## Unit Overview

Essential Questions:

**Lesson Plans and Seeds**

**Download Seeds, Plans, and Resources (zip)**

**Content Emphasis By Clusters in Grade 4**

**Progressions from Common Core State Standards in Mathematics**

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 this unit, students build on their understanding of number and the four operations, geometry, and measurement by solving problems involving measurement conversions from a larger unit to a smaller unit. Students in Grade 4 develop mental images and benchmarks about a meter and a kilometer, as well as expressing larger measurements in smaller units within the metric system.

Students will extend their understanding of area from grade 3 where they multiplied sides of rectangles to find the area of rectangles with whole number sides. In grade 4 students will apply the area formulas for area and perimeter to real life problems representing the area formula as a multiplication equation with an unknown factor. Students should work on problems that will lead them to create these equations rather than being told the rule and procedure.

A strong emphasis should be made on connecting the Domains of Number and Operations in Base Ten, Measurement and Data, and Geometry in this unit, as it supports work done both at the beginning and end of Grade 4.

**Teacher Notes: **

__http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5_2012__

_07_21.pdfto see the development of the understanding of Measurement and Data (measurement part) as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.

_07_21.pdf

**Enduring Understandings:**

*At the completion of the unit on Measurement and Conversions, the student will understand that:*

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

**4.NBT.B.5**Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

**4.NBT.B.6**Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

**4.NF.A.1**Explain why a fraction a/b is equivalent to a fraction

*(n × a)/(n × b)*by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

**4.NF.B.3**Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

**Possible Student Outcomes:**

The student will be able to:

**Evidence of Student Learning:**

*The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.*

**Fluency Expectations and Examples of Culminating Standards:**

**multi-digit whole numbers**using

**the standard algorithm**.

**Common Misconceptions:**

**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*

*nstructional 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*

*PARCC public release items*

*Maryland Public release items*

Topic |
Standard |
Link |
Notes |
---|---|---|---|

Who Is the Tallest? | 4.MD.A.1 | http://www.illustrativemath ematics.org/illustrations/1508 |
This task provides a context for translating between different units. While there are in principle multiple approaches (using each of the different units for measurement), the 4.MD.1 standard calls for converting a larger unit to a smaller unit. Students who convert all of the heights to inches are meeting the expectations of the standard, and students solving it in other ways are exceeding the expectations of the standard. |

Margie Buys Apples | 4.MD.A.2 | http://www.illustrativemath ematics.org/illustrations/873 |
This task gives students an opportunity to work with familiar fractions and decimals in a context involving money. This task could be used early in the year for formative assessment or as a transition to more complex problems. It also provides a good opportunity to review the connection between familiar fractions and decimals. |

Karl’s Garden | 4.MD.A.3 4.OA.A.3 |
http://www.illustrativemath ematics.org/illustrations/876 |
The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. |

**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**

**standard algorithm:** an algorithm is a systematic scheme for performing computations, consisting of a set of rules or steps.

*properties of operations:*

Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system.

Associative property of addition (a + b) + c = a + (b + c)

Commutative property of addition a + b = b + a

Additive identity property of 0 a + 0 = 0 + a = a

Existence of additive inverses For every a there exists –a so that a + (–a) = (–a) + a = 0

Associative property of multiplication (a ▢▢b) ▢▢c = a ▢▢(b ▢▢c)

Commutative property of multiplication a ▢▢b = b ▢▢a

Multiplicative identity property of 1 a ▢▢1 = 1 ▢▢ = a

Existence of multiplicative inverses For every a ≠▢▢ there exists 1/a so that a ▢▢1/a = 1/a ▢▢a = 1.

Distributive property of multiplication over addition a ▢▢(b + c) = a ▢▢b + a ▢▢c

multi-digit whole numbers: a whole number comprised of more than one digit. Example: 27 and 246,910 are both multi-digit whole numbers.

**Part II – Instructional Connections outside the Focus Cluster**

** multiplicative comparison:** comparing the size of a product to the size of one factor on the basis of the size of the other factor.

Example: If 2 bags of candy cost $4.00

then 8 bags of candy would cost $16.00

**is a number sentence stating that the expressions on either side of the equal sign are, in fact, equal.**

*equation:***comparing the size of a sum to the size of one of addend on the basis of the size of the other addend.**

*additive comparison:*Example: Johnny is 10 years old. His brother, Sean is 6 years old.

When Johnny is 16 years old, Sean will be 12 years old.

**the value of a digit as determined by its position in a number. Example: in the number “101” the one is worth either 100 or 1, depending upon its position.) base ten numerals: a base of a numeration system is the number that is raised to various powers to generate the place values of that system. In the base ten numeration system the base is ten. The first place is 100 or 1 (the units place), the second is 10¹ or 10 (the tens place, the third is 10² or 100 (the hundreds place), etc. This determines the place value of the different positions in a number. Example: One number written as a base ten numeral would be**

*place value:**6,427*.

**the arrangement of counters, blocks, or graph paper squares in rows and columns to represent a multiplication or division equation. Examples:**

*rectangular arrays:***a rectangular array of square units that represents a product/quotient. Example:**

*area model:*Additional Resources:

__Free Online Resources:____http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,3547876-,00.html__Reproducible blackline masters

__http://lrt.ednet.ns.ca/PD/BLM_Ess11/table_of_contents.htm__mathematics blackline masters

__http://yourtherapysource.com/freestuff.html__Simple activities to encourage physical activity in the classroom

__http://www.mathsolutions.com/index.cfm?page=wp9&crid=56__Free lesson plan ideas for different grade levels

__http://www.nctm.org/__National Council of Teachers of Mathematics

__http://www.k-5mathteachingresources.com__Extensive collection of free resources, math games, and hands-on math activities aligned with the Common Core State Standards for Mathematics

__http://elementarymath.cmswiki.wikispaces.net/Standards+for+Mathematical+Practice__Common Core Mathematical Practices in Spanish

__http://mathwire.com/__Mathematics games, activities, and resources for different grade levels

__http://www.pbs.org/teachers/math/__interactive online and offline lesson plans to engage students. Database is searchable by grade level and content

__http://www.k8accesscenter.org/training_resources/MathWebResources.asp__valuable resource including a large annotated list of free web-based math tools and activities.

__http://www.cast.org/udl/index.html__Universal Design for Learning

__http://www.nsa.gov/academia/_files/collected_learning/elementary/geometry__

/measure_conver.pdfLesson plan for measurement conversions.

/measure_conver.pdf

__Math Related Literature: __

__Game Time__! Notes: This book helps students explore the relationships between the various units of time—seconds, minutes, hours, days, and weeks—and how clocks and calendars represent these units.

__Polly’s Pen Pal__.

Notes: This book features Polly and her pen-pal Ally, who lives in Montreal, Canada. The concept of using rough equivalents in terms of familiar objects and distances helps students become familiar and comfortable with the metric system.

__References: __

__http://www.ncpublicschools.org/acre/standards/common-core-tools/#unmath__