The worksheet presents three completed representation cards: three groups of 4, four groups of 3 using the same 12 counters, and a separate unequal 4/4/3 case. Local checks compare the group interpretation and product with the displayed arrangement, while the explanation remains for teacher discussion.
State what each factor means here
For this activity, the first factor means number of groups and the second means counters in each group. That is the displayed convention for these cards, not a universal notation rule. Illustrative Mathematics connects equal groups and arrays to expressions and asks how the drawing matches the equation. This activity uses original counter layouts rather than its diagrams or exercises.
Teacher-confirm the vocabulary, level and access arrangements. Boundaries and text labels identify the groups without depending only on color. Keep actual learner fields blank at the start, and separate the teacher reference from the attempt. Read the arrangement before showing its matching expression.
Read three trays of four
M1 places C01–C04 in Tray 1, C05–C08 in Tray 2 and C09–C12 in Tray 3. There are three groups, each containing four. Repeated addition is 4 + 4 + 4 = 12; the activity expression is 3 × 4 = 12. Every counter ID appears once.
If a learner enters four groups of three for this card, the product still equals 12, but the tray description does not match. Feedback should ask the learner to count tray boundaries and then count one tray. This gives the teacher a representation question instead of an unsupported conclusion about the learner's overall ability.
Rearrange the same twelve counters
M2 forms four rows: C01/C05/C09, C02/C06/C10, C03/C07/C11 and C04/C08/C12. All twelve IDs remain. The rows now give four groups of three, with 3 + 3 + 3 + 3 = 12 and 4 × 3 = 12 under this activity's convention.
Compare M1 and M2 with the product covered. The grouping descriptions differ while the object set and total stay the same. The text lists let a reviewer check that no counter was added or lost during the rearrangement. Switching cards loads the correct boundaries and question instead of reusing a previous card's feedback.
Give unequal groups their own response
M3 is a separate eleven-counter example: its trays contain 4, 4 and 3 counters. Three trays are present, but no single count applies to all of them. Choose “Unequal groups” instead of forcing a counters-each number. The total is 4 + 4 + 3 = 11.
Three equal groups of four would require 12 counters, one more than M3 contains. Do not describe M3 as M1 rotated with a counter disappearing; it is its own card. Ask which tray prevents the proposed 3 × 4 model from fitting. The teacher key explains that the third tray has 3, not 4.
Keep the attempt tied to the card
Enter groups, items each or unequal, total and a brief reason, then use Check representation. Blank required fields remain unanswered. Changing an answer clears the prior feedback for that card; a fresh check uses current entries. Checking the same item twice is not a fourth worksheet task.
The key gives expressions and repeated-addition references for M1 and M2; M3 instead shows its unequal counts, total, and why 3 × 4 does not fit. The explanation field is not semantically graded, and a matched total does not prove the written reasoning. Reset clears all attempts and teacher-reveal state, leaving the original three cards intact. Maintain any actual responses and teaching decisions in the school's required record rather than relying on temporary page state.
Copy this prompt
Create a complete original HTML example in US English for this task: Interactive multiplication worksheets. Return one self-contained HTML file. Include all styles, data and JavaScript in the file. Use no remote dependencies. Return the working page, not an outline.
M1 three trays C01–C04/C05–C08/C09–C12: groups 3, each 4, total 12, 3 × 4, 4 + 4 + 4. M2 same 12 IDs in rows C01, C05, C09; C02, C06, C10; C03, C07, C11; C04, C08, C12: groups 4, each 3, total 12, 4 × 3. M3 separate C01–C11 with tray counts 4, 4, 3: groups 3, unequal, total 11. First factor groups, second each is a local convention.
Draw original labeled trays/rows and individual counter IDs, with equivalent text lists. Use buttons for M1–M3. Ask for group count, items each or an explicit unequal-groups choice, total and reasoning. Check only fixed representation fields. Explain expressions and repeated addition for M1/M2; for M3, show unequal counts 4/4/3, total 11, and reject 3 × 4. A correct total with reversed group interpretation needs targeted feedback. Checking a completed fixed-field attempt reveals that card’s reference in feedback, including after an incorrect attempt. A separate Teacher reference disclosure can also reveal it explicitly. Do not grade prose. Blank remains unanswered, edits clear feedback, card changes restore that card’s own attempt, reset clears all. No timed facts, streaks, invented extra counter, persistence, grading service or actual class results.
Use a page design suited to this particular task, readable text at least 16 px, generous spacing, visible keyboard focus and explicit labels. At 360 px, stack the content without page-level horizontal scrolling. Use type="button" click handlers for actions. Keep source facts and sample results distinct from actual observations. Leave unknown details visible rather than inventing them. Controls update only this temporary page; distinguish local changes from actual records. Provide concise task-specific feedback and a reset that clears entered answers and stale results.
Rebuild the groups with the counters
Give learners the same twelve labeled counters and ask them to rebuild M1 as M2. While preparing the counter activity with a colleague, render the HTML group diagrams in NOS to compare those two arrangements. Record both the number of groups and the number in each group. Then show M3 and ask which tray prevents an equal-group description and how many counters would be needed to change that.