6th grade math help: ratios, negative numbers and expressions
Get tutoring help for your child →Sixth grade marks the start of middle school math for many students, and the content changes character. Ratios, rates and negative numbers appear, and letters start standing in for numbers. Students who were comfortable with arithmetic can feel lost when problems become more about relationships than calculation. Here is what the year usually covers and how to keep a child on track.
Main ideas in sixth grade
In most states, standards based on or close to the Common Core expect sixth graders to:
- Understand ratios and rates, using tables, tape diagrams and double number lines, and find unit rates such as cost per ounce or miles per hour.
- Divide fractions by fractions, and explain the result with a model or a story.
- Work with negative numbers, placing them on a number line, comparing them and understanding absolute value.
- Write and evaluate expressions with variables, such as 3x + 5, and solve one-step equations like x + 7 = 12.
- Find area, surface area and volume of shapes including triangles and prisms with fraction edges.
- Begin statistics, describing data with mean, median and range.
Where sixth graders commonly struggle
Ratios are a new way of thinking: a child may see 2 to 3 and 4 to 6 as different because the numbers changed. Dividing fractions is often taught as "flip and multiply," which works but leaves students unable to tell whether an answer makes sense. Negative numbers feel strange, so many students say −8 is greater than −3. In expressions, 3x might be read as 3 plus x, or a student may not see that the same letter stands for the same number throughout a problem.
Red flags in the first year of middle school
- Grades drop sharply compared with fifth grade.
- Your child can follow examples but freezes on a problem worded differently.
- Fractions and decimals from earlier grades still cause errors.
- Your child stops asking questions in class or avoids starting math homework.
Our study skills guide can help with the organization side of middle school.
What to ask a middle school math tutor
- How will you check for gaps from fifth grade fractions and decimals?
- How do you explain ratios so they feel natural?
- Will you work on reading word problems, not just computing?
- How do you help a student who has decided they dislike math?
Ways to make sixth grade math concrete
- Unit price hunts: at the store, work out which size of a product is the better deal.
- Recipes and ratios: if lemonade uses 2 cups of juice for every 5 cups of water, how much water for 6 cups of juice?
- Temperatures and elevations: talk about below-zero weather or places below sea level.
- Guess my rule: say a number, your child applies a secret expression, and you figure out the rule.
- Ask "does that make sense?" after every answer, especially with fraction division.
Proportions and percents grow out of this year's ratio work; see seventh grade math next.
Tell us your child’s grade, ZIP code and the subject that feels hardest. Wherever you live in the U.S., we’ll search for a tutoring provider near you. Families near Bay Ridge, Brooklyn can connect with Huntington Learning Center.
Start the questionnaireRelated guides
- 5th grade math help: decimals, fraction operations and volume
- 7th grade math help: proportions, percents and equations
- Study skills: helping a student who understands but still struggles
- All parent guides