All Topics

Place Value

K–5th

Place value is the operating system of our number system — every computation skill depends on it.

18 articles

Skills your child will master

  • Understanding ones, tens, and hundreds
  • Reading and writing numbers in expanded form
  • Comparing and ordering multi-digit numbers
  • Rounding to the nearest 10, 100, and 1,000
  • Place value through millions and decimals

Uses base-ten blocks and place-value charts so kids physically see how 10 ones become 1 ten — the big idea that makes regrouping click.

Comparing Numbers

K–2nd1

How to Teach Comparing Numbers (Greater Than, Less Than, Equal)

Many kids memorize the alligator trick but cannot actually tell which number is bigger or why. Here is how to teach number comparison so your child truly understands quantity, not just symbols.

5 min readK–2nd

Expanded Form

1st–3rd1

What Is Expanded Form in Math?

Expanded form breaks a number into its place value components. Here is what it means, why it matters, and how it connects to place value understanding.

2 min read1st–3rd

Place Value Basics

1st–3rd2

What Is Place Value?

A quick reference explaining place value — the idea that a digit's value depends on its position. The foundation of our entire number system.

2 min read1st–3rd

How to Teach Place Value So It Actually Sticks

Place value is the foundation of all multi-digit math. Here is how to teach it so your child truly understands why the 3 in 35 means thirty, not three — with an interactive place value mat you can try right now.

5 min read1st–3rd

Grade Expectations

2nd–2nd1

What Your Second Grader Should Know in Math

A clear guide to the math skills your second grader should master — from adding and subtracting within 1000 to early multiplication thinking, place value, and standard measurement. Know what is on track.

6 min read2nd–2nd

Powers of Ten

2nd–4th1

How to Teach Multiplication by 10, 100, and 1000

Multiplying by powers of 10 is one of the most important shortcuts in math. Here is how to teach it so your child understands the pattern — not just the 'add a zero' trick.

2 min read2nd–4th

Rounding

2nd–4th1

How to Teach Rounding Numbers

Most kids learn the rounding rule ('5 or more, round up') without understanding why we round or what rounding means. Here is how to teach rounding as a thinking skill, not just a procedure.

4 min read2nd–4th

Decimal Place Value

3rd–5th1

How to Teach Place Value with Decimals

Decimal place value extends the same system your child already knows — but to the right of the decimal point. Here is how to teach it so tenths and hundredths feel as natural as tens and hundreds.

3 min read3rd–5th

Assessment Help

8th–Pre-K3

Signs Your Child Has Math Gaps (And How to Find Them)

Math gaps are invisible until they cause visible problems. Here are the specific signs that your child has gaps in their math foundation — and a systematic way to find and fill them.

4 min read

How to Test Your Child's Math Level at Home

Grade-level labels hide skill-level reality. Here is a practical method for finding where your child actually is in math — skill by skill — without expensive testing or professional assessments.

8 min read

How to Know If Your Child Is Behind in Math (And What to Do)

Grade-level expectations are not the same as readiness. Here is how homeschool parents can identify real math gaps, separate them from normal variation, and address them without panic.

6 min read

Common Pitfalls

8th–Pre-K1

The Biggest Mistakes Homeschool Math Programs Make

Most math curricula — even popular ones — share fundamental design flaws that create gaps, frustration, and shallow understanding. Here are the mistakes to watch for and what to do about them.

8 min read

Emotional Support

8th–Pre-K1

My Child Hates Math — Here's What's Actually Going On

When your child says they hate math, they are usually telling you something specific. Here is how to decode the real problem and fix it — without turning math time into a battle.

8 min read

Hands-On Learning

8th–Pre-K1

How to Use Math Manipulatives at Home

Base-ten blocks, fraction bars, counters — manipulatives turn abstract math into something your child can touch. Here is which ones to use, when, and how.

3 min read

Homeschool Tips

8th–Pre-K1

Transitioning to Homeschool Math: What You Need to Know

Switching from school math to homeschool math is both liberating and terrifying. Here is the practical guide to making the transition smooth — what to assess, how to choose a curriculum, and what mistakes to avoid.

4 min read

Learning Gaps

8th–Pre-K1

Your Child Is Not Bad at Math — They're Missing a Prerequisite

When a child struggles with a math concept, the problem is almost never that concept. It is a gap in something they were supposed to learn earlier. Here is how prerequisite gaps work and how to find the real issue.

7 min read

Learning Progression

8th–Pre-K2

The Problem with Grade-Level Math (And What to Do Instead)

Grade-level math forces every child through the same progression at the same pace. Here is why that creates gaps, how to identify them, and what mastery-based learning looks like in practice.

7 min read

How Math Skills Build on Each Other — The Hidden Progression

Math is not a list of topics. It is a dependency chain where every concept builds on earlier ones. Understanding this progression changes how you teach, diagnose gaps, and choose what to work on next.

8 min read

Your child's path through place value — automated

Lumastery builds a personalized path through these skills. They practice daily. You get weekly reports. No lesson planning required.

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