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Math Logic Problems

Welcome to our Math Logic Problems worksheets. All the problems on this page require children to use their reasoning and logic thinking skills to solve.

There are a range of worksheets on this page with varying levels of difficulty from 1st grade up to 5th grade.

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Logic puzzle problems are a set of problems which involve children using their reasoning and logical thinking skills.

Sometimes children who struggle in other areas of math, such as number work, find that this is an area which they excel in.

Some of the math logic problems on this page work like traditional logic puzzles with table grids to fill in, but most of the sheets simply involve children using their thinking and resoning to solve the problems on the page.

All the logic puzzle worksheets on this page come with an answer sheet.

newton thinking image

The problems on this page all involving solving Logic Problems.

Some of the sheets on this page include tables and way to support children with their recording and organising their work.

Some of the sheets have a space for children to record their own thinking and working out, with no support in recording.

The level of the worksheets goes from 1st grade to 5th grade (UK Years 1 to 6).

Using these sheets will help your child to:

  • deveolop their reasoning and thinking skills;
  • support and develop recording skills;
  • solve a range of logic puzzles.

Logic Problems Worksheets

1st grade problems, share the treasure.

Share the Treasure involves sharing out 20 gold bars equally into 4 piles. The second part of the activity involves sharing out the bars using four rules.

  • Share the Treasure 1
  • PDF version
  • Who Chose Which Shape #1

Who Chose Which Shape is a logic problem where children have to work out which salamander chose which shape from the clues given.

2nd Grade Problems

  • Birthday Girl

Birthday Girl is an activity which involves finding the correct ages of all the people in the challeges using the clues that are given.

  • Share the Treasure #2

Share the Treasure is a logic acitivity where the aim is to share some treasure according to certain criteria.

  • Who Chose Which Shape #2

Who Chose Which Shape is a math logic problem where children have to work out which salamander chose which shape from the clues given.

3rd Grade Problems

  • Color that Shape

Color that Shape is a coloring activity which uses logical thinking to work out which shape needs to be shaded which color.

Join Me Up is an logical puzzle where the aim is to place the numbers from 1 to 7 into the puzzle so that no consecutive numbers are next to each other.

  • Spot the Digits

Spot the Digits is a logic activity where children have to find out the values of the letters a, b, c and d. The values can be determined by using the 3 clues.

4th Grade Problems

Quadra's magic bag challenges.

Quadra's Magic Bag Challenges involves using thinking and reasoning skills to work out two math challenges. The challenges also involve an element of trial and improvement, and also some addition.

  • Quadra's Magic Bag Challenge
  • Four Dogs Problem

Four Dogs Problem is a logic problem which involves using the clues to work out the owners for each of the four dogs.

Who Caught the Biggest FIsh?

Who Caught the Biggest Fish is a logical number problem where you need to use trial and improvement strategies to work out the order of size of the fish from the clues given about their weights.

  • Who Caught the Biggest Fish?

5th Grade Problems

  • Who Chose Which?

Who Chose Which is a logical number activity where you need to use the clues to work out which numbers each of the salamanders chose.

  • Birthday Bonanza

Birthday Bonanza is a logic problem which requires logical thinking to work out who got which present and how old each of them was.

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Other Word Problems by the Math Salamanders

Finding all possibilities problems.

This is our finding all possibilities area where all the worksheets involve finding many different answers to the problem posed.

The sheets here encourage systematic working and logical thinking.

The problems are different in that, there is typically only one problem per sheet, but the problem may take quite a while to solve!

  • Finding all Possibilities problems

Math Real-Life Word Problems by Grade

We have a variety of different problem solving worksheets, including 'real-life' problems.

The sheets go from 1st through 5th grade.

  • Math Problems for Children 1st Grade
  • 2nd Grade Math Word Problems
  • Math Word Problems for kids 3rd Grade
  • 4th Grade Math Word Problems
  • 5th Grade Math Problems

Fraction Problems

Here you will find a range of fraction word problems to help your child apply their fraction learning.

The worksheets cover a range of fraction objectives, from adding and subtracting fractions to working out fractions of numbers. The sheets support fraction learning from 2nd grade to 5th grade.

  • Fraction Riddles for kids (easier)
  • Free Printable Fraction Riddles (harder)

Ratio Problems

Here you will find a range of ratio word problems to help your child understand what a ratio is and how ratios work.

The sheets support ratio learning at a 5th grade level.

We hope you have enjoyed our Math Logic Problems on this page. Please leave a comment at the bottom of the page if you like them!

