The post What Are Composite Numbers? appeared first on Magoosh Math.
]]>Composite numbers are whole numbers that have at least three factors. Prime numbers have two factors: one and itself. For example, the only factors for 2 is 1 and 2 (1 x 2). However, 4 has 3 factors: 1, 2, and 4 (1 x 4 and 2 x 2). When you want to determine whether a number is prime or composite, you must figure out how many factors that number has.
From 1 to 100, the following are composite numbers:
4, 6, 8, 9, 10
12, 14, 15, 16, 18, 20
21, 22, 24, 25, 26, 27, 28, 30
32, 33, 34, 35, 36, 38, 39, 40
42, 44, 45, 46, 48, 49, 50
51, 52, 54, 55, 56, 57, 58, 59, 60
62, 63, 64, 65, 66, 68, 69, 70
72, 74, 75, 76, 77, 78, 80
81, 82, 84, 85, 86, 87, 88, 90
91, 92, 94, 95, 96, 98, 99, 100
The best way to figure out if it’s a composite number is to perform the divisibility test. To do this, you should check to see if the number can be divided by these common factors: 2, 3, 5, 7, 11, and 13. If the number is even, then start with the number 2. If the number ends with a 0 or 5, try dividing by 5. If the number can’t be divided by any of these 6 numbers, then the number is most likely a prime number.
Test your skills with the divisibility test with the following 4 examples:
Since the number ends with a 3, we know that it isn’t an even number. Therefore, it’s not divisible by 2. Also, it doesn’t end with a 0 or 5, so it isn’t divisible by 5 either. So, we can move onto the next lowest number: 3.
243/3 = 81
Since the number has more than 2 factors, we know that it’s a composite number. The factors of 243 are 1, 3, 8, 27, 81, 243 (1 x 243, 3 x 81, 9 x 27).
As we perform the divisibility test with 283, we find that
283/2 = 141.5
283/3 = 94.33
283/5 = 56.6
283/7 = 40.43
283/11 = 25.72
283/13 = 21.76
Since none of the quotients are whole numbers, we can confidently say that 283 is a prime number.
We can weed out 2 and 5 as factors for 187. Then, we move onto the rest of the numbers. We end up with the following quotients:
187/3 = 62.33
187/7 = 26.71
Then, we get to 11 and find 187/11 = 17. The factors of 187 are 1, 11, 17, and 187, so it’s a composite number.
Once again, the number is odd and doesn’t end with 0 or 5. We can try to multiply it by 3, 7, 11, and 13, but we end up with a remainder or a decimal point. Since there are no other whole number factors, the only factors are 1 and 113, making it a prime number.
So, what are composite numbers? Composite numbers are whole numbers that have at least three factors. Performing the divisibility test will help you determine whether or not a number is a prime or composite number.
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]]>The post 6 Properties of Parallelograms to Help You Identify Them appeared first on Magoosh Math.
]]>Parallel lines are lines that are always the same distance apart and never touch. If the sides of a parallelogram were lines that continued on, the ones opposite of each other would never touch. These lines would remain the same distance away from each other no matter how far they extended. If your quadrilateral has opposite sides that are parallel, then you may have a parallelogram.
In geometry, congruent means that two things are identical. If you were to superimpose the shapes on top of each other they would match up exactly. This is true for a parallelogram’s sides. Each of the opposite sides are the same in length. If you were to break the shape apart and place the opposite sides on top of each other, you would find that they line up perfectly.
The angles that are opposite of each other are also congruent. To find out if your quadrilateral is a parallelogram, you could get out your protractor and measure each angle. The angles opposite of each other will have the same measurement. It’s common for a parallelogram to have two acute angles and two obtuse angles. Therefore, the acute angles should have the same measurement, and the obtuse angles should also have the same measurement.
To find another one of the properties of parallelograms, draw an imaginary line through the shape to cut it in half. Then, look at the consecutive angles (or the ones that are next to each other). If the shapes are supplementary, then the shape might be a parallelogram.
