## What’s happening in math?

The school year begins with a week of fun activities to build and support positive attitudes about math. The activities help students think about the following ideas and use them all through the year:

• I can work with others to solve a math challenge.
• I can use math in my everyday life.
• I can look for patterns and make connections to make sense of math problems.
• I can share my thinking with words and representations using the language of math.
• I can persevere to solve a challenging math problem.

### Number: Whole numbers – Place value

Next, students look at how to represent numbers in different ways.

All numbers are made of digits. In the number 368 there are three digits: 3, 6, and 8, in different places. Each place has a name. In the number 368, the 6 is in the tens place, so it is worth 6 groups of ten (60).

Hundreds place Tens place Ones place
3 6 8

As numbers get bigger the group of hundreds, tens, and ones places is repeated in a pattern. Each group is called a period.

Each period has a name, like thousands, millions, and billions. We don’t say the name of the ones period. This is why a number like 27,509,368 is said as “twenty-seven million five hundred nine thousand three hundred sixty-eight”.

 Millions Thousands Ones Hundreds place Tens place Ones place Hundreds place Tens place Ones place Hundreds place Tens place Ones place 2 7 5 0 9 3 6 8

There is also a special relationship between the places. When moving one place to the left, the value of the place is ten times as much as it was before. For example, when a 6 in the ones place moves to the next place on the left its value changes from 6 ones to 6 tens. 60 is worth ten times as much as 6.

Students study these ideas to understand numbers to the billions and beyond. They also use different methods to show numbers. One way is to use exponents. Exponents are a short way to write large numbers. For example, 10 × 10 × 10 × 10 is equal to 10,000 so it can also be written as 104. The small 4 is the exponent. These are all different ways of writing large numbers:

• Expanded form: 6,000 + 400 + 30 + 7 = 6,437
• Expanded notation: (6 × 1,000) + (4 × 100) + (3 × 10) + (7 × 1) = 6,437
• Expanded notation with exponents: (6 × 103) + (4 × 102) + (3 × 101) + (7 × 100) = 6,437

## Math at home

Find articles or videos that involve large numbers. Examples include city or state populations, distances in our solar system, or the number of objects such as cell phones or cars there are in different countries. Discuss how the numbers are shown and how to say the number aloud. Some large numbers you find may be shown as 238.8 million. Another way to write this number is 238,800,000 and it can be read as two hundred thirty-eight million eight hundred thousand.