You sit on the floor next to your child and a pile of tiles. They build, you watch, and you want to help without taking over. So what should you actually say? This guide gives you the words, the questions and one simple game, so ordinary play turns into thinking.
Why the words around a build matter
Building already uses math: shapes, sizes, counting, where things go. Talk is what makes that math visible. A chapter on early math summarizes research showing that the amount of math-related talk from teachers is significantly related to the growth of children's math knowledge (Klibanoff and colleagues, 2006).1 The same chapter cites work finding that math ability at kindergarten entry predicts later school success even better than early reading does (Duncan and colleagues, 2007).1
The catch: kids do not get much of this talk by default. One cited study found teachers spent 8% of daily classroom time on math and 21% on literacy (Early and colleagues, 2005).1 Home is a good place to add more, and it costs nothing but words.
Spatial talk matters early. In a study of more than a hundred 3-year-olds, children who were better at copying block structures were also better at early math.5 Parents of low-income toddlers reported using significantly fewer words such as "above" and "below."5 The good news is that these are learned skills, not fixed talents.
spatial abilities improve with practice1
Words that place things in space
Position words tell your child where one piece sits in relation to another. A kindergarten milestone in the Work Sampling System is that a child "shows understanding of and uses direction, location, and position words."1 You do not need to teach them as a lesson. Just narrate what you see.
Higher than something, or lower than something.
Say it: “Which tile is above the red one? What is below your car?”Right next to something, or in the middle of two things.
Say it: “Can you put a square between the two triangles?”Hidden at the back of something, or closer to you than it.
Say it: “What is behind your tower? Can I see it from here?”Comparing height: one is taller, the one that beats them all is tallest.4
Say it: “Which tower is taller? Which one is the tallest of all three?”How long something is from end to end.4
Say it: “How many tiles long is your road?”Add a think-aloud now and then. A think-aloud is when the adult describes their own problem solving while doing it, a strategy the chapter recommends for supporting children's thinking about their thinking.1 Try: "I want a roof here. I need something wide enough to cover both walls, so I am looking for a longer piece."
Ask questions that start thinking, not quizzes
A study of K-5 science classrooms found that when the teacher ran a quick ask, answer, move on pattern, talk stayed at the lowest level.1 In the strongest classrooms, the authors write, the complexity of the first question mattered less than how the answer was followed up.1 The follow-up is where thinking happens.
- What shape is this?
- How many tiles is that?
- Is that right?
- What color is the square?
- Quick, what comes next?
- How did you figure that out?
- How do you know it will fit?
- What would happen if you took one away?
- Could you make that shape a different way?
- What did you notice?
A national report on STEM education describes "on-the-fly" questions teachers use to check understanding: "how do you know?" and another one worth memorizing.2 The same report notes that hands-on activity by itself is not enough: children also need to make sense of what they did and explain it.2
how can you support that idea?2
Then wait. Researchers cited in the K-5 study suggest children need turns of talk extended for 10 seconds or more to form and connect ideas.1 And skip the stopwatch: successful math teachers work to disrupt the idea that being fast means being good at math.2
The first question opens the door. The follow-up is where your child walks through it.
- "Tell me how you built that."
- "How do you know?"
- "What is above it? What is below it?"
- "Guess first: how many tiles tall will it be? Now let's count."
- "Can you swap some pieces instead of starting over?"
- "Show me with your finger which piece you mean."
- "Hmm, I am not sure. Let's test it."
Try it tonight: copy my build, then shape swap
Copy my build and shape swap
- About 20 magnetic or wooden tiles, including squares and triangles
- Two small cars or toy figures (optional)
- Paper and pencil for a quick tally
- Build a small 4 to 6 piece structure where your child can see it. Narrate as you go: "The triangle goes above the square, beside the blue one."
- Ask your child to copy it exactly. When they finish, compare together: "Is your triangle above or beside the square?"
- Switch roles. Your child builds, you copy, and they check you using position words.
- Shape swap: hand over two triangles and ask "Can you make a square out of these?" Then ask "How do you know it is a square?"
- Cover a big square or rectangle with only triangles. Then ask your child to swap pairs of triangles for squares and tally each version in two columns.
- Look at the tally together: "What do you notice?" Stop while it is still fun.
- Adult supervision: keep tiles away from younger siblings who still mouth toys, and check that no magnets are loose or exposed.
Why the tally? In a second grade lesson described in one chapter, students covered a puzzle with pattern blocks and kept wiping the board to start over, until a classmate noticed that two triangles match one rhombus.1 The class charted every solution and spotted the rule.1
| Triangles | Rhombuses |
|---|---|
| 10 | 1 |
| 8 | 2 |
| 6 | 3 |
| 4 | 4 |
| 2 | 5 |
What to listen for at each age
The Work Sampling System, an assessment tool reproduced in one chapter, lists geometry and measurement milestones from age 3 to third grade.1 Use them as things to listen for, not a test. The tables stop at third grade, so the 8-10 row describes the upper end of that range.
Can: Uses direction, location and position words. Composes and decomposes shapes. Orders and compares objects by size, length, capacity and weight. By first grade, measures with simple tools in non-standard and standard units.1
Try: Copy my build, two triangles into a square, and measuring a road in car lengths before using a ruler.
Can: Reasons with shapes and their attributes. Explores and solves spatial problems using manipulatives and drawings. Uses tools and techniques to estimate and measure.1
Try: Sketch the build before making it, estimate its height in inches, then measure and talk about how close the guess was.13
A related early math curriculum for ages 32 to 72 months, described in another chapter, includes goals you can slip into any build: counting backwards from 10, measuring with hands and footsteps, comparing a guess with the real measurement, and making a square by combining two triangles.1 It is a Turkish national curriculum, so treat it as a source of ideas, not a US standard.
Move the idea between hands, pictures and words
One framework for understanding in math says a child really knows an idea when they can show it in several forms and move between them.3 Each hop is a chance for a little math talk:
- Hands. Build the shape with tiles.
- Picture. Draw it on paper.
- Words. Say what it is: "Four sides, all the same length."
- Symbols. Count the pieces and write the number.
- Real life. Find the same shape at home, like a window or a box.3
Estimating fits here too. A primary grade lesson plan in the same book has children estimate first, measure, then write how close the estimate was.3 At home that becomes: "Guess how many tiles long the bridge is. Now count. Were you close?"
If you want a kit for this
Everything above works with blocks, boxes or tiles you already own, but if you want pieces made for shape swaps and car roads, this is the one we sell.
Build it with / Ages 5-7Magnetic Travel Tiles with CarsFlat shapes that stand up into roads and garages.$41.99GoP Toys sells the kit mentioned above. None of the sources cited tested our products.