Applying one rule across a whole page
Grade 1 logic puzzles ask a child to hold a single rule in mind and apply it consistently across every item on the page, rather than judging each item in isolation the way Kindergarten's row-by-row puzzles do. That's the step up: the rule doesn't change, but the number of things it has to be checked against does, and staying consistent across a full grid is a genuinely harder version of the same underlying skill.
Find and Cross Out
A grid of shapes is shown along with one rule (for example, a target shape and color), and the task is to cross out every single item in the grid that matches — not just the first one found. Every puzzle is built to guarantee at least a few real matches, so a child isn't hunting for something that might not exist; the challenge is thoroughness, checking every item rather than stopping after the first hit.
Growing Sequences (What Comes Next?)
A short row of numbers follows one consistent pattern — always adding the same amount, or always adding a growing amount — with the last box left blank for a child to fill in. This is an early, concrete introduction to algebraic thinking: spotting a rule from a few examples and predicting what comes next, the same reasoning that underlies far more advanced pattern and sequence work later on.
Number Pattern (Pick the Answer)
Number Pattern takes the same skip-counting and arithmetic-sequence reasoning as Growing Sequence and turns it into a multiple-choice puzzle instead of an open blank — three numbers are shown, a rule connects them, and a child picks the correct next number from three lettered options (A, B, C) rather than writing one in. The distractors aren't random: one is usually the previous value repeated (a common "forgot to add" mistake), and one uses a slightly wrong step size, so picking correctly means actually confirming the rule against all three options, not just recognizing the right-looking number.
Why three puzzle types, together
Cross-Out, Growing Sequence, and Number Pattern look different but train the same underlying move from three directions: Cross-Out gives the rule and asks a child to apply it exhaustively; Growing Sequence gives examples and asks a child to produce the missing number themselves; Number Pattern gives the same kind of sequence but asks a child to recognize the correct answer among plausible wrong ones. Working all three regularly builds the full loop — recognizing a pattern, producing an answer, and discriminating a right answer from a close-but-wrong one — rather than just one piece of it.
A teacher's guide to Grade 1 logic worksheets
A first grader can do something a kindergartner mostly cannot: hold a rule in mind and apply it, over and over, without losing it. "Cross out every green square" is a sentence a six-year-old can read or have read to them, and then act on for forty-eight shapes in a row, without being distracted by green circles or red squares. That steadiness, being able to follow a rule across a whole page, is a milestone in thinking, and it is what the Grade 1 puzzles are built to practice.
This page gathers the three Grade 1 puzzles: Find and Cross Out, What Comes Next? (a growing number sequence) and Pick the Next Number. This guide explains what each is teaching, how to introduce it, what mistakes to expect, and how the puzzles lead into the number reasoning of later years. The Pick the Next Number puzzle has its own full guide on the Grade 1 number pattern page, and this page concentrates on the other two.
A Find and Cross Out page: forty-eight shapes in six rows of eight, and a rule printed under the title.
What changes at Grade 1
At Pre-K and Kindergarten, a puzzle asks a child to see a difference: this one is not like the others. At Grade 1, puzzles ask for more.
- Hold a rule in words. The instruction is a sentence, and the child must remember it.
- Apply it many times. Not once, but across a grid of dozens of items.
- Combine two features. Not just "green," but "green and square."
- Find a rule from examples. In number sequences, the rule is not given. The child works it out.
- Use number. Counting on, skipping and finding differences.
That is a big step, and the three puzzles are chosen so that it can be taken one foot at a time.
Find and Cross Out
Each page has a grid of six rows of eight shapes, forty-eight in all, in circles and squares of several colors. Under the title is a rule, such as "Cross out every green square." The child goes through the grid and crosses out every shape that matches.
Why it works. The task seems easy, and for a child who is just beginning, it is not. The rule has two conditions, a color and a shape, and both must be true. A green circle is not a green square. A red square is not a green square. The child has to check both things for every shape, and not slip into crossing out everything green or everything square.
What a child learns.
- Reading and holding a rule. The words of the rule must be kept in mind through the whole page.
- Two attributes at once. Color and shape are independent. This is a first lesson in combining conditions, the logic behind "and."
- Systematic scanning. A good solver goes row by row, left to right, without skipping. A hasty one jumps around and misses some.
