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Vol. I — Autumn 2026
Danicarl Publishing

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No. 52 · Mathematics teacher and parent edition

The teacher and parent edition of Grade 1 Math.

Grade 1 Math

Place Value, Addition and Subtraction within 20, Time and Shapes

Grade 1 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 1 student, ages 6-7
Pages
152
Published
2026
Catalogue
No. 52
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 1 Math

Chapter at a Glance · Dani Carl

Chapter at a Glance

  • Chapter: 1
  • Strand: Foundations
  • Difficulty: Level 1 of 5
  • Builds on: Counting to 100 by ones and tens

Try This First

Try this short activity before reading the lesson.

> Get a cup of dry beans or a box of paper clips. Count out ten and put them in a pile. Make as many piles of ten as you can. Then count the piles: "ten, twenty, thirty..." and count the leftovers on by ones. Say the number you land on out loud.

Math Lab: Count on past one hundred

Predict first. You are counting beads and you reach $99$. Say the next three numbers in your head before you read on.

<div class="math-model"><p><strong>Counting on across 100.</strong></p><div class="model-bar"><span class="model-cell">99</span><span class="model-cell">100</span><span class="model-cell">101</span><span class="model-cell">102</span></div></div>

Model and solve. One more than $99$ is $100$. After $100$ the counting starts again, just like the numbers you already know: one hundred one, one hundred two. You write them $101$ and $102$.

Explain. Why is one hundred one written $101$ and not $1001$?

Your turn. Count on from $97$ to $103$.

Check after trying. $97, 98, 99, 100, 101, 102, 103$.

The Big Idea

Counting is a road, and every number is the next stop on it. After $99$ the road does not stop. The next stop is $100$, then $101$, $102$, and on to $120$. The numbers after one hundred sound like "one hundred and then a small number": one hundred one, one hundred two.

Writing a number past one hundred takes three digits, no more. One hundred fourteen is $114$: a $1$ for the hundred, then $14$. It is not $10014$. Say the hundred, then write the rest in the two places after it.

You can start counting anywhere on the road. Start at $87$ and keep walking: $88$, $89$, $90$, $91$. You do not have to go back to $1$ to know what comes after $89$.

For grown-ups. Counting past 100 is where a child first meets the pattern that every later number system repeats: the ones roll from 9 back to 0 and the tens tick up by one. Students count forward from any number, read and write numerals to 120, and say how many objects are in a group that big. Place value, the hundred chart and every two-digit sum stand on this.

Words to Know

  • numeral: The written number, made of digits: $114$ is the numeral for "one hundred fourteen".
  • count on: Start at a number and keep counting from there instead of starting at $1$. Counting on from $87$: $88, 89, 90$.
  • decade number: A number that ends in $0$: $40$, $70$, $110$. The ones start again from $1$ after each decade number.

Outcomes and Milestones

  • Students can: count forward from any number within 120, read and write numerals to 120, and count a group of up to 120 objects by tens and ones.
  • Watch for: saying “one hundred, two hundred” after 100 instead of 101; writing one hundred fourteen as 10014.
  • Ready when: they can start at 87 and count aloud to 120 without a chart, and write 109 and 113 from the spoken words.

Worked Examples and Your Turn

Study each example, then try the paired problem.

Example 1: Count on from the middle

Problem: Start at $66$ and count on to $75$.

