Essential Questions: Why do I measure?
Why do I need standardized units of measurement?
How does what I measure influence how I measure?
What types of problems are solved with measurement?
What are tools of measurement and how are they used?
How do units within a system relate to each other?
When is an estimate more appropriate than an actual measurement?
What strategies help estimate measurements?
When will I use angle measurement in real-life problem solving?
Why do I need to know how to convert units of measurement?
Lesson Plan A.3: Area and Perimeter Problems
Lesson Seed A.2: Elapsed Time
Download Seeds, Plans, and Resources (zip)
Content Emphasis By Clusters in Grade 4
Progressions from Common Core State Standards in Mathematics
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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.
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.
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):
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:
Interdisciplinary connections fall into a number of related categories:
Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:
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
equation: is a number sentence stating that the expressions on either side of the equal sign are, in fact, equal.
additive comparison: comparing the size of a sum to the size of one of addend on the basis of the size of the other addend.
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.
place value: 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 6,427.
rectangular arrays: the arrangement of counters, blocks, or graph paper squares in rows and columns to represent a multiplication or division equation. Examples:
area model: a rectangular array of square units that represents a product/quotient. Example:
Math Related Literature: