Grade 5 Math
Grade 5 • Module 1 Place Value and Decimal Fractions
In Module 1, students’ understandings of the patterns in the base ten system are extended from Grade 4’s work with place value to include decimals to the thousandths place. In Grade 5, students deepen their knowledge, e.g., 1 tenth times any digit on the place value chart moves the digit one place value to the right.
In Module 1, students’ understandings of the patterns in the base ten system are extended from Grade 4’s work with place value to include decimals to the thousandths place. In Grade 5, students deepen their knowledge, e.g., 1 tenth times any digit on the place value chart moves the digit one place value to the right.
Topic A opens the module with exploration of the multiplicative patterns of the base ten system using manipulatives and a place value chart. Students notice that multiplying by 1,000 is the same as multiplying by 10 × 10 × 10. Since each factor of 10 shifts the digits one place to the left, multiplying by 10 × 10 × 10— can be recorded in exponential form as 103. This shifts the position of the digits to the left 3 places, thus changing the digits’ relationships to the decimal point.
Topic B moves into the naming of decimal fraction numbers in expanded form (e.g., 4.23 = 4 ones 2 tenths 3 hundredths), and word forms and concludes with using like units to compare decimal fractions. Now, in Grade 5, students use exponents and the unit fraction to represent expanded form (e.g., 2 × 102 + 3 × (1/10) + 4× (1/100) = 200.34). Also, students reason about differences in the values of like place value units and express those comparisons with symbols (>, <, and =).
In Topic C, students generalize their knowledge of rounding whole numbers to round decimal numbers initially using a vertical number line to interpret the result as an approximation and then eventually moving away from the visual model.
Topic D, uses general methods for addition and subtraction with whole numbers to decimal addition and subtraction (e.g., 7 tens + 8 tens = 15 tens = 150 just as 7 tenths + 8 tenths = 15 tenths = 1.5).
Topic E bridges the gap between Grade 4 work with multiplication and the standard algorithm by focusing on an intermediate step— reasoning about multiplying a decimal by a one-digit whole number. The area model, with which students have had extensive experience since Grade 3, is used as a scaffold for this work.
Topic F concludes this module with a similar exploration of division of decimal numbers by one-digit whole-number divisors. Students solidify their skills with an understanding of the algorithm before moving on to long division involving two-digit divisors in Module 2.
Place Value Pirates
Partial Quotients Strategy
