2015-2016 Curriculum Blueprint
Grade: 3
Course: Mathematics
Topic 6 – Connect Area to Multiplication and Addition
Flexible Time
Line
12 days
Topic Overview
Students will develop a deep understanding of the concept of area. Students will begin with concrete models and then move to pictorial and abstract models.
Students come to understand how area is related to multiplication and addition.
Vertical Progression
nd
2 Grade
 Students work with equal groups of objects arranged in arrays.
 Students find the total number of objects by writing equations using rows or columns.
4th Grade
 Students will apply the area formula for a rectangle to solve real-world and mathematical problems.
Learning Goal
Essential Question
Students will demonstrate how area can be measured and found using various
How can area be measured and found?
strategies.
Topic 6 Scale
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the standards
Step 1: Problem-Based Learning “Solve and Share”
 area
within the topic. Lessons and problems used for instruction
Problem-Based Learning Lesson Flow Map
 unit square
and assessment should be determined through collaborative
Conceptual understanding is developed when mathematics is
 square unit
unit planning.
introduced in the context of solving a real problem in which
 estimate
ideas related to the new content are embedded. Conceptual
Topic 6: Connect Area to Multiplication and Addition
Lesson 6-1: Cover Regions
Lesson 6-2: Area: Nonstandard Units
Lesson 6-3: Area: Standard Units
Lesson 6-4: Area of Squares and Rectangles
Lesson 6-5: Apply Properties: Area and the Distributive
Property
Lesson 6-6: Apply Properties: Area of Irregular Shapes
Lesson 6-7: Math Practices and Problem Solving: Look For
and Use Structure
understanding results because the process of solving a problem
requires students to connect their prior knowledge with the new
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Each lesson in the book begins with a Solve and Share. See the
links below for additional tasks to be used as needed:
Math Formative Assessment System (MFAS) Tasks by Standard
Illustrative Mathematics Tasks by Standard
Step 2: “Visual Learning Bridge”
Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the
lesson through the use of the worked-out problem in the
textbook.
Deconstructed Standards
MAFS.3.MD.3.5 (DOK 1) Recognize area as an attribute of plane figures and understand concepts of area measurement.
a) A square with a side length of 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of square units.
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Define “unit square.”
Define area.
Relate the number (n) of unit squares to the area of a plane figure.
MAFS.3.MD.3.6 (DOK 1) Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
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Measure areas by counting unit squares.
Use unit squares of cm, m, in, ft. and other sizes of unit squares to measure areas.
MAFS.3.MD.3.7 (DOK 3) Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side
lengths.
b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and
represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area
models to represent the distributive property in mathematical reasoning.
d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the nonoverlapping parts, applying this technique to solve real world problems.
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Find the area of a rectangle by tiling it in unit squares.
Find the side lengths of a rectangle in units.
Compare the area found by tiling a rectangle to the area found by multiplying the side lengths.
Relate area of a rectangle to multiplication and addition by modeling the distributive property.
Multiply side lengths to find areas of rectangles.
Multiply using an area model (array)
Recognize that areas of each rectangle in a rectilinear (straight line) figure can be added together to find the area of the figure
Find areas of rectangles.
Add areas of rectangles.
Solve real world and mathematical area problems by multiplying side lengths of rectangles.
Use rectangular arrays to represent whole-number products in multiplication problems.
Decompose rectilinear figures into non-overlapping rectangles
Use the technique of decomposing rectilinear figures to find the area of each rectangle to solve real world problems.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.4.1 Model with mathematics.
MAFS.K12.MP.7.1 Look for and make use of structure.
Additional Resources & Links
Discovering Area
Introductory lesson (retrieved from Illustrative Mathematics) designed to assist
students in discovering the multiplication algorithm for area. Recommended to be
implemented prior to direct instruction on area.
Lesson Plan
Demonstration Video (Safari Montage)
Georgia Unit
Unit 3
 Olympic Cola Display
 Array Challenge
 Read All About It
(Many other lessons in this Georgia unit pertain to this topic)
EngageNY
Module 4: Topic A & B
All topics in this module pertain to this topic
www.pearsonrealize.com
Home-School Connection Page
Reteaching Pages
Marzano Proficiency Scales Bank
Math Formative Assessment System (MFAS) Tasks by Standard
CPALMS - MFAS includes tasks that teachers can implement with their students, and
rubrics that help the teacher interpret students’ responses.
Illustrative Mathematics Tasks by Standard
The site illustrates standards with impeccably crafted tasks, videos, lesson plans, and
curriculum modules.
Common Core Flip Books Provides additional information and sample problems for
every standard
FSA Test Item Specifications
Higher Order Questions & Writing Connections
Link to Webb’s DOK Guide
* Higher order questions should be utilized to foster a deep,
conceptual understanding of the topic. Encouraging students to
express their mathematical thinking in writing helps them solidify
their learning.
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How can the area of an object be measured without counting
squares?
How is the commutative property of multiplication evident in an
area model?
How can the area of a rectangle represent the Distributive
Property?
What are two ways to find the area of an irregular shape?
How can you break a problem into simpler problems?
How do the lengths of a rectangle’s sides affect its area?
Write to explain how multiplication is related to area.
Spiral Review
*Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and
procedures.
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Daily Review 6-1 through 6-7