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    • ▾5th grade
      • ▸Decimal place value
        • •Decimal place value
        • •Hashi puzzles
        • •Decimals to thousandths
        • •Rounding decimals
      • ▸Multi-digit multiplication and division
        • •Multiplying whole numbers by 10, 100, and 1000
        • •Multiplying and dividing decimals by 10, 100, and 1000
        • •Convert fractions to decimals, 10, 100, or 1000 in the denominator
        • •Multiplication, partial products method
        • •Long division
      • ▸Decimal arithmetic
        • •Decimal arithmetic
        • •Dividing whole numbers to get a decimal
      • ▸Add and subtract fractions
        • •Add and subtract fractions, abstract
        • •Adding and subtracting mixed numbers with regrouping
        • •Add and subtract fractions, word problems
      • ▸Multiply fractions
        • •Multiplication as scaling
        • •Areas and perimeters, fractional side lengths
        • •Multiply fractions, abstract
        • •Multiply fractions, word problems
      • ▸Divide fractions
        • •Understanding fractions as division, word problems
        • •Dividing whole numbers by unit fractions
        • •Dividing unit fractions by whole numbers
        • •Dividing mixed numbers
      • ▸Volume
        • •Volume by counting unit cubes
        • •Volume of right rectangular prisms by multiplying
        • •Volume of composite right rectangular prisms
        • •Volume, word problems
      • ▸Coordinate plane
        • •Plot coordinates
        • •Plot coordinates from word problems
      • ▸Algebraic thinking
        • •Intro to parentheses
        • •Distributive property without variables
        • •Convert between words and arithmetic expressions
        • •Linear equations, tables
      • ▸Measurement and data
        • •Unit conversion
        • •Represent and reason with line plots
      • ▾Properties of shapes
        • •Geometric definitions
        • •Classifying shapes
        • •Classifying triangles
        • •Classifying polygons
        • •Symmetries of regular polygons
        • •Quantifiers
     › 5th grade › Properties of shapes

    Geometric definitions

    Students will learn the distinction between lines, line segments, and rays. Then students will learn how to identify them in figures. After that, students will learn the distinction between parallel and perpendicular lines. Then students will learn how to identify them in figures. Students should also learn how to identify right triangles and non-right triangles. This topic is our first formal definition of parallel. Previously, parallel was understood informally to recognize trapezoids. Conclude by giving your students this challenge. Its only prereq is understanding lines of symmetry.

    Watch these Khan Academy videos:

    • Parallel & perpendicular lines intro
    • Parallel & perpendicular lines
    • Lines, line segments, & rays
    • Acute, right, & obtuse angles
    • Recognizing angles
    • Drawing parallel line segments
    • Classifying quadrilaterals

    Do these Khan Academy exercises:

    • Identify parallel and perpendicular lines
    • Identify points, lines, line segments, rays, and angles
    • Angle types
    • Recognize angles in figures
    • Types of angles by measure
    • Draw parallel and perpendicular lines
    • Properties of shapes

    Next, give your students this challenge:

    Domino Pick by NRICH

    Conclude by leading this investigation:

    Life expectancy in different countries
    by MathPickle

    4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

    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.

    Lessons and practice problems