Supplementary angles are two angles that add up to 180-degrees. Let’s say that two of the consecutive angles have measurements of 35-degrees and 145-degrees. If we add these together (35 + 145), the sum is 180-degrees. Therefore, we have supplementary angles.
Now pretend to draw an imaginary line from one angle to its opposite, congruent angle. This line should create two congruent triangles within the shape.
From there, proceed to draw another imaginary line from the supplementary angle to its opposite, congruent angle. These two imaginary lines should bisect one another. (To bisect is to cut something into two equal parts.) If this is the case with the diagonal lines, then (along with the previous five properties) you have a parallelogram.
The last property only matters if there is a right angle in your quadrilateral. If you have one angle that is a right angle, then all the rest of the angles should be right angles, too. Why? Because we know that the opposite angles are congruent. We also know that consecutive angles are supplementary, and 90 + 90 = 180. Therefore, all four angles would have a measurement of 90-degrees.
Let’s recap. You’ll know that your quadrilateral is a parallelogram if it has these properties of parallelograms:
1. The opposite sides are parallel.
2. The opposite sides are congruent.
3. The opposite angles are congruent.
4. Consecutive angles are supplementary (add up to 180-degrees).
5. The diagonals bisect each other.
6. And all four angles measure 90-degrees IF one angle measures 90-degrees.
Look for these 6 properties of parallelograms as you identify which type of polygon you have.
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]]>The post 7 Examples of Everyday Math to Practice with Your Student appeared first on Magoosh Math.
]]>Pull out your favorite recipe and let your student help you make something delicious. Along the way, you’ll see how often you work with fractions, addition, subtraction, and more. You need to get the measurements just right to make sure that the finished product turns out edible. If you want to give your student extra practice, try doubling or halving the recipe, too. This gets especially tricky when dealing with the fractions of teaspoons and tablespoons.
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Whether you’re balancing a checkbook or putting together a budget, it’s important to know how to use math to help you. Have your child help you pay bills, allowing them to add up the amount you need to pay. You could also have them calculate the average amount paid each month, or how many hours they would need to work to pay the bill if they received X amount of dollars per hour.
Purchasing new furniture takes a lot of math. First, you need to measure the space. Then, you need to figure out what kind of furniture you need to get to fill the space. How big should it be? What size should the furniture be? As you pick out the new pieces, you need to measure the doorways and angles to make sure that the furniture can get into the room, too.
On top of decorating with new furniture, you can use math when calculating how much flooring to purchase or measuring the wall space for a new picture collage. Whatever you decide to do, let your child help you with the decorating process to get a taste for everyday math.
Learning to tell time is part of the math curriculum. However, you also need to learn about fractions in order to tell others what time it is. For example, it’s important to know that a quarter of an hour is 15 minutes or that a half an hour is 30 minutes. Then, you know what people are talking about when they say, “It’s a quarter to 4.”
You may also find an understanding of math helpful to calculate time. Whether you’re trying to beat your mile time or deciding how long to grill a steak, you should know that there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.
Next time you go shopping, think about how often you use math. You need to calculate prices, quantities, your budget, and more. You need to think about coupons and discounts, figuring out how much the shirt costs if it’s 30% off of the original ticketed price. As you walk through the store, discuss the math with your child. Let them help you calculate the prices and figure out how much the total will be before the sales associate rings you up.
When planning a trip, there are lots of details involved. First off, you need to think about your budget. Add together the cost of the hotel room, travel expenses, food, entertainment, and more. If you’re driving to your destination, have your student help you calculate the mileage and how much you should expect to pay in gas along the way. If you have a set budget, have your student help you work out the plan to stay within your budget and have money needed for extra expenses on the trip.
Whether you’re playing or watching a sport, you may find yourself doing math without even knowing it. For example, you might say, “we’re down by 5” or “we need two touchdowns to win.” If you enjoy baseball, you can use math to calculate the batting averages, too. As you watch or play sports with your student, identify ways that math is used by the players and officials throughout the game.
It may be surprising for students to find out that there are examples of everyday math all around us. Help your child identify the ways math is used from day to day, so they can understand the importance of mastering the important math concepts.
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]]>The post Where Can You Find 5th Grade Math Games? appeared first on Magoosh Math.
