How to Pass Fourth Grade Math

Last Updated: August 31, 2023 References

Fourth grade math builds upon concepts you learned in prior grade levels, like third grade, second grade, first grade, and kindergarten. Fourth grade math covers concepts like mixed arithmetic problems, areas and perimeters of shapes, multiplication and division with remainders, decimal addition and subtraction, place value, comparing fractions, writing decimals as fractions, and measuring angles. ^{[1]
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Research source} If you weren't doing well in third grade math or are struggling now in fourth grade math, now is the chance to improve. If you have great study skills and use opportunities to improve your grade, you can easily pass middle school math, high school math, and beyond! ^{[2]
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Section 1 of 4:

Fourth Grade Math Concepts (Common Core)

These math concepts are taught in public schools across the U.S. in fourth grade. ^{[3]
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Research source} Public schools in the U.S. follow the Common Core curriculum/guidelines for teaching various subjects, such as math and language arts.

1
Understand place value. Place value is how the position of a digit in a number affects how large or small it is. For example, in the number "12", 1 is in the tens place, so it has a value of 10. You multiply the number in the tens place by 10. The 2 is in the ones place, so you multiply 2 by 1. Any number multiplied by 1 equals itself, which is the Identity Property of Multiplication. All the numbers from 1-9 are 1-digit numbers. Numbers from 10-99 are 2-digit numbers, numbers from 100-999 are 3-digit numbers, etc.
- For example, if you're counting apples, the "ones" digit represents how many individual apples you have. The "tens" digit represents how many groups of 10 apples you have, the "hundreds" digit represents how many groups of 100 apples you have, and so on. ^{[4]
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- You may use place value blocks or tables to represent numbers. ^{[5]
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Know how to round large numbers. In fourth grade, you may learn how to round numbers to the nearest hundred or the nearest thousand. First, look at the digit to the right of the place value you're rounding to. If you're rounding to the nearest hundred , the right of the hundreds place is the tens place. If the digit to the right of the place value is less than 5 (4 or less), keep the digit the same. Any digits after that one are rounded down to 0. If the digit is 5 or more, increase the value by 1 of the place value you're rounding to.
- For example, 1235 is rounded to 1200 if you're rounding to the nearest hundred. The number to the right of the place value you're rounding to is the tens place. The tens place contains the number 3. 3 is less than 5 (4 or less), so it stays the same. All of the digits to the right of the place value you're rounding to (the hundreds place, 2 in this case) become 0, so the result is 1200.
- 1523 is rounded to 2000 if you're rounding to the nearest thousand. The number to the right of the place value you're rounding to is the hundreds place. The hundreds place contains the number 5. Numbers 5 or greater are rounded up, so since the hundreds place has a number 5 in it, you increase the place value you're rounding to by 1. You're rounding to the thousands place, which contains a 1. 1 + 2 is 2, and all the digits to the right of 1 become 0. So, 1523 rounded to the nearest thousand is 2000. ^{[6]
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3
Learn how to add and subtract large numbers. Adding and subtracting numbers with more than 2 digits is the same process- you just need to pay attention to the borrowing of numbers, and the carrying of ones. Add your numbers vertically to make it easier. Doing it horizontally will increase the chances of you making mistakes during your calculations. Write neatly and use graph paper to line your numbers up if you can. Many schools tell students to use graph paper to line up digits and to draw coordinate planes in third, fourth, and fifth grade, so buy some or get a graph paper notebook if you need it.
- Start from the very right digits. If the sum of those digits is greater than 9 (more than 1 digit), you'll need to carry a 1 to the next digits. ^{[7]
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Learn how to multiply 1 and 2-digit numbers . You may have mastered 1-digit multiplication and your times-tables in third grade and second grade, but in case you haven't mastered this, you can review 1-digit multiplication now. After you've mastered 1-digit multiplication, you can use those facts to do 2-digit multiplication.
- It is similar to adding numbers with multiple digits; you still have to carry a number if the numbers have a product that is more than one digit (more than 9). One difference is that you do this twice. ^{[8]
