Word Problems for Kindergarten and Primary School Students (Ages 5–9)
What Are Word Problems?
A word problem is a short story that usually includes some numbers. At the end there’s a question that calls for a numerical answer. Most of the time, you use the numbers in the story and simple arithmetic to figure it out. For example:
Santa is getting 8 gifts ready and wants to put 3 tangerines in each. How many tangerines does he need for all the gifts?
Someone took 8 tree ornaments out of a box, and 12 ornaments are left. How many ornaments were in the box to begin with?
At school, word problems are often sorted by type (addition on one side, subtraction on the other; first one-step, then two-step). But what really matters is variety. We don’t want kids to get used to grabbing two numbers and picking an operation without thinking. A problem might have one number, two, or three. For example:
A pirate and a parrot had the same number of gold bars. The pirate took two bars from the parrot. Who has more now? By how many?
In everyday life, we run into both word problems and non-text problems. Maybe you need to cut a recipe in half, or figure out when to leave home so you won’t be late for a concert. These tasks are different from typical textbook problems in how the information shows up:
You often need to bring in extra data, like a bus schedule, and choose what’s relevant from a lot of information.
Much of the information isn’t text at all. It might be pictures, graphs, tables, or even short videos, like an online recipe.
Why Does It Matter for Kids?
Research shows that strong language understanding has a bigger impact on success with word problems than fast calculation skills. To really grasp a problem, kids often need to read or listen more than once, break the text into parts, mark what matters, retell it in their own words, act it out, model it with objects, and sketch pictures or simple diagrams.
A common tip is to look for “key words,” like “more means add” or “left means subtract.” That might help for a single quiz, but it isn’t a strong long-term strategy. It can turn problem solving into a mechanical jump from the story to a formula without building a mental model of what’s happening. It can even mislead kids. For example, “how many more” is about comparing quantities, which often calls for subtraction, not addition.
When analyzing a problem, it helps to cross out extra details and circle the important ones. Ask kids to explain what happened, act it out with puppets or toys, pick a matching picture, or retell the story in their own words. You can also tell numberless arithmetic stories to focus attention on meaning and models first. Another helpful move is to give kids the beginning of a story and ask them to invent the rest.
Schema-based instruction gives kids a toolbox of common story structures, such as “total” (combining two or more sets) or “change” (adding to or taking from a set). To choose a schema, kids need to read the whole text. The schema then points to different operations depending on what is known and what is being asked. At the same time, kids should also meet problems that don’t fit neat schemas. This pushes them to invent their own strategies and, sometimes, new schemas.
Finally, kids benefit most from problems that feel like real life. Real-world tasks are harder than simplified textbook stories, but working through them builds deeper understanding and more useful problem-solving habits.
How Do We Teach?
At the beginning, kids learn to answer questions about a picture. These don’t have to be numerical — “What color is the girl’s hat?” works just fine. Over time, the picture gets richer, more objects appear, and a full story unfolds that kids need to notice and understand. It helps to put a few illustrations from a simple story in order and build the story from the images. Arithmetic stories can also pop up in play as kids use simple props, like acorns or pebbles for food and leaves or shells for plates.
Hands-on pretend play is a powerful bridge to word problems. A chair can be a train car, a stick can be a horse. So when a kid hears a story, it feels natural to show strawberry ice cream as red dots and pistachio as green ones. Imagination helps kids picture what happens next: adding items, taking some away, or sharing things equally into two piles. They might count hidden rabbits by their ears, or imagine unseen giraffes and ostriches by looking at hats and shoes.
Many kids need time to understand money and its symbolic value. They are used to counting identical objects, so it is tricky when different coins and bills have different values. Here is a typical confusion. For example, a little girl once wondered why her mom needed to work. At the store she saw her mom hand over one paper bill and then receive a handful of coins and bills as change. To her it looked like there was more money afterward. To build this concept, it helps to picture a coin labeled 5 as a small box with five 1s inside.
Money is a great model for many operations. To find the total cost, you add prices. If every item costs the same, you multiply. Change comes from subtraction. When you ask “How many can I buy for 100?”, you are doing division with a remainder.
We also include lots of problems that lay the groundwork for equations. Think of balanced scale puzzles where you have to find the weight of an object, or “mystery box” problems where identical boxes hold the same number of candies and you know the totals for different sets of boxes. This is early practice not only for equations but also for systems of equations later on.
