Up, Down, and Around
Explore Spatial Thinking
When children crawl under a table, fit toys in a box, or figure out how to get through a narrow path, they are thinking about how to move through or fill up a certain space. Moments like these support spatial thinking—how we understand where objects are and how they move or fit together.
- Audience
- Caregiver
- Subject
- Math
- Age
- KindergartenPre-KPreschoolToddler
- Languages
- Brazilian PortugueseEnglishHaitian CreoleSimplified ChineseSpanish
- Materials
- Paper cups, bowls, painter's tape, blanket, sticky notes
Many adults feel anxious about math, often because of past experiences. But here is the good news: you don’t need to be a math expert to help your child! Just be curious together. Notice the shapes and numbers around you, and talk about them while you play. When math is part of everyday life, it feels less scary for both of you. Laugh, explore, and don’t worry about mistakes.
Try these activities!
Cup towers
- Explore different ways to place lots of paper cups.
- Place cups right side up or upside down.
- Stack cups bottom to bottom or top to top.
- Line up cups on the floor or table. Make a straight line, a circle, or place them randomly!
- As you place cups together, notice and talk about how they fit, balance, and make shapes: “When I put the cups on top of each other, they make a tall tower” or “These three cups look like a triangle!”
- Knock the cups down and start again!
Obstacle course
- Use painter’s tape to draw out a path on the floor.
- Place bowls and paper cups to create obstacles along the path. Use sticky notes to mark where your child needs to jump.
- Add things to go around, like stuffed animals or boxes. Use a step stool or a pillow to go over and a mylar blanket to crawl under.
- You and your child can go over, under, and in between furniture or items as you move through the obstacle course.
- Explore how you and your child’s bodies fit, move, and change direction in different spaces. Redesign the obstacle course and try it again!
What’s under there?
- Place a bowl and paper cup upside down.
- Ask your child to pick objects from the kit and hide them under the bowl or paper cup so they are completely covered.
- Do an exciting reveal by saying, “Ta-da!”
- Talk about what fits under the bowl or cup. Do the same objects fit under both? Can you fit more than one object? Are some items too big to fit?
- Try objects from around the house or containers of different sizes!
“Where will you place the cup?”
“You jumped so far!”
“Let's see if it fits!”
Everyday interactions
Clean-up time is a great way to practice putting items in different containers, drawers or shelves and seeing how they fit together. Adults often say, “Put the blocks in the bin” or “That bin goes on the shelf between the books”—this is exactly what spatial thinking is about! Your child might stack bins so they don’t fall, fit puzzles back in their boxes, or place books so they stand up straight. As they decide where each toy goes, they are thinking about size, shape, and how things fit.
Related Resources
CaregiverActivityBig, Small, and in Between
Young children learn about measuring before they ever use rulers or scales. They practice these skills by pouring water, stacking blocks, or filling containers. Children use their senses and simple tools to explore size, weight, length, temperature, and more. They notice if something is big or small, heavy or light, long or short, or more or less.
CaregiverActivityPutting Together, Taking Apart
Adding and subtracting happens every day! It’s not just about equations like “1 + 1 = 2.” Young children learn about math by exploring how amounts change—like putting more colors onto their painting (addition) and giving a block from their pile to a friend (subtracting). As children explore putting together and taking apart groups of objects, they practice basic skills that help them get ready for the math they will learn in school.
CaregiverActivityCircles, Squares, and More!
Shapes are everywhere! Some shapes have names—like circle, square, or triangle. Some shapes don’t have names—like the puddles on the ground or the outline of a favorite toy. Children naturally experience shapes when fitting blocks together, sitting in a circle at story time, or trying to fit a square peg into a round hole. Exploring shapes helps them observe, compare, and interact with the world around them.
CaregiverActivitySame and Different
Matching and sorting are key skills that help children learn how things are the same or different. Children might sort and match by color, size, shape, or what things are used for. When they do this, they are learning to compare items, understand groups, notice patterns, and organize information—all important ideas in early math and problem-solving.
CaregiverActivity1, 2, 3!
Numbers and counting help us understand ideas like amounts and sizes. When your child says “one, two, three” while touching three blocks, it helps them see that numbers have meaning. This early practice makes it easier for children to learn other math ideas, like adding, subtracting, and measuring.
EducatorGuideMath Everywhere – Playgroup Guide
You can use or adapt this playgroup structure to maximize playful learning about early math during your playgroup. Be sure to also visit the Math Everywhere collection to download the accompanying Family Activity Sheets. This playgroup guide includes:
CaregiverActivitySnip, Stick, Scribble!
In school, children do lots of activities. They write, draw, paint, and build with different materials. As children do these things, they use tools–scissors to cut paper, paintbrushes to mix colors, and pencils to write letters and numbers.
CaregiverActivityI Can Do It
At home, children can often get one-on-one help with what they need. At school, teachers have many children to care for and may not be able to assist right away. This is why it is important for children to learn to do tasks like zip jackets, put on shoes, and open snack containers. These everyday tasks use fine motor skills—small movements of the fingers, hands, and wrists.