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Learn how to divide by 2 digit-numbers . This is very similar to dividing by 1-digit numbers. As long as you've memorized your 1-digit multiplication times tables, this will be simple. First, check the first digit of your dividend. Since 2-digit-numbers are larger than 1-digit numbers, your divisor will not fit into the first digit. Next, check the first and second digits of your number. Repeat these steps until you've used all of the digits of your dividend.
- For example, if you're dividing 520 ÷ 25, check to see if 25 fits into 5 (the first digit of your dividend). 25 is too large to fit into 5, so check the 1st and 2nd digits. Does 25 fit into 52? Yes, it fits! 25 multiplied by 2 is around 50, which is not too small nor too large to fit into 52. Write 2 on top of the 2nd digit, and subtract 52 by 50 to see what number you have remaining. 52-50 is 2. Next, bring the 3rd digit down next to the 2. The 3rd digit is 0. Does 25 fit into 20? No, so write 0 on top of the 0 from the number 520. Subtract 0 from 20. The answer is 20, so your answer is 20 with a remainder of 20. ^{[9]
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- You can check your answer by multiplying your divisor with your quotient (the answer to a division problem) and adding back the remainder if there is one. 25 x 50 is 500, and 500 + 20 (the remainder) is 520, so our answer is correct.
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Compare fractions with like and unlike denominators. For fractions with like denominators, the process of comparing them is easy. Since the denominators are the same, you just have to compare the numerators. For example, ${\frac {3}{5}}$ is larger than ${\frac {1}{5}}$ since 3 is greater than 1. For fractions with unlike denominators, you may have to convert both of them to fractions with the same denominator by multiplying by a fraction equivalent to 1.
- If you're a visual learner, you can use pie charts or number lines to compare fractions.
- For example, you can convert ${\frac {3}{5}}$ and ${\frac {2}{3}}$ to ${\frac {9}{15}}$ and ${\frac {10}{15}}$ by multiplying ${\frac {3}{5}}$ by ${\frac {3}{3}}$ and ${\frac {2}{3}}$ by ${\frac {5}{5}}$ to get a common denominator of 15. Then you will see that 10 is greater than 9, so ${\frac {2}{3}}$ is greater than ${\frac {3}{5}}$ .
- You can also compare fractions by seeing if one is greater than ${\frac {1}{2}}$ . ${\frac {3}{5}}$ is greater than ${\frac {1}{2}}$ , as ${\frac {1}{2}}$ of ${\frac {3}{5}}$ is ${\frac {1.5}{5}}$ . As 3 is greater than 1.5, ${\frac {3}{5}}$ is greater than ${\frac {1}{2}}$ ^{[10]
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7
Learn some basic geometry definitions. You will learn some new terms and definitions in geometry. This won't be proving how angles are congruent like in a middle/high school geometry course, although it will prepare you for one in the future. There are some useful terms you will need to know and jot down in your math notes, such as the meanings of a line, point, segment, ray, and angle.
- A line extends forever from both sides. You label a line like this: ${\textstyle {\overleftrightarrow {AB}}}$ . This reads as "Line AB". A segment is a part of a line, and it is not infinite. A line segment has two endpoints. You label a segment like this: ${\overline {AB}}$ . This reads as "Segment AB". A ray has one endpoint and continues on forever in the opposite direction. You label a ray like this: ${\textstyle {\overrightarrow {AB}}}$ .
- Parallel lines do not intersect or touch anywhere. Perpendicular lines form 90-degree angles at their intersections.
- An angle is formed by two rays connecting at the same endpoint. You label an angle like this: ∠ABC. There are 3 types of angles: acute (less than 90 degrees), right (equal to 90 degrees), and obtuse (greater than 90 degrees).
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Learn how to classify triangles and quadrilaterals. Triangles can be classified by side length and angle measure. Classifying triangles into a few different groups is necessary because it will be easier to solve for different sides and angles if you know what type of triangle they are. There are a few types of quadrilaterals (shapes with 4 sides); parallelograms, trapezoids, rectangles, and squares.
- If a triangle has 3 sides of the same length, then it is equilateral . If a triangle has 2 sides of the same length, then it is isosceles . If a triangle has all three sides with different lengths, then it is scalene . ^{[12]
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- If a triangle contains 3 acute angles, then it is an acute triangle. If a triangle contains 1 obtuse angle, then it is an obtuse triangle. Lastly, if a triangle contains 1 right angle, then it is a right triangle.
- A parallelogram has exactly two pairs of parallel sides. A trapezoid only needs to have exactly one pair of parallel sides. A rhombus needs to have four equal sides. A rectangle has 4 right angles (angles that measure 90 degrees). Lastly, a square needs to have 4 equal sides and 4 right angles.
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Section 2 of 4:

