Measure a collection, record what was measured, organise the results and ask a question the records can actually answer. This investigation joins two familiar Primary 1 topics—length and picture graphs—without treating them as unrelated worksheet chapters. It gives the child a reason to align a ruler carefully: an inaccurate measurement will affect the record, the category and the final graph.
This page is a practical companion to the length and scale-reading guide and the picture-graph interpretation guide. It belongs to the Primary 1 Mathematics Learning Hub. The earlier guides explain the topic foundations; this investigation provides a complete classroom sequence, a worked dataset, checks and independent practice.
The twelve-strip dataset below is a constructed teaching example, not a report of measurements made by eduKate pupils. A real group can measure its own strips and obtain different results. The important requirement is that every result can be traced back to an identified object and a stated unit.
Curriculum boundary and purpose
Primary 1 includes length in centimetres and reading picture graphs. Building a graph from a measured collection is used here as a teaching application, not presented as a separate compulsory assessment requirement. Consult the MOE primary mathematics syllabus, Primary One section, for the official topic scope.
The investigation has three distinct questions. How long is each strip? How many strips fall into each length category? What comparisons can we make from those records? The first answer uses centimetres; the second uses a count of strips. Keeping these units separate is one of the central mathematical jobs.
Do not try to complete the whole article in one sitting. Use measuring and recording as one session, sorting and graphing as another, and interpretation or error analysis as a later session. The suggested division is a practical option, not a claim that every child needs the same lesson duration.
Prepare a collection that can be checked
An adult prepares twelve paper strips with straight ends and labels them A to L. Keep the labels away from the edges that will be aligned to the ruler. The letters identify objects; they are not algebraic variables. A child should be able to pick up strip F and match it to the record for F.
Use a centimetre ruler and a flat surface. Real paper strips should be measured physically. Do not ask a learner to measure the apparent length of a picture on a phone or computer screen: display size and zoom change the visible length. The numerical examples on this page are stipulated data, not a printable scale drawing.
Prepare a recording sheet with three columns: strip label, first measurement in cm, and checked measurement in cm. Add a short notes area for a disagreement or a method correction. A record of an amended measurement is useful; silently erasing the original can hide the reason a later graph changed.
For a simpler start, use six strips rather than twelve. Keep the same relationship between object, label, measurement and record. Increasing the number of objects should not be used to compensate for an unclear measuring procedure.
Session 1: Establish the two endpoints
Place one end of a strip at the zero mark of the ruler and keep the scale alongside the strip. Locate the other end before reading its position. If the strip ends at nine centimetres, its length is nine centimetres. Say both the number and the unit.
Check that the starting point is the printed zero, not necessarily the physical edge of the ruler. Some rulers have extra material before zero. Starting from the edge can produce a different reading even if the learner counts accurately along the printed scale.
Now place an eight-centimetre strip from the three-centimetre mark to the eleven-centimetre mark. The endpoint is eleven, but the length is eight. Count the intervals from three to eleven or calculate 11 − 3 = 8. Then move the same strip back to zero and verify the eight-centimetre endpoint.
The movement separates position from length. The strip has moved, so its endpoints on the scale changed. Its physical length did not change. This is the same distance idea developed in the number-line guide.
Count intervals rather than printed marks
From the two-centimetre mark to the seven-centimetre mark there are five one-centimetre intervals. The labelled marks include two, three, four, five, six and seven, but counting those six positions does not give the distance. The distance is measured by the five spaces between successive positions.
Ask the learner to trace each interval with a finger or pencil above the ruler. One interval takes the count from two to three; the fifth finishes at seven. This makes the start an identified position rather than an extra unit of length.
A deliberate wrong example can help: an adult says the strip is six centimetres because six numerals are visible. Ask the learner to show the error. A correct explanation identifies the difference between a scale mark and the interval it helps delimit.
Nearest centimetre without pretending every object is exact
Some real strips will end between whole-centimetre marks. For a nearest-centimetre measurement, inspect which whole-centimetre mark is closer. If the endpoint is between eight and nine and clearly nearer nine, record approximately nine centimetres for that measurement task.