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 400 100" width="400" height="100" role="img" aria-label="Number line from 65 to 76. Nine small hops go from 66 to 75, one number at a time." font-family="Source Sans 3" font-size="14"><line x1="10" y1="70" x2="390" y2="70" stroke="#333" stroke-width="1.5"/><polygon points="392,70 385,73.5 385,66.5" fill="#333" stroke="#333" stroke-width="1"/><polygon points="8,70 15,66.5 15,73.5" fill="#333" stroke="#333" stroke-width="1"/><line x1="22" y1="63" x2="22" y2="77" stroke="#333" stroke-width="1.5"/><text x="22" y="92" text-anchor="middle" font-size="13" fill="#333">65</text><line x1="54.4" y1="63" x2="54.4" y2="77" stroke="#333" stroke-width="1.5"/><text x="54.4" y="92" text-anchor="middle" font-size="13" fill="#333">66</text><line x1="86.7" y1="63" x2="86.7" y2="77" stroke="#333" stroke-width="1.5"/><text x="86.7" y="92" text-anchor="middle" font-size="13" fill="#333">67</text><line x1="119.1" y1="63" x2="119.1" y2="77" stroke="#333" stroke-width="1.5"/><text x="119.1" y="92" text-anchor="middle" font-size="13" fill="#333">68</text><line x1="151.5" y1="63" x2="151.5" y2="77" stroke="#333" stroke-width="1.5"/><text x="151.5" y="92" text-anchor="middle" font-size="13" fill="#333">69</text><line x1="183.8" y1="63" x2="183.8" y2="77" stroke="#333" stroke-width="1.5"/><text x="183.8" y="92" text-anchor="middle" font-size="13" fill="#333">70</text><line x1="216.2" y1="63" x2="216.2" y2="77" stroke="#333" stroke-width="1.5"/><text x="216.2" y="92" text-anchor="middle" font-size="13" fill="#333">71</text><line x1="248.5" y1="63" x2="248.5" y2="77" stroke="#333" stroke-width="1.5"/><text x="248.5" y="92" text-anchor="middle" font-size="13" fill="#333">72</text><line x1="280.9" y1="63" x2="280.9" y2="77" stroke="#333" stroke-width="1.5"/><text x="280.9" y="92" text-anchor="middle" font-size="13" fill="#333">73</text><line x1="313.3" y1="63" x2="313.3" y2="77" stroke="#333" stroke-width="1.5"/><text x="313.3" y="92" text-anchor="middle" font-size="13" fill="#333">74</text><line x1="345.6" y1="63" x2="345.6" y2="77" stroke="#333" stroke-width="1.5"/><text x="345.6" y="92" text-anchor="middle" font-size="13" fill="#333">75</text><line x1="378" y1="63" x2="378" y2="77" stroke="#333" stroke-width="1.5"/><text x="378" y="92" text-anchor="middle" font-size="13" fill="#333">76</text><path d="M54.4,70 Q70.5,52 86.7,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="86.7,70 78.4,66.7 84.4,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M86.7,70 Q102.9,52 119.1,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="119.1,70 110.8,66.7 116.7,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M119.1,70 Q135.3,52 151.5,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="151.5,70 143.1,66.7 149.1,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M151.5,70 Q167.6,52 183.8,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="183.8,70 175.5,66.7 181.4,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M183.8,70 Q200,52 216.2,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="216.2,70 207.9,66.7 213.8,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M216.2,70 Q232.4,52 248.5,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="248.5,70 240.2,66.7 246.2,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M248.5,70 Q264.7,52 280.9,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="280.9,70 272.6,66.7 278.5,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M280.9,70 Q297.1,52 313.3,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="313.3,70 304.9,66.7 310.9,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><path d="M313.3,70 Q329.5,52 345.6,70" fill="none" stroke="#e06666" stroke-width="2"/><polygon points="345.6,70 337.3,66.7 343.3,61.4" fill="#e06666" stroke="#e06666" stroke-width="1"/><circle cx="54.4" cy="70" r="5" fill="#e06666" stroke="#333" stroke-width="1"/><circle cx="345.6" cy="70" r="5" fill="#93c47d" stroke="#333" stroke-width="1"/></svg>

Solution:

  • Say $66$, then the next number: $67$. Why: counting on means starting where you are, not at $1$.
  • Keep going by ones: $68, 69$. The next number after a $9$ in the ones is the next decade number, $70$.
  • Carry on: $71, 72, 73, 74, 75$. Stop at $75$.

Answer: $66, 67, 68, 69, 70, 71, 72, 73, 74, 75$.

> Notice: Every time the ones reach $9$, the next number ends in $0$ and the tens go up by one.