- Sustained attention. Forty-eight items is a lot for a six-year-old.
- Self-checking. At the end, the child goes back and checks that none was missed.
How to introduce it.
- Read the rule aloud. "Cross out every green square."
- Ask the child to say it back. "Green and square."
- Find one together. Point to a green circle. "Is this a green square?" "No, it's a circle." Point to a green square. "Yes!"
- Show the scanning. Run a finger along the first row. "I look at each one, one at a time."
- Let the child do the page.
- Check at the end. Go through the grid again, looking for any green square without a cross.
Strategies.
- Go row by row. Use a finger, or a ruler, under the row.
- Cross out as you go. Do not wait. Mark each match as you find it.
- Say the rule at the start of each row. "Green square."
- Look for the tricky ones. Which ones are green but not square? Which are square but not green?
- Count at the end. "How many did I cross out?" Compare with a friend.
- Use a different mark. A single line, or a cross, to avoid confusion with the shapes.
Common mistakes.
- Crossing out all green shapes. The child has attended to color only. Re-read the rule, and emphasize "square."
- Crossing out all squares. The child has attended to shape only.
- Missing some. The child has scanned too quickly. Go back, and use a finger.
- Crossing out a near-match. A yellow square, perhaps, mistaken for a green one. Check the colors by name.
- Losing the rule halfway. Re-read the instruction.
These are all useful information, and a good teacher treats them as such. "I see you crossed out the green circles. Let's look at the rule again."
Growing sequences: What Comes Next?
Each page has six rows of numbers, three shown and a blank. The child looks at the three numbers, works out how the sequence is going, and writes the fourth.
A What Comes Next page. In each row, the numbers grow by the same amount each time, and the child writes the fourth.
Look at the rows on the sample.
| Row |
Shown |
The step |
Next |
| 1 |
5, 10, 15 |
up by 5 |
20 |
| 2 |
5, 11, 17 |
up by 6 |
23 |
| 3 |
7, 10, 13 |
up by 3 |
16 |
| 4 |
9, 11, 13 |
up by 2 |
15 |
| 5 |
9, 15, 21 |
up by 6 |
27 |
| 6 |
4, 8, 12 |
up by 4 |
16 |
In every row, the numbers grow by the same amount each time. That amount is the step, and finding it is the whole puzzle.
Why it works. A growing sequence is the first piece of algebra a child meets. It asks for a rule that applies to all the terms, and it asks the child to find it from examples. The approach is always the same: look at how much it changes, check that the change is the same each time, and apply it once more.
What a child learns.
- The idea of a constant step. The difference between neighbors is the same.
- Finding the difference. Subtracting a number from the next one.
- Applying a rule. Adding the step to the last number.
- Checking. Testing the rule on a second pair.
- Number sense. Counting on and skip counting with different steps.
- Mental arithmetic. Adding 5 or 6 to a number within 30.
How to introduce it.
- Look at the first row. "5, 10, 15. What is happening?"
- Find the step. "How much did it go up from 5 to 10?" "5." "From 10 to 15?" "5." "So each time it goes up by 5."
- Apply it. "What is 15 plus 5?" "20."
- Write it in the box.
- Check by saying the whole row. "5, 10, 15, 20."
Strategies.
- Find the gap. Count on from the first number to the second.
- Check with the second gap. If both gaps match, the rule holds.
- Use a number line. Draw jumps from one number to the next.
- Use a hundred chart. Mark the numbers, and see the pattern.
- Say the sequence aloud. "Four, eight, twelve..." Many children can hear what comes next.
- Use fingers. Count on to add the step.
Common mistakes.
- Adding the wrong step. The child worked out the step from the first number only. Check the second gap too.
- Counting the gap wrongly. The difference between 9 and 15 is 6, but a child may count 9 as the first number: 9, 10, 11, 12, 13, 14, 15, and say 7. Use a number line, and count the jumps, not the numbers.
- Repeating the last number. The child writes 15 again. Ask them to say the pattern.
- Guessing. A very fast answer with no explanation. Ask, "How do you know?"
- An addition error. The child found the right step, but added incorrectly. That is a math issue, not a logic one. Revisit addition within 20.
