Math // Data & Statistics

Picture & Bar Graphs

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph

Ages
7 to 8
Type
Representation
Builds on
1 topic
Leads to
1 topic
Standards
1 code

Quick check

Can the learner draw a simple bar chart or picture graph to show information — like how many of each colour of sweet are in a bag — and answer questions from it?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Draw a picture graph with a symbol representing one unit for each data point
  • Draw a bar graph with labelled axes and a single-unit scale
  • Use a bar graph to answer comparison questions (e.g. 'How many more votes did cats get than dogs?')

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

1 topic

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Picture & Bar Graphs

Ages 7 to 8 // Representation

Leads to

1 topic

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 7-8, learners draw picture graphs (one symbol = one unit) and bar graphs (labelled axes, single-unit scale) with up to four categories, then use the finished graph to solve put-together, take-apart and compare ('how many more') problems. The core skill is translating both ways: from organised counts to a scaled visual, and from the visual back to a count that answers a question. Teaching builds the graph from the children's own data, insists on equal-width bars rising from a common baseline read against the scale, and models 'how many more' as the difference (the gap) between two bars rather than the taller bar's value.

Common misconceptions

  • Answers 'how many more' with the taller bar's value instead of the difference between the bars
  • Reads a bar's value off by one (counts gridlines instead of the value the top reaches, or bars not starting at zero)
  • Draws bars of unequal width, floating off the baseline, or unevenly spaced, so height no longer means count
  • Draws picture-graph symbols of different sizes or unaligned, so rows can't be compared by length

Useful representations

  • Bar graph with single-unit scale on squared paper
  • Picture graph with one symbol per unit, aligned in rows
  • Two bars aligned to show the difference for 'how many more'
  • Frequency table as the source the graph is drawn from

Teaching practices

  • Build the graph from data the children collected, mapping each unit to one square/symbol so height means count
  • Insist on the grammar of a bar graph: equal-width bars, common baseline, evenly spaced, axes labelled, single-unit scale
  • Read values by tracking the bar top across to the scale, and model comparison as the difference between two bars
  • Pose put-together (combine two categories), take-apart and compare ('how many more') problems on the finished graph

Activities to try

  1. 1

    Build a bar graph from our data on gridded paper

    Why it works: Height means count: a bar's top read against the scale gives the number of items in that category. This only works if every bar starts from the shared zero baseline. Equal widths keep the bars fair to compare by eye, so that only height carries the count.

    1. Collect or use a given data set with up to four categories (e.g. favourite pets: cats 9, dogs 6, fish 4, birds 2)
    2. On squared/gridded paper or a gridded canvas, draw one bar per category, shading one square per unit so each bar's height equals its count
    3. Keep every bar the same width, rising from a common baseline (zero line), evenly spaced, and label both axes with a single-unit scale
    4. Read a chosen bar's value back by tracking its top straight across to the scale number, and check it matches the original count
  2. 2

    'How many more' as the gap between two bars

    Why it works: A comparison answer is the difference between two bars (the gap at the top), not the height of the taller bar; put-together and take-apart questions use the same read-the-scale skill with addition or subtraction.

    1. On a finished bar graph, pick two categories and state a comparison question, e.g. 'how many more children chose cats than dogs?'
    2. Line the two bars up side by side and count the squares by which the taller bar sticks up above the shorter one
    3. Write the answer as a subtraction, e.g. cats 9 − dogs 6 = 3, and say in words that 3 is 'how many more'
    4. Repeat with a put-together question ('how many chose cats and dogs together?') and a take-apart question ('15 children chose cats or dogs; use the cats bar to find how many of them did NOT choose cats, then check with the dogs bar') to practise combining and separating counts
  3. 3

    Picture graph with uniform, aligned symbols

    Why it works: Symbols must be uniform and aligned so that a row's length faithfully represents its count; 'how many more' is still the difference between the two counts, read as the extra symbols in the longer row.

    1. Represent the same data as a picture graph, placing exactly one equal-sized symbol per unit in each category's row
    2. Align symbols in rows so the length of a row can be compared at a glance
    3. Read a category's count by counting its symbols, and answer a 'how many more' question by lining up the two rows and counting only the EXTRA symbols in the longer row (the difference, not the longer row's total)
    4. Discuss what goes wrong if symbols are different sizes or not lined up

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
2.MD.10

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