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    • ▾3rd grade
      • ▸Addition, subtraction, estimation
        • •Mentally add within 1000
        • •Round to the nearest 10 or 100
        • •Add and subtract within 1000, abstract
      • ▸Multiplication
        • •Multiplication using rectangular arrays and equal groups, concrete and visual
        • •Multiplication as repeated addition
        • •Multiply, abstract
      • ▸Division
        • •Divide using equal groups
        • •Division as repeated subtraction
        • •Divide, abstract
      • ▾Fractions
        • •Equal shares of shapes and unit fractions
        • •Plot fractions on the number line
        • •Relating fractions to 1
        • •Representing whole numbers as fractions
        • •Comparing fractions with like numerators, denominators, or both
      • ▸Relating multiplication and division
        • •Missing number problems, multiplication and division
        • •Relating multiplication to division
        • •Use properties to multiply and divide
        • •Multiply one-digit numbers by multiples of 10
      • ▸Arithmetic patterns and problem solving
        • •Two-step word problems
        • •Arithmetic and geometric sequences
        • •Patterns in addition and multiplication
        • •Intro to the triangular numbers
        • •Intro to the Fibonacci sequence
        • •Intro to Pascal's triangle
      • ▸Geometry
        • •Shape heirarchy
        • •Area of composite rectangles by counting unit squares
        • •Area and units of measure
        • •Area as multiplication
        • •Area, perimeter, and how they're related
      • ▸Time, measurement, and data
        • •Tell and write time, minute increments
        • •Measure and estimate volumes and masses
        • •Scaled bar and picture graphs
        • •Line plots with fractions
     › 3rd grade › Fractions

    Equal shares of shapes and unit fractions

    Students will learn how to determine whether circles, rectangles, and polygons are cut into equal parts, and if they are, what fraction is shaded. Also, students will learn how to identify which of several shaded figures represents a given a fraction. Conclude by giving this challenge, then this one. That last problem mentions regular hexagons, but it's not essential to the problem. You could say that every tile is the same, without mentioning "hexagons."

    Watch these Khan Academy videos:

    • Intro to fractions
    • Cutting shapes into equal parts
    • Identifying unit fractions word problem
    • Recognizing fractions greater than 1
    • Recognize fractions
    • Identifying numerators and denominators

    Do these Khan Academy exercises:

    • Cut shapes into equal parts
    • Identify unit fractions
    • Fractions in contexts
    • Recognize fractions
    • Understand numerators and denominators
    • Recognize fractions greater than 1

    Conclude by leading this investigation:

    Dot to Dot Precise Measurement Puzzles
    by MathPickle

    3.NF.A.1: Understand unit fractions, such as 1/b, as the quantity formed by 1 part when a whole is partitioned into b parts. Understand a/b as a parts, each of size 1/b.

    3.G.A.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

    Lessons and practice problems