Add and Subtract with Objects
What Is Addition and Subtraction with Objects?
Addition and subtraction are number operations written with + and −. For kids, these ideas click when they’re tied to real things they can see and move. If there are 8 plums and someone eats 5, there are 3 left. That’s subtraction.
Stories help these ideas stick. Picture this: Two sailors are on watch and spot a pirate ship. They wake the captain and 7 more sailors. How many people are ready to defend the ship? That’s addition.
Want more on using stories in math? Read our guide.
As numbers grow, visuals still matter. Big quantities are easier to grasp when we group them into tens, hundreds, and so on. That’s where base ten blocks shine.
Learn more about base ten blocks and place value.
Why Does It Matter for Kids?
Kids build abstract understanding step by step. Educators often call this the Concrete–Pictorial–Abstract (CPA) path.
Concrete: Kids act on real objects. They join one group to another to add, or move some objects away to subtract.
Pictorial (Representational): Kids picture the same actions in their mind or use photos, drawings, pictograms or schemas to stand in for real items.
Abstract: Kids work with numbers and the symbols “+” and “−” without visual support. They understand procedures, compose and decompose numbers in their head, and solve problems using symbols.
Research shows that moving from concrete to pictorial to abstract improves accuracy, reasoning, and confidence in the early and middle grades. It helps kids build stable, reliable number sense. When we skip straight to symbols and bypass the hands-on and visual stages, kids often feel unsure about the basics. Misunderstandings stack up and can lead to math anxiety. A steady CPA progression keeps learning clear and secure.
How Do We Teach?
Early on, we hold off on formal notation, especially operation signs, so kids can build rich “counting stories” and make friends with numbers. Even without symbols, they remember that 5 breaks into 1 and 4 or 2 and 3, and that these are the only splits.
Once kids connect a quantity with the digit that names it, we introduce + and −. We practice moving back and forth between a concrete model and a written expression, so symbols always point to meaning.
When numbers grow, we keep the visuals. With many objects, structure is key. We group by tens so the place-value makeup of each number is easy to see.
First Steps
Addition and Subtraction in Pictures
Subtraction often tells a “before and after” story: there were some things, some were taken, now fewer remain. To show what is gone, we leave traces like apple cores or candle stubs.
Visual addition and subtraction
Visual subtraction
Try arranging pinecones on small leaf “plates.” Even after you “eat” a few, you still see how many were there and how many were eaten. That makes it easy to find how many are left.
Many subtraction problems mirror complement problems: How many berries do we add to 2 to make 8?
Addition is even easier to picture because the sets you combine can differ in color or shape.
In real life we often add three or more sets. You can introduce several small addends early. Аsk a few kids to show a favourite number with their fingers, then count the fingers together.
Counting with pictures
Increase and decrease
Quantities & addition
Add up with 2 addends within 10 (objects only)
Order of numbers (up to 10)
Add one or two
Counting up to 5
Make four
Deep Understanding
Symbols: Numbers and Operation Signs
When kids know their digits well, they can tackle subtraction problems that require more than simple counting and call for imagination. For example, the label on the box shows the original number of pencils. You can see how many were taken out. How many remain inside?
Game to try: Put 10 candies on the table and cover some with a bowl. Guess how many are under the bowl, then lift it to check.
Visual addition and subtraction
Visual subtraction
As we bring in + and −, we keep using groups of objects in place of numerals. This softens the shift from concrete to abstract. Matching tasks help, too: pair a numeric expression (8 − 4) with a model that shows it (8 cubes with 4 crossed out). And give zero its own moment: adding 0 keeps the number the same. Small insights like this build big confidence.
Addition basics
Addition sign
Subtraction
Basic subtraction within 10
Subtraction
Model subtraction up to 10 (objects and numbers)
Practical problems with and without zero
Zero
Confident Mastery
Adding and Subtracting with Base Ten Blocks
Once there are more than 10 objects, it’s hard to “see” the total at a glance. Grouped objects solve that problem. Base ten blocks let kids add and subtract with tens and ones in a way that feels organized and clear.
Addition
Fluent addition (up to 20)
You can also use building blocks of length 5 and 10 for quick models. Counting sticks or matches tied into bundles of ten work well, and bead triangles that make a ten (1+2+3+4) do the same job. These tools keep ideas visual for two-digit and even three-digit numbers. Having a concrete model to return to is a powerful antidote to math anxiety.
Hundred
Tens and ones
Place value
Subtraction: two digits
Big numbers
Regrouping
Big numbers
Regrouping
Big Ideas
Lowering the level of abstraction is a helpful habit across math, not just in the early grades. When a problem feels stuck, bring it back to something you can see and touch, then climb back to symbols.
For word problems, act out the scene like a mini play or sketch a quick picture.
In motion problems, switch roles and imagine yourself as each driver.
When writing a computer program, “dry run” it step by step.
With large data sets, draw a graph and let each dot stand for one real item — for example, one city in a population graph or one animal in a zoo’s meat-consumption graph.
Algebra gets clearer if you picture numbers and variables as weights on a balance scale.
Geometric reasoning comes easier with a diagram in front of you.
Kids grasp 3D geometry better when the classroom has models of polyhedra. Even better when they build the models themselves.
When exploring a broad theory (for example, all transformations of space), keep returning to concrete examples and special cases such (as rotations, reflections, and scalings).
These habits keep math grounded and meaningful, helping kids build skills they can rely on far beyond just addition and subtraction.