Finally, we do not stop at single answer problems. We give problems with multiple correct answers too. Sometimes one example is enough, but more often we ask kids to find all solutions, or at least check every possibility to see whether it fits the story.
First Steps
Match the Story to the Picture and Count
Solving word problems is closely tied to hands-on and pretend play. When kids step into a favorite character’s shoes, they can follow the story of a problem and act it out.
We invite kids into a quick make-believe snack game. Any small objects can be the snacks, and small bowls or paper circles can be the plates. As kids serve and share, they count, add, and take away.
Counting with pictures
Increase and decrease
We start simple. Kids listen to a short word problem and then point to the objects in a picture that they need to count.
Next come actions. Kids might remove a few items by covering them with a hand or share the items equally between two people. Sometimes the answer is shown as a picture rather than a number.
Some problems are trickier than they look. Consider this one: Emily has two brothers and three sisters. How many kids are in the family? Many people add two and three and forget to include Emily. With a picture, kids can find Emily, her brothers, and her sisters, count everyone, and get the right answer.
Visual addition and subtraction
Visual addition
Subtraction basics
Taking away
Halves and multiples
Halves
Counting with a twist
Brothers and sisters
Deep Understanding
Engage Imagination and Sketch Simple Models
Imagination sits at the heart of word problems. A kid who can picture an invisible lamb asleep in a box drawn on paper can just as easily picture the pencils that remain in a box after three have been taken out.
Visual addition and subtraction
Visual subtraction
Sometimes a problem asks kids to imagine unseen giraffes and ostriches by using clues like hats and shoes, then remember that each giraffe has four legs and each ostrich has two. Other times the task is to update the picture that is already there: add one berry to each jar, or picture how many wheels there will be if two more bikes arrive.
Money can be tricky, and imagination helps here as well. A coin labeled 5 can be pictured as a small box with five 1s inside.
While reading, turn the story into a quick sketch: draw an ice cream cone with three scoops, cross out two, then count how many are left. The picture makes the answer clear.
Hats, legs and other problems
Heads and legs
Counting with pictures
Number puzzles
Practical money problems
Tasks with coins
Schemes
Model word problems
Confident Mastery
From Text to Meaning to Models to Symbols
In a comic-strip format, we can tell rich, challenging stories that quietly ask kids to work with unknowns. It feels less abstract when the unknowns are shown as little boxes instead of x’s. For example, two red boxes hold 16 candies in total and the boxes are equal, so each box has 8. A red box and a green box together have 27 candies, and the red box has 8. That means the green box has 19.
Addition & subtraction
Systems of equations
Kids also tackle practical shopping puzzles. The goal is to choose the largest number of items you can buy with a fixed amount of money. At heart, this is division with a remainder, and kids learn to reason about what fits the budget and what does not.
They also meet age problems that use relationships like “older by N years” or “N times as old.”
In many problems it helps to adjust the numbers first. Swap a big number for a smaller one and look for a pattern. For example, cutting a log into two pieces takes one cut, and into three pieces takes two cuts. The pattern is easy to spot. The number of cuts is one less than the number of pieces. You begin with one piece, and each cut adds one more.
It is also useful to meet problems with more than one correct answer. Sometimes the story says that one quantity is greater than another but does not say by how much. In that case there are many possibilities, and kids practice listing or checking all the options that fit the conditions.
Family week
Age word problems
Practical money problems
Count in the picture
Counting with a twist
Cuts
Counting with a twist
Real-life addition
Big Ideas
Stories run through our culture, from books and comics to movies. We also write our own stories about the near future, like planning a kid’s birthday party. To make that plan real, we often do some math: count the guests, figure out how many cupcakes and party favors we need, check prices, and set a budget. In that sense, word problems are not just for school. They are a life skill.
The path from story to sketch to symbols comes together in algebra, where variables help us handle more complex situations. Many areas of math, including functions, probability, and differential equations, begin with a real-world scenario: the behavior of a sound wave in water, a gambler in a casino, or a population of whales in the ocean.
Finally, even if AI can solve a well written problem, we still need everyday common sense, quick estimation skills, and hands-on practice with small, simple arithmetic problems to judge whether the model and the answer make sense.
