Little Newtons · Class 1 · Number Sense · Grades 1–2
Number Sense to 20 — Counting Forward & Back and Comparing Quantities (Little Newtons Class 1, Grades 1–2) — 25 Practice Questions with Hidden Answers
Number sense to 20 is the foundation of every later grade 1–2 math class. A child with strong number sense can count from 1 to 20 forward and backward, touch each object once as they count (one-to-one matching), tell you how many without recounting, and compare two groups to say which has more, which has fewer, or whether they are equal. This Little Newtons Class 1 pack teaches counting the teen numbers, counting backward from 10 and 20, one-to-one matching, comparing quantities with more/fewer/equal, the symbols <, >, and =, and gives 25 practice questions with click-to-reveal step-by-step answers.
This class is part of the Little Newtons arc at SOMATH — School of Math on the Upper West Side. Class 1 is the very first class in the grade 1–2 year — it is where we make sure every child has the number sense that the next 47 classes will build on. It is taught in-person at 226 W 79th St. Call (646) 668-6151 or book a free 30-minute evaluation to see if your grade 1–2 child is a fit.
What’s in this class pack
- Why number sense to 20 is Class 1
- Counting forward from 1 to 20 (and the teen trap)
- The number line 0 to 20 — a map of the numbers
- Counting backward from 10 and 20
- One-to-one matching — how to count objects correctly
- Comparing quantities — more, fewer, equal
- The symbols <, >, and = (the alligator trick)
- The 6 most common grade 1–2 number-sense mistakes
- 25 practice questions with hidden answers
- Answer key summary
- Frequently asked questions
1. Why number sense to 20 is Class 1
What is number sense?
Number sense is a feel for what numbers mean and how they relate to each other. A child with number sense to 20 can:
- Say the number words in order, forward from 1 to 20 and backward from 20 to 0.
- Point to each object exactly once while counting (one-to-one matching).
- Know that the LAST number they said is HOW MANY there are (cardinality).
- Look at a small group (up to about 5) and know how many without counting.
- Say which of two numbers is more, which is fewer, or if they are the same.
These five skills together are the whole foundation of grade 1–2 math. Place value (Class 2), make-ten addition (Class 3), doubles (Class 4), subtraction (Class 5), and word problems (Class 6–7) all assume the child has them cold. That is why Class 1 is dedicated to them.
2. Counting forward from 1 to 20 (and the teen trap)
The 20 number words
Here is the full list your child needs to say, in order, without stopping:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Sounds easy. But English is unfair to 6-year-olds in three places:
- 11 (eleven) and 12 (twelve) don’t fit the pattern. They’re not “oneteen” and “twoteen.” They just have to be memorized.
- 13 (thirteen) and 15 (fifteen) change the base word. Not “threeteen” and not “fiveteen.”
- 14, 16, 17, 18, 19 follow the pattern (four+teen, six+teen…) — the word says the ones digit FIRST but the number is written with the 1 first.
These are the “teen trap” numbers. If your child stumbles anywhere between 11 and 19, that is where to practice.
Reading two-digit numbers 11 through 20
Every teen number is really 1 ten and some ones. That’s the connection to Class 2 (place value). For now, in Class 1, we just want the words and the digits to match up:
| Digits | Word | Read as |
|---|---|---|
| 11 | eleven | 1 ten and 1 one |
| 12 | twelve | 1 ten and 2 ones |
| 13 | thirteen | 1 ten and 3 ones |
| 14 | fourteen | 1 ten and 4 ones |
| 15 | fifteen | 1 ten and 5 ones |
| 16 | sixteen | 1 ten and 6 ones |
| 17 | seventeen | 1 ten and 7 ones |
| 18 | eighteen | 1 ten and 8 ones |
| 19 | nineteen | 1 ten and 9 ones |
| 20 | twenty | 2 tens |
In Class 1 we don’t need the words “tens” and “ones” yet — that’s Class 2. But we DO need the child to know that 14 comes after 13 and before 15, and that 14 and 41 are different numbers.
3. The number line 0 to 20 — a map of the numbers
A number line is a picture of the numbers in order. It is the single most useful picture in grade 1–2 math. It shows counting, comparing, adding, and subtracting all in one image.
