Introduction As our children go about their daily lives exploring and discovering things around them, they are exposed to the world of mathematics. And since mathematics has become increasingly important in this technological age, it is even more important for our children to learn math at home, as well as in school. Children whose families read to them, help them with homework, talk to their teachers, and participate in their learning in other ways have a tremendous advantage in school.  We know that one of the most powerful forces we have to strengthen student achievement is a family's fundamental desire to prepare their children to succeed in the world. Many families know that the first step toward success for their children when they enter school is to master basic skills, such as reading and math. Helping Your Child Learn Math provides proven ideas and activities for families to help their children succeed in math. Today, math includes much more than arithmetic. Even in elementary school, children should be learning beginning concepts in algebra, geometry, measurement, and statistics. In addition, they should be learning how to solve problems by applying a knowledge of math to new situations, to understand math concepts, to reason mathematically, and to communicate mathematical ideas by talking and writing about math. Demand for skills in mathematics, science, and technology are continually increasing. To be successful in college and the workplace, students should take at least three years of rigorous high school math, aiming for calculus and even Advanced Placement mathematics.  By the end of the eighth grade, students should have mastered the fundamentals of algebra and geometry to be ready for high school and on track for college and the workforce. Perhaps one of the most important ways that families can reinforce mathematics achievement is simply by having a positive attitude that children can master challenging math.  Too often, we undermine our children's interest in math by using statements such as "math is hard" or "I didn't like math either." Research shows that when we believe all children can learn challenging materials and we set high expectations, children rise to the occasion. This resource includes activities for families with elementary school-aged children. These activities use materials found inside your home and also make learning experiences out of everyday routines, such as grocery shopping and cooking. The activities are designed for you to have fun with your child while reinforcing mathematical skills.  This is part of a series aimed at helping families participate in their children's learning. Hopefully  you and your children will enjoy the activities suggested here and will develop many more of your own. Thank you for being an involved family. Your commitment will encourage your children to reach their full potential.   How Do I Use This Resource? This material is for parents of children in kindergarten through fifth grade.  It  is divided into introductory material that explains the basic principles behind the current approaches to math, sections on activities you can do with your children, and lists of other resources.  It includes a variety of activities that will help children learn and apply mathematical concepts such as geometry, algebra, measurement, statistics, and probability in a useful and fun way. All of the activities here relate math to everyday life and complement many of the math lessons that children are learning in school. These fun activities use materials that are easy to find. They can be done in the home, at the grocery store, while traveling, or just for the fun of it. The activities are arranged by levels of difficulty. Look for the suggested grade levels on each page that indicate the level of difficulty. The activities you choose and the level of difficulty depend on your child's ability. If your child seems ready, you might want to skip the easier exercises and go straight to the more challenging ones. Each activity includes a tip box with a simple explanation of the mathematical concept behind the activity, so that when your child asks, "Why are we doing this?" you can explain. Mathematics is everywhere, and every day is filled with opportunities to help children experience it.  Help your child explore math and have fun at the same time.  The activities in this section are intended to be enjoyable and inviting and use items that can be found in your home. While doing the activities, keep in mind that an understanding of math and a sense that math is enjoyable will help children develop skills that they will need for success their entire lives.

Attitude Counts

How do you feel about math? Your feelings will have an impact on how your children think about math and themselves as mathematicians. Take a few minutes to answer these questions:

      Do you think everyone can learn math?
      Do you think of math as useful in everyday life?
      Do you believe that most jobs today require math skills?

If you answer "yes" to most of these questions, then you are probably encouraging your child to think mathematically. Positive attitudes about math are important for your child's success. 

Mathematics as Problem Solving, Communication, and Reasoning

Helping your child learn to solve problems, to communicate mathematically, and to demonstrate reasoning abilities are fundamental to learning mathematics. These attributes will improve your child's understanding of and interest in math concepts and thinking. Before beginning the activities in this book, let's first look at what it means to:

      Be a Problem Solver,
      Communicate Mathematically, and
      Demonstrate Reasoning Ability.

A problem solver is someone who questions, investigates, and explores solutions to problems; demonstrates the ability to stick with a problem to find a solution; understands that there may be different ways to arrive at an answer; considers many different answers to a problem; and applies math to everyday situations and uses it successfully. You can encourage your child to be a good problem solver by involving him or her in family decision making using math.

To communicate mathematically means to use words, numbers, or mathematical symbols to explain situations; to talk about how you arrived at an answer; to listen to others' ways of thinking and perhaps alter their thinking; to use pictures to explain something; and to write about math, not just give an answer. You can help your child learn to communicate mathematically by asking your child to explain a math problem or answer. Ask your child to write about the process she or he used, or to draw a picture of how he or she arrived at an answer to a problem.

Reasoning ability means thinking logically, being able to see similarities and differences about things, making choices based on those differences, and thinking about relationships among things. You can encourage your child to explain his or her answers to easy math problems and to the more complicated ones. As you listen, you will hear your child sharing his or her reasoning.

Important Things To Know

1. Problems Can Be Solved in Different Ways While some problems in math may have only one solution, there may be many ways to get the right answer. Learning math is not only finding the correct answer, it's also a process of solving problems and applying what you have learned to new problems.