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Math and Logic Problems

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3.E: Symbolic Logic and Proofs (Exercises)

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3.1: Propositional Logic

Consider the statement about a party, “If it's your birthday or there will be cake, then there will be cake.”

  • Translate the above statement into symbols. Clearly state which statement is \(P\) and which is \(Q\text{.}\)
  • Make a truth table for the statement.
  • Assuming the statement is true, what (if anything) can you conclude if there will be cake?
  • Assuming the statement is true, what (if anything) can you conclude if there will not be cake?
  • Suppose you found out that the statement was a lie. What can you conclude?
  • \(P\text{:}\) it's your birthday; \(Q\text{:}\) there will be cake. \((P \vee Q) \imp Q\)
  • Hint: you should get three T's and one F.
  • Only that there will be cake.
  • It's NOT your birthday!
  • It's your birthday, but the cake is a lie.

Make a truth table for the statement \((P \vee Q) \imp (P \wedge Q)\text{.}\)

Make a truth table for the statement \(\neg P \wedge (Q \imp P)\text{.}\) What can you conclude about \(P\) and \(Q\) if you know the statement is true?

If the statement is true, then both \(P\) and \(Q\) are false.

Make a truth table for the statement \(\neg P \imp (Q \wedge R)\text{.}\)

Like above, only now you will need 8 rows instead of just 4.

Determine whether the following two statements are logically equivalent: \(\neg(P \imp Q)\) and \(P \wedge \neg Q\text{.}\) Explain how you know you are correct.

Make a truth table for each and compare. The statements are logically equivalent.

Are the statements \(P \imp (Q\vee R)\) and \((P \imp Q) \vee (P \imp R)\) logically equivalent?

Simplify the following statements (so that negation only appears right before variables).

  • \(\neg(P \imp \neg Q)\text{.}\)
  • \((\neg P \vee \neg Q) \imp \neg (\neg Q \wedge R)\text{.}\)
  • \(\neg((P \imp \neg Q) \vee \neg (R \wedge \neg R))\text{.}\)
  • It is false that if Sam is not a man then Chris is a woman, and that Chris is not a woman.
  • \(P \wedge Q\text{.}\)
  • \((\neg P \vee \neg R) \imp (Q \vee \neg R)\) or, replacing the implication with a disjunction first: \((P \wedge Q) \vee (Q \vee \neg R)\text{.}\)
  • \((P \wedge Q) \wedge (R \wedge \neg R)\text{.}\) This is necessarily false, so it is also equivalent to \(P \wedge \neg P\text{.}\)
  • Either Sam is a woman and Chris is a man, or Chris is a woman.

Use De Morgan's Laws, and any other logical equivalence facts you know to simplify the following statements. Show all your steps. Your final statements should have negations only appear directly next to the sentence variables or predicates (\(P\text{,}\) \(Q\text{,}\) \(E(x)\text{,}\) etc.), and no double negations. It would be a good idea to use only conjunctions, disjunctions, and negations.

  • \(\neg((\neg P \wedge Q) \vee \neg(R \vee \neg S))\text{.}\)
  • \(\neg((\neg P \imp \neg Q) \wedge (\neg Q \imp R))\) (careful with the implications).

Tommy Flanagan was telling you what he ate yesterday afternoon. He tells you, “I had either popcorn or raisins. Also, if I had cucumber sandwiches, then I had soda. But I didn't drink soda or tea.” Of course you know that Tommy is the world's worst liar, and everything he says is false. What did Tommy eat?

Justify your answer by writing all of Tommy's statements using sentence variables (\(P, Q, R, S, T\)), taking their negations, and using these to deduce what Tommy actually ate.

Determine if the following deduction rule is valid:

The deduction rule is valid. To see this, make a truth table which contains \(P \vee Q\) and \(\neg P\) (and \(P\) and \(Q\) of course). Look at the truth value of \(Q\) in each of the rows that have \(P \vee Q\) and \(\neg P\) true.

Determine if the following is a valid deduction rule:

Can you chain implications together? That is, if \(P \imp Q\) and \(Q \imp R\text{,}\) does that means the \(P \imp R\text{?}\) Can you chain more implications together? Let's find out:

I suggest you don't go through the trouble of writing out a \(2^n\) row truth table. Instead, you should use part (a) and mathematical induction.

We can also simplify statements in predicate logic using our rules for passing negations over quantifiers, and then applying propositional logical equivalence to the “inside” propositional part. Simplify the statements below (so negation appears only directly next to predicates).