Avoid awkward halfway cases in the introductory collection. They introduce a recording convention that can distract from learning to align and read the ruler. If a real endpoint is difficult to judge, record the uncertainty and recheck the position rather than turning an uncertain observation into a confident exact value.
A rounded measurement is not a claim that the physical object is exactly that many centimetres long. For this investigation, category assignments will use the recorded whole-centimetre values. State that convention before graphing so that the categories are applied consistently.
Session 2: Record before comparing
Let the learner measure one strip, say the result and place it beside the matching label on the recording sheet. Only then move to the next strip. This procedure keeps the identity of the object connected to its measurement.
When a partner checks a strip, the partner should read the scale independently before comparing answers. Agreeing with a visible first answer is not the same as making a second measurement. If the two readings differ, inspect the starting point, alignment, endpoint and unit.
Do not resolve a disagreement by automatically choosing the larger value or taking a vote. The correct record depends on the object and measurement procedure. A clear method correction is more useful than an unexplained agreement.
For example, one learner records eleven centimetres and another records eight. The strip was placed from three to eleven. The eleven came from reading the endpoint as length. Repositioning the strip at zero or subtracting the start establishes eight centimetres. The correction has a mathematical reason.
The complete worked dataset
Use this stipulated dataset for the graph and practice questions. All lengths in this table are whole-centimetre teaching values. A class measuring its own collection should retain its own results rather than change them to match the example.
| Strip | Length in cm | Category |
|---|---|---|
| A | 3 | 1–5 cm |
| B | 4 | 1–5 cm |
| C | 5 | 1–5 cm |
| D | 6 | 6–10 cm |
| E | 7 | 6–10 cm |
| F | 8 | 6–10 cm |
| G | 8 | 6–10 cm |
| H | 10 | 6–10 cm |
| I | 11 | 11–15 cm |
| J | 12 | 11–15 cm |
| K | 12 | 11–15 cm |
| L | 14 | 11–15 cm |
Read the record in two directions. Given strip F, find its length: eight centimetres. Given a length of eight centimetres, find every strip with that value: F and G. This checks whether the learner can use the table as a record rather than simply read down a column.
Ask which strip is longest and which is shortest. Strip L is fourteen centimetres and strip A is three centimetres. Their difference is eleven centimetres. This is a comparison of lengths, not a count of how many objects appear in the table.
Session 3: Define categories before placing objects
The example uses three categories: recorded lengths from one to five centimetres, from six to ten centimetres, and from eleven to fifteen centimetres. The endpoints are included. Five belongs to the first category; ten belongs to the second; eleven begins the third.
These categories do not overlap for the whole-centimetre values in this dataset. Avoid labels such as “small” and “large” without a rule. Different readers may use those words differently. A category becomes checkable when the inclusion rule is stated.
Place the physical strips into three areas using their recorded values. Check each placement against its label on the table. A strip with a value of eight must not be counted twice just because another strip also measures eight. Equal lengths can belong to two different objects.
Count the objects in each category: A, B and C give three; D, E, F, G and H give five; I, J, K and L give four. The category counts add to twelve, matching the twelve strip labels. This checks the completeness of classification, not the accuracy of each original measurement.
Session 4: Build and read the picture graph
The graph below answers a specific question: how many strips fall into each recorded-length category? Each filled circle represents one strip. The circles do not each represent one centimetre. The numerical count column provides the same information in text.
| Length category | Picture row | Number of strips |
|---|---|---|
| 1–5 cm | ● ● ● | 3 |
| 6–10 cm | ● ● ● ● ● | 5 |
| 11–15 cm | ● ● ● ● | 4 |
The middle category contains the most strips because five is the largest frequency. The first category contains the fewest because three is the smallest frequency. This does not mean the middle category contains the longest strip. Frequency and length are different quantities.
There are two more strips in the middle category than in the first: 5 − 3 = 2. There are nine strips in the middle and final categories together: 5 + 4 = 9. Every answer here counts strips, even though the category names include centimetres.