Three rules of the number line
- Numbers get bigger as you move to the RIGHT.
- Numbers get smaller as you move to the LEFT.
- Each space between two tick marks is one step (one “hop”) — each hop is 1.
“Counting forward” is hopping to the right. “Counting backward” is hopping to the left. Later, in Class 3, adding will be “hop right” and in Class 5, subtracting will be “hop left.”
4. Counting backward from 10 and 20
Backward from 10
Backward from 10, all together:
10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
This is the launch-countdown sequence — it’s worth practicing out loud (in the car, at bath time, before bed) until it feels as automatic as forward counting.
Backward from 20
Backward from 20, all the way to 0:
20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
The hardest spot is usually 13 → 12 → 11 → 10, because those teen numbers don’t announce their own pattern. If your child freezes at that spot, walk them backward on the number line with their finger.
Why backward matters: backward counting IS subtraction in disguise. When we later say 7 − 3 = 4, we mean “start at 7 and hop back 3: 6, 5, 4.” A child who can’t count backward has no picture for what subtraction is doing.
5. One-to-one matching — how to count objects correctly
What one-to-one matching means
One-to-one matching (or “one-to-one correspondence”) means: for each object I count, I say exactly one number. Not two. Not zero. Exactly one.
The two mistakes a grade 1 child makes are:
- Skipping an object. Their finger moves faster than their mouth — they say “one, two, three” while touching FOUR objects. They report 3 when the real answer is 4.
- Counting an object twice. Their mouth moves faster than their finger — they say “one, two, three, four” while touching only three objects. They report 4 when the real answer is 3.
The move-and-count fix
The fix is to physically SEPARATE counted objects from uncounted objects. Give your child two lines on a piece of paper — a “to count” line and a “counted” line. As they count each object, they MOVE it from left to right and say the number. When the “to count” line is empty, whatever number they said last is the answer.
This works because it makes it physically impossible to count the same object twice OR to skip one. Do it for two or three weeks. After that, most kids don’t need it anymore.
Cardinality — the last number is HOW MANY
After counting is done, ask “how many?” A child with number sense answers immediately with the last number they said. A child who is still developing number sense will start counting again from 1. That’s a sign they don’t yet know that the whole point of counting is to arrive at a total — not just to say the number words in order. If your child recounts, ask them “what was the last number you said?” and gently point out that that number IS the answer.
6. Comparing quantities — more, fewer, equal
The three comparison words
When we compare two groups of things, exactly one of three things is true:
- The first group has more than the second.
- The first group has fewer (or “less”) than the second.
- The two groups are equal (the same).
Note the grownup vocabulary: fewer is for things you can count (fewer apples, fewer cookies); less is for things you can’t count one-by-one (less water, less sand). In grade 1–2 we use both, but “fewer” is more precise for counted objects.
Method 1: match one-to-one
Line up the two groups next to each other. Pair off — one from group A with one from group B. Whoever has leftovers has more. If nobody has leftovers, they are equal.
Example. Group A: 🍎🍎🍎🍎🍎🍎🍎 (7 apples). Group B: 🍎🍎🍎🍎🍎 (5 apples). Pair them up: 5 pairs, and Group A has 2 leftover apples. So Group A has MORE. Group B has FEWER. And Group A has 2 more than Group B.
Method 2: use the number line
Count each group. The one whose number is FARTHER to the RIGHT on the number line is bigger. In our example, 7 is to the right of 5 — so 7 is more than 5.
Once counting is solid, this second method is much faster and it’s exactly what the comparison SYMBOLS in the next section formalize.
7. The symbols <, >, and = (the alligator trick)
The three symbols
| Symbol | Meaning | Example |
|---|---|---|
| > | greater than (more than) | 9 > 7 — nine is greater than seven |
| < | less than (fewer than) | 7 < 9 — seven is less than nine |
| = | equal to (the same) | 5 = 5 — five is equal to five |
The alligator trick
Pretend the symbol is an alligator’s mouth. The alligator is greedy — it always wants to eat the BIGGER number. So the mouth OPENS toward the bigger number and the pointy end points at the smaller one.
9 > 7 (mouth opens toward 9, the bigger number)
7 < 9 (mouth opens toward 9, still the bigger number)
The equals sign = has two lines of exactly the same length — that’s the picture for “both sides are the same.”
