Wayne RESA

Unit PlannerEDM4 Math 5

Wayne Resa - Math / Grade 5 / Mathematics / EDM4 Math 5 / Week 28 - Week 31
5 Curriculum Developers
Unit Abstract

In this unit, children learn two methods for multiplying mixed numbers. They use these methods to find the areas of rectangles with fractional side lengths and to solve problems involving fractional data in line plots. Students also review attributes of 2-dimensional figures and classify shapes in a hierarchy based on properties. Finally, students graph points on coordinate grids to visualize numerical patterns and represent real world problems.The following big ideas will be covered in this unit:

- Fractional side lengths can be multiplied to find the area of a rectangle.
- Previous understandings of multiplication can be applied to multiply a fraction by a fraction. (mixed numbers)

- Shapes are classified into large categories and subcategories according to the properties they share, such as properties of sides, angles, and symmetry.
- Two-Dimensional figures can fit into more than one category.

- A line plot displays a data set of measurements in fractions of a unit (1/2, ¼, 1/8).
- Graphical representations can be used to make predictions and interpretations about real world situations.

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Expectations/Standards
MI: Mathematics
MI: Grade 5
Operations & Algebraic Thinking
5.OA.B. Analyze patterns and relationships.
Number & Operations—Fractions
5.NF.B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.4b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.NF.B.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
5.NF.B.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Measurement & Data
5.MD.B. Represent and interpret data.
Geometry
5.G.A. Graph points on the coordinate plane to solve real-world and mathematical problems.
5.G.A.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.G.B. Classify two-dimensional figures into categories based on their properties.
5.G.B.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
5.G.B.4. Classify two-dimensional figures in a hierarchy based on properties.
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Practice Standards

Students will have opportunities to:

  • Create mathematical representations using numbers, words, pictures, symbols, gestures, tables, graphs, and concrete objects. (MP.2)
  • Make sense of the representations you and others use. (MP.2)
  • Make connections between representations. (MP.2)
  • Look for and express regularity in repeated reasoning (MP.8)
  • Create and justify rules, shortcuts and generalizations (MP.8)
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Concepts from Previous Units

- Previous understandings of multiplication can be applied to multiply a fraction by a fraction.
- Multiplication is an operation by which one factor scales the second up or down.

- Tiling can be used to find the area of rectangles with fractional side lengths.
- A line plot displays a data set of measurements in fractions of a unit (1/2, ¼, 1/8).
- The data from the line plot can be used to identify a typical measurement.
- Location can be determine in a plane or in space using coordinate systems.
- Graphical representations can be used to make predictions and interpretations about real world situations.

From Previous Grades:

- Geometric figures can be analyzed and classified based on their properties.

- Edges (sides), angles, and symmetry can be used to classify geometric figures.

- Two lines are parallel if they never intersect and are always equidistant.

- Two lines are perpendicular if they intersect in right angles (90°).

- Lines of symmetry for a 2-dimensional figure occur when a line can be drawn across the figure such that the figure can be folded along the line into matching parts.

Connections to Upcoming Units

- Formulas for area and volume can be applied to solve real world problems.

- A rectangle can be decomposed into two congruent triangles. Therefore, the area of the triangle is ½ the area of the rectangle.

Later Grades:

- The independent variable is the variable that can be changed; the dependent variable is the variable that is affected by the change in the independent variable.

- The independent variable is graphed on the x-axis; the dependent variable is graphed on the y-axis.

- There are four quadrants in the Cartesian Coordinate System. The quadrant for a given ordered pair can be determined based on the signs of the coordinates.

- A net is a two-dimensional representation of a three-dimensional figure.

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Key Terms / Vocabulary

adjacent, attribute, category, common denominator, corresponding terms, corresponds, cubit, decrease, equilateral triangle, fathom, formula, hierarchy, great span, increase, isosceles triangle, joint, kite, natural measure, parallel, parallelogram, partial products, partial-products multiplication, polygon, precision, property, quadrilateral, rectangle, relationship, rhombus, rule, sequence, square, standard unit, subcategory, term, tick mark, tiling, trapezoid, unit fraction, vertex, right angle, acute angle, obtuse angle, scalene triangle, pattern, product, area, length, width


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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Lesson Plan Sequence

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.

Gr 5 Unit 7: Multiplication of Mixed Numbers; Geometry; Graphs
Monitoring Student Work Tool
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Language Support

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.

Language Objectives & Sentence Stems
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