New Hampshire Grade 6 Math

A unit rate puts two ratios on the same one-item basis. The invented offers here contain different numbers of identical notebooks. Comparing the total package prices alone answers which package costs less overall, not which notebook has the lower unit price.

Try this original activity

Package A contains five identical notebooks for $7.50. Package B contains eight of the same notebooks for $11.20. Find the price per notebook for each package. Which has the lower unit price, and by how much? Assume whole packages only and no additional charges.

Work through the reasoning

For A, divide $7.50 by five notebooks: $1.50 per notebook. For B, divide $11.20 by eight: $1.40 per notebook. B’s unit price is lower by $0.10 per notebook. The units explain the order of division: dollars divided by notebooks gives dollars per notebook. Multiplying back checks each offer: 5 × $1.50 = $7.50 and 8 × $1.40 = $11.20. Package A still has the smaller total price. A lower unit price does not imply a lower immediate payment when packages contain different quantities. The stated comparison assumes the notebooks are identical, so quality or size differences do not alter the mathematical task.

Check the common mistake

Dividing five by 7.50 computes notebooks per dollar, a different rate from the one requested. Also avoid reporting $3.70, the package-price difference, as the savings per notebook. If a learner needs only five notebooks and packages cannot be split, B supplies three extra; the unit-rate comparison alone does not decide which purchase meets that need. These classroom prices are invented and do not describe current store offers.

Try a related case

Compare ten identical notebooks for $15.00 with six for $8.40. Their unit prices remain $1.50 and $1.40 respectively. Explain why multiplying or dividing both quantity and cost by the same factor preserves the unit rate. Keep the distinction between rate and package payment.

Selected Common Core references for this activity

New Hampshire’s current school-approval rules, Ed 306.34, allow local boards to use the adopted 2010 Common Core mathematics standards or approved alternative academic standards. Confirm the school’s standards choice and local competencies first. The selected Common Core references below were checked in the original publisher’s 2010 document. They identify this activity’s focus, rather than a complete local course. Read the full requirements, mathematical practices, examples, and progression with the school’s curriculum.

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 2025–2026 public NH SAS manual describes general mathematics testing in Grades 3–8, including Grade 6, using a computer-adaptive assessment. Confirm the learner’s assigned pathway, tools, and the school’s current administration directions. The reviewed manual is the 2025–2026 edition; confirm later-year directions with the school. 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 public NH SAS manual resource page.

Read New Hampshire local curriculum rules 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.