Children's Math: Grades 3-8

Most parents are interested in fully understanding the mathematics topics being taught to to their children. Read on for a review of common types of math taught at each grade level with some examples and explanations for each age.

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Parents often want to help their children excel in math at school. The first step to assisting a child is to understand the skills and work that is being presented to them. By knowing what is expected of your child in each grade, you can work with them over breaks if it takes them longer to understand math concepts. Additionally, it will allow you to monitor their advancement in math.

Since it is hard for a struggling child to describe to parents the math concepts they are supposed to learn but cannot understand, and teachers can be hard to get a hold of due to busy schedules, parents have to look elsewhere to understand what's expected. Each state has different mathematical standards for various grade levels, but the various mathematical coursework and basics remain roughly the same.

The following paragraphs describe what children usually learn in the third through the eighth grade, and offers sample math problems that may be assigned to your student in homework, a quiz, or a test. This is based on California's mathematical standards. If you have specific questions about another state's math standards, your school's secretary may know how to access such information. For quick reference, paragraphs are arranged by grade level and are labeled accordingly.

Third Grade Math

The third grade is full of new mathematical concepts. Some of these math basics are likely to include:

  • Time
  • Multiplication and division
  • Decimals, fractions, and measurements
  • Adding and subtracting whole numbers
  • Adding and subtracting money
  • Basic understanding of graphs

There are numerous ways to create mathematical problems that reflect a child's understand of each concept. One way is the use of timed addition, subtraction, multiplication, and division tests. Other homework problems may include word problems and simple computations. The following are examples of third grade word problems and computations that incorporate one or several of the math concepts mentioned above:

  • Mary played with 35 blocks. Bob played with 90 blocks. Harry played with 68 blocks. How many blocks were played with in all?
  • Jill bought 8 pencils. She put 1 pencil in each folder. How many folders did Jill need?
  • 201 - 83 = ?
  • $1.50 + $5.00 = ?

Fourth Grade Math

Much of fourth grade math looks like a review of third grade math. However, as a child progresses through the fourth grade, teachers will make their work more complicated. The following are some math fundamentals a parent should expect to see in their child's math homework:

  • Place value and time
  • Adding and subtracting whole numbers
  • Adding and subtracting money
  • Adding and subtracting decimals
  • Negative numbers
  • Factoring of small numbers
  • Perimeter and area,
  • X and Y graphs
  • Introductory geometry
  • More fractions and decimals

Teachers and parents can test a fourth grader's comprehension of these math skills. Timed addition, subtraction, multiplication, and division tests are common, as are various word and straight computation assignments. By the fourth grade, many of these homework problems mix various concepts. Putting several math skills into one problem lets a parent or teacher see if a child truly understands each concept, because the individual answers depend upon each other for the correct final result. These more complex problems also test student's analytical problem solving skills. Math problems presented to fourth grade youth are similar to the following problems:

  • A bus left the station and picked up 6 people. At its next stop, 2 people got off of the bus, then 5 more people got onto the bus. At the third stop, 5 people got off and 3 got on the bus. How many people now are on the bus?
  • Linda picked flowers from her garden. She gave 6 flowers to her mom, 3 flowers to Susan, and has 8 flowers left. How many flowers did Linda pick?
  • 63 / ? = 7
  • 0.50 = 3/?

Fifth Grade Math

By the fifth grade students have usually mastered both addition and subtraction, so the focus is on multiplication and division. Teachers introduce new multiplication and division problems and other concepts in various ways. Here are some of the specific mathematical skills that a fifth grade kid is likely to learn or be introduced to during the year:

  • Percents
  • Volume and areas
  • Adding and subtracting decimals
  • Multiplying and subtracting decimals
  • Continuation of long division
  • Continuation of geometry
  • Mixed numbers
  • Multiplication of fractions
  • Ratio
  • Probability

Math quizzes, tests, and homework combine these mathematical skills to challenge children to think. However, these increasingly difficult problems should not be overwhelming for your student. If your student is becoming frustrated with the work their teacher assigns, you can help them conquer their math by formulating additional problems for them to solve. Both word and regular computation problems should be designed to strengthen your child's analytical math skills. Examples of such problems are:

  • If you begin with this one-digit integer and then multiply it by 3, then add 8, divide it by 2, and finally subtract 6, you will get the first integer back. Find this integer.
  • 1.3 x 2.75 = ?
  • 6/8 x 1/4 = ?

