Nevada Grade 7 Math

A percent calculation uses a base amount. When one change follows another, the second percent may use a new base. This invented purchase example states both the order and the rate; its tax rate is a classroom assumption, not a statement about Nevada tax law.

Try this original activity

A backpack has an original price of $80. A store gives 25% off, then applies an assumed 5% tax to the discounted price. No other fees apply. Find the final total. Explain why adding the two percentages does not describe the calculation.

Work through the reasoning

The discount is 25% of $80: 0.25 × 80 = $20. Subtracting it gives a discounted price of $60. The assumed tax is 5% of that $60, not 5% of $80: 0.05 × 60 = $3. The total is $63. Equivalently, multiply 80 × 0.75 × 1.05 = 63. The discount base is eighty dollars, while the tax base is sixty dollars. Subtracting twenty percentage points from the original price would give $64, which does not match the stated sequence. The order and bases explain the difference. The total lies above the discounted price and below the original price, giving a quick reasonableness check.

Check the common mistake

A 25% discount leaves 75% to pay, not 25%. Also avoid adding the three-dollar tax to the original eighty dollars. The activity excludes other fees and specifies an assumed rate; a real purchase needs its actual terms. Reversing two percentage multipliers can give the same numeric product when their mathematical bases follow that model, but that observation does not authorize changing a store’s specified tax or discount rules.

Try a related case

Use the same stated sequence with a $120 item. A 25% discount removes $30, leaving $90. The assumed 5% tax is $4.50, so the total is $94.50. Label the base used at each step before comparing the result with 120 × 0.75 × 1.05.

Selected references from Nevada mathematics standards

The Nevada Department of Education’s mathematics directory links the Nevada Academic Content Standards for Mathematics. The selected references below identify the worked activity’s focus. The full document includes requirements, examples, mathematical practices, and grade-level progression. Read it alongside the school’s curriculum; one worked activity does not establish complete course alignment or grade-level proficiency.

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.

The Nevada Department of Education identifies Smarter Balanced mathematics assessment for Grades 3–8, including Grade 7. Its public overview describes a computer-adaptive assessment. Confirm the learner’s assigned pathway and current school administration directions, including any alternate assessment pathway. 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 Nevada assessment overview.

Read Nevada 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.