  • \(\neg \exists x \forall y (\neg O(x) \vee E(y))\text{.}\)
  • \(\neg \forall x \neg \forall y \neg(x \lt y \wedge \exists z (x \lt z \vee y \lt z))\text{.}\)
  • There is a number \(n\) for which no other number is either less \(n\) than or equal to \(n\text{.}\)
  • It is false that for every number \(n\) there are two other numbers which \(n\) is between.
  • \(\forall x \exists y (O(x) \wedge \neg E(y))\text{.}\)
  • \(\exists x \forall y (x \ge y \vee \forall z (x \ge z \wedge y \ge z))\text{.}\)
  • There is a number \(n\) for which every other number is strictly greater than \(n\text{.}\)
  • There is a number \(n\) which is not between any other two numbers.

Suppose \(P\) and \(Q\) are (possibly molecular) propositional statements. Prove that \(P\) and \(Q\) are logically equivalent if and only if \(P \iff Q\) is a tautology.

What do these concepts mean in terms of truth tables?

Suppose \(P_1, P_2, \ldots, P_n\) and \(Q\) are (possibly molecular) propositional statements. Suppose further that

is a valid deduction rule. Prove that the statement

is a tautology.

3.2: Proofs

Consider the statement “for all integers \(a\) and \(b\text{,}\) if \(a + b\) is even, then \(a\) and \(b\) are even”

  • Write the contrapositive of the statement.
  • Write the converse of the statement.
  • Write the negation of the statement.
  • Is the original statement true or false? Prove your answer.
  • Is the contrapositive of the original statement true or false? Prove your answer.
  • Is the converse of the original statement true or false? Prove your answer.
  • Is the negation of the original statement true or false? Prove your answer.
  • For all integers \(a\) and \(b\text{,}\) if \(a\) or \(b\) is not even, then \(a+b\) is not even.
  • For all integers \(a\) and \(b\text{,}\) if \(a\) and \(b\) are even, then \(a+b\) is even.
  • There are numbers \(a\) and \(b\) such that \(a+b\) is even but \(a\) and \(b\) are not both even.
  • False. For example, \(a = 3\) and \(b = 5\text{.}\) \(a+b = 8\text{,}\) but neither \(a\) nor \(b\) are even.
  • False, since it is equivalent to the original statement.
  • True. Let \(a\) and \(b\) be integers. Assume both are even. Then \(a = 2k\) and \(b = 2j\) for some integers \(k\) and \(j\text{.}\) But then \(a+b = 2k + 2j = 2(k+j)\) which is even.
  • True, since the statement is false.

Consider the statement: for all integers \(n\text{,}\) if \(n\) is even then \(8n\) is even.

  • Prove the statement. What sort of proof are you using?
  • Is the converse true? Prove or disprove.

Let \(n\) be an integer. Assume \(n\) is even. Then \(n = 2k\) for some integer \(k\text{.}\) Thus \(8n = 16k = 2(8k)\text{.}\) Therefore \(8n\) is even.

  • The converse is false. That is, there is an integer \(n\) such that \(8n\) is even but \(n\) is odd. For example, consider \(n = 3\text{.}\) Then \(8n = 24\) which is even but \(n = 3\) is odd.

Your “friend” has shown you a “proof” he wrote to show that \(1 = 3\text{.}\) Here is the proof:

I claim that \(1 = 3\text{.}\) Of course we can do anything to one side of an equation as long as we also do it to the other side. So subtract 2 from both sides. This gives \(-1 = 1\text{.}\) Now square both sides, to get \(1 = 1\text{.}\) And we all agree this is true.

What is going on here? Is your friend's argument valid? Is the argument a proof of the claim \(1=3\text{?}\) Carefully explain using what we know about logic. Hint: What implication follows from the given proof?

Suppose you have a collection of 5-cent stamps and 8-cent stamps. We saw earlier that it is possible to make any amount of postage greater than 27 cents using combinations of both these types of stamps. But, let's ask some other questions:

  • What amounts of postage can you make if you only use an even number of both types of stamps? Prove your answer.
  • Suppose you made an even amount of postage. Prove that you used an even number of at least one of the types of stamps.
  • Suppose you made exactly 72 cents of postage. Prove that you used at least 6 of one type of stamp.

Suppose that you would like to prove the following implication:

For all numbers \(n\text{,}\) if \(n\) is prime then \(n\) is solitary.

