27.3 Data Analysis and Probability
Key Takeaways
- PECT 0012.8 tests strategies, materials, tools, and technologies for data analysis and probability: collect, organize, represent, and interpret data, and describe chance with likely/unlikely/certain/impossible plus simple experiments.
- PreK–4 representations run object graphs → picture graphs → tally charts → bar graphs → line plots (Grade 2–4); scaled bars and fractional line plots are later-elementary, not the first display.
- Questions about data — how many, how many more, how many fewer, what is most/least common — are the interpretation target; a decorated graph with no question is not 0012.8.
- Probability at this grain is certain, likely, unlikely, and impossible, tested with a bag, spinner, or cube experiment; do not teach independent events, expected value, or high-school combinatorics.
- The typical PreK–4 summary of categorical class data is the mode (the most frequent category) and counts — the arithmetic mean is not a PreK–4 requirement and is the over-teaching trap.
27.3 Data Analysis and Probability
Quick answer: PECT 0012.8 tests strategies, activities, teaching materials, tools, and technologies that support PreK–4 data analysis and probability. Children collect, organize, represent, and interpret data with object graphs, picture graphs, bar graphs, tally charts, and line plots (line plots at Grade 2–4 grain). They ask questions about data. Probability is likely / unlikely / certain / impossible plus simple experiments. The mean is not required for PreK–4 typically — mode and category counts are the honest summary. Do not over-teach high-school statistics.
Plan from PA Core CC.2.4 Measurement, Data, and Probability (measurement itself sat on 0012.7; this descriptor is data and chance). PreK–Grade 2 also uses data ideas inside Mathematical Thinking and Expression in the 2024 Pennsylvania Learning Standards for Early Childhood. Pearson did not publish a count of 0012.8 items. Module 3 is 45 selected-response questions covering 0012–0014 together.
Collect, organize, represent, interpret — in that order
Data work is a cycle, not a coloring page of a pre-drawn bar graph.
- Ask a question children can actually answer (What fruit did you bring? How many people in your household? How long is your pencil to the nearest inch?).
- Collect with a real set: cubes, sticky notes, a show of hands, a survey clipboard.
- Organize — sort, tally, order.
- Represent — choose a display that matches the grain.
- Interpret — answer how many, how many more/fewer, what is most/least common, and what this does not tell us.
If children never asked a question, they are decorating. If they never interpret, they are coloring bars.
| Display | What it is | Typical grain | Watch-for |
|---|---|---|---|
| Object graph | The actual objects (shoes, apples, cubes) in rows or columns | PreK–K, still useful later | Objects must be one-to-one and lined up from a baseline |
| Picture graph (pictograph) | Pictures stand for objects | Grade 1–2; scaled pictures (one apple = 2 votes) later | A key that says 1 picture = 2 must be taught, not assumed |
| Tally chart | Marks in fives | Grade 1–2 | Crossing the fifth tally is the structure; random slashes are not tallies |
| Bar graph | Bars from a baseline; one axis categories, one axis counts | Grade 1–3; scaled bars (1 square = 2 or 5) Grade 3 | Bars same width; baseline at 0; title and labels |
| Line plot | Xs (or marks) above a number line | Grade 2–4; Grade 4 can use fractional units | It is not a line graph of change over years |
Line plot vs line graph (hard trap). A line plot is a number-line display of how many of each measurement (X X X above 4 inches). A line graph of temperature across a week is a different representation, sometimes used in science weather work, not the Grade 2 PA Core data display. If a stem says line plot, think Xs on a number line.
Circle/pie graphs are not the PreK–4 workhorse. They require part-whole fraction sense that is still growing. A colorful pie is not automatically better than a bar. Histograms, box plots, scatter plots, and two-way relative-frequency tables are later. Do not put them on a kindergarten menu to look rigorous.
Worked example: a Grade 2 fruit graph
The class asks, Which fruit did we choose for snack? Twenty children vote.
| Fruit | Tally (groups of five) | Count |
|---|---|---|
| Apples | five-bar and 3 | 8 |
| Bananas | five-bar | 5 |
| Grapes | 4 marks | 4 |
| Oranges | 3 marks | 3 |
| Total | 20 |
They build an object graph (real fruit or cubes), then a picture graph (one fruit picture = 1 vote), then a bar graph with fruit names on the bottom and counts up the side from 0 to 8.
