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Gr. 5 Unit: Perform operations with multi-digit whole numbers and with decimals to hundredths

Unit Overview

Essential Questions:

What makes a computational strategy both efficient and effective?

How do mathematical ideas interconnect and build on one another to produce an answer?

How can the four operations in decimals related to one another?

How does one recognize the strategy to be used for a specific operation?

How can models help us understand decimals?

How can we determine the reasonableness of an answer when solving a problem?

How are decimals different from whole numbers?

Lesson Plans and Seeds

LP 5.NBT.B.5-7 Multiplying Decimals to Hundredths

Lesson Seed B.5: Standard Algorithm for Multiplication Based on Place Value

Lesson Seed B.7: Addition & Subtraction with Decimals

Download Seeds, Plans, and Resources (zip)

Unit Overview

Content Emphasis By Clusters in Grade 5

Progressions from Common Core State Standards in Mathematics

Send Feedback to MSDE’s Mathematics Team

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

Unit Overview

In prior grades, students used various strategies to multiply. This unit builds on prior understandings of multiplying whole numbers fluently which means a correct answer in a reasonable amount of steps. The unit focuses on performing whole number division using equations, arrays and concrete models. Addition, subtraction, multiplication, and division of decimals to hundredths should be used with concrete models or drawings and strategies relating the strategy to a written method and explaining the reasoning used.

Teacher Notes:

Students should be fluent in multiplying whole numbers.

Students should be able to find quotients of whole numbers with up to four-digit dividends and two-digit divisors.

Students should be able to add, subtract, multiply, and divide decimals to numbers to the hundredths.

Students should understand place value in order to perform operations with decimals.

Students should understand the difference between place value to the left of the decimal and to the right of the decimal.

Teacher will draw on student background knowledge of whole numbers to perform decimal operations.

Enduring Understandings:

At the completion of this unit performing operations with multi-digit whole numbers and with decimals to hundredths:

Fluency includes both understanding of and the ability to appropriately us numbers.

Prior knowledge should allow students to be able to transition to using decimals more effectively.

A decimal quantity can be represented in various ways.

The magnitude of number affects the outcome of operations on them.

Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):

5.NBT.B.6 UThe extension from one-digit divisors to two-digit divisors requires care. This is a major milestone along the way to reach fluency with the standard algorithm in grade 6.

Possible Student Outcomes:

The student will be able to:

understand whole number division with four-digit dividends and two-digit divisors.

use multiplication of multi-digit numbers using the standard algorithm fluently.

utilize their knowledge of whole numbers to add, subtract, multiply, and divide decimals numbers to hundredths.

Evidence of Student Learning;

Fluency Expectations and Examples of Culminating Standards:

PARCC has no fluency expectations related to graphing points on the coordinate plane to solve problems.

Common Misconceptions:

Students May:

compute the sum or difference of decimals by lining up the right-hand digits as they would with whole numbers.

misunderstand how to estimate to see if their answer is close to being correct.

misunderstand the value of decimal numbers.

misunderstand the difference in value of digits to the left of the decimal versus to the right of the decimal.

Interdisciplinary Connections:

Interdisciplinary connections fall into a number of related categories:

Literacy standards within the Maryland Common Core State Curriculum.

Science, Technology, Engineering, and Mathematics standards.

Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.

Sample Assessment Items:

The items included in this component will be aligned to the standards in the unit and will include:

Items purchased from vendors.

PARCC prototype items.

Items purchased from vendors.

Maryland Public release items.

Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)

Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.

Part I – Focus Cluster

Perform Operations with Multi-Digit Whole Numbers and with Decimals to Hundredths

NOTE: None of the vocabulary, terminology, and concepts in this cluster are new, nor should they be particularly problematic for instruction of the related standards.

Part II – Instructional Connections outside the Focus Cluster

NOTE: None of the vocabulary, terminology, and concepts in this cluster are new, nor should they be particularly problematic for instruction of the related standards.

Additional Resources:

http://commoncoretools.files.wordpress.com/2012/06/ccss_progression
_g_k6_2012_06_27.pdf

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Last Updated 7/21/2019 8:19 PM