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Problem Solving & Modeling/Data Analysis

What it means
How to help

What they're learning

We all know it’s important for kids to master division, fractions, and equations. But math is more than memorizing facts or even procedures. Math also teaches an essential skill: problem solving. Sixth graders are expected to be able to solve problems even when the path to solving the problem isn’t clear. Students should be comfortable asking and answering questions such as: What is this problem asking me to do? How do I know this is correct? Does this make sense? How else can I solve this?

Modeling and data analysis means taking a real-world problem and using math to solve it — by creating a graph, drawing a picture, using a number line, creating a table, or building a model. In sixth grade, students apply the concepts and procedures they’ve learned to solve real-world problems.

See how a sixth grader solves a word problem involving ratios.

Sample problems

Analyze and efficiently solve problems

Sixth graders are expected to figure out how to solve problems that don’t tell them which procedures or techniques to use. Students need to identify the important information in problems, figure out which steps to take, and choose what tools to use (for example, pictures, graph paper, or a ruler) to find the answer. Many problems, such as the sample problem below, can be solved using a variety of techniques. Your child should be able to read a problem and find the answer using a technique that works for him. He should also be able to make sense of other approaches and show multiple ways to solve a problem.

Sample problem 1: Analyzing a problem and looking for ways to efficiently solve it


Relationship between quantities

Students learn to show and make sense of how quantities change in relationship to one another using graphs and tables. For example, in the sample problem below students are asked to find the rate of two bikers using the data presented.

Sample problem 2: Making sense of quantities and their relationships


Sample problem 3: Modeling, or using mathematics to solve real-world problems


If your child didn’t meet the problem solving and modeling/data analysis standard...

  • Your child may have trouble making sense of a situation and determining what problem needs to be solved. (See sample problems 1 and 2.)
  • Your child may have trouble evaluating her answer to see if it’s reasonable.
  • Your child may need help figuring out or understanding new, different, or more efficient ways to solve problems. (See sample problem 2.)
  • Your child may have trouble understanding how to interpret or create a graph, chart, table, or equation that shows the relationship between two quantities. (See sample problem 3.)
  • Your child may have trouble sticking to it when he gets stuck.
How to help

Start with a great attitude

The math gene is a myth! There’s a common misconception that some people are born with a math brain and some aren’t. Not true. With support, practice, and encouragement, kids can — and will — learn math.

Sprinkle math into everyday activities

  • Is your child the artsy type? Talk to him about how ratios are important in art. Can he draw two pictures that are in a scale of 3 to 1? There’s a ratio! Two parts red paint to three parts blue paint: another ratio!
  • Help your child see how you use problem solving in everyday life. Let’s say you’re food shopping and see two brands of macaroni and cheese on sale. One brand is normally $1.99 and is 30 percent off. The other brand is normally $2.99 and is 20 percent off. Ask your child to figure out which is the better buy.
  • Choose a city that experiences true winter (maybe your hometown), and look up the temperatures on the five coldest days last winter. Create a number line with your child and put those five temperatures on the line and compare them.

Boost those skills

  • Have your child check out this fun video about reasoning with rates.
  • Encourage your child to mess around with equations using this visual calculator:
  • Get your child to practice dividing money amounts, algebraic expressions, fractions, and more with these 43 skill-builder games and activities at Be a Learning Hero.

Talk to the teacher

Teachers want to work with you to help your child. Ask for specific information about your child’s strengths and weaknesses. Ask for suggestions on math exercises you can do at home. Maybe there’s a card game or board game that helps with reasoning skills. Get some advice on how to talk to your child in a way that encourages her.