Illinois Grade 4 Math

An array can show why two whole numbers are factors of a total. Looking for every possible rectangular arrangement also helps students explain why the list is complete. This activity connects multiplication, divisibility, and number classification through twenty-four counters.

Try the worked activity

Arrange 24 counters in complete rectangular arrays with whole-number rows and columns. List all factor pairs without repeating rotations, explain why 24 is composite, and decide whether it is a multiple of 6.

Follow the reasoning

The arrays give 1 × 24, 2 × 12, 3 × 8, and 4 × 6. Reversing each array changes its orientation but repeats the same pair. Testing five does not produce a whole-number partner. By six, the partner four repeats a pair already found; larger row counts produce reversed pairs rather than new ones. The factors are 1, 2, 3, 4, 6, 8, 12, and 24. Because 24 has factors besides one and itself, it is composite. It is a multiple of six because 6 × 4 = 24.

Check the explanation

A factor is a whole number that divides 24 evenly in this setting. A multiple is a product such as 24 or 48 in the sequence of multiples of six. The two words describe different relationships. One complete array is not enough to classify a number as prime: every positive whole number has a one-row array. Also remember that one has exactly one positive factor and is neither prime nor composite; it is an important exception to an overly broad rule about having no factor other than one and itself.

Use the next session

1. Build or draw a complete array for a possible row count.
2. Record its whole-number partner and avoid duplicate rotations.
3. Use the factor list to justify the number’s classification.

Test 23 counters. Check possible row counts through four and explain why no new complete pair appears before the partners would reverse; its only positive factor pair is 1 and 23, so it is prime. Then compare 23 with 24 and explain why their nearby positions on the number line do not determine their classifications. Ask whether 24 is a multiple of five and justify the answer with whole-number multiplication or division. Extend the investigation within the official one-to-one-hundred range, explaining the completeness of each list rather than memorize a classification.

Selected references from Illinois’s adopted mathematics document

The Illinois mathematics standards directory links the Illinois Learning Standards document incorporating Common Core. These selected references identify the worked activity’s focus. The expectations include numbered requirements, examples, and mathematical practices. Read the full document and confirm the school’s current instructional sequence.

Sources checked October 6, 2026. Read complete requirements, clarifications, limitations, and mathematical practices alongside the school’s sequence. This selected activity is an entry point for instruction.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; open each activity’s directions to understand its timer, tools, question count, and scoring.

Grade 4 is within Illinois’s IAR mathematics testing range. The linked learning resources have their own directions and scoring; a practice score does not establish an official state performance level. Read Illinois’s assessment overview.

Keep one example of the student’s reasoning with the practice result. Choose a smaller model, a related question, or a new context according to the difficulty revealed in the worked activity.