Fourth Grade Math Concepts (Advanced/Gifted)

If you're in a public elementary school in the United States, your school will follow the Common Core standards. However, if you're in a private, charter, or magnet school, the curriculum for math may be different and more challenging than public school fourth grade math standards. If you're in a public school honors/gifted math course, you could be taught harder math concepts too.

1
Recognize patterns. You may learn about how to recognize patterns in a number sequence. There may be a common factor that is multiplied to get the next numbers in the sequence, or it may alternate between 2 numbers being added, subtracted, multiplied, or divided by. The sequence could be arithmetic (a common factor being added or subtracted) or geometric (a common factor being multiplied or divided).
- For example, in the sequence $0,9,18...$ each number is added by 9 to get to the next number. So, the next 4 numbers in the sequence would be 18 + 9 (27), 27 + 9 (36), 36 + 9 (45), and 45 + 9 (54).
- In the sequence $100,90,80...$ each number is subtracted by 10 to get to the next number. So, the next 4 numbers would be 70, 60, 50, and 40.
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Solve equal groups problems. Equal groups problems ask how to divide a number into equal groups. The formula is "the number of groups x the number in each group = total". These are basically multiplication word problems- they either ask you to find the number of groups, the total amount, or how many values are in each divided group.
- For example, you may be asked to solve this problem: At Lincoln School, there are 4 classes of fifth graders with 30 students in each class. Altogether, how many students are in the 4 classes? 4 classes (the # of groups) x 30 students (# of students in each group) = 120 students (the total).
3
Learn how to divide by 2 digit-numbers . This is very similar to dividing by 1-digit numbers. As long as you've memorized your 1-digit multiplication times tables, this will be simple. First, check the first digit of your dividend. Since 2-digit-numbers are larger than 1-digit numbers, your divisor will not fit into the first digit. Next, check the first and second digits of your number. Repeat these steps until you've used all of the digits of your dividend.
- For example, if you're dividing 520 ÷ 25, check to see if 25 fits into 5 (the first digit of your dividend). 25 is too large to fit into 5, so check the 1st and 2nd digits. Does 25 fit into 52? Yes, it fits! 25 multiplied by 2 is around 50, which is not too small nor too large to fit into 52. Write 2 on top of the 2nd digit, and subtract 52 by 50 to see what number you have remaining. $52-50$ is $2$ . Next, bring the 3rd digit down next to the 2. The 3rd digit is 0. Does 25 fit into 20? No, so write 0 on top of the 0 from the number 520. Subtract 0 from 20. The answer is 20, so your answer is 20 with a remainder of 20. ^{[13]
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- You can check your answer by multiplying your divisor with your quotient (the answer to a division problem) and adding back the remainder if there is one. $25\times 50$ is 500, and $500+20$ (the remainder) is 520, so our answer is correct.
4
Add and subtract decimals. Adding and subtracting decimal numbers is very similar to adding and subtracting whole numbers. You still have to line up the digits correctly- the digits before and after the decimal have to be lined up. Then, you carry a one/borrow a one like you usually do when adding regular numbers.
- For example, $3.15+2.30=5.45$ . $5+0$ (the placeholder if there's no number there) is $5$ . Next, $1+3$ is $4$ . Lastly, $3+2$ is $5$ . The answer is $5.45$ .
5
Use properties of numbers. Properties of numbers can make it easier for you to do arithmetic and word problems. You may learn basic properties such as the Distributive Property of Multiplication and the Associative Property of Addition and Multiplication. The Distributive Property states that multiplying a sum of 2 or more numbers by another number is equivalent to each number being multiplied by another number. The Associative Property of Addition states that rearranging the parentheses/indices/brackets in an addition problem will not change the answer. The Associative Property of Multiplication states that rearranging the parentheses in a multiplication problem will not change the answer.
- An example of the distributive property is $3(1+2)$ . You can first add the 2 numbers in the parenthesis first (because of PEMDAS or BODMAS), which equals 3. You can then multiply 3 by 3 which equals 9. If you multiplied $3\times 1$ and $3\times 2$ , you would see that the answers are $3$ and $6$ . Then, you add the products together, which also equals 9. $9=9$ , so the distributive property is true.
- An example of the Associative Property is 2 + (3 + 2). 2 + 5 = 7. If you regrouped the numbers into (2 + 3) + 2, you will also get 7. This also works for multiplication; $2\times$ ( $3\times 2$ ) is equivalent to $2\times 3$ $\times 2$ , which both equal 12.
6
Multiply and divide fractions. Multiplying fractions is easy, as you just need to multiply the numerators and the denominators together! You don't need to change the fractions for you to multiply them (as with adding and subtracting fractions with unlike denominators). Dividing fractions is a bit trickier. You'll have to multiply the 1st fraction by the 2nd fraction's reciprocal (the numerator and the denominator switched).
- For example, ${\frac {1}{2}}\times {\frac {3}{4}}$ is ${\frac {3}{8}}$ , as $1\times 3$ is 3 (the numerator), and $2\times 4$ is 8 (the denominator).
- ${\frac {1}{2}}$ ÷ ${\frac {3}{4}}$ equals ${\frac {1}{2}}\times {\frac {4}{3}}$ , which equals ${\frac {4}{6}}$ . ${\frac {4}{6}}$ can also be written as ${\frac {2}{3}}$ .
7
Use exponents and square roots. Exponents are basically repeated multiplication. So, $2^{2}$ is 2 multiplied 2 times. $2\times 2$ is 4. $2^{3}$ is $2\times 2\times 2$ , and so on. Square roots divide a number 2 times. So, √9 is √3 x 3, as 3 is multiplied twice to get 9. √25 is 5, √36 is 6, and so on.
- This is also the reason why the units while solving the area of a shape are squared. You're multiplying the length and the width of a shape, which squares the units. $2cm\times 2cm=4cm^{2}$ , as you're multiplying the numbers and the units twice.
- If you're solving for the volume of a 3D shape, the units are cubed. For example, $2cm\times 2cm\times 2cm=4cm^{3}$ .
8
Recognize types of polygons and angles. This will be basic geometry that will help you with harder geometry courses in the future. Polygons are shapes formed by straight-line segments. They close, so all of the lines of a shape have to be connected for it to be called a polygon. Polygons are classified by their sides. Angles are formed by two rays (lines with one endpoint). There are many different types of angles. There are also different types of lines, including parallel and perpendicular lines.
- Triangles (3-sided), quadrilaterals (4-sided), pentagons (5-sided), hexagons (6-sided), heptagons (7-sided), octagons (8-sided), nonagons (9-sided), decagons (3-sided), and dodecagons (12-sided) are all examples of polygons.
- Angles are classified by their angle measure. Acute angles are angles less than 90 degrees. Right angles equal 90 degrees. Obtuse angles measure more than 90 degrees. Straight angles measure 180 degrees.
- Parallel lines never touch. Perpendicular lines intersect and form right angles (angles that have measures of exactly 90 degrees). Oblique lines are neither parallel nor perpendicular.
9
Draw line and bar graphs. These types of basic graphs show data. The data is usually given to you in tables. You may need to draw line graphs in math, such as when finding out the relationships between numbers. Line graphs may be drawn to find the total distance and velocity traveled (physics). Bar graphs show amounts of things, and they compare different things.
- No matter which graph you're drawing, you always have to label the x-axis and the y-axis. You should give it a name relating to the data. For example, "Number of Pets Each Student Has" or "Amount of Money Earned" would be nice titles.
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Section 3 of 4:

Acing Fourth Grade Math

1
Take notes. Even if your teacher doesn't require notes or if only your middle school and beyond require them, you should still take a couple of notes. Use flashcards to record definitions (like the definitions of parallel and perpendicular lines) and jot down 2-4 examples of how to solve math problems. Use a small spiral notebook to write down important definitions, formulas (e.g. the formula for the area of a rectangle), and example problems for you to practice solving by yourself or with the whole class.
- You can highlight or underline key terms with a highlighter or a pen to make notes less boring!
2

