Math Activities That Build the Underlying Skills

By Laura Lurns · Reviewed by Philip Weaver · Last reviewed 2026-09-29

What are the underlying skills?

In our view, arithmetic is built on a few skills underneath it. They are part of math itself. To us, later math builds on them.

A feel for how big a number is. It means knowing that 8 is close to 10 and far from 80. It means knowing which of two numbers is bigger without working it out. This is part of what people call number sense.

Seeing small amounts at a glance. It means knowing there are three dots without counting them. This skill has a name: subitizing. We count it as part of number sense too. Is it hard for children with dyscalculia? One review says some studies find that, but not all (Dowker, 2024). One study compared 68 children with dyscalculia and 412 without (Lamb, Krieger and Kuhn, 2023). It found no evidence of trouble with subitizing. The one difference was slower counting of about four to nine dots. That study looked at each child once. So we count subitizing as one skill among several.

Breaking numbers apart. It means knowing that 7 is 5 and 2, or 4 and 3. Many teachers call these number bonds.

Tens and ones. It means knowing that the 4 in 43 stands for four tens. This is place value.

Facts that mean something. It means knowing 6 + 7 without counting, and knowing what it stands for.

Early number sense predicts later math achievement, in Jordan and Devlin's (2023) summary of the research. That is a link over time, not a test of teaching it.

A German medical guideline summary lists trouble with several of these among the typical features of dyscalculia (Haberstroh and Schulte-Körne, 2019). By its account, one mistake is not a sign. It judges mistakes by how varied, lasting and frequent they are.

The activities, skill by skill

Each of these is built to be worked alongside your child's math instruction, not in place of it. None needs special materials.

Which is more? Grab two handfuls of dried pasta. Ask which has more, before anyone counts. Then count to check. Or turn over two playing cards each. The bigger card takes both. Ask which is bigger, 7 or 4. Then ask about 38 and 83.

How many, at a glance? Roll one die. Ask how many dots, fast, without counting. Make dot cards with sticky dots. Show a card for a second, then hide it. Start with three or four dots. Then try five and six in a dice pattern.

Hide and find. Count out seven buttons together. Hide some under a cup. Ask how many are hiding. Then do it again with the same seven. An egg carton cut down to ten cups works too. Fill some cups. Ask how many more make ten.

Count on and count back. Start counting at 17, not at 1. Ask what comes just before 60. Ask what is one more than 99.

Tens and ones. Bundle straws into tens with a rubber band. Build 43 as four bundles and three loose straws. Then write it down. Dimes and pennies do the same job.

Where does it go? Draw a line. Write 0 at one end and 100 at the other. Ask where 50 goes. Then try 25, then 90.

Facts, with the meaning beside them. Practice a few facts at a time. Keep the buttons nearby. When a fact does not come, build it with the buttons, then say it. In our view, a math fact sticks when the child understands it and practices it.

Everyday math. Double a recipe. Count the change at the store. Ask how many minutes until dinner.

Objects, then a drawing, then the numbers

Our working order is objects first, then a drawing, then the written numbers.

Put all three on the same problem. Move the buttons and say what is happening. Draw it. Then write the sum. In our view, that keeps each number tied to what it stands for.

When something is too hard, go back to the objects. Take them away once your child stops reaching for them.

How to run a session

Our suggestion, from our own reasoning rather than a tested method, has four parts.

• Keep each session short, and say when it will end. To us, a child who knows the size of the task finds it easier to start.
• Say what will be in the session before it starts.
• Keep practice apart from testing. In our view, if every bit of math is a test, avoiding it makes sense.
• Do not let homework be the only math of the day.

Pitch it right. In our view, aim for work that takes effort and a strategy to do. To us, work that is too easy teaches little. Work that is too hard tells a worried child what they already fear.

Watch what you say. We suggest skipping "I was bad at math too." It is meant kindly. To us, it hands a child a ready reason to stop.

Keep old work. Children rarely notice their own math improving. The work gets harder as they get better. Keep an older page, and put it next to today's. Praise cannot stand in for a child's own evidence.

Timed practice has its place. In our view, speed should never become what a child thinks math is.

What the research we hold says, and where it stops

We hold no study that tests the games on this page. That is a gap in what we hold, not a finding that they do not work. Here is some of what we do hold.

A German medical guideline summary looked at help for dyscalculia (Haberstroh and Schulte-Körne, 2019). Practice made of math tasks did better than training other skills, like working memory. The guideline says high-quality trials are still lacking. It recommends that trained specialists give this help, one to one. For that help, it recommends sessions of at least 45 minutes. The games on this page are home practice, not that kind of specialist help.

One trial taught number sense to kindergartners who were behind in math (Dyson and colleagues, 2015). The group that also practiced number facts kept an edge over the group that did not, at a follow-up test. It was one trial, with young children who were behind, not diagnosed.

An expert briefing looked at ways to help with dyscalculia (Iuculano, 2020). Two number games in it did not carry over to sums; one number-line training did. None of them was a game on this page. The briefing also describes a small tutoring study that mixed number ideas with fact practice. Arithmetic improved in its 15 children, but no group went without the tutoring to compare. The briefing says this research is still young. Play the games on this page alongside math instruction, not in place of it.

One review pooled small, older trials of parent programs at home (Nye, Turner and Schwartz, 2006). The children were in elementary school. Programs that had parents do learning activities with their child raised school results. The clearest gains were in reading. For math, the gain was less certain, and came mostly from one study.

When activities are not enough

Each of these is a reason to ask for help on its own.

• Little change, even with steady practice and good teaching.
• Math well below your child's other schoolwork.
• Extreme upset about math.
• Complete avoidance of math.
• Worry about math that spreads into the rest of learning.
• A teacher who raises a concern about math.
• A skill that was there and has gone. Our position is that a lost skill goes to a doctor first, not a tutor.

Tell your child's teacher what you have seen and what you have tried. In our view, if you are worried enough to ask, a professional evaluation is worth asking about.