In this video, teachers will learn classroom strategies for teaching decimal addition and subtraction in this professional development video from Making Math Matter.
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.
Throughout Module 2, Topic C, students make connections between what they know of whole number multiplication to its parallel role in multiplication with decimals by using place value to reason and make estimations about products (5.NBT.7). Knowledge of multiplicative patterns from Grade 4 experiences, as well as those provided in Grade 5 Module 1, provide support for converting decimal multiplication to whole number multiplication. Students reason about how products of such converted cases must be adjusted through division, giving rise to explanations about how the decimal must be placed.
In Module 2, Topic D, students explore multiplication as a method for expressing equivalent measures. For example, they multiply to convert between meters and centimeters or ounces and cups with measurements in whole number, fraction, and decimal form (5.MD.1). These conversions offer opportunities for students to not only apply their newfound knowledge of multi-digit multiplication of both whole and decimal numbers but to also reason deeply about the relationships between unit size and quantity (i.e., how the choice of one affects the other). Students are given the opportunity to review the multiplication of a whole number by a fraction, a skill taught in Grade 4.
Module 2, Topic G uses the knowledge students have accumulated about whole number division with double-digit divisors and extends it to the division of decimals by double-digit divisors (5.NBT.7). Parallels between sharing or grouping whole number units and sharing or grouping decimal units are the emphasis of Topic G. Students quickly surmise that the concepts of division remain the same regardless of the size of the units being shared or grouped. Placement of the decimal point in quotients is based on students’ reasoning about when wholes are being shared or grouped and when the part being shared or grouped transitions into fractional parts. Students reason about remainders in a deeper way than in previous grades. Students consider cases in which remainders expressed as whole numbers appear to be equivalent; however, equivalence is disproven when such remainders are decomposed as decimal units and shared or grouped.
In Module 2, Topic H, students apply the work of the module to solve multi-step word problems using multi-digit division (5.NBT.6). Cases include unknowns representing either the group size or the number of groups. In this topic, an emphasis on checking the reasonableness of their solutions draws on skills learned throughout the module, which includes using knowledge of place value, rounding, and estimation. Students relate calculations to reasoning about division through a variety of strategies including place value, properties of operations, equations, and area models.
In this interactive activity, students will be led through steps to add and subtract decimals to the hundredths place. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the activity 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 multiply decimals to the hundredths place. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.
In this lesson, students will calculate savings for different products when using coupons. They will also decide what factors will influence the choices they make when choosing products. Students will practice adding, subtracting, multiplying, and dividing monetary amounts using decimals to the hundredths place.