8. The 6 most common grade 1–2 number-sense mistakes
- Skipping a teen number. Most often 15 or 13. Fix: count together on the number line, tapping each number as you say it.
- Saying 60 instead of 16 (or 40 instead of 14). The “-teen” and “-ty” sounds are close. Fix: hold up two hands for 10 and add fingers — 16 is a full 10 plus 6 more; 60 comes much later.
- Counting the same object twice (or missing one). Fix: the move-and-count method — slide each object into a “counted” pile as you say its number.
- Recounting after saying the total. The child doesn’t yet trust that the last number IS the answer. Fix: ask “what was the last number you said?” and confirm it is the total.
- Flipping > and <. The alligator is looking the wrong way. Fix: always check that the OPEN mouth faces the BIGGER number.
- Assuming “more objects” means “bigger objects.” 3 elephants vs. 7 ants — the answer to “which has more?” is 7 ants (more of them). We are comparing COUNT, not size. Fix: point to each object and count together.
9. Practice — 25 questions with hidden answers
Read the question with your child. Encourage them to answer out loud or point on a number line first. Click “Show answer & work” only after they’ve tried.
Question 1 — counting forward
Count out loud from 1 to 20. What number comes right after 13?
Answer: 14 (fourteen).
Right after 13 comes 14, then 15, then 16. On the number line, 14 is one hop to the RIGHT of 13.
Question 2 — the teen trap
Fill in the missing number: 11, 12, ___, 14, 15.
Answer: 13 (thirteen).
The teen numbers in order are 11, 12, 13, 14, 15, 16, 17, 18, 19. 13 is the tricky one because it’s “thirteen” not “threeteen.”
Question 3 — number after 19
What number comes right after 19?
Answer: 20 (twenty).
After 19 the teens end and we jump to a new word, twenty. In Class 2 we’ll see that 20 is really 2 tens with no leftover ones.
Question 4 — counting backward from 10
Count backward from 10 to 0. What comes right after 7 when you count backward?
Answer: 6 (six).
Backward from 10: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0. After 7 comes 6. On the number line, 6 is one hop to the LEFT of 7.
Question 5 — counting backward from 15
Fill in the missing number: 15, 14, ___, 12, 11.
Answer: 13 (thirteen).
Going backward one at a time from 15: 15, 14, 13, 12, 11. Same teen-trap number as Question 2, but now going the other direction.
Question 6 — two numbers before
What number is TWO less than 12?
Answer: 10 (ten).
Start at 12 and hop back twice: 12 → 11 → 10. Two less than 12 is 10. This is a first taste of subtraction, which is Class 5.
Question 7 — before and after
What number comes BEFORE 16 and what number comes AFTER 16?
Answer: 15 comes before 16 and 17 comes after 16.
On the number line, 15 is one hop to the LEFT of 16 and 17 is one hop to the RIGHT.
Question 8 — writing the teen number
Which number is bigger — 14 or 41?
Answer: 41 is bigger. 14 is much smaller.
14 means “1 ten and 4 ones” (fourteen). 41 means “4 tens and 1 one” (forty-one). The DIGITS look almost the same but the number is completely different. In grade 1 we usually don’t work with 41 yet, but the child should know that writing a number in the wrong order changes it.
Question 9 — count the objects (one-to-one)
There are 12 counting bears on the table. Your child is asked “how many?” and answers 11. What likely happened, and what should you do?
Answer: they most likely skipped an object. Have them count again, moving each bear from left to right as they say the number.
Off-by-one usually means their finger moved faster than their mouth. The move-and-count fix (slide each bear into a “counted” pile) makes it physically impossible to skip.
Question 10 — cardinality (the last number)
Emma counts “one, two, three, four, five, six, seven” while touching 7 blocks. Then you ask “how many blocks?” and she starts counting again from one. What’s the correct answer, and what does Emma need to learn?
Answer: 7. Emma needs to learn that the LAST number she said IS the answer.
This is called cardinality — the idea that counting produces a total. Whenever Emma says the number words in order, the very last one she said IS how many. Ask her “what was the last number you said?” and confirm that that is the answer.
Question 11 — one-to-one with pairing
There are 6 hats and 6 heads. If every head wears exactly one hat, will any hats be left over? Will any heads be without a hat?
Answer: no leftover hats and no bare heads. Every head has a hat.
This is the picture of one-to-one matching. When two groups pair up perfectly with no leftovers, the two groups are EQUAL. 6 hats = 6 heads.
Question 12 — comparing by matching
There are 8 forks and 5 spoons on the table. Which group has more, and how many more?
Answer: forks have more, by 3.
Pair each spoon with a fork: 5 pairs. That leaves 3 forks with no spoon partner. So there are 3 more forks than spoons. 8 is bigger than 5, and 8 − 5 = 3.
Question 13 — comparing on the number line
Which is bigger — 9 or 12?
Answer: 12 is bigger.
On the number line, 12 is farther to the RIGHT than 9. The number farther right is always bigger.
Question 14 — how many more
How many MORE is 15 than 12?
Answer: 3 more.
Start at 12 and count up to 15: 13, 14, 15 — that’s 3 hops. So 15 is 3 more than 12.
Question 15 — how many fewer
There are 4 red apples and 10 green apples. How many FEWER red apples are there than green?
Answer: 6 fewer red apples.
Count from 4 up to 10: 5, 6, 7, 8, 9, 10 — that’s 6 hops. There are 6 fewer red apples than green. (Also: 6 more green than red. Both are correct ways to say it.)
Question 16 — more vs. bigger objects
There are 3 elephants and 7 ants on a picture. Which group has MORE?
Answer: the ants — there are more of them.
“More” means more OBJECTS, not bigger objects. There are 7 ants and only 3 elephants, so there are more ants. This is the classic trap where kids answer “elephants” because elephants are big.
Question 17 — the equal sign
Fill the blank with the correct symbol (<, >, or =): 8 ___ 8.
Answer: 8 = 8 (the equals sign).
The two numbers are the same, so we use =. The equals sign has two lines of the same length because both sides are the same.
Question 18 — the alligator, greater than
Fill the blank with the correct symbol (<, >, or =): 13 ___ 9.
Answer: 13 > 9 (thirteen is greater than nine).
13 is the bigger number. The alligator’s mouth opens toward the bigger number, so the wide side faces 13 and the point faces 9. That’s the > sign.
Question 19 — the alligator, less than
Fill the blank with the correct symbol (<, >, or =): 6 ___ 14.
Answer: 6 < 14 (six is less than fourteen).
14 is the bigger number. The alligator’s mouth opens toward 14, so the point faces 6 and the wide side faces 14. That’s the < sign.
Question 20 — ordering three numbers
Put these three numbers in order from smallest to biggest: 11, 5, 17.
Answer: 5, 11, 17.
On the number line, 5 comes first (farthest left), then 11, then 17 (farthest right). So from smallest to biggest: 5, 11, 17.
Question 21 — find the number between
What number is between 14 and 16 on the number line?
Answer: 15.
Right between 14 and 16 is 15. The three numbers in a row are 14, 15, 16.
Question 22 — missing number (backward)
Fill in the missing number: 20, 19, 18, ___, 16, 15.
Answer: 17.
Counting backward: 20, 19, 18, 17, 16, 15. Between 18 and 16 is 17.
Question 23 — word problem, comparing
Sofia has 9 stickers. Her brother Leo has 6 stickers. Who has more, and how many more do they have?
Answer: Sofia has more, by 3 stickers.
9 is more than 6. Count up from 6 to 9: 7, 8, 9 — that’s 3 hops. Sofia has 3 more stickers than Leo.
Question 24 — write the number for a picture
A picture shows 1 group of 10 dots and 3 extra dots on the side. What number does the picture show?
Answer: 13 (thirteen).
One 10 plus 3 more is 10 + 3 = 13. This is exactly how the teen numbers work — every teen is 1 ten and some extra ones. That’s the bridge to Class 2 (place value).
Question 25 — challenge, order five numbers
Put these five numbers in order from biggest to smallest: 12, 7, 19, 4, 15.
Answer: 19, 15, 12, 7, 4.
Look at the number line 0 to 20. The number farthest to the RIGHT is biggest — that’s 19. Then working leftward: 15, then 12, then 7, then 4. From biggest to smallest: 19, 15, 12, 7, 4.