Write out the beginning and end of the argument if you were to prove the statement,

  • By contrapositive
  • By contradiction

You do not need to provide details for the proofs (since you do not know what solitary means). However, make sure that you provide the first few and last few lines of the proofs so that we can see that logical structure you would follow.

Prove that \(\sqrt 3\) is irrational.

Suppose \(\sqrt{3}\) were rational. Then \(\sqrt{3} = \frac{a}{b}\) for some integers \(a\) and \(b \ne 0\text{.}\) Without loss of generality, assume \(\frac{a}{b}\) is reduced. Now

So \(a^2\) is a multiple of 3. This can only happen if \(a\) is a multiple of 3, so \(a = 3k\) for some integer \(k\text{.}\) Then we have

So \(b^2\) is a multiple of 3, making \(b\) a multiple of 3 as well. But this contradicts our assumption that \(\frac{a}{b}\) is in lowest terms.

Therefore, \(\sqrt{3}\) is irrational.

Consider the statement: for all integers \(a\) and \(b\text{,}\) if \(a\) is even and \(b\) is a multiple of 3, then \(ab\) is a multiple of 6.

  • State the converse. Is it true? Prove or disprove.

Prove the statement: For all integers \(n\text{,}\) if \(5n\) is odd, then \(n\) is odd. Clearly state the style of proof you are using.

We will prove the contrapositive: if \(n\) is even, then \(5n\) is even.

Let \(n\) be an arbitrary integer, and suppose \(n\) is even. Then \(n = 2k\) for some integer \(k\text{.}\) Thus \(5n = 5\cdot 2k = 10k = 2(5k)\text{.}\) Since \(5k\) is an integer, we see that \(5n\) must be even. This completes the proof.

Prove the statement: For all integers \(a\text{,}\) \(b\text{,}\) and \(c\text{,}\) if \(a^2 + b^2 = c^2\text{,}\) then \(a\) or \(b\) is even.

Prove: \(x=y\) if and only if \(xy=\dfrac{(x+y)^2}{4}\text{.}\) Note, you will need to prove two “directions” here: the “if” and the “only if” part.

The game TENZI comes with 40 six-sided dice (each numbered 1 to 6). Suppose you roll all 40 dice.

  • Prove that there will be at least seven dice that land on the same number.
  • How many dice would you have to roll before you were guaranteed that some four of them would all match or all be different? Prove your answer.

Suppose that each number only came up 6 or fewer times. So there are at most six 1's, six 2's, and so on. That's a total of 36 dice, so you must not have rolled all 40 dice.

Suppose you roll 10 dice, but that there are NOT four matching rolls. This means at most, there are three of any given value. If we only had three different values, that would be only 9 dice, so there must be 4 different values, giving 4 dice that are all different.

Prove that \(\log(7)\) is irrational.

We give a proof by contradiction.

Suppose, contrary to stipulation that \(\log(7)\) is rational. Then \(\log(7) = \frac{a}{b}\) with \(a\) and \(b \ne 0\) integers. By properties of logarithms, this implies

Equivalently,

But this is impossible as any power of 7 will be odd while any power of 10 will be even. Therefore, \(\log(7)\) is irrational.

Prove that there are no integer solutions to the equation \(x^2 = 4y + 3\text{.}\)

Prove that every prime number greater than 3 is either one more or one less than a multiple of 6.

For each of the statements below, say what method of proof you should use to prove them. Then say how the proof starts and how it ends. Bonus points for filling in the middle.

  • There are no integers \(x\) and \(y\) such that \(x\) is a prime greater than 5 and \(x = 6y + 3\text{.}\)
  • For all integers \(n\text{,}\) if \(n\) is a multiple of 3, then \(n\) can be written as the sum of consecutive integers.
  • For all integers \(a\) and \(b\text{,}\) if \(a^2 + b^2\) is odd, then \(a\) or \(b\) is odd.
  • Proof by contradiction. Start of proof: Assume, for the sake of contradiction, that there are integers \(x\) and \(y\) such that \(x\) is a prime greater than 5 and \(x = 6y + 3\text{.}\) End of proof: … this is a contradiction, so there are no such integers.
  • Direct proof. Start of proof: Let \(n\) be an integer. Assume \(n\) is a multiple of 3. End of proof: Therefore \(n\) can be written as the sum of consecutive integers.
  • Proof by contrapositive. Start of proof: Let \(a\) and \(b\) be integers. Assume that \(a\) and \(b\) are even. End of proof: Therefore \(a^2 + b^2\) is even.