Questions that are 0012.8 interpretation:
- How many children chose apples? 8
- Which fruit was chosen most? Apples (that is the mode — the most frequent category)
- How many more chose apples than oranges? 8 − 3 = 5
- How many chose apples or bananas? 8 + 5 = 13
- How many children voted? 20 (check against the class list)
- Did anyone choose pears? 0 — that category is not in the display; do not invent a bar
What not to ask yet: What is the mean fruit? Averaging 8, 5, 4, and 3 to get 5 apples-worth of fruit is a nonsense mean on categorical data. Even on numerical data (pencil lengths), the arithmetic mean is typically a later-grade statistic in PA Core. PreK–4 summaries are counts, comparisons, and the typical category (mode). Grade 4 line plots of measurements may ask how many are at a value and how many more; they do not require mean-median-mode-range as a four-pack.
A Grade 2–4 line plot of pencil lengths (nearest inch) might show Xs: 4, 4, 5, 5, 5, 5, 6, 6, 7. Questions: How many pencils are 5 inches? 4. How many are 6 or longer? 3. What is the shortest? 4 inches. That is 0012.8. Computing the mean length as 5.22 and calling it the typical pencil is the over-teach.
Probability — language and simple experiments
Chance in PreK–4 is vocabulary plus a trial, not a sample-space listing of 36 dice outcomes.
| Word | Meaning | Child example |
|---|---|---|
| Certain | It will happen | Drawing a cube from a bag that holds only cubes |
| Likely | Chance is high, not guaranteed | 9 red and 1 blue: drawing red is likely |
| Unlikely | Chance is low, still possible | Drawing the 1 blue |
| Impossible | It cannot happen | Drawing green from a bag with only red and blue |
| Equally likely (later primary) | Same chance | A fair 2-color spinner split in half |
Simple experiments: a bag of colored cubes, a two- or three-section spinner, a coin (heads/tails), a number cube with 1–6 as which is more likely only when the faces are not equally represented (a cube with five 1s and one 6 makes 1 likely). Record tallies of 10 pulls with replacement so the bag does not silently change. Compare the tally to the prediction: likely events can still miss in a short run — that is chance, not a broken bag. Do not teach independent vs dependent events, permutations, combinations, expected value, or conditional probability. Those are high-school stats dressed as rigor.
Connect data to chance. After 20 fruit votes, it is impossible that the next child in this class chose a fruit that was not offered; it is likely they chose an apple if the class is similar tomorrow — but tomorrow is a new collection. Keep the language honest. Do not say apples are certain because they won yesterday.
Developmental grain
| Age band | Honest data and chance | Too abstract |
|---|---|---|
| PreK–K | Sort real objects into rows; count which row is more; certain vs impossible with a bag you can see | Mean, pie charts, percent |
| Grade 1–2 | Tally, picture graph, bar graph, how-many-more; likely/unlikely with a visible bag | Scaled graphs as the first display; line graphs of decades |
| Grade 3–4 | Scaled bar graphs; line plots of measurements; simple experiments with a recorded tally | Mean-median-mode-range battery; box plots; theoretical probability as fractions of equally likely outcomes as the only entry |
Scenarios
PreK. Children take off one shoe and make two rows: sneakers vs other. They see which row is longer. Object graph; more/less; no bar-graph template.
Grade 2. The fruit vote above, then a bag with 8 red and 2 yellow cubes. Children predict yellow is unlikely but possible, pull 10 times with replacement, and tally. One group pulls yellow twice and wants to call yellow likely. The teacher returns to the bag composition — the experiment was a short run, not a rewrite of likely.
Grade 4. Pencil-length line plot; scaled bar graph of how we travel to school (1 square = 2 children); a spinner with three equal sections for a fair game and a spinner with a tiny slice for a not-fair game. Still no mean of travel modes.
English learners and children with IEPs still collect. Real objects, picture keys, and a partner placing Xs on the line plot keep the target. A completed adult-made histogram is not an accommodation if the child never sorted.
Exam traps for 0012.8
- A pre-drawn graph with no collection and no question.
- Mean (or median/range batteries) on favorite color or other categories.
- Treating line plot as a line graph.
- Pie charts, histograms, box plots as the PreK–4 default.
- Probability as percent, combinations, or expected value.
- Calling an unlikely event impossible because it did not happen in five trials.
- Dumping 0012.7 measurement formulas or 0012.6 operations into a data stem (operations serve how-many-more; they are not the objective).
Plan: Children will ask [question], collect [objects or votes], show them on [object/picture/bar/tally/line plot], and answer [how many / how many more / what is typical]. For chance, they will use [bag/spinner] to sort events as certain, likely, unlikely, or impossible. If you only have a mean formula or a decorative pie, you are not yet teaching 0012.8.
Which sequence best matches PreK–4 data analysis on 0012.8?
A bag holds 8 red cubes and 2 yellow cubes. A Grade 2 child will draw one cube. Which statement best matches PreK–4 probability language?
After the 20 fruit votes (apples 8, bananas 5, grapes 4, oranges 3), which summary best matches typical PreK–4 data analysis?