10. Answer key summary
| # | Answer | # | Answer | # | Answer |
|---|---|---|---|---|---|
| 1 | 14 | 10 | 7 (last number said) | 19 | 6 < 14 |
| 2 | 13 | 11 | equal, no leftovers | 20 | 5, 11, 17 |
| 3 | 20 | 12 | forks by 3 | 21 | 15 |
| 4 | 6 | 13 | 12 | 22 | 17 |
| 5 | 13 | 14 | 3 more | 23 | Sofia, by 3 |
| 6 | 10 | 15 | 6 fewer | 24 | 13 |
| 7 | 15 before, 17 after | 16 | ants (7 > 3) | 25 | 19, 15, 12, 7, 4 |
| 8 | 41 is bigger | 17 | 8 = 8 | ||
| 9 | skipped a bear; recount | 18 | 13 > 9 |
11. Frequently asked questions
What is number sense to 20 and why is it Class 1?
Number sense to 20 is the ability to count from 1 to 20 forward and backward, count objects with one-to-one matching, know that the last number said is HOW MANY, and compare two quantities. It’s Class 1 because every later grade 1–2 class — place value, addition, subtraction, word problems — assumes it. Without it, later classes feel like magic steps with no meaning.
How do I know if my child has number sense to 20?
Four quick checks: (1) can they count 1 to 20 out loud without stumbling on the teens? (2) can they count 14 objects by touching each one once? (3) can they count backward from 10 to 0? (4) can they say which is more when you show them two piles like 7 vs. 9? A wobble on any of these is exactly where Class 1 focuses.
Why are the teen numbers 11 through 19 so hard?
Because English is inconsistent there. 11 and 12 (“eleven” and “twelve”) don’t follow any pattern. 13 and 15 change the base word (“thirteen,” “fifteen” — not “threeteen” and “fiveteen”). And 14 through 19 say the ones digit first but write the ten first. The teens are the single most common gap we see in incoming Little Newtons students.
What is one-to-one matching?
One-to-one matching (or one-to-one correspondence) means every object gets exactly one number when you count it. Not two. Not zero. Exactly one. The two common mistakes are skipping an object or counting the same object twice. The fix is the move-and-count method: physically slide each object from a “to count” pile to a “counted” pile as you say its number.
How do you compare quantities without recounting?
Two ways. Method 1: match one-to-one — line the groups up in pairs, and whichever has leftovers has more. Method 2: use the number line — count each group and the number farther to the RIGHT is bigger. Once counting is solid, the number-line method is faster.
How do you teach < and > so kids don’t flip them?
Use the alligator picture. The symbol is a hungry alligator’s mouth, and a hungry alligator always eats the BIGGER number. So the wide open side faces the bigger number and the point faces the smaller one. 9 > 7 (mouth toward 9) and 7 < 9 (mouth still toward 9). Usually 1–2 weeks of alligator practice locks it in.
Why does counting backward matter so much?
Because backward counting is subtraction in disguise. When we later say 7 − 3 = 4, we mean “start at 7 and hop back 3.” A child who can’t count backward has no picture for what subtraction is doing. Backward from 10 should feel as easy as forward from 1 by the end of Class 1; in Class 2 we extend it to 100.
What comes after Class 1 in the Little Newtons arc?
Class 2 is place value to 100 (tens and ones with base-10 blocks) — it takes the “1 ten and some ones” idea from Class 1 and extends it. Class 3 is make-ten addition, Class 4 is doubles and near-doubles up to 20, Class 5 is subtraction within 20. See our Little Newtons course page for the full 48-class ladder.
About SOMATH — School of Math
SOMATH — School of Math is a math-focused school on the Upper West Side of Manhattan for students in grades 1–12. Class 1 is part of the Little Newtons arc (grades 1–2), taught in small groups by cofounder Marcelo Ambrozio (Northwestern-trained, 15+ years teaching NYC math) and the SOMATH team, and led by cofounder Vivianne Wright (Harvard).
Location: 226 W 79th St, 1st Floor, New York, NY 10024 · Upper West Side
Phone: (646) 668-6151 · Email: hello@schoolofmath.us
Book: Free evaluation · Schedule · Home
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