Linking to skip counting
Many of the growing sequences are exactly skip counting: 5, 10, 15 is counting by 5s, and 4, 8, 12 is counting by 4s. A child who has practiced skip counting will find these rows easy, and a child who has not will find them harder. The skip counting pages are an excellent companion.
But not all rows are skip counting. A row such as 5, 11, 17 begins at 5 and goes up by 6. It is a general pattern, not a table. The difference matters. A skip counting row can often be solved by recall ("it's the 5s"), but a general row has to be reasoned. A child who can do both has the basics of number patterns.
Reading a number sequence aloud
A very useful habit is to say the sequence, and listen for the step. A child who whispers "five... eleven... seventeen..." and hears the gap of six is using their ear as well as their eye.
- Say the numbers in a steady rhythm. Clap on each.
- Say the gap between each. "Five to eleven is six. Eleven to seventeen is six."
- Say the next. "Seventeen, and six more is twenty-three."
- Say the whole thing. "Five, eleven, seventeen, twenty-three."
It sounds simple, and it is very effective. The act of saying the numbers makes the pattern audible.
Mental math tools for sequences
Finding the step is a thinking skill, but adding the step is arithmetic, and a child who is slow at the second may lose the thread of the first. A few mental math tools make sequences smoother.
- Counting on from the larger number. To add 6 to 17, start at 17 and count: 18, 19, 20, 21, 22, 23.
- Bridging through ten. To add 6 to 17, add 3 to reach 20, and then 3 more. That is 23.
- Using a known double. To add 6 to 9, think "9 and 6 is one more than 5 and 10," or "it's 10 and 5, so 15."
- Skip counting. If the step is 5, the numbers end in 0 or 5, and a child can hear it.
- Finding the gap by counting up. From 9 to 15, count up: 10, 11, 12, 13, 14, 15. Six jumps.
- Subtracting. 15 − 9 is also 6. A child can check the gap in two ways.
These are the same strategies that appear in the Grade 1 math pages, and a child who has them will find the sequences quick and satisfying.
A closer look at the cross-out grid
The cross-out puzzle looks like a simple search, but it hides an interesting piece of logic. Take the rule "Cross out every green square." In a grid of forty-eight shapes, each shape is one of two things, a circle or a square, and one of several colors. For each shape, the child has to ask two questions.
- Is it green?
- Is it a square?
Only if the answer to both is yes does it get crossed out. This is the logic of "and." A shape that passes only one test is a near miss, and the grids are full of them. A green circle passes the first and fails the second. A red square passes the second and fails the first.
You can show this with a simple chart on a scrap of paper.
|
Green |
Not green |
| Square |
Cross out |
Leave |
| Circle |
Leave |
Leave |
Only one box of four says "cross out." Seeing it as a chart helps some children, and the same idea reappears in Grade 3 as a Venn diagram, where overlapping circles show things that pass both tests. The Grade 3 logic page picks up that thread.
A child who finishes quickly might be asked: "How many did you cross out? Do you think you found them all? How could you be sure?" Counting and checking, row by row, is a good habit, and it introduces the idea of an exhaustive search.
A sample fifteen-minute session
A session with a six-year-old, using a Find and Cross Out page.
- Minute 0 to 2. Warm up by sorting real objects. Spread out a handful of red and blue blocks, some squares and some circles. "Find all the blue squares." Ask how many.
- Minute 2 to 4. Read the rule on the page together. Ask the child to say it in their own words.
- Minute 4 to 6. Do the first row together. Say "green and square" at each shape. Let the child cross out the matches.
- Minute 6 to 11. Let the child do the remaining rows, with a finger under each one. Resist pointing out missed shapes.
- Minute 11 to 14. Check together. Go through the grid again, and count the crossed-out ones.
- Minute 14 to 15. Ask the child to make a rule for you: "Cross out every red circle." Make a small grid on scrap paper, and let them test it.
Notice that the child ends the session as the rule-maker. That is a meaningful shift, and it is a good sign of understanding.
A four-week plan
For a family or a teacher who wants a loose plan, here is one way to work through the Grade 1 logic puzzles. It is not a requirement.
- Week 1: Find and Cross Out. Three short sessions. Focus on reading the rule and scanning in order.
- Week 2: What Comes Next? Three sessions. Begin with skip counting rows, such as steps of 5 and 2. Say each row aloud.