A standard deck of 52 cards consists of 4 suites (hearts, diamonds, spades and clubs) each containing 13 different values (Ace, 2, 3, …, 10, J, Q, K). If you draw some number of cards at random you might or might not have a pair (two cards with the same value) or three cards all of the same suit. However, if you draw enough cards, you will be guaranteed to have these. For each of the following, find the smallest number of cards you would need to draw to be guaranteed having the specified cards. Prove your answers.

  • Three of a kind (for example, three 7's).
  • A flush of five cards (for example, five hearts).
  • Three cards that are either all the same suit or all different suits.

Suppose you are at a party with 19 of your closest friends (so including you, there are 20 people there). Explain why there must be least two people at the party who are friends with the same number of people at the party. Assume friendship is always reciprocated.

Your friend has given you his list of 115 best Doctor Who episodes (in order of greatness). It turns out that you have seen 60 of them. Prove that there are at least two episodes you have seen that are exactly four episodes apart.

Suppose you have an \(n\times n\) chessboard but your dog has eaten one of the corner squares. Can you still cover the remaining squares with dominoes? What needs to be true about \(n\text{?}\) Give necessary and sufficient conditions (that is, say exactly which values of \(n\) work and which do not work). Prove your answers.

What if your \(n\times n\) chessboard is missing two opposite corners? Prove that no matter what \(n\) is, you will not be able to cover the remaining squares with dominoes.

Discrete Mathematics/Logic/Exercises

  • 1 Logic Exercise 1
  • 2 Logic Exercise 2
  • 3 Logic Exercise 3
  • 4 Logic Exercise 4
  • 5 Logic Exercise 5
  • 6 Logic Exercise 6
  • 7 Logic Exercise 7

Logic Exercise 1 [ edit | edit source ]

{\displaystyle \scriptstyle \wedge }

Back to Logic .

Logic Exercise 2 [ edit | edit source ]

Logic exercise 3 [ edit | edit source ], logic exercise 4 [ edit | edit source ].

Back to Logic Page 2 .

Logic Exercise 5 [ edit | edit source ]

The following predicates are defined:

Write each of the following propositions using predicate notation:

1 Jimmy is a friend of mine.

2 Sue is wealthy and clever.

3 Jane is wealthy but not clever.

4 Both Mark and Elaine are friends of mine.

5 If Peter is a friend of mine, then he is not boring.

6 If Jimmy is wealthy and not boring, then he is a friend of mine.

Logic Exercise 6 [ edit | edit source ]

Logic exercise 7 [ edit | edit source ].

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These workbooks have been compiled and tested by a team of math experts to increase your child's confidence, enjoyment, and success at school. Third Grade Math Made Easy provides practice at all the major topics for Grade 3 with emphasis on basic multiplication and division facts. It includes a review of Grade 2 topics, a preview of topics in Grade 4, and Times Tables practice. Learn how the workbook correlates to the Common Core State Standards for mathematics.

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Test Your Mathematical Logic With Solutions

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Welcome to our "Test Your Mathematical Logic with Solutions" quiz! If you're passionate about mathematics and enjoy solving logical puzzles, this quiz is tailor-made for you. Whether you're a student brushing up on your math skills, a professional looking to challenge your problem-solving abilities or just someone who loves a good mental workout, this quiz offers an engaging experience. Ready to take our interesting math logic test quiz, designed to test your math skills? Take this math logic test and see how well you can compute numbers in your head, how good you are at sequences, and if you can Read more do basic math word problems. Our quiz features a series of intriguing mathematical problems, ranging from basic arithmetic to more advanced logical challenges. Are you ready to put your mathematical logic to the test and sharpen your mind? Challenge yourself, track your progress, and discover new problem-solving techniques in this interactive quiz. Share your results with friends or colleagues to see who can solve the most problems correctly and quickly. If you think you have good control over this subject, then you must take up this quiz. Don't worry. Thismath logic quiz consists of just a few simple questions that require fundamental math knowledge. Whether you're preparing for an exam, looking to enhance your mathematical abilities, or just craving a fun and educational experience, our "Test Your Mathematical Logic with Solutions" quiz is the perfect choice. Dive in and explore the world of mathematical logic today!

There are 60 marbles in a bowl. Their colors are red, blue, and yellow. 1/3 of the marbles are yellow, and 1/4 of the marbles are blue. How many red marbles are there in the bowl?