2. Wrong Answers Can Help! While accuracy is always important, a wrong answer could help you and your child discover what your child may not understand. The wrong answer tells you to look further, to ask questions, and to see what the wrong answer is saying about the child's understanding. It is highly likely that when you studied math, you were expected to complete lots of problems using one, memorized method and to do them quickly. Today, the focus is less on the quantity of memorized problems and memorized methods and more on understanding the concepts and applying thinking skills to arrive at an answer.

• Sometimes, a child may arrive at the wrong answer to a problem, because the child misunderstands the question being asked. For example, when children see the problem 4+____ = 9, they often respond with an answer of 13. That is because they think the problem is asking, "What is 4+9?" instead of "4 plus what missing number equals 9?"
  
• Ask your child to explain how a math problem was solved. The explanation might help you discover if your child needs help with the procedures; the number skills, such as addition, subtraction, multiplication, and division; or the concepts involved. In working with your child, you may learn something the teacher might find helpful. A short note or call will alert the teacher to possible ways of helping your child learn math more easily.
  
• Help your children be risk takers. Help them see the value of trying to do a problem even if it is difficult for them. Give your child time to explore the different approaches to solving a problem. Your child's way might differ from yours, but if the answer is correct and the strategy or way of solving it has worked, it may be a great alternative. By encouraging children to talk about what they are thinking, we help them to have stronger math skills and become independent thinkers.

  3. Doing Math in Your Head Is Important

  • Have you ever noticed that today very few people take their pencil and paper out to solve problems in the grocery store, restaurant, department store, or in the office? Instead, most people estimate in their heads, or use calculators or computers.
    
  • Using calculators and computers demands that people put in the correct information and that they know if the answers are reasonable. Usually people look at the answer to determine if it makes sense, applying the math in their heads (mental math) to the problem. This, then, is the reason mental math is so important to our children as they enter the 21st century. Using mental math can make children become stronger in everyday math skills.

  4. It's Okay to Use a Calculator

  • It's okay to use calculators and computers to solve math problems. In fact, students are taught to use calculators at young ages and are often required to use them to do homework and take tests. The Scholastic Assessment Test (SAT), for example, permits the use of calculators for its timed tests. Many schools teach computer courses that include how to do spread sheets, statistical display, and computer-assisted designs for mechanical drawing and graphics. Schools often sell calculators to families at a low cost or supply them for all students to use. Knowing how to use a calculator and computer is a benefit for all students.
    

  Help Your Child Achieve in Math

  Visit your child's school. Meet with your child's teacher to see if your child is actively involved in math. Find out how you can help your child to better understand math problems.
  Set high standards for your child in math. Make sure your child is mathematically challenged and encourage his or her interest and pursuit of math. By the end of the 10th grade, your child should be expected to have studied algebra and geometry.
  Help children see that math is very much a part of everyday life. From statistics in sports to the sale price of clothing, from the calories in food to the amount of gas needed to travel from one city to another, math is important to us every day. Help your child make these connections to math.
  Point out that many jobs require math. From the scientist to the doctor, from the plant manager to the newspaper salesman, from the computer programmer to the hardware store owner, many jobs require a strong foundation in math. Help your child see that math leads to many exciting career opportunities.
  Stimulate your child's interest in technology. Encourage your child to use calculators and computers to further learning.
  Play games that help children develop decision making and mental math skills. There are many games sold commercially, such as board games, that involve patterns and probability. Play games from your own family traditions such as counting games and games that keep score. Try schoolyard games such as jump rope, hopscotch, and jacks. Games require children to use strategies to make decisions, solve problems, and develop an understanding about numbers and how to use them (number sense) and computational skills.
  Positive attitudes about math will reinforce encouragement. Your feelings will have an impact on how your children think about math and themselves as mathematicians. Positive attitudes about math are important in encouraging your child to think mathematically.

  How Will Math Look in Your Child's Classroom?

  As a result of the recent effort in mathematics teaching to include understanding in the teaching of math, from basic through advanced levels, the picture of your child's math class may, indeed, look different from what you remember when you were in school. For instance:

   

  Children will be expected to know their math facts: Children will be learning their math facts with an understanding of how facts relate to each other.
  Children will be doing more than arithmetic: Children will be seeing that math is much more than arithmetic (knowing the facts and number operations); it involves estimation, geometry, probability, statistics, and more.
  Children will be striving to achieve high goals: Children will be achieving high standards of understanding, complexity, and accuracy set for them by their parents, teachers, schools, and states.
  Children will be actively involved in the study of mathematics: Children will be doing tasks that involve investigations. They will be talking and writing explanations for their thinking.
  Children will be working with one another: Children will be collaborating to make discoveries, draw conclusions, and discuss math.
  Children will be evaluated in a variety of ways: Teachers will use many different ways to determine if children know and understand math concepts. Some of these will include writing samples, projects, or written tests. Not all evaluation will be the same for every classroom or every child.
  Children will be using calculators to solve problems: They will be using calculators not as crutches but as tools to solve more complex problems with bigger numbers than they could do otherwise. Children with good knowledge of math facts, number sense, and reasoning about math will be able to use the calculator most effectively.
  Children will be using computers: They will be developing databases, spreadsheets and computer graphics, while solving problems.