- Week 3: Mixed. One session of each, with more attention to the harder rows, where the start is not the step.
- Week 4: Pick the Next Number. See the Grade 1 number pattern page, and use the multiple-choice puzzles to practice checking.
At the end, a child might make a puzzle of each type for someone else. Making a puzzle is a good test of whether the idea has been understood.
Making your own puzzles
A child who can create a puzzle has understood its rule. Here is how to set a child up to make their own.
For a cross-out grid.
- Draw a grid of four rows and five columns.
- Fill each box with a circle or a square, in two or three colors.
- Choose a rule, such as "Cross out every blue circle."
- Swap with a friend.
For a sequence.
- Choose a start and a step. "Start at 4, and go up by 3."
- Write the first three numbers: 4, 7, 10.
- Leave a blank for the fourth.
- Check that the answer is 13.
For a rule-finding game.
- One player thinks of a rule, such as "add 2."
- The other says a number, and the first replies with the answer.
- Keep going until the second can guess the rule.
These games take only a minute, and they make a child the author of the thinking. They are also a lot of fun.
A routine for a puzzle session
A short, steady session is best.
- Warm up orally. Count by 2s, 5s and 10s together.
- Choose one puzzle type for the day.
- Do the first example together, thinking aloud.
- Let the child do two or three more.
- Check. Ask the child to explain one answer.
- Look at a mistake, if there was one.
- Finish with a quick challenge. "I'm thinking of a pattern. It starts at 3 and goes up by 4. What are the next three?"
Ten to fifteen minutes is enough for a six-year-old.
Pick the Next Number
The third Grade 1 puzzle is a multiple-choice version of a number pattern. The page shows three numbers and a blank, and offers three choices, A, B and C, from which the child must pick the next. For example, 13, 21, 29... A) 35, B) 37, C) 34.
A Pick the Next Number page: three numbers, a blank, and three choices.
It is related to the growing sequence, but it adds something: the child has to choose, and the wrong choices are tempting. A full guide to this puzzle, including how the wrong answers are built and how to teach around them, is on the Grade 1 number pattern page.
Connecting to other parts of the curriculum
Grade 1 logic links to a great many things.
- Math. Number patterns lead to skip counting, multiplication and algebra. Find and Cross Out is a lesson in classification. See the Grade 1 math pages.
- Patterns. The emoji pattern pages build the same habit of finding a rule.
- Reading. Following written instructions, and attending to every item in a row.
- Science. Sorting by two attributes is the first step in classification. Which animals are both furry and four-legged?
- Computing. A rule applied to every item is an algorithm, and finding "every green square" is what a computer program does.
For teachers
A Grade 1 class can use these puzzles in many ways.
- Early finishers. A page is a quiet, engaging task.
- Centers. A page, a pencil and a partner.
- Whole-class warm-up. Display a sequence on the board, and ask the class to find the step.
- Differentiation. Give some children a page of sequences with small steps, and others a page with larger steps, by choosing different numbered pages.
- Discussion. Ask a child to explain how they found the step.
- Assessment. A page shows whether a child can find a constant difference.
- Homework. A single puzzle is a gentle task.
For parents
You do not need to be good at puzzles.
- Read the rule aloud together.
- Ask, "What do you notice?"
- Resist telling the answer.
- Let your child explain.
- Do one of your own. Make up a sequence for them.
- Keep it playful. Ten minutes at the table with a snack.
Questions that come up
My child crosses out the wrong ones. Re-read the rule together, and emphasize both parts. Use a finger to go one by one.
My child finds the sequences easy. Move to Grade 2, where the steps are bigger and the puzzles more complex.
My child can't find the step. Use a number line, and count the jumps between the first two numbers.
Do I need to correct everything? Pick one or two to review. A calm "let's check" is plenty.
How many puzzles a week? Two or three, with a mix of types.
What if my child hates puzzles? Try a game version, or let them make a puzzle for you.
What does the pattern step have to do with multiplication? Skip counting is repeated addition, and repeated addition is multiplication. A child who can find the step is on the way.
A Grade 1 puzzle asks a child to follow a rule, or to find one. It is a very small piece of work, and it is the beginning of a very large idea: that the world has structure, and a careful mind can find it.