]]>Marble Math is an app that you can download to your phone or tablet. The game asks your student to move a marble through a maze while practicing math facts in the process. Not only will your child get math review, but he or she will also stretch critical thinking skills in the process.
The Hoodamath website offers games for multiplication, factoring, fractions, decimals, and more. The games have fun animation with great music and sounds. The website does have lots of ads, which you can remove by paying the yearly subscription fee of $20. If you don’t mind the ads, then you can play the games for free.
After creating a free account with Splash Math, parents can either download the app or allow students to play the games online. After logging into the site, choose your student’s grade and topic. Some of the things that are available for review include multiplication, division, fraction, geometry, addition, place value, and decimals. The games are simple, but they are aligned with common core math standards.
Some of the 5th grade math topics covered on ABCYa.com include decimals, fractions, math patterns, division, multiplication, number values, and equal ratios. These games are simple but have fun animation students will enjoy. A few of the games you can try are Fraction Fling, Dirt Bike Proportions, Puppy Chase, Math Facts Basketball, Monster Mansion Mash, and Prime Number Ninja.
If you’d rather find a board game to play, there are plenty available from which you can choose. For example, Prime Climb is a popular option that many 5th grade teachers use in the classroom for review, too. The game allows students to practice prime factorization, multiplication, and division while racing to make it to the end first. Other board games worth checking out include Super Genius Multiplication, Equate, and Lightning Fast Math.
If you like board games but don’t want to purchase one, you can print your own, too. The Futuristic Math site has several game boards that you can print at home. Then, find some dice and game pieces and you’re ready to go!
When your student is struggling in math, it’s important to find a fun and stress-free method to help them. These 5th grade math games can be just the thing to help your student review in a relaxed setting, while enjoying some good family time as well!
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]]>The post How to Find the Measure of an Angle appeared first on Magoosh Math.
]]>There are four types of angles. Knowing the difference helps you estimate the measurement of an angle. Here are the four types of angles and the measurements to help you classify each one.
The best way to measure an angle is to use a protractor. To do this, you’ll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle’s measurement to the nearest degree.
Triangles received their name from the three angles that they possess. These three angles should add up to 180-degrees. Oftentimes, you’ll have the measurements of two angles. However, you’ll have to figure out the measurement of the third angle. The equation to use is:
angle A + angle B + angle C = 180-degrees.
For example, say you have the following triangle. What is the measurement of angle C?
If you plug these numbers into the equation, you get the following equation:
Squares and rectangles have four right angles. If you add up the angles, you get 90 + 90 + 90 + 90 = 360. A quadrilateral also has four angles. Therefore, the shape’s angles add up to 360-degrees even if there are no right angles. To determine the missing angle of a quadrilateral, you can use the following equation:
angle A + angle B + angle C + angle D = 360-degrees.
Check out the following example. Can you figure out the missing angle in this quadrilateral?
To find the missing angle, plug the angle measurements into the equation:
Whether you’re working with a ray, triangle, or quadrilateral, there are methods you can use to discover the missing measurement of an angle. If you’re wondering how to find the measure of an angle on a ray, triangle, or quadrilateral, try using a protractor or the equations we’ve discussed. They should work, and help make your life a little easier!
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Your child’s teacher knows where your child excels and what your child may need to review. Don’t be afraid to contact the teacher. Let the teacher know that you want to help your child succeed and ask about what you should focus on as you work with your child. The teacher may have other ideas for improvement that you can implement at home.
For many students, math is a chore. Because of this, it might be difficult to get your child to practice math outside of class. However, there are lots of fun resources available on math websites and apps. For example, check out Sushi Monster to help your child review math facts in a fun and interesting way. Find a website or app that your child enjoys and sit with them as they use it to support their learning and growth.
While working with elementary school children, I’ve found that one of the hardest parts of word problems is deciding what you’re supposed to do with the numbers given. Should you add them together? Do you need to subtract them? To get around this, work with your child to identify keywords that will tell you what to do. For addition, some of the keywords include
And for subtraction, you may see phrases like “how many more…?” or “how much less…”. You can also look for some of the following keywords:
Help your child memorize these keywords and practice identifying them in word problems.