Ask the learner to explain the title, a category label, a symbol and a numerical answer. If they answer that three circles means three centimetres, return to the key. The picture row counts objects whose lengths fall into a range; it does not draw the objects to scale.
What the graph preserves and what it loses
The table preserves each labelled strip’s recorded length. The grouped picture graph preserves only how many strips fall into each category. From the graph alone, we cannot recover whether the final category contains lengths eleven, twelve, twelve and fourteen or another set of four values within that category.
Therefore the exact longest length of fourteen centimetres comes from the table, not from the grouped graph alone. This is a useful boundary question. A learner should know which representation contains the information needed, rather than assuming every representation tells the whole story.
The graph also cannot establish the mass, colour or material of a strip. Those attributes were not recorded. There is no need to introduce advanced statistics to teach this limit: ask what was measured and what was merely imagined.
Session 5: Follow a correction through the investigation
Suppose an adult accidentally draws four symbols in the first category instead of three. The graph then totals thirteen while the table contains twelve objects. Comparing the graph with the record exposes the extra symbol. Remove the representation error from the classroom worksheet after identifying its cause.
Now consider a different hypothetical change. Replace strip H, previously ten centimetres, with a strip recorded as eleven centimetres, keeping the label H. The number of labelled strips is still twelve, but H moves from the middle category to the final category.
The new category counts are three, four and five. One category loses a member and another gains one. The total count remains twelve. This is not the same event as adding an extra strip to the collection, which would increase the total.
Record the changed measurement before redrawing the graph. That order preserves the evidence trail: object or measurement changes first, table changes next, category count changes next, and graph changes last. A graph should not be adjusted merely to make a preferred pattern appear.
Session 6: Ask a new question of the same records
Return to the original dataset. Ask how many strips are shorter than eight centimetres and how many are eight centimetres or longer. The first group contains A, B, C, D and E: five strips. The second contains F, G, H, I, J, K and L: seven strips.
The old three-category graph does not show this split directly because its middle category combines lengths on both sides of the new boundary. Return to the labelled table. The original records support a new classification without remeasuring the objects.
This demonstrates a practical reason to retain records. A summary can answer its intended question while being too coarse for a later one. The child need only understand that the first graph grouped some information together and the table kept the individual values.
Twenty practice questions
Questions about the labelled strips use the original twelve-strip dataset unless a change is explicitly stated. The hypothetical changes do not silently modify later questions. Read each question as its own task.
1. A strip begins at zero and ends at the nine-centimetre mark. What is its length?
2. A strip begins at three centimetres and ends at eleven centimetres. What is its length?
3. Another strip begins at four centimetres and ends at twelve centimetres. Compare its length with the strip in Question 2.
4. How many one-centimetre intervals lie between the two-centimetre and seven-centimetre marks?
5. A strip aligned at zero ends between eight and nine centimetres, clearly nearer nine. What is its measured length to the nearest centimetre?
6. You are drawing a seven-centimetre line starting at zero. At which centimetre mark should its other endpoint be?
7. Which labelled strip in the example table is longest, and how long is it?
8. Which labelled strip is shortest, and how long is it?
9. What is the difference between the longest and shortest recorded lengths?
10. How many labelled strips are recorded altogether?
11. How many strips belong to the 1–5 cm category?
12. How many strips belong to the 6–10 cm category?
13. How many strips belong to the 11–15 cm category?
14. How many more strips are in the middle category than in the first?
15. How many strips are in the middle and final categories together?
16. A graph shows four symbols in the first category although the table records three strips there. What correction is needed?
17. The first graph row has three symbols. Does that mean three strips or three centimetres? Use the key.
18. Which categories contain strip C at five centimetres and strip H at ten centimetres?
19. In a separate version of the task, H changes from ten to eleven centimetres and every other value stays the same. What are the three new category counts?
20. Using only the grouped picture graph, can you determine that the longest strip is exactly fourteen centimetres? Explain.
Explained answers
1. Nine centimetres. With the starting endpoint at zero, the ending position of nine corresponds to a nine-centimetre distance. The unit is part of the answer.
