Montana Grade 5 Math

Two expressions with the same numbers can describe different actions. Before calculating, identify what is inside each group and how many times that group occurs. This original packing example makes the difference visible.

Try this original activity

Plan A packs five envelopes, each containing 14 large stickers and 6 small stickers. Plan B packs five envelopes with 14 stickers in each, then adds 6 loose stickers outside the envelopes. Match the plans with 5 × (14 + 6) and 5 × 14 + 6. Explain the expressions before evaluating them.

Work through the reasoning

Plan A matches 5 × (14 + 6). The parentheses group the contents of one envelope: 14 large plus 6 small stickers. Multiplying that whole group by 5 counts the five identical envelopes. Plan B matches 5 × 14 + 6: the first term counts the five groups of 14, and the final 6 is added once. Calculating afterward checks the interpretation: A has 5 × 20 = 100 stickers, while B has 70 + 6 = 76. The plans differ by 24 stickers because A includes five sets of six small stickers, whereas B includes one set of six loose stickers. Explaining the groups tells why the answers differ.

Check the common mistake

Do not say the two expressions must match because they contain the same three numbers. Parentheses change which quantity is multiplied. In Plan A, adding six after finding 5 × 14 omits four of the five groups of small stickers. In Plan B, multiplying the loose six by five invents extra loose stickers. An answer that gives only 100 and 76 misses the task of interpreting the expressions.

Try a related case

Describe 3 × (8 + 2) and 3 × 8 + 2 in words. One possible pair is three bags with eight blue and two yellow counters in each, versus three bags of eight blue counters and two yellow counters added once. Explain the grouping before checking totals of 30 and 26.

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 5. 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.