It’s important to master the basic math facts, such as addition and subtraction, before moving onto more complex problems. If your child needs help memorizing them, consider breaking out the flashcards. Run through the cards on a regular basis, focusing on the ones with which your child struggles. Flashcards can be a great way to practice when you’re waiting in line or need something to pass the time on a trip.
At some point in your schooling career, you probably asked your math teacher “when will I ever use this in the real world?” Sound familiar? Before your child starts asking that question, it would be helpful to show your child how math is applicable in life. When you’re at the grocery store, ask your child to compare prices.
Have your child count the money in your wallet. Have your child estimate heights or divide your pie for dessert. Of course, you could break out games like Monopoly and assign your child to be the banker, too.Look for ways to incorporate math concepts into real-world situations, so your child gets the needed practice while understanding why the concepts are important to learn.
When you think about how often you calculate prices, cut pizza into perfectly even portions, balance your checkbook, or determine how much of one thing to buy, you know that math is important. Help your child learn the 2nd grade math curriculum so your child can excel in math and use it in real-world scenarios, too!
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A prime number is one that only has two factors: one and itself. This means that the number can’t be divided evenly by any number but one.
Prime numbers are the building blocks of numbers. You can break down all numbers to prime numbers. There are an infinite number of prime numbers, but they are less frequent as numbers get larger. For these reasons, mathematicians have enjoyed studying and discovering other prime numbers.
So how do you find prime numbers? Let’s look at the numbers up to 100. As Eratosthenes discovered, there are a few multiples that you can look for to weed out the numbers that are not prime numbers. Start with a chart up to 100:
First, cross out the numbers that are multiples of 2 (hold off on 2):
Then, skip 5 but remove the rest of the multiples of 5:
Next, cross out the multiples of 3 starting with 6:
And finally, locate the multiples of 7 (not including 7). Go ahead and cross those out, too:
Now, look at the numbers that are left. These are the prime numbers to 100. Those numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
If you continue to test for prime numbers beyond 100, see if you can evenly divide the number into groups.
If a number isn’t a prime number, it’s probably going to be a composite number. Composite numbers are simply ones that have more than 2 factors. For example, the factors of 4 include 1 x 4 and 2 x 2. Since there are more factors than just one and itself, 4 would be considered a composite number (even if it has only 3 factors: 1, 2, and 4).
Years ago, mathematicians classified zero and one as prime numbers. However, now these numbers aren’t considered to be prime or composite numbers. To be a prime number, a number should have just 2 factors: 1 and itself. However, 1 = 1 x 1. Therefore, 1 only has 1 factor: itself. Therefore, it can’t be a prime or a composite number.
Zero acts in the same way: 0 = 0 x 0. Because it only has 1 factor, 0 is also difficult to classify as either a prime or composite number.
As you study numbers, start by classifying whether each number is a prime or composite number. If it’s a composite number, try to break it down to its prime number factors. Soon, you’ll become a pro with prime numbers. So, when someone asks “what are prime numbers?” you can teach them all about it!
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]]>The post Adding Fractions: Everything You Need to Know appeared first on Magoosh Math.
]]>Fractions are used to denote parts of a whole. If you have less than a whole pie, you can use fractions to show how much pie you really have. Some fractions include:
When Jerry is ready to add the fractions together, there are certain things he needs to know to be sure that he ends up with enough wood.
Adding fractions is pretty simple as long as you start with like denominators. The denominator is the bottom number, and the numerator is the number on top. Let’s say you have the following problem:
Since the denominators are the same (6), all you have to do is add the numerators together:
Maybe you bought two pies: a cherry pie and an apple pie. After a few of your guests have helped themselves to dessert, you find that one pie has 2 slices left out of the 6 slices you cut and the other has 3 slices out of 6 left. By adding them together, you know that you have 5 slices left that you can share with others.
After adding the fractions together, it’s important to give your answer in the simplest form. So, you need to make sure that the solution is reduced to the lowest terms. For example,
Before moving on to the next equation, you need to check your answer and make sure that it can’t be simplified any further. To do this,
For the above example, the GCF is 6.
