Delaware Grade 8 Math

Work through the example

An imaginary rectangular panel measures 6 centimeters by 8 centimeters. A line joins opposite corners. Find the length of that diagonal, treating the corner as a right angle.

Connect the model and calculation

The two perpendicular sides of the triangle are 6 and 8 centimeters. The diagonal is opposite the right angle, so it is the hypotenuse c. Use 6² + 8² = c²: 36 + 64 = 100, so c² = 100 and c = 10 centimeters. Taking the positive square root fits a length. The diagonal is longer than either leg but shorter than the 14-centimeter route along the two edges.

Understand an incorrect answer

Adding 6 + 8 measures the edge route, not the diagonal. Reporting 100 centimeters stops at the squared quantity; 100 is c² in square centimeters, not c in centimeters. Using 8 as c merely because it is the larger given number misidentifies the hypotenuse. The unknown diagonal is opposite the right angle, and the theorem depends on that right-angle condition.

Transfer the idea to another example

Keep one perpendicular side at 6 centimeters and give a diagonal of 10. Solve 6² + b² = 10², obtaining b² = 64 and b = 8. This time subtract the known leg’s square from the hypotenuse’s square rather than adding both known squares. Then compare with a triangle that is not stated to be right-angled. Explain why the same calculation cannot simply be assumed. Label the right angle and unknown side before doing any arithmetic.

Selected Delaware Grade 8 references

The Delaware mathematics standards directory links the Common Core publisher. Delaware’s standards regulation, section 1.1.1.1, identifies adoption for the 2010–11 school year. Use the adopted document alongside the school’s instructional plan. These labels summarize the activity’s focus; read the complete expectations and mathematical practices in the publisher’s mathematics document.

Sources checked October 5, 2026. This selected activity is an entry point for instruction, not a complete curriculum checklist.

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 8 is within Delaware’s Smarter Balanced 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 Delaware’s official summative 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.