Montana Grade 4 Math

A factor pair gives two whole-number dimensions for an array with the same total. Use a systematic search so that finding one pair does not get mistaken for finding every pair. The original example below uses 18 counters.

Try this original activity

List every positive whole-number factor pair for 18. Use the pairs to list its factors and explain whether 18 is prime or composite. How do you know when the search starts repeating pairs?

Work through the reasoning

One row of 18 gives 1 × 18. Two rows of 9 give 2 × 9, and three rows of 6 give 3 × 6. Four and five do not divide 18 evenly. At six rows of three, the pair 6 × 3 reverses 3 × 6, so the search is repeating a known pair. The complete factor list is 1, 2, 3, 6, 9, and 18. Eighteen is composite because it has positive factors besides 1 and itself. The same pairs also show that 18 is a multiple of 2, 3, 6, and 9. A drawing of three equal rows of six can check one pair, while the ordered search checks that no smaller first factor was skipped.

Check the common mistake

Six is a factor, but 18 + 6 is not the calculation that checks it; 18 ÷ 6 = 3 is. Reversing a pair changes the array’s orientation without producing new factors. Composite does not mean even: 9 is an odd composite number because 3 × 3 = 9. The number 1 is neither prime nor composite, since it has only one positive factor. Do not stop after the first pair, because every positive whole number has 1 times itself.

Try a related case

List the pairs for 24: 1 × 24, 2 × 12, 3 × 8, and 4 × 6. Check divisibility at 5 and notice the repetition at 6 × 4. Then list the distinct factors in order and explain why they support the composite classification.

Selected references from Montana mathematics standards

Montana’s Office of Public Instruction identifies July 1, 2026 as the implementation date for its revised mathematics standards. The selected references below were checked in the current PK–12 mathematics document linked from the OPI mathematics directory. Use the 2026 implementation document when checking a code; earlier Montana documents use a different set of references. 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.

OPI identifies MAST English language arts and mathematics assessment for Grades 3–8, including Grade 4. The required-assessments directory also identifies alternate assessment pathways. Follow the school’s current assigned pathway, instructional sequence, and administration directions. Independently published practice may use its own timer, tools, question count, and scoring; these are not official administration specifications or a prediction of a state performance level. Read the current OPI assessment overview.

Read OPI mathematics guidance for later guidance. 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.