Graphs, Charts, and Tables
Warm-up
Display two graphs showing the same data: a bar graph and a pictograph. Ask: what is the same? (Same data.) What is different? (Visual format.) Which makes it easier to see which category is largest? (Bar graph.) Which is more visually interesting? (Pictograph.) Different formats serve different purposes.
Explore
Full data cycle: (1) Pose a class question, (2) collect data with tally marks, (3) organize in a table, (4) represent as a bar graph AND a pictograph, (5) compare the two representations, (6) answer 5 questions (Levels 1, 2, 3). Discuss: which representation made the questions easiest to answer?
Formalize
Scale introduction: if our pictograph shows 40 students but we only have space for 8 pictures, how many students does each picture represent? (40/8 = 5.) Each picture = 5 students. Now read: a category with 3 pictures has 3 x 5 = 15 students. Scale unlocks pictographs for larger data sets.
Graphs, Charts, and Tables
Graph critique: show a misleading bar graph (bars not starting at zero). Ask: does this look like twice as many? Let us check the actual numbers. The visual impression is wrong because the axis does not start at zero. Critical graph reading begins in Grade 3.
Practice
Students collect class data, build a bar graph and a pictograph, answer questions at all three levels, and write one sentence about what the data shows that surprised them. Exit ticket: a pictograph has 4 pictures with scale 1=3. What is the total?
Exit ticket
Students collect class data, build a bar graph and a pictograph, answer questions at all three levels, and write one sentence about what the data shows that surprised them. Exit ticket: a pictograph has 4 pictures with scale 1=3. What is the total?
Step 1: Collect the raw data — favourite season, recorded as an unordered LIST on the board exactly as votes arrive: summer, winter, summer, spring… (18 votes). Note how unreadable the raw list is: that's the point of what follows.
Step 2: Organize into a tally chart: summer 𝍸|| (7), winter 𝍸 (5), spring |||| (4), fall || (2). Now totals are countable — but comparisons still take effort.
Step 3: Draw the bar graph on grid paper: one axis lists seasons, the other counts (label it!), one grid square = 1 vote, bars drawn to exact height. NOW "summer beat fall by 5" is visible from across the room.
Step 4: Reflect on the pipeline: same 18 votes, three forms — the list REMEMBERS, the tally COUNTS, the graph COMPARES. Each step trades detail for readability (the graph no longer knows who voted third).
Exit: hand students a messy list of 20 items; produce all three forms and answer one comparison question from the graph alone.
The graph: books borrowed per weekday — Mon 12, Tue 8, Wed 15, Thu 8, Fri 20.
Level 1 (read the bars): "How many on Wednesday?" → 15. Warm-up only.
Level 2 (compute between bars): "How many more Friday than Tuesday?" → 20 − 8 = 12. "Which two days tied?" → Tue and Thu. "Total for the week?" → 12+8+15+8+20 = 63.
Level 3 (reason beyond the bars): "Why might Friday spike?" (Weekend reading ahead.) "The librarian can restock shelves on her quietest day — which should she pick?" (Tue or Thu.) "Predict next Monday." (Around 12 — IF weeks behave alike, an assumption worth saying out loud.)
The grading secret to share with students: level-1 questions check eyesight; level-2 check arithmetic; level-3 check THINKING. Every graph deserves all three interrogations — and level 3 answers must always name their assumption.
Setup: two bar graphs of the same juice-sales data (apple 10, grape 12). Graph A's count axis runs 0–14; graph B's runs 9–13, and suddenly grape's bar towers at TRIPLE apple's height.
Step 1: Read both graphs' actual numbers: identical data — 10 vs 12 in each. Verify by reading tops of bars against the axes.
Step 2: Find the trick: graph B's axis starts at 9, not 0. The bars show only the slivers ABOVE 9, so a difference of 2 masquerades as a landslide.
Step 3: The rule for honest Grade-3 graphs: the count axis starts at ZERO, so bar heights truly represent the amounts.
Step 4: Practice being un-foolable: give three published-style mini-graphs and ask "what impression does the PICTURE give? What do the NUMBERS say? Do they match?"
Why teach skepticism this young: students meet more graphs in ads than in math class. Checking the axis before believing the bars is a life skill wearing a math costume.