Rate this question:

What is the next number in the following sequence? 4,16;  5, 25;  6, 36;  7, 49;  8, ____. 

What is 26x8, how many legs (total) do 4 dogs, 2 elephants, 15 cats, and 26 people have, john works 4 days per week. he drives 10 miles round trip per day. if gas is $2.50 per gallon and his car gets 20 miles to the gallon, how much would he have spent on gasoline in 2 weeks getting back and forth to work, what is the next letter in the following sequencej, f, m, a, m, j, ______, what is 204x51, 100 divided by 0= _________. , jack goes fishing on saturday and catches 32 fish. on sunday, he catches 1/4 the amount of fish he catches on saturday. on monday, he catches 1/2 the fish he caught on saturday and sunday combined. how many fish did he catch on monday, ned has a fruit stand. normally he sells apples for 40 cents a piece, but today he has apples on sale for 5 for $ 1. there are no limits on quantity. how much money would you have saved if you had bought 16 apples at the sale price.

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Logic puzzles for kids: a strategy for improving problem solving skills in 2024.

In order for elementary students to improve their problem solving skills, they need to grow in their logical thinking, critical thinking, and reasoning skills. How do you promote these skills in your classroom? One of the best ways to address these skills during math is through the implementation of logic puzzles for kids, also known as missing number puzzles or number logic puzzles. They provide students with opportunities to fine-tune these important skills in fun and engaging ways and greatly improve problem solving skills for kids and logic for kids at the elementary level. 1st, 2nd, 3rd, 4th, and 5th grade students love solving logic puzzles designed for kids!

This blog post will answer the following questions:

  • What is logic?
  • Can you give an example of logic?
  • What is math logic?
  • What is it important to teach logic, critical thinking, and reasoning?
  • How can I teach my students logic in fun and engaging ways?

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What is Logic?

Logic is a tool that helps people make sense of information by analyzing relationships and structures to make conclusions in a systematic way. Logical thinking, critical thinking, and reasoning are integral foundational skills in math. As a result, it is very important to begin teaching these skills at the elementary level. A fun way to do this is through logic puzzles for kids and math puzzles for kids!

What is an Example of Logic?

A real life example of someone not using logic is if someone sees a drum set they like at the store. It’s not on sale so they don’t buy it. The person finds the same drum set at another store and it is 50% off; however, the actual cost of the drum set is cheaper at the first store. They buy the one that is on sale without analyzing the actual cost of the drum set. This example clearly demonstrated why logic is so important!

What is Math Logic?

Math logic is applying the principles of logic to mathematical situations. In simpler terms, it is critically analyzing and thinking through problems that involve math to make sense of the problem. A fun way for your elementary students to practice math logic is through math logic puzzles for kids!

practice math logic problems

What is the Importance of Teaching and Practicing Logic, Critical Thinking, and Reasoning?

Practicing logic, critical thinking , and reasoning is essential for students for many reasons. Practicing these skills stimulates and trains their brains to naturally work towards making sense of the world around them and prepares them for being logical and critical thinkers and decision makers. It also helps them develop a growth mindset around math.

practice math logic problems

5 Reasons to Teach Logic in Math

Here are 5 reasons why it’s important to teach elementary students logic in math:

  • Prepares students for more complex mathematics (e.g. proofs in geometry).
  • Develops students’ critical thinking and reasoning skills.
  • Provides an opportunity for cooperative learning.
  • Equips students with a strong mathematical foundation.
  • Fine tunes students’ problem solving skills and stimulates their brain.

practice math logic problems

5 Reasons to Teach Critical Thinking in Math

Here are 5 reasons why it’s important to teach elementary students critical thinking in math:

  • Develops students’ ability to connect ideas.
  • Enhances students’ ability to clearly articulate arguments and thinking.
  • Leads to future academic and professional success.
  • Contributes to students’ ability to problem solve and make effective decisions.
  • Promotes creativity among students working in a group.

practice math logic problems

5 Reasons to Teach Reasoning in Math

Here are 5 reasons why it’s important to teach elementary students reasoning in math:

  • Increases students’ ability to articulate why their answer makes sense.
  • Develops students’ understanding that math makes sense and is made up of patterns, properties, and formulas.
  • Leads students with the skills needed for future academic and professional success.
  • Enhances students’ ability to problem solve and make quality decisions.

practice math logic problems

3 Fun Ways to Teach Logic

Below are 3 fun ways to teach elementary students logic skills.

