗

The comparison model asks a different kind of question: how much more or how much less? If Maya has eight pencils and Jordan has five, how many more does Maya have? Comparison subtraction problems can be more challenging to visualize because you’re not physically taking objects away from a single group; instead, you’re examining the relationship between two separate quantities.

This model becomes especially powerful when children learn to line up objects or draw bars to compare. By placing Maya’s eight pencils in one row and Jordan’s five pencils directly below them, the difference becomes visually obvious. The three pencils that extend beyond Jordan’s row represent the answer to “how many more.”

Complementary addition: counting up 🔗

Perhaps the most elegant model is complementary addition, which flips subtraction on its head by asking, “What do we add to reach our goal?” If you have seven apples and need twelve for a recipe, complementary addition asks: what goes with seven to make twelve?

This approach particularly helps children who find subtraction challenging because understanding the relationship between addition and subtraction makes problem-solving easier. Many students discover that counting up feels more natural than counting back, and once they grasp this strategy, they prefer it for mental math.

Subtraction stories and games 🔗

One of the most effective ways to help children practice subtraction is through storytelling and play. Stories give context and meaning to numbers, transforming abstract problems into engaging narratives that children want to solve.

Create simple subtraction stories from children’s daily experiences. “There were eight birds sitting on the fence. Three flew away to find food. How many birds are still on the fence?” These stories don’t need to be complex; they just need to be relatable and interesting to young learners.

Games add an element of excitement and repetition without tedium. Consider dice games where children roll to see how many objects to remove from a collection, or card games where they subtract the smaller number from the larger. Board games naturally incorporate counting back as players move their pieces, reinforcing subtraction concepts through play.

Store games are particularly valuable because they combine subtraction with real-world math. Set up a pretend store where children “buy” items with play money. If they start with ten dollars and spend three dollars, how much money remains? This scenario connects mathematical operations to practical life skills.

Interactive subtraction activities 🔗

Movement-based games make subtraction memorable. Try “Ten in the Bed” where children act out the song, with one child rolling off the bed each verse. Musical chairs naturally teaches subtraction as chairs are removed one by one. Even simple playground activities like “Duck, Duck, Goose” can reinforce counting and subtraction concepts.

Technology can also support learning through educational apps and online games that provide immediate feedback and adaptive challenges. However, these digital tools work best when balanced with hands-on, concrete experiences that allow children to manipulate physical objects.

Using visual aids and number strips 🔗

Visual representations bridge the gap between concrete objects and abstract numbers. They help children move from needing physical manipulatives to being able to solve problems mentally or on paper.

Number lines are among the most versatile visual tools for subtraction. Number lines help students move from the concrete stage to a more abstract understanding of subtraction. Children can start at the larger number and jump backward, counting each jump until they reach their destination. For the problem twelve minus five, a child would start at twelve and make five jumps backward, landing on seven.

Number strips and tracks 🔗

Number strips provide a simplified version of the number line that’s particularly helpful for beginners. These are simply sequences of numbered boxes that children can use to physically track their counting. Some teachers create number strips with removable pieces, allowing children to cover or remove numbers as they subtract.

Ten frames offer another powerful visual tool, especially for developing number sense within ten. These two-by-five grids help children quickly visualize quantities and understand how numbers relate to ten, which becomes crucial for more complex subtraction later on.

Pictorial representations 🔗

Before children can work comfortably with abstract numbers, they benefit from drawing pictures to represent problems. If the question is “nine minus four,” a child might draw nine circles and then cross out four of them, counting the remaining circles to find the answer.

As children’s skills develop, these pictures can become more symbolic. Instead of drawing detailed objects, they might use simple dots, tally marks, or base-ten block sketches. This gradual shift from realistic drawings to mathematical symbols represents significant cognitive growth.

Bar models for complex problems 🔗

Bar models become especially valuable as subtraction problems grow more complex. These rectangular representations show the relationships between quantities in a problem. For a comparison problem, two bars of different lengths placed side by side immediately show which quantity is larger and help children visualize the difference.

The beauty of bar models is their flexibility. They work equally well for simple problems with small numbers and for multi-step word problems involving larger numbers. As children progress through elementary school, bar models continue to support their mathematical thinking across various operations and concepts.

What do you think? How might understanding multiple models of subtraction help children tackle more complex mathematical problems in the future? Can you think of everyday situations where children naturally encounter different types of subtraction without realizing it?

References

1. https://www.maine.gov/doe/pl/math/subtraction
2. https://www.scholastic.com/parents/school-success/learning-toolkit-blog/addition-and-subtraction-models-and-strategies.html
3. https://www.therecoveringtraditionalist.com/best-way-to-teach-subtraction/