Practice, practice, practice! If you only do 5 problems, you're probably not getting enough practice. Do your math homework every single day , even if you don't want to do it. Do your math homework, whether it's 10 problems or 15; this way, you'll review what you've learned in class. If you have time, you can even do extra problems. Your teacher may provide early finishers with extra worksheets for practice, or you may have to do random problems in your math textbook. You could also search online for more practice problems relating to what you're learning about.
3
Organize your workspace. If your workspace is piled full of random papers, school supplies, and trash, you're never going to find what you need. Put all of your school supplies into another pencil case (or you could use your school ones instead), throw away all trash into a dustbin, and use a shelf or a cabinet to organize your school books. You could put all math-related things on one shelf, all language arts-related things on another shelf, and all science-related things on the last shelf.
- If you have more shelves, put items like miscellaneous folders or old assignments.
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Section 4 of 4:

Finding Help

1
Ask an older sibling or an older relative. Since your siblings are older than you, they've probably learned the same things as you; it's just that they've learned the material earlier than you. If your older sibling maintains nice grades, they are suitable for you to ask questions to. They may be in middle school, or they could be in high school or even college already. Talk to your sibling if you need help. Ask them after they've finished their homework or on the weekends. If your siblings do not know how to explain the content, a parent or another relative could help.
- You could ask your 14-year-old brother, "Sid, I'm having trouble with adding fractions. Could you help me?". You could ask your 12-year-old sister, "Amanda? Can you help me solve this multiplication problem?". You could also ask your uncle, "Uncle Roger, I don't understand what this question is asking. Can you help me?"
- Keep in mind that if you annoyed your sibling recently, they are less likely to help you, as they still have a grudge against you. Wait a couple of days to see if they feel better, then ask.
2
Raise your hand if you have a question. Most schools usually allow students to ask plenty of questions. If you have one, don't be shy to raise your hand up high for your teacher to see. Don't be scared that your question is "weird" or "stupid". It's likely that more shy students have a similar question to yours, so if you stand out from the shy crowd and raise your hand, the students and you will get a satisfying answer. Besides, not asking questions will leave you confused, so you won't know how to answer questions on homework and tests. This will lead to bad grades, and eventually, a bad report card.
- If you're really shy, send an email to the teacher, call the teacher, or host an online meeting with your teacher for help. Elementary schools don't have office hours (a free period, usually during breaks, lunch, and/or after school to ask questions), so you'll need to find a suitable time to talk.
- You can also ask after class for individualized help.
3
Search for answers online. The internet is full of information in the digital age these days, so you're guaranteed to find at least a few sites that pertain to your topic. Just searching for a few words will lead to millions of results popping up in the search engine. Math websites like Khan Academy and IXL teach math from Pre-K to high school, so you'll find many results.
- Many of the math websites will contain practice problems, so if you sign up for an account on those websites, you can practice a bunch of these problems.
4
Hire a tutor. Sometimes, you may fall behind on fourth grade math. You may struggle to understand earlier concepts taught, leading to a buildup of things that you don't understand. This is why your grades will drop if you are unable to get help or don't ask questions. Ask your guardians to hire a tutor for you. Tutors, unlike teachers, have plenty of time to answer your questions. Their job is to literally tutor kids, tweens, teens, or adults and review concepts they don't understand. The whole tutoring session will be for you (or a few other kids) to ask questions, instead of just a couple of minutes to ask like in class. Some tutors are in-person, while others are free or online.
- Don't feel ashamed that you need a tutor. Sometimes, tutors can really help you boost your grades. You may find that you don't even need a tutor anymore once you get to 5th grade or middle school.
- Sometimes, you need a tutor for middle school and beyond, and that's ok too! Just make sure you still try your best on all assignments. If you're earning bad grades, you don't want to add to that by slacking off!
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How to Pass Fourth Grade Math

Steps

Fourth Grade Math Concepts (Common Core)

Fourth Grade Math Concepts (Advanced/Gifted)

Acing Fourth Grade Math

Finding Help

Expert Q&A

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