Topic A Grouping Units in Tens and Ones Topic A builds on work with tens and ones that students completed in modules 3 and 4. At first students reason about units in the context of time. They learn through experience that smaller units can compose larger units. For example, they discover that 1 hour is made of 60 minutes and 1 half hour is made of 30 minutes. Lessons build on the idea that smaller units can be used to compose larger units by considering the place value units of tens and ones. Students work with sets of objects to compose groups of 10 and represent two-digit totals in different ways. For example, 26 ones can also be represented as 1 ten 16 ones or 2 tens 6 ones. Working with numbers that have more than 9 ones prepares students for adding and subtracting with larger numbers in later grades. However, students come to understand that the digits we use to write a number, such as the 2 and the 6 in 26, show how many tens and ones there are when the number is expressed in its “most composed” form. This leads to recognition that the value of digits can be determined based on their place in the number. The value of the digit 2 can be expressed as 2 tens or 20. The value of the digit 6 can be expressed as 6 ones or simply 6. Students compose (or decompose) a total such as 26 by place value units: 20 and 6 or 2 tens 6 ones. Using different representations of the same total invites students to consider equivalence and deepens their number sense.
50 pennies 50 ones
5 dimes 5 tens
Several place value models that increase in complexity help students internalize the basic understanding that 10 ones are equivalent to 1 ten.
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