In this lesson, students will examine the amount of annual and seasonal rainfall in four cities to compare decimals to the hundredths place. Students will add and round digits to the thousandths place. Students will utilize technology by navigating to a specific United States climate website to get relatively current and accurate data.
This unit was created as part of the ALEX Interdisciplinary Resource Development Summit.
Naming decimal fractions in expanded, unit, and word forms in order to compare decimal fractions is the focus of Module 1, Topic B (5.NBT.3). Familiar methods of expressing expanded form are used, but students are also encouraged to apply their knowledge of exponents to expanded forms (e.g., 4,300.01 = 4 × 103 + 3 × 102 + 1 × 1/100). Place value charts and disks offer a beginning for comparing decimal fractions to the thousandths but are quickly supplanted by reasoning about the meaning of the digits in each place, noticing differences in the values of like units and expressing those comparisons with symbols (>, <, and =).
In Module 1, Topic C, students generalize their knowledge of rounding whole numbers to round decimal numbers to any place. In Grades 3 and 4, vertical number lines provided a platform for students to round whole numbers to any place. In Grade 5, vertical number lines again provide support for students to make use of patterns in the base ten system, allowing knowledge of whole-number rounding (4.NBT.3) to be easily applied to rounding decimal values (5.NBT.4). The vertical number line is used initially to find more than or less than halfway between multiples of decimal units. In these lessons, students are encouraged to reason more abstractly as they use place value understanding to approximate by using nearest multiples.
Naming those nearest multiples is an application of flexibly naming decimals using like place value units. To round 3.85 to the nearest tenth, students find the nearest multiples, 3.80 (38 tenths 0 hundredths) and 3.9 (39 tenths 0 hundredths), and then decide that 3.85 (38 tenths 5 hundredths) is exactly halfway between and, therefore, must be rounded up to 3.9.
In Module 1, Topics D through F mark a shift from the opening topics of Module 1. From this point to the conclusion of the module, students begin to use base ten understanding of adjacent units and whole-number algorithms to reason about and perform decimal fraction operations—addition and subtraction in Topic D, multiplication in Topic E, and division in Topic F (5.NBT.7).
In Topic D, unit form provides the connection that allows students to use what they know about general methods for addition and subtraction with whole numbers to reason about decimal addition and subtraction (e.g., 7 tens + 8 tens = 15 tens = 150 is analogous to 7 tenths + 8 tenths = 15 tenths = 1.5). Place value charts and disks (both concrete and pictorial representations) and the relationship between addition and subtraction are used to provide a bridge for relating such understandings to a written method. Real-world contexts provide opportunities for students to apply their knowledge of decimal addition and subtraction as well in Topic D.
A focus on reasoning about the multiplication of a decimal fraction by a one-digit whole number in Module 1, Topic E provides the link that connects Grade 4 multiplication work and Grade 5 fluency with multi-digit multiplication. Place value understanding of whole-number multiplication coupled with an area model of the distributive property is used to help students build direct parallels between whole-number products and the products of one-digit multipliers and decimals (5.NBT.7). Once the decimal has been placed, students use an estimation-based strategy to confirm the reasonableness of the product through place value reasoning. Word problems provide a context within which students can reason about products.
Topic F concludes Module 1 with an exploration of the division of decimal numbers by one-digit whole-number divisors using place value charts and disks. Lessons begin with easily identifiable multiples such as 4.2 ÷ 6 and move to quotients that have a remainder in the smallest unit (through the thousandths). Written methods for decimal cases are related to place value strategies, properties of operations, and familiar written methods for whole numbers (5.NBT.7). Students solidify their skills with an understanding of the algorithm before moving on to division involving two-digit divisors in Module 2. Students apply their accumulated knowledge of decimal operations to solve word problems at the close of the module.
In this interactive activity, students will be led through steps to change fractions to decimals, then put the decimal numbers in order by comparing their magnitude. Students will learn to compare two decimals to the hundredths place by reasoning about their size. There are teaching activities as well as practice activities available. There is a handout that reviews the strategies taught during the activity that can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.
In this interactive activity, students will be led through steps to learn the place value of decimals to the thousandths place. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.