The National Council of Teachers of Mathematics, the world's largest organization devoted to improving mathematics education, is developing a set of mathematics concepts, or standards, that are important for teaching and learning mathematics. There are two categories of standards:

**thinking math** standards and

**content math** standards. The thinking standards focus on the nature of mathematical reasoning, while the content standards are specific math topics. Each of the activities in this section touches one or more content areas and may touch all four thinking math areas.

The four thinking math standards are

*problem solving, communication, reasoning, and connections*. The content math standards are

*estimation, number sense, geometry and spatial sense, measurement, statistics and probability, fractions and decimals, and patterns and relationships*. We have described them and then provided general strategies for how you as a parent can create your own activities that build skills in each of these areas.

Thinking Mathematics

**Problem solving** is key in being able to do all other aspects of mathematics. Through problem solving, children learn that there are many different ways to solve a problem and that more than one answer is possible. It involves the ability to explore, think through an issue, and reason logically to solve routine as well as nonroutine problems. In addition to helping with mathematical thinking, this activity builds language and social skills such as working together.

**What parents can do:**
- Children are naturally curious about everyday problems. Invite your children to figure out solutions to everyday situations. You can do this by talking about the problem, asking your children for ways to solve it, and then asking how they came up with those solutions.
- Encourage your children to suggest problems and ask questions, too. Your children will learn how to figure things out and will learn that many problems can be solved several different ways.

**Communication** means talking with your children and listening to them. It means finding ways to express ideas with words, diagrams, pictures, and symbols. When children talk, either with you or with their friends, it helps them think about what they are doing and makes their own thoughts clearer. As a bonus, talking with children improves their vocabulary and helps develop literacy and early reading skills as well.

**What parents can do:**
- Talk with your children and listen to what they have to say.
- Reading children's books that rhyme, repeat, or have numbers in them (available at your local library) is a great way to communicate using mathematics.
- All communication doesn't have to be in words. You can represent math in ways other than talking. Your children can make diagrams or draw pictures to solve problems or represent numbers. They can use concrete objects like pieces of paper or even fingers to represent numbers.

**Reasoning** is used to think through a question and come up with a useful answer. It is a major part of problem solving.

**What parents can do:**
- To promote reasoning, ask your children questions and give them time to think about the answer. By simply asking questions and listening to answers, you are helping your children learn to reason.
- Ask your children to figure out why something is the way it is and then check out their ideas. Let them think for themselves, rather than try to figure out what answer you want to hear.

**Connections:** Mathematics is not isolated skills and procedures. Mathematics is everywhere and most of what we see is a combination of different concepts. A lot of mathematics relates to other subjects like science, art, and music. Most importantly, math relates to things we do in the real world every day. Connections make mathematics easier for children to understand because they allow children to apply common rules to many different things.

**What parents can do:**
- Ask children to think about and solve problems that arise in your everyday activities. For example, ask children to help you put the groceries away. They will practice sorting-the cereal boxes and the soup cans-and experiment with relative size and shape and how the big boxes take up more room than the smaller ones.
- Look for mathematics in your everyday life and don't worry about what the particular aspect of mathematics might be. Something as simple as pouring water into different sized cups and thinking about which cup will hold more is a low-key activity that actually involves estimation, measurement, and spatial sense.

**Math Activities for Ages Two to Five:**