Michigan Grade 4 Math

Can the two piece counts be added immediately?

A ribbon piece is 4/10 meter long. A second piece is 17/100 meter long. Find their combined length, leaving out any overlap or extra length for joining. A learner writes 21/110 meter by adding both numerators and both denominators. Explain why that method does not describe the two measured lengths.

Explain the solution

The two fractions initially count differently sized units. Four tenths of a meter is forty hundredths of a meter because each tenth contains ten hundredths. Rename 4/10 as 40/100 without changing its length. Now both amounts use hundredths: 40/100 + 17/100 = 57/100 meter. The combined length is 0.57 meter. The denominator stays 100 because the unit being counted is still a hundredth of a meter. On a meter strip partitioned into one hundred equal parts, the first piece covers forty parts and the second covers seventeen; together they cover fifty-seven. The sum is shorter than one whole meter, which also agrees with the model.

Notice the reasoning

Adding denominators would create a new unit size that was not used to measure either piece. Ask the learner to identify what a tenth and a hundredth mean before calculating. Multiplying the numerator and denominator of 4/10 by ten produces an equivalent fraction; it does not make the ribbon ten times longer. Decimal notation must preserve the place values: 0.4 equals 0.40, while 0.04 represents only four hundredths. The worked activity uses denominators ten and one hundred, the specific scope of this selected Grade 4 expectation. General fraction addition with all unlike denominators is not required by this expectation.

Try a related task

Replace the second piece with 23/100 meter. Forty hundredths plus twenty-three hundredths gives 63/100 meter, or 0.63 meter. Check the new answer by shading a separate hundred-part strip. Then ask how much more ribbon would complete one meter: thirty-seven hundredths remain. State that this follow-up uses the same whole meter and the same hundredth units. Choose related equivalent-fraction and decimal practice from the lesson directory, and keep the student’s model with the numerical answer to show whether the common unit is understood.

Selected references from Michigan mathematics standards

The Michigan mathematics standards directory links the current mathematics document, adopted by the State Board of Education in 2010 and currently linked in the state’s academic standards 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.

The currently linked 2025–26 state guide identifies M-STEP English language arts and mathematics in Grades 3–7, including Grade 4. Follow the school’s current assigned assessment pathway and 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 currently linked state assessment guide.

Read MDE assessment updates 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.