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| In this unit, children explore the geometric attributes of polygons and classify quadrilaterals into categories based on their attributes, they identify and measure the perimeters of polygons, and distinguish between perimeter and area. They develop multiple strategies to determine the areas of rectangles and extend those ideas to determine the areas of rectilinear shapes. The following big ideas will be covered in this unit: - Area is the two-dimensional space inside a region.
- Area is measured by covering or tiling.
- When finding the area of a rectangle, the dimensions represent the factors in a multiplication problem.
- The length around a polygon can be calculated by adding the lengths of its sides.
- Quadrilaterals can be classified according to the lengths of their sides.
- The broad category of “quadrilaterals” includes all types of parallelograms, trapezoids, and other four-sided figures.
- Polygons can be described and classified by their sides and angles.
- Polygons can be put together or taken apart to make other polygons.
- A Rectilinear is a polygon that has all right angles and is composed of more than one rectangle.
- The area of the rectilinear figure can be found by decomposing them into non-overlapping rectangles and adding the areas of the parts. *Please Note: Lessons 4-1 and 4-2 were moved to Unit 7. The explorations from Lesson 4-3 are embedded in Practice Opportunities section. |
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| Operations & Algebraic Thinking 3.OA.C. Multiply and divide within 100. 3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 3.OA.D. Solve problems involving the four operations, and identify and explain patterns in arithmetic. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order. 3.MD.C. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.C.5. Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.C.5a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. 3.MD.C.5b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 3.MD.C.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.C.7. Relate area to the operations of multiplication and addition. 3.MD.D. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 3.MD.D.8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 3.G.A. Reason with shapes and their attributes. 3.G.A.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. |
Students will have opportunities to:
- Explain their mathematical thinking clearly and precisely. (MP6.1)
- Use an appropriate level of precision for their problem. (MP6.2)
- Use clear labels, units, and mathematical language. (MP6.3)
- Think about accuracy and efficiency when they count, measure, and calculate. (MP6.4)
- Look for mathematical structures such as categories, patterns, and properties. (MP7.1)
- Use structures to solve problems and answer questions. (MP7.2)
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| - Multiplication is related to addition and involves counting groups of like size and determining how many there are in all.
- Models such as an array is used to represent multiplication.
- Multiplication and division can be used to solve word problems involving situations involving equal groups and arrays. Concepts from Previous Grades:
- Geometric figures can be analyzed and classified based on their attributes.
- 2-dimensional shapes can be identified by the number of its sides, vertices, and angles.
- Shapes help us describe, represent, and make sense of our world.
- Shapes can be combined to make new shapes.
- Shapes can be decomposed into other shapes.
- A rectangle can be tiled with squares lined up in rows and columns. | - Area of rectangles can be found by multiplying the side lengths.
- The area model can be used to partition larger factors in a multiplication problem.
- Area models are related to addition and multiplication.
- Shapes can be partitioned into parts with equal areas and the area of each part can be expressed as a unit fraction of the whole.
-The measurement of an unknown side length can be determined when given the perimeter of the polygon. |
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| Angle, approximate, area, array, attributes, benchmark, composite unit, decompose, face, kite, parallel, parallelogram, perimeter, polygon, precise, quadrilateral, rectangle, rhombus, right angle, side, square unit, trapezoid, vertex, skip-count, repeated addition, length, width, distance, surface Bold Font: Listed in teacher's EDM4 edition Normal Font: not listed in teacher’s edition as a vocabulary word but will be helpful for students in explanations |
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| The following lesson plan sequence is obtained from Everyday Mathematics 4. Each lesson is aligned with a learning objective to inform the teachers on what students should be able to at the end of the lesson. The student objective informs the students of their learning goals for the day and it should be reviewed before, during and at the end of the lesson. Each lesson includes a mathematics task that should be implemented to meet the learning objectives. Teachers can select from the practice opportunities to reinforce the learning goals of the day. |
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| The following language supports are for English Language Learners but could also be used to support any struggling learner in mathematics. The strategies are obtained from the SIOP model. The language objectives will support students' academic language development. The sentence stems and starters provides the support many students need to be able to participate in discussions and writing about mathematics. |
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