Grade 6 Math Word Problems: Tips, Tricks, and Answers

Math word problems are about more than just doing calculations. They are also about applying your math knowledge to real-world situations. Math word problems are important for 6^th graders because they help them to:

• Learn how to use different math concepts and skills in various contexts
• Develop their logical thinking and reasoning abilities
• Enhance their communication and literacy skills
• Prepare them for standardized tests and future math courses

Math word problems also make math more exciting and relevant. They show us how math can solve everyday problems and challenges. They also expose us to different topics and scenarios we may not encounter in our regular math lessons.

Solving Grade 6 math word problems can be intimidating, especially involving multiple steps or operations. But don't worry. Some general strategies will help your students confidently approach any word problem. Here are some of them:

• Please encourage them to read the problem carefully and identify the given information, the unknowns, and the question.
• They should rewrite the problem in their own words or summarize it in a sentence.
• Let them choose a suitable method or strategy to solve the problem. Some standard methods are guessing and checking, making a table or chart, drawing a picture or diagram, using a formula or equation, working backward, or using logical reasoning.
• They must show their work and explain each step clearly. Use appropriate units, labels, symbols, and terms.
• Lastly, tell them to check their answer by plugging it back into the problem or using a different method. Ensure their answer makes sense and answers the question.

Some word problems may seem too complex or confusing at first glance. They may have too much information, too many steps, or too many operations. In such cases, breaking down the problem into smaller and simpler parts is helpful. Here are some tips on how to do that:

• Look for keywords or phrases that indicate what operation or concept is involved in each part of the problem. For example, words like "total," "sum," "add," or "plus" indicate addition.

  Words like "difference," "subtract," "take away," or "minus" indicate subtraction.

  Words like "product," "multiply," "times," or "of" indicate multiplication.

  Words like "quotient," "divide," "per," or "out of" indicate division.

  Words like "ratio," "fraction," "percent," or "part" indicate fractions or decimals.

  Words like "equal," "same as," or "is" indicate equations.

  Words like "more than,” “less than," "greater than," or "smaller than" indicate inequalities.

  Words like "average," "mean," or "median" indicate statistics.

  Words like "area," "perimeter," "volume," or "surface area" indicate geometry, etc.

• Use parentheses, brackets, or other symbols to group the parts of the problem that belong together. For example, if the problem says:
• John has 12 apples, and Mary has 8 apples. They want to share their apples equally among themselves and their two friends. How many apples will each person get?

  You can rewrite it as:

• (John has 12 apples) + (Mary has 8 apples) = (total number of apples) / (4 people) = (number of apples per person)

This way, you can see the structure of the problem more clearly and focus on one part at a time.

• Solve each part of the problem separately and write down the intermediate results. For example, using the previous problem:
• (John has 12 apples) + (Mary has 8 apples) = (total number of apples)
• 12 + 8 = 20
• (total number of apples) / (4 people) = (number of apples per person)
• 20 / 4 = 5

  This way, you can keep track of your work and avoid making mistakes.

• Combine the intermediate results to get the final answer. For example, using the previous problem:
• (number of apples per person) = 5

  This way, you can answer the question and check your answer.

There are many types of word problems that you may encounter in grade 6 math. Some of the most common ones found on Mathskills4kids.com are:

• Ratio and proportion problems: These problems involve finding the relationship between two quantities with the same unit or measure. For example, if 12 pencils cost $3, how much do 20 pencils cost?
• Percent problems: These problems involve finding the part, whole, or percent of a quantity. For example, if 30% of a class is boys, and there are 24 students, how many boys are there?
• Fraction problems: These problems involve adding, subtracting, multiplying, or dividing fractions. For example, how much pizza do you have left if you have 2/3 of a pizza and eat 1/4?
• Decimal problems: These problems involve adding, subtracting, multiplying, or dividing decimals. For example, if you buy a shirt for $12.50 and a pair of jeans for $24.75, how much change do you get from $50?
• Measurement problems: These problems involve converting between different units of measurement or finding the perimeter, area, or volume of shapes. For example, if a rectangle has a length of 15 cm and a width of 10 cm, what is its area in square meters?
• Algebra problems: These problems involve finding the value of an unknown variable or expression. For example, if x + 5 = 13, what is the value of x?

No matter what type of word problem your 6^th graders are faced with, they can use the following steps to solve it:

1. They should read the problem carefully and identify the given information and the question.
2. They must choose a variable to represent the unknown quantity and write an equation or expression that relates the given information and the question.
3. They can now solve the equation or expression and find the variable's value.
4. They can check their answer by plugging it back into the equation or expression to see if it makes sense.
5. They can now write their answer in complete sentences and include the appropriate units.

Sometimes, it can be helpful to use diagrams and models to visualize the problem and make it easier to solve. Some examples of diagrams and models for solving math word problems are:

• Tape diagrams: These are horizontal or vertical bars showing the relationship between two quantities. For example, you can use a tape diagram to show how much money each person gets when $60 is shared equally among 4 people.
• Number lines: These horizontal lines show numbers and their relative positions. For example, you can use a number line to show how to add or subtract fractions with different denominators.
• Tables: These are grids that show data in rows and columns. For example, you can use a table to show how to find equivalent ratios or fractions.
• Charts: These are graphical representations of data using bars, circles, lines, or other shapes. For example, you can use a chart to show how to find the percent of a quantity or compare different quantities.
• Drawings: These are sketches or illustrations that show shapes or objects. For example, you can use a drawing to show how to find a shape's perimeter, area, or volume.

Here are some sample Grade 6 math word problems with answers and explanations available at Mathskills4kids.com:

1. A cookie recipe calls for 2 cups of flour for every 3 cups of sugar. How much flour is needed for 9 cups of sugar?

   Answer: 6 cups of flour

   Explanation: This is a ratio problem. We can use a tape diagram to show the relationship between flour and sugar.

   Flour →|<---2 cups--->|<---2 cups--->|<---2 cups---> = 6

   Sugar→|<---3 cups--->|<---3 cups--->|<---3 cups---> = 9

   We can see that for every 3 cups of sugar, we need 2 cups of flour. So, for 9 cups of sugar, we need 6 cups of flour.

2. A shirt is on sale for 40% off its original price of $25. What is the sale price of the shirt?

   Answer: $15

   Explanation: This is a percent problem. We can use a formula to find the sale price of the shirt.

   Sale price = Original price - Discount

   Discount = Percent off x Original price

   We know the percent off is 40%, and the original price is $25. So, we can plug these values into the formula and solve for the sale price.

   Discount = 40% x $25

   Discount = 0.4 x $25

   Discount = $10

   Sale price = $25 - $10

   Sale price = $15

Here are some tips that can help students improve their problem-solving skills in grade 6 math:

• Please encourage them to practice regularly and try different types of word problems.
• They should review the concepts and skills they have learned and apply them to new situations.
• They can use different strategies and methods to solve word problems and compare their results.
• Let them ask for help from the teacher, parents, or peers if they get stuck or confused.
• They should learn from their mistakes and try to avoid them in the future.