Michigan Grade 2 Math

Where did the extra two tens come from?

Four classroom trays contain 26, 34, 18, and 22 paper shapes. Find the total number of shapes. Then explain a method that adds the tens and ones separately. These are invented classroom counts; the important question is how the quantities combine, not how quickly the answer can be written.

Explain the solution

The tens contribute 20 + 30 + 10 + 20 = 80 shapes. The ones contribute 6 + 4 + 8 + 2 = 20 shapes. Combining 80 and 20 gives 100. The ones total contains two groups of ten, so it can be represented as two additional tens. The original eight tens become ten tens, