• TOC
  • Courses
  • Blog
  • Twitch
  • Shop
  • Search
    • Courses
    • Blog
    • Subreddit
    • Discord
    • Log in
    • Sign up
    • ▾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 › Time, measurement, and data

    Scaled bar and picture graphs

    First, students will learn how to make picture graphs.

    Creating picture and bar graphs by Khan Academy

    Create picture graphs (picture more than 1) by Khan Academy

    Next, students will learn how to solve basic word problems that involve reading a picture graph.

    Solving problems with picture graphs by Khan Academy

    Read picture graphs by Khan Academy

    After that, students will learn how to solve multi-step word problems that involve reading a picture graph.

    Watch these Khan Academy videos:

    • Interpreting picture graphs: paint
    • Interpreting picture graphs: notebook

    Read picture graphs (multi-step problems)

    Next, students will learn how to choose an appropriate scale for picture graphs. For example, if the data contains 25, 75, 100, 150, 200, the appropriate scale would be 25.

    Outside of math education, I have only seen pictograms and picture graphs with whole numbers of objects. For example, 1 in 9 people might be represented by 8 people being grayed out. I have never seen a quantity depicted by halves of shapes, such as in this video, and this one. Should we teach picture graphs with half shapes?

    Next, give your students this challenge:

    Six to Four by NRICH

    Conclude by leading this investigation:

    The Broken Sword (addition, division, mini-mathematical universe)
    by MathPickle

    3.MD.B.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

    Additional lessons and practice problems