1. Logic Puzzles

Logic puzzles for kids are a great way for students to build logic skills. These fun and engaging math logic puzzles invite students to think critically about numbers, learn through trial and error, and use logic to systematically solve a problem. They are great because students love critical thinking puzzles and they even help them practice having a growth mindset in math.

2. Number Talks

Number talks are another great way to teach logic skills. Hosting number talks at the beginning of a math lesson is a great way to model and discuss how to approach problems and situations in a logical and methodical way. Remember to ask students follow up questions to their responses: Why do you think that? How do you know? Part of mastering logical thinking is being able to justify their answers and explain it to others in a clear and concise way.

3. Board Games

There are tons of fun and easy board games out there that provide opportunities for students to practice logical thinking. Some of my favorites are Mastermind, Blokus, Monopoly, Qwirkle, Battleship, and Connect Four. Board games also provide a great way for kids to develop problem solving skills when working with partners or small groups.

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If you need printable and digital math resources for your classroom, then check out my time and money-saving math collections below!

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We would love for you to try these logic puzzle resources with your students. Your students will have so much fun with these find the missing number puzzle activities and you will love that they come with an answer key. This resource offers them opportunities to practice logic, critical thinking, and reasoning skills, as well as math fact fluency practice . You can download logic puzzle worksheets specific to your grade level (along with lots of other math freebies) in our free printable math resources bundle using this link: free printable math activities for elementary teachers .

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Puzzles are beneficial for children. They exercise both sides of the brain, improve memory, and raise IQ scores. Solving puzzles requires concentration, improves short-term memory, problem solving, and at the same time is relaxing. If done regularly, puzzles can improve cognition and visual-spatial reasoning.

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  1. Math Logic Problems

    Welcome to our Math Logic Problems worksheets. All the problems on this page require children to use their reasoning and logic thinking skills to solve. There are a range of worksheets on this page with varying levels of difficulty from 1st grade up to 5th grade. Math Logic Problems

  2. Practice Logic

    Practice Logic Courses Take a guided, problem-solving based approach to learning Logic. These compilations provide unique perspectives and applications you won't find anywhere else. Logic What's inside Introduction Puzzles and Riddles Multi-Level Thinking The Rational Detective Logic II What's inside Introduction Syllogisms and Sets Logic Machines

  3. Practice Exercises for Mathematical Logic

    Solutions Featured Sites: EducationWorld Math Award Certificates Free math worksheets, charts and calculators Practice Exercises for Mathematical Logic. Check your answers with with the solution box.

  4. Aplusclick Math and Logic Problems for Grade 1 to 12

    Math and Logic Problems. A+Click helps students become problem solvers without any ads and without signing-up. More than 16,000 challenging questions with answers for students in grades 1 through 12, starting from the very simple to the extremely difficult. The problems concentrate on understanding, usefulness, and problem solving.

  5. Quiz & Worksheet

    question 1 of 3 Which of the following is a logic proposition? A: Sam only eats square foods B: Once upon a time C: Circles roll A B C A and B A and C Next Worksheet Print Worksheet 1. If the...

  6. Math and Logic Puzzles

    Symmetry Jigsaw Puzzles Logic Puzzles Sam Loyd Puzzles Shape Puzzles Einstein Puzzles Number Puzzles Tricky Puzzles Algebra Puzzles Card Puzzles Assorted Math Puzzles and Quizzes

  7. Getting started with Logical Reasoning (article)

    Course: LSAT > Unit 1 Lesson 6: Logical Reasoning - Articles Getting started with Logical Reasoning Introduction to arguments Catalog of question types Types of conclusions Types of evidence Types of flaws Identify the conclusion | Quick guide Identify the conclusion | Learn more Identify the conclusion | Examples

  8. Free Math Worksheets

    Khan Academy's 100,000+ free practice questions give instant feedback, don't need to be graded, and don't require a printer. Math Worksheets. Khan Academy. Math worksheets take forever to hunt down across the internet. Khan Academy is your one-stop-shop for practice from arithmetic to calculus. Math worksheets can vary in quality from ...

  9. Practice Logic

    The beginning of our introductory math journey is Logic. Through these challenging problem solving exercises, you'll construct the critical thinking skills that are the basis for mathematical reasoning. You'll use limited information to make predictions - eliminating the impossible to uncover the truth. This course builds up to some truly ...

  10. Practice Propositional Logic

    Truth Tables. Solving Propositional Logic Word Problem. Proof by Contradiction. Mathematical Logic and Computability. Mathematical Logic and Computability II (continuation) Propositional Logic Using Algebra.

