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Representing numbers with objects (age 8+)

REPRESENTATIONAL
Mathematics›Data & Statistics|Ages 8—9|ID: mt_r8XnXwRA6g

Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables

Mastery Evidence

  • Draw a bar graph where each square represents 5 pets
  • From a scaled pictogram, answer: how many more children chose football than tennis?
  • Solve a two-step problem: how many votes in total for the top two choices?

Assessment Prompt

“If [child] looked at a bar chart showing how many books different children read last month, could they work out the total, find the difference between the most and least, and draw their own chart with a scale like "each square = 2 books"?”

Prerequisites3

Show full prerequisite tree
  • Pictograms and tally charts hard

    Constructing simple pictograms/tables is prerequisite to scaled versions

    • Pictograms and tally charts (age 6+) hard

      Constructing pictograms, tally charts, and bar charts requires these display vocabulary terms

    • Sorting into categories hard

      Constructing pictograms and tally charts requires classifying and counting objects first

      • Comparing groups: more or fewer soft

        Sorting categories by count benefits from ability to compare quantities

        • Counting objects to 20 soft

          Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

          • How Many in Total? hard

            Answering 'how many?' requires the cardinality principle

            • One-to-one counting hard

              Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • One-to-one counting hard

            Counting objects to answer 'how many?' requires one-to-one correspondence

      • Counting objects to 20 hard

        Counting objects in each category requires being able to count sets of objects

        • How Many in Total? hard

          Answering 'how many?' requires the cardinality principle

          • One-to-one counting hard

            Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

        • One-to-one counting hard

          Counting objects to answer 'how many?' requires one-to-one correspondence

    • Sorting Data into Categories soft

      Data representation formats (pictograms, tally charts) support organising data

      • How Many in Total? soft

        Counting data in categories requires understanding cardinality

        • One-to-one counting hard

          Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

      • Pictograms and tally charts (age 6+) hard

        Organising and representing data requires data, tally, frequency, and category vocabulary

      • Sorting into categories hard

        Organising data in categories builds on classifying and counting objects in categories

        • Comparing groups: more or fewer soft

          Sorting categories by count benefits from ability to compare quantities

          • Counting objects to 20 soft

            Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

            • How Many in Total? hard

              Answering 'how many?' requires the cardinality principle

              • One-to-one counting hard

                Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

            • One-to-one counting hard

              Counting objects to answer 'how many?' requires one-to-one correspondence

        • Counting objects to 20 hard

          Counting objects in each category requires being able to count sets of objects

          • How Many in Total? hard

            Answering 'how many?' requires the cardinality principle

            • One-to-one counting hard

              Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • One-to-one counting hard

            Counting objects to answer 'how many?' requires one-to-one correspondence

  • Pictograms and tally charts (age 6+) hard

    Drawing scaled bar charts and pictograms requires axis, scale, label, and frequency vocabulary

  • Picture & Bar Graphs hard

    Single-unit bar graphs are prerequisite to scaled bar graphs

    • Sorting Data into Categories hard

      Drawing picture/bar graphs extends organising and representing data

      • How Many in Total? soft

        Counting data in categories requires understanding cardinality

        • One-to-one counting hard

          Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

      • Pictograms and tally charts (age 6+) hard

        Organising and representing data requires data, tally, frequency, and category vocabulary

      • Sorting into categories hard

        Organising data in categories builds on classifying and counting objects in categories

        • Comparing groups: more or fewer soft

          Sorting categories by count benefits from ability to compare quantities

          • Counting objects to 20 soft

            Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

            • How Many in Total? hard

              Answering 'how many?' requires the cardinality principle

              • One-to-one counting hard

                Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

            • One-to-one counting hard

              Counting objects to answer 'how many?' requires one-to-one correspondence

        • Counting objects to 20 hard

          Counting objects in each category requires being able to count sets of objects

          • How Many in Total? hard

            Answering 'how many?' requires the cardinality principle

            • One-to-one counting hard

              Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

          • One-to-one counting hard

            Counting objects to answer 'how many?' requires one-to-one correspondence

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