Massachusetts Grade 4 Math

How much of the turn is missing?

Three rays start at the same vertex. The middle ray splits a 95-degree angle into two adjacent, nonoverlapping angles. One smaller angle measures 38 degrees. Find the other angle and explain why subtraction is appropriate. The whole turn and its two parts are specified; this is not a drawing to estimate by eye.

Explain the solution

The two nonoverlapping parts together make the 95-degree angle. If the unknown part is x degrees, then 38 plus x equals 95. Subtract the known 38-degree part from the whole: 95 minus 38 equals 57. The unknown angle measures 57 degrees. Check by adding the parts: 38 plus 57 equals 95. All three measurements describe turns about the shared vertex. Changing the drawn ray lengths would not change those angle measures. A student can trace the turn from the first outside ray to the middle ray, then continue to the second outside ray to connect the addition with the arrangement.

Notice the reasoning

Adding 38 and 95 treats the whole as though it were another missing part. Return to the labels whole, known part, and unknown part before selecting an operation. The subtraction works because the parts are adjacent, share the vertex, and cover the whole without overlap. Two unrelated angles with measures 38 and 57 do not automatically form this angle. Students should also distinguish degrees from a ray’s length. A sketch can illustrate the relationship, but the given measures determine the calculation even if the sketch is not drawn to scale.

Try a related task

Create a different whole angle with one labeled known part and an unknown adjacent part. Write an equation, solve it, and check that both parts sum to the whole. Then ask what changes when the middle ray moves while the outside rays remain fixed: one part grows as the other shrinks, and their total stays constant. Use a protractor where appropriate to connect measured turns with the additive model. Choose related angle practice from the existing resources and retain the student’s explanation with the numerical answer.

Selected references from Massachusetts mathematics standards

The Massachusetts mathematics standards directory links the current mathematics document, adopted in March 2017 and currently listed in the state’s frameworks directory. 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.

Grade 4 is within the statewide MCAS mathematics assessment range. MCAS is untimed within a regular school day. Independently published practice may use its own timer, tools, question count, and scoring; these are not official administration rules or a prediction of a state performance level. Read Massachusetts’s 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.