  11. PDF MATHEMATICAL LOGIC EXERCISES

    Mathematics is the only instructional material that can be presented in an entirely undogmatic way. The Mathematical Intelligencer, v. 5, no. 2, 1983 MAX DEHN Chapter 1 Introduction The purpose of this booklet is to give you a number of exercises on proposi-tional, first order and modal logics to complement the topics and exercises

  12. Truth Tables Practice Problems With Answers

    There are eight (8) problems for you to work through in this section that will give you enough practice in constructing truth tables. Problem 1: Write the truth table for. Answer. Problem 2: Write the truth table for. Answer. Problem 3: Write the truth table for. Answer.

  13. 3.E: Symbolic Logic and Proofs (Exercises)

    14. We can also simplify statements in predicate logic using our rules for passing negations over quantifiers, and then applying propositional logical equivalence to the "inside" propositional part. Simplify the statements below (so negation appears only directly next to predicates). ¬ ∃ x ∀ y ( ¬ O ( x) ∨ E ( y)).

  14. Discrete Mathematics/Logic/Exercises

    1 Which of the following are propositions? (a) Buy Premium Bonds! (b) The Apple Macintosh is a 16 bit computer. (c) There is a largest even number. (d) Why are we here? (e) 8 + 7 = 13 (f) a + b = 13 2 p is "1024 bytes is known as 1MB" q is "A computer keyboard is an example of a data input device".

  15. 25 Logic Puzzles (with Answers) for Adults

    1. Logic Puzzle: There are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks are there? Answer: Three. Two ducks are in front of the last duck; the...

  16. Logic Problems

    Share Logic and problem-solving scenarios that aren't related to writing code. Why Logic Problems? A logic problem is a general term for a type of puzzle that is solved through deduction. Given a limited set of truths and a question, we step through the different scenarios until an answer is found.

  17. Wolfram Problem Generator: Unlimited AI-generated Practice Problems

    Wolfram Problem Generator: Unlimited AI-generated Practice Problems Upgrade to Pro Apps Tour Sign in Online practice problems with answers for students and teachers. Pick a topic and start practicing, or print a worksheet for study sessions or quizzes.

  18. Logic Problems

    Read the clues to solve the logic problems in this printable math worksheet. Children can use guess-and-check to find the answers, or they can use a systematic approach by eliminating numbers that do not meet the conditions given. ... Third Grade Math Made Easy provides practice at all the major topics for Grade 3 with emphasis on basic ...

  19. Test Your Mathematical Logic With Solutions

    C. 28. D. 32. Correct Answer. B. 25. Explanation. Since 1/3 of the marbles are yellow and 1/4 of the marbles are blue, the remaining fraction of marbles must be red. To find the number of red marbles, we need to subtract the number of yellow and blue marbles from the total number of marbles. 1/3 of 60 is 20, and 1/4 of 60 is 15.

  20. Logic Puzzles for Kids: A Strategy for Improving Problem Solving Skills

    These fun and engaging math logic puzzles invite students to think critically about numbers, learn through trial and error, and use logic to systematically solve a problem. They are great because students love critical thinking puzzles and they even help them practice having a growth mindset in math. 2. Number Talks

  21. Logic Puzzles and more

    Learning through play, crafted by child development experts. This Math Kangaroo Wooden Puzzle provides hours of entertainment. Includes a booklet listing challenges for little ones and for grown-ups. Tico Bricks are tiny building blocks. This set offers the challenge of using the 290+ pieces to build a pair of kangaroos: a mom and a child.

  22. Brilliant

    Learn math at your own pace. Personalized learning paths tailored to your level. Master concepts in minutes a day with bite-sized, interactive lessons in algebra, geometry, logic, probability, and more. Get started Math. Data Analysis. Computer Science. Programming. Science & Engineering. Join over 10 million people learning on Brilliant.

  23. Quia

    Math-Logic Problem Practice. Try these logic problems to practice! Tools. Copy this to my account; E-mail to a friend; Find other activities; Start over; Print; Help; This activity was created by a Quia Web subscriber. Learn more about Quia:

  24. Basic Math Programming Practice Problem Course Online

    Get hands-on experience with Basic Math programming practice problem course on CodeChef. Solve a wide range of Basic Math coding challenges and boost your confidence in programming. ... Basic Math includes problems on topics like arithmetic, sequences, and counting, which are fundamental to proper understanding of algorithmic logic. 4.7 (11 ...