Sixth Grade Math

Sixth grade often marks the beginning of middle school, which means more difficult classes and higher expectations. It is this grade level that students truly begin to form study skills and habits. Therefore, it is increasingly important for parents of sixth grade children to monitor their kids' math work. Sixth grade math blends many concepts including:

  • Multiplication and division of fractions
  • Least common multiples; greatest common divisors
  • Algebraic expressions and equations
  • Graphing of algebraic results
  • Geometric patterns
  • The use of angles, range, mean, median, mode, statistical analysis of sample populations
  • Use of probabilities to make predictions.

Sixth grade math teachers help their students understand these concepts through various word and computation problems. These problems are much like those from earlier grades but tend to be larger questions with more complicated operations or equations.

  • Jenny bought seven t-shirts, one for each brother. The shirts cost $9.95 each. The cashier charged an additional $5.23 in sales tax. Jenny left the store with $15.12. How much money did she arrive with?
  • Ralph had 5 math tests. He received the following scores on the tests: 80, 75, 86, 91, and 82. What is Ralph's mean math test score?
  • Give the range of these numbers: 45, 82, 13, 56, 73, 11, 27?

Seventh Grade Math

Mathematical concepts and skills continue to evolve through the seventh grade. This grade usually marks a beginning of pre-algebra and an introduction to more advanced math. Students are expected to have mastered addition, subtraction, multiplication, division, and concepts related to fractions and decimals. According to California standards, seventh grade youth will be presented with the following:

  • Scientific notation
  • Evaluation of algebraic expressions
  • Algebraic terminology
  • Graphing and interpreting linear and some nonlinear functions
  • Problem solving with simple linear equations and involving inequalities over rational numbers
  • Measurement conversions
  • The Pythagorean theorem.

As can be inferred from this list, pre-algebra can be difficult for students to grasp. This is why teachers implement tests and quizzes. Parents can help prepare their students for these exams by going through their homework assignments with them. If it seems that the child is having difficulties understanding a concept, more math questions pertaining to that skill should be given to the student. Math problems can be simple or come in more complex forms, like word problems. The following are examples of appropriate supplemental problems for the average seventh grader.

  • Three ducks and two ducklings together weigh 32 kg. Four ducks and three ducklings together weigh 44 kg. All of the ducks weigh the same and all of the ducklings weigh the same. What do two ducks and one duckling weigh?
  • In 1969 10 pounds of flour cost $0.75. In 1970 the price increased 15%. In 1971 the 1970 price decreased by 5%. What did 10 pounds of flour cost in 1971?
  • In a right triangle, given that the hypotenuse is 5, one of the other sides is given as 3, then how long is the remaining side?
  • ((5-3) x 2)2 = ?

Eighth Grade Math

By the eighth grade, many school districts format their math classes by subject instead of by grade level. The majority of eighth grade students focus on a continuation of pre-algebra activities and skills, while many other eighth graders have advanced to Algebra I. While the work varies greatly from one eighth grade youth to another, the following are some math concepts that an eighth grader may be working with or expected to understand:

  • Solving equations through the use of inverse operations
  • Distributive property
  • Commutative property
  • Associative property
  • Surface area and volume of three-dimensional objects
  • Prime factorization
  • Equivalencies of fractions and percents and decimals
  • Polygon classification
  • Two-step equations
  • The slope of a line
  • Number Conversion

These algebraic skills are impacted into eighth grade youth through quizzes and homework problems that prepare them for their unit tests. The questions asked in these assignments look much like the following:

  • A piece of construction paper is .01 mm thick. It's cut in half, then one piece is placed atop the other. These pieces are cut in half, then all four of the pieces are put in a pile. These four are again cut in half and placed in a pile, and so on. After all of the pieces have been cut and then piled for the tenth time, what is the pile's height in cm?
  • Silver's Cleaners decided to raise their price for dry cleaning a sports coat a dollar - from $4.00 to $5.00. The same percent increase was applied to dry cleaning jackets. The old cost of dry cleaning each jacket was $10.00. What is the new dry cleaning cost for a jacket?
  • Mr. MacDonald recorded test scores for his eighth grade class which had 25 students. He used the scores recorded to calculate a class average of 72. Sandra's score of 86 was incorrectly marked to be 36. What should the correct average for the test have been?
  • What is the volume of a 9 x 9 x 9 cube?

Now that you know what could be expected of your student, you'll be able to proceed to help with their assignments so they can master these important mathematical skills. If you find that you are unable to clearly explain these concepts to your student, try reading through their math book alone or with your student. There are usually basic examples of each concept presented within a chapter. Still struggling with your child? Math tutoring may be an effective way to help your child advance through school and understand all of the fundamental math concepts they are failing to understand.

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