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 360 90" width="360" height="90" role="img" aria-label="Number line from 57 to 64. A red dot marks 58, where you start. An empty ring marks 63, where you stop." font-family="Source Sans 3" font-size="14"><line x1="10" y1="50" x2="350" y2="50" stroke="#333" stroke-width="1.5"/><polygon points="352,50 345,53.5 345,46.5" fill="#333" stroke="#333" stroke-width="1"/><polygon points="8,50 15,46.5 15,53.5" fill="#333" stroke="#333" stroke-width="1"/><line x1="22" y1="43" x2="22" y2="57" stroke="#333" stroke-width="1.5"/><text x="22" y="72" text-anchor="middle" font-size="13" fill="#333">57</text><line x1="67.1" y1="43" x2="67.1" y2="57" stroke="#333" stroke-width="1.5"/><text x="67.1" y="72" text-anchor="middle" font-size="13" fill="#333">58</text><line x1="112.3" y1="43" x2="112.3" y2="57" stroke="#333" stroke-width="1.5"/><text x="112.3" y="72" text-anchor="middle" font-size="13" fill="#333">59</text><line x1="157.4" y1="43" x2="157.4" y2="57" stroke="#333" stroke-width="1.5"/><text x="157.4" y="72" text-anchor="middle" font-size="13" fill="#333">60</text><line x1="202.6" y1="43" x2="202.6" y2="57" stroke="#333" stroke-width="1.5"/><text x="202.6" y="72" text-anchor="middle" font-size="13" fill="#333">61</text><line x1="247.7" y1="43" x2="247.7" y2="57" stroke="#333" stroke-width="1.5"/><text x="247.7" y="72" text-anchor="middle" font-size="13" fill="#333">62</text><line x1="292.9" y1="43" x2="292.9" y2="57" stroke="#333" stroke-width="1.5"/><text x="292.9" y="72" text-anchor="middle" font-size="13" fill="#333">63</text><line x1="338" y1="43" x2="338" y2="57" stroke="#333" stroke-width="1.5"/><text x="338" y="72" text-anchor="middle" font-size="13" fill="#333">64</text><circle cx="292.9" cy="50" r="5" fill="#ffffff" stroke="#333" stroke-width="1.5"/><circle cx="67.1" cy="50" r="5" fill="#e06666" stroke="#333" stroke-width="1"/><text x="67.1" y="30" text-anchor="middle" font-size="13" fill="#333">start</text><text x="292.9" y="30" text-anchor="middle" font-size="13" fill="#333">stop</text></svg>

Your Turn:

  • Prompt: Start at $58$ and count on to $63$.
  • Answer: $58, 59, 60, 61, 62, 63$.

Example 2: Past one hundred, from 87

Problem: Start at $87$ and count aloud to $120$. What are the three numbers after $99$?

Solution:

  • Count up to the next decade: $87, 88, 89, 90$.
  • Keep counting by ones: $91, 92, \ldots, 99$.
  • After $99$ comes $100$. Why: ten tens make one hundred, and the road keeps going.
  • Now the small numbers start again after the hundred: $101, 102, 103$, and so on to $110$, then $111, \ldots, 120$.

Answer: The three numbers after $99$ are $100, 101, 102$. The count ends $\ldots, 118, 119, 120$.

> Verification & Check: Each number after $100$ is $100$ plus a small number: one hundred one is $100$ and $1$ more, one hundred two is $100$ and $2$ more.

Your Turn:

  • Prompt: Start at $95$ and count on to $105$.
  • Answer: $95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105$.

Example 3: Count a big pile by tens and ones

Problem: Noah has $6$ bags with ten crayons in each bag, and $4$ loose crayons. How many crayons?

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 220 170" width="220" height="170" role="img" aria-label="Six ten-rods and four single cubes: 6 bags of ten crayons and 4 loose crayons."

The chapter continues in the book.

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The teacher and parent edition of Grade 1 Math. It holds all eleven student chapters, from numbers to 120 and tens and ones through adding and subtracting within 20, the equals sign, length, time to the half hour, picture graphs and halves and quarters, with each Your Turn answer printed under its problem and the answer printed under every Try It on Paper problem.

Each chapter adds four sections for the adult. Chapter at a Glance gives the chapter in brief. Outcomes and Milestones states what the child can do afterwards, a common misconception to watch for, and a "ready when" check. Exam and Contest Profile gives a short note on how the chapter's skills are usually asked on standardized tests. At the Table is a script for the helping adult: a hands-on start, questions to ask in order, and what to do when a child is stuck.

A Master Topic Matrix in the front matter shows which earlier topics 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 1 Math — front cover
Front cover
Grade 1 Math — back cover
Back cover
Grade 1 Math — a page from the interior
A page from the interior