2. Eight centimetres. The length is the distance between the positions: 11 − 3 = 8. Eleven is the endpoint reading, not the length of an object that started at three.
3. The lengths are equal: eight centimetres each. Twelve minus four also equals eight. Different starting positions can represent the same distance.
4. Five intervals. Count two-to-three, three-to-four, four-to-five, five-to-six and six-to-seven. Counting both endpoint marks as units would count positions instead of intervals.
5. Approximately nine centimetres. Nine is the nearer whole-centimetre mark. The rounded record does not claim the object is exactly nine centimetres long.
6. Seven. A line from zero to the seven-centimetre mark has a length of seven centimetres. This should be drawn with a physical ruler, not inferred from the on-screen width of text.
7. Strip L, fourteen centimetres. The labelled table gives the individual measurements needed to identify the longest strip precisely.
8. Strip A, three centimetres. Three is the smallest recorded length. The answer identifies both the object and the measured value.
9. Eleven centimetres. Fourteen minus three equals eleven. This is a difference in length, so the unit is centimetres rather than strips.
10. Twelve strips. Labels A through L identify twelve separate objects. The total can also be checked by adding the category frequencies: 3 + 5 + 4 = 12.
11. Three strips. A, B and C have recorded lengths of three, four and five centimetres. Five is included in the first category.
12. Five strips. D, E, F, G and H fall in the middle category. F and G are distinct strips even though both have a recorded length of eight centimetres.
13. Four strips. I, J, K and L fall in the final category. Their four symbols represent four objects, not a combined length of four centimetres.
14. Two more strips. The middle frequency is five and the first frequency is three. Their difference is 5 − 3 = 2.
15. Nine strips. Combine the middle frequency of five and the final frequency of four. This question asks for a total across selected categories, not a difference.
16. Remove one extra symbol from that classroom graph. The first row should contain three symbols to match its three recorded objects. Check the other rows and the overall total as well.
17. Three strips. The key states that one symbol represents one strip. The centimetre range names the category; it does not change the symbol’s unit.
18. C belongs to 1–5 cm; H belongs to 6–10 cm. The category endpoints are included. The next categories begin at six and eleven respectively.
19. Three, four and five strips. H leaves the middle category and joins the final category. The first category remains three. The new total is still twelve because no additional labelled object has been introduced.
20. No. The grouped graph shows that four strips are in the 11–15 cm category, but it does not preserve their individual measurements. The exact maximum of fourteen centimetres is available from the table.
Read the error before choosing the repair
If Questions 1 to 4 fail, inspect alignment and the distinction between position and distance. Let the child move the same strip along the ruler and compare the resulting endpoint readings. A change in ruler position should not be mistaken for a change in physical length.
If measuring succeeds but graph totals do not match the table, inspect object identity and recording. One omitted strip or one duplicate label can affect several later answers. Do not repair only the final arithmetic while leaving an inconsistent dataset underneath it.
If the learner confuses centimetres with strips, point to a measured value in the table and a frequency in the graph. Ask what each number counts or measures. The two uses of number coexist in the investigation, so they need explicit labels.
If Question 20 is difficult, compare two different possible tables that share the same category frequencies. The graph can remain unchanged while the longest individual length changes within its category. This makes the information limit visible without requiring abstract statistical terminology.
A small-group and home version
In a small group, rotate the roles of measurer, recorder and checker. Every learner should eventually perform each role. The recorder should repeat the value and unit before writing; the checker should verify the procedure rather than approve the answer by habit.
At home, use fewer labelled paper strips or safe stationary objects with clear endpoints. Keep an original record, build one graph and ask one total question and one difference question. An adult may write the labels while the child supplies the mathematics; record that support when using the task to observe independence.
Stop and remeasure when the setup is unclear. The purpose is not to create a neat graph at any cost. It is to show how a representation earns its reliability through identifiable objects, units, consistent categories and checks against the original record.
For more on creating a dataset before graphing, use the data collection and picture-graph construction guide. Return to the Primary 1 Mathematics Learning Hub for the complete route.
