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Vol. I — Autumn 2026
Danicarl Publishing

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No. 54 · Mathematics teacher and parent edition

The teacher and parent edition of Grade 2 Math.

Grade 2 Math

Numbers to 1,000, Fluency, Measurement and Equal Shares

Grade 2 Math by Dani Carl — cover
Written by
Dani Carl
Genre
Mathematics teacher and parent edition
Series
The Danicarl Omni-Mastery Series
For
Adult reader (teacher, parent or tutor) working with a Grade 2 student, ages 7-8
Pages
152
Published
2026
Catalogue
No. 54
Edition details
Trim
8.5 x 11 in
Binding
Paperback · Matte

The opening

Chapter at a Glance

Try this short activity before reading the lesson.

Grade 2 Math

Chapter at a Glance · Dani Carl

Chapter at a Glance

  • Chapter: 1
  • Strand: Foundations
  • Difficulty: Level 1 of 5
  • Builds on: Tens and ones

Try This First

Try this short activity before reading the lesson.

> Get some paper and cut ten small squares. Put them in a row and count them: that row is a ten. Make ten rows. That is a hundred. Now show $124$ with one hundred, two tens and four loose squares.

Math Lab: Too many tens

Predict first. A number has 2 hundreds, 14 tens and 3 ones. Is it more or less than 300?

<div class="math-model"><p><strong>Place-value boxes: hundreds, tens, ones.</strong></p><div class="model-bar"><span class="model-cell">2 hundreds</span><span class="model-cell">14 tens</span><span class="model-cell">3 ones</span></div><p class="model-caption">Only 0 to 9 can stay in one place.</p></div>

Model and solve. Ten of the $14$ tens make $1$ hundred, so $14$ tens is $100 + 40$. Then $200 + 100 + 40 + 3 = 343$. That is more than $300$.

Spot the mistake. Someone writes the number as 2143. Which box has too many pieces to stay in its place?

Your turn. A number has 3 hundreds, 12 tens and 5 ones. Draw the boxes, trade ten tens for a hundred, and write the number.

Check after trying. $12$ tens is $1$ hundred and $2$ tens, so $300 + 100 + 20 + 5 = 425$. In 2143 the $14$ tens were written as two digits; ten of them had to become a hundred first, giving $343$.

The Big Idea

A number up to $1{,}000$ has three places: hundreds, tens and ones. The digit tells you how many; the place tells you of what. In $630$ the $3$ is not three. It is three tens, which is thirty.

Ten ones make a ten. Ten tens make a hundred. Ten hundreds make a thousand. Every time you have ten of something, you trade it for one of the next bigger thing.

Expanded form writes the number as its parts: $358 = 300 + 50 + 8$. If a place has nothing in it, you write a $0$ to hold the place. Four hundred seven is $407$, not $47$.

A three-digit number is hundreds, tens and ones, and a hundred is ten tens. In this chapter you read and write numbers to 1,000 in digits, words and expanded form, and say what each digit is worth. The same three columns stretch to a million in Grade 4 and to decimals after that, so the habit of naming the place, not just the digit, starts here.

Words to Know

  • digit: One of the symbols $0$ to $9$. The number $407$ has three digits.
  • place: Where a digit sits: ones, tens or hundreds. The place says what the digit is worth.
  • expanded form: The number written as its parts added together: $358 = 300 + 50 + 8$.

Outcomes and Milestones

  • Students can: read and write numbers to 1,000 in digits, words and expanded form, and give the value of any digit.
  • Watch for: writing four hundred seven as 4007 or 47; reading the 3 in 630 as "three" rather than thirty.
  • Ready when: they write 12 tens and 5 ones as 125 without counters, and give the expanded form of 809.

Worked Examples and Your Turn

Study each example, then try the paired problem.

Example 1: Say what the digit is worth

Problem: In $274$, what is the $7$ worth?

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Solution:

  • Name the places from the right: $4$ ones, $7$ tens, $2$ hundreds.
  • The $7$ is in the tens place. Seven tens is $70$. Why: a ten is ten ones, and seven of them is seventy.

Answer: The $7$ is worth $70$.

> Notice: Ask "seven of what?" every time. Seven ones, seven tens and seven hundreds are all written with a $7$.

Your Turn:

  • Prompt: In $593$, what is the $9$ worth?
  • Answer: Nine tens, which is $90$.

Example 2: Words to digits, digits to words

Problem: Write six hundred fifteen in digits. Then write $290$ in words.

Solution:

  • Six hundred fifteen: six hundreds, then fifteen, which is one ten and five ones. So $6$, $1$, $5$: $615$.
  • $290$: two hundreds and nine tens and no ones. Say the hundreds, then the tens: two hundred ninety. Why: the $0$ means there are no ones to say.

Answer: $615$; two hundred ninety.

Your Turn:

  • Prompt: Write three hundred eight in digits, and $740$ in words.
  • Answer: $308$; seven hundred forty.

Example 3: Tens and ones, when there are more than nine tens

Problem: A number is made of $12$ tens and $5$ ones. What is the number? Then write the expanded form of $809$.

Solution:

  • Twelve tens is too many for one tens place. Trade ten of the tens for a hundred. Why: ten tens make a hundred. That leaves $1$ hundred and $2$ tens.
  • Now the number is $1$ hundred, $2$ tens, $5$ ones: $125$.
  • For $809$: eight hundreds, no tens, nine ones. Write only the parts that are there: $800 + 9$.

Answer: $125$; and $809 = 800 + 9$.

> Notice: The $0$ in $809$ is a placeholder. It keeps the $8$ in the hundreds place. It adds nothing to the expanded form.

> Verification & Check: Count twelve tens out loud: $10, 20, \ldots, 120$. Then five more is $125$.

The chapter continues in the book.

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The teacher and parent edition of Grade 2 Math. It contains all eleven student chapters (numbers to 1,000, fact fluency, adding and subtracting within 100 and 1,000, two-step story problems, arrays, measurement with rulers, time and money, graphs, and equal shares), with each Your Turn answer printed under its problem and the answer printed under every Try It on Paper problem.

Four sections per chapter are for the adult. Chapter at a Glance sums up the chapter. Outcomes and Milestones says what the child can do afterwards, the misconception to watch for, and a "ready when" check. Exam and Contest Profile gives a short note on how these skills are usually asked on standardized tests. At the Table is a script: a hands-on start, questions to ask in order, and what to try when a child is stuck.

The front matter adds a Master Topic Matrix showing what each chapter builds on.

Look inside.

Actual edition

The cover and pages below are rendered from the print-ready files for this edition—not a stock mockup.

Grade 2 Math — front cover
Front cover
Grade 2 Math — back cover
Back cover
Grade 2 Math — a page from the interior
A page from the interior