Essential Questions:
Lesson Plan A.1: Elapsed Time
Lesson Seed A.1: How Much Time Routine and Problems
Lesson Seed A.2-3: Measurement Centers
Lesson Seed A.2: Solving Problems for Volume and Mass at a Measurement Center
Lesson Seed A.2: Solving Problems Using Volume
Unit Overview
Content Emphasis By Clusters in Grade 3
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.
In this unit, the students apply their understanding of whole number operations in order to reason about and solve problems involving measurement. Students in Grade 3 continue to develop personal benchmarks and measurement estimation skills. They build on the work that was done with time in Grade 2, and now learn to tell time to the nearest minute, and measure time intervals in minutes. They also begin using standard units of grams, kilograms, and liters in order to measure units of volume, mass, and liquids. Students justify their solutions using drawings or diagrams, such as representing problems on a number line or creating a drawing of a beaker with a measurement scale of milliliters.
Grade 3 students also measure lengths using rulers marked with halves and fourths of an inch. They use their developing knowledge of fraction and number lines to extend their work from the previous grade by working with measurement data involving fractional measurement values. To make a line plot from the data in the table, the student can ascertain the greatest and least values in the data, then construct the line plot with those two values as the endpoints and tick marks appropriately spaced, adding additional Xs or dots for the remaining data collected. Students can pose questions about data presented in line plots, such as how many students obtained measurements larger than 14 ^{1}/_{2} inches. Also in Grade 3, students draw scaled picture graphs (also known as pictographs) and scaled bar graphs in which the symbol in the picture graph or the square in the bar graph could represent, for example, 5 pets. Again students can pose questions that can be answered about the graph by interpreting the data displayed.
The student will be able to:
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.
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
product: the result when two numbers are multiplied. Example: 5 x 4 = 20 and 20 is the product.
measurement quantities: examples could include inches, feet, pints, quarts, centimeters, meters, liters, square units, etc.
Zero Property: In addition, any number added to zero equals that number.
Example: 8 + 0 = 8
In multiplication, any number multiplied by zero equals zero. Example: 8 x 0 = 0
Identity Property: In addition, any number added to zero equals that number. Example: 8 + 0 = 8
In multiplication, any number multiplied by one equals that number. Example: 8 x 1 = 8
Commutative Property: In both addition and multiplication, changing the order of the factors when adding or multiplying will not change the sum or the product.
Example: 2 + 3 = 5 and 3 + 2 = 5; 3 x 7 = 21 and 7 x 3 = 21
Associative Property: in addition and multiplication, changing the grouping of the elements being added or multiplied will not change the sum or product.
Examples: (2 + 3) + 7 = 12 and 2 + (3 + 7) = 12; (2 x 3) x 5 = 30 and 2 x (3 x 5) = 30
Distributive Property: a property that relates two operations on numbers, usually multiplication and addition or multiplication and subtraction. This property gets its name because it ‘distributes’ the factor outside the parentheses over the two terms within the parentheses. Examples:
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.
fluently: using efficient, flexible and accurate methods of computing
estimation strategies: : to estimate is to give an approximate number or answer. Some possible strategies include front-end estimation, rounding, and using compatible numbers. Examples:
whole: In fractions, the whole refers to the entire region, set, or line segment which is divided into equal parts or segments.
Part II – Instructional Connections outside the Focus Cluster
partitioning: dividing the whole into equal parts.
quotient: the number resulting from dividing one number by another.
share: a unit or equal part of a whole.
partitioned: the whole divided into equal parts.
arrays: the arrangement of counters, blocks, or graph paper square in rows and columns to represent a multiplication or division equation. Examples:
inverse operation: two operations that undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
Examples: 4 + 5 = 9; 9 - 5 = 4 6 x 5 = 30; 30 ÷ 5 = 6
fact families: a collection of related addition and subtraction facts, or multiplication and division facts, made from the same numbers. For 7, 8, and 15, the addition/subtraction fact family consists of 7 + 8 = 15, 8 + 7 = 15, 15 – 8 = 7, and 15 – 7 = 8. For 5, 6, and 30, the multiplication/division fact family consists of 5 x 6 = 30, 6 x 5 = 30, 30 ÷ 5 = 6, and 30 ÷ 6 = 5.
decomposing: breaking a number into two or more parts to make it easier with which to work. Example: When combining a set of 5 and a set of 8, a student might decompose 8 into a set of 3 and a set of 5, making it easier to see that the two sets of 5 make 10 and then there are 3 more for a total of 13.
Decompose the number = ^{3}/_{5}; ^{3}/_{5} = ^{1}/_{5} + ^{1}/_{5} + ^{1}/_{5}
composing: Composing (opposite of decomposing) is the process of joining numbers into a whole number…to combine smaller parts. Examples: 1 + 4 = 5; 2 + 3 = 5. These are two different ways to “compose” 5.
equation: is a number sentence stating that the expressions on either side of the equal sign are in fact equal.
area: the number of square units needed to cover a region. Examples:
tiling: highlighting the square units on each side of a rectangle to show its relationship to multiplication and that by multiplying the side lengths, the area can be determined. Example:
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