It’s important to make sure that the fraction cannot be reduced lower. This is especially true if you don’t find the GCF, so you should continue to divide the top and bottom by the same number until you reduce the fraction as much as possible.
A mixed number is one that contains a fraction as well as a whole number, such as:
Adding these numbers can be difficult. To simplify the process, first convert the number to an improper fraction. An improper fraction has a numerator that is larger than the denominator. Because of this, it’s important to simplify the fraction after finding the solution since you’ll probably end up with another mixed number. Check out this equation:
In this equation, you know that 1 = 4/4. Therefore, 2 = 8/4. Add the fraction to the converted whole number:
After finding the solution, it’s time to simplify the fraction. In this case, the final solution is simply the whole number 3.
Knowing the basic principles of adding fractions is important, but oftentimes equations have fractions with different denominators. When this happens, what should you do? Before adding fractions together, you need to have like denominators.
One of the easiest ways to find common denominators is by multiplying the first denominator by the second denominator and vice versa. When doing this, it’s important to multiply the numerator and denominator by the same number so the value doesn’t change. If you’re unsure what this means, take a look at this example:
Say we start with the following equation:
Since the fractions have different denominators, the first thing that we need to do is convert the fractions to get common denominators. To do this, look at the denominators and multiply each by the other denominator. And, multiply the numerator by the same number as its denominator to keep the value the same:
Once the fractions have the same denominator, add the numerators together:
The final solution is an improper fraction, so you need to convert it to a mixed number and simplify the solution:
By dividing the numerator and denominator by 2, you can simplify the solution to:
Take a look at the following 5 practice examples. If you need to convert the denominators, make sure that you complete this step first. Then, solve and simplify!
Since the fractions don’t have like denominators, the first thing to do is convert the fractions. The simplest way to do this would be to multiply the fractions by the opposite denominator. Remember to multiply the numerator and denominator by the same number. You may also notice that both numbers are factors of 30, so you could multiply them by the appropriate factor to get a denominator of 30 (6 x 5 and 10 x 3).
After the fractions have like denominators, add the numerators together. Since the sum is an improper fraction, change it to a mixed number before simplifying the fraction.
In this practice problem, you need to change the fractions to have like denominators. Of course, you could multiply the denominators by each other. However, since 3 is a factor of 12, you can multiply just one of the fractions to get like denominators before solving the equation and simplifying.
Since the sum is an improper fraction, you need to reduce the equation to a mixed number and simplify the final fraction.
For practice problem 3, the equation has a mixed number, so start by making an improper fraction. Since 1 = 4/4, we can surmise that 2 = 8/4. Add this number to the numerator (3). Then, it’s time to ensure that there are like denominators for the equation. Similar to the previous example, 4 is a factor of 12. Therefore, you can multiply the first fraction’s numerator and denominator by 3 to convert the fraction.
The sum is an improper fraction. Thirty-eight can be divided by 12 three times, (12 × 3 = 36). This gives you a remainder of 2. Then, check to see if this is the simplest form.
Once again, you can start solving the equation by converting the fractions into like denominators. Multiply each fraction by the other fraction’s denominator to get a new denominator of 56.
After converting the fraction, add the numerators together and see if you can simplify the fraction.
The solution is an improper fraction. Therefore, first make the number into a mixed number. Then, simplify the solution. The factors of 56 include 1, 2, 4, 7, 8, 14, 28, and 56. The factors of 25 include 1, 5, and 25. Since they don’t have common factors, the final solution is:
For the final practice problem, start by converting the mixed number into an improper fraction. For this equation, 1 = 8/8 so 3 = 24/8.
Next, make sure that the fractions have like denominators. You can multiply each fraction by the other fraction’s denominator. Then, add the products together.
With the solution as an improper fraction, simplify it into a mixed number:
Then, simplify! The factors of 51 include 1, 3, 17, 51. And, the factors of 72 include 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Both numbers can be divided by 3. Divide the numerator and denominator by 3 giving you:
Since 17 is prime, the fraction is as simplified as it can be.
How did you do with the practice questions? What questions do you have about adding fractions? Tell us in the comments below.
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]]>Help your child understand the importance of learning math for the real-world. Your child may struggle with figuring out measurements on a worksheet, but cooking doesn’t feel like work and yields delicious results!
Have your child join you as you calculate prices at the grocery store. For instance, ask them how much 3 gallons of milk will cost if it costs $2 per gallon? Practice fractions with a pie or a quarter pound cheeseburger, or measure items around the house. Make the work hands-on so your child understands how to use math outside of the classroom.
You can find simple math games online to help your child master various concepts. Or, make your own. A simple one that you could play in the car involves choosing a number. Then, take turns saying multiplication pairs that equal the number you chose.
Think about ways to practice the math concepts your child is struggling with as you’re on the road, waiting in line, or hanging out at home. Make it fun, so your child can practice in a stress-free way.
Word problems often confuse young students. It can be difficult to determine what the problem is asking them to do. Help your child practice these at home. You can find grade-appropriate examples online. Then, have your child read the problem out loud. This is a great way to help your child slow down, and you can find out what your child is struggling to understand.
Work together to determine what the problem requires. In the process, you can model your thinking about it for your child. As your child gets more and more confident, make sure to help less and less. However, you could ask leading questions to help your child when he or she gets stuck.
One of the most important things about 3rd grade math is learning how to think. By the end of 3rd grade, the expectation is that your child will be able to think and reason out a problem to find the solution. To help your child learn to talk about math and explain solutions, it can be helpful to have your child take the reins as the teacher. Play school with your child as the teacher. Have your child explain a topic to you. You could even get a problem wrong, so your child can explain how to find the correct answer next time.
Whether you’re driving to grandma’s or spending time at home, you can also use a tablet or computer for math apps and websites. Find ones that offer practice with concepts that your child needs to review. There are lots of fun ones available that will engage your child and provide the practice needed to master the concepts.
If you’re unsure where to start as you work with your child, don’t hesitate to reach out to your child’s teacher. Find out how your child is doing and what resources may be available for you to help. Partnering with your child’s teacher is a great way to know more about your child’s level and what you can do to help your child get where he or she needs to be. Then, find methods that work with your child to practice and master the concepts in 3rd grade math.
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]]>The post 6 Tips for Using Math Flashcards with Your Child appeared first on Magoosh Math.
]]>You can sift through a large stack of cards every day, but it’s going to end up being a waste of time. Rather than spending time going over facts your student already knows, focus on ones that your student hasn’t already mastered.
One way to do this would be by creating two containers—one for the facts your child has mastered, and the other for ones that he or she is still working on. As your child masters each math fact, move it to the mastery box. Then, your child can observe his or her progress while focusing on the facts that need to be mastered.
Adding to the mastery box may be encouraging, but students tend to lose motivation as the math facts get harder and they know fewer facts. As this happens, you can find ways to motivate your child to continue working hard.
For example, create a bingo card with answers. Then, hold up the math fact. Have your child state the answer before finding the corresponding number on the card. Of course, providing a prize or treat when your child gets a bingo could be a fun motivation, too!
When you’re running short on time, there are great apps to use for math flashcards. Or, you could purchase pre-made ones at the store or online. However, children can get a lot out of creating their own flashcards. For one thing, it helps them create neural pathways, making it easier to retrieve the information later when they’re running through the flashcards with you.
Maybe your child likes to run through the flashcards on their own. Maybe your child is shy or timid. However, speaking out loud can help your child memorize the math facts. This way your child is seeing the fact, saying the fact, and hearing it. Together, this will help your child make connections to remember these facts each time.
If flashcards aren’t working or your child needs a break, there are other ways to practice math facts. Try these ideas:
Remember that flashcards are just one of the ways to review. It may not work for every student, so try using other methods, too. Maybe your child will excel with worksheets or practice quizzes instead. Find out what works with your child to help them memorize the math facts quickly.
Math can be fun! As you use math flashcards with your student, make the process fun, and your child will learn and memorize the math facts in the process. Tell us about your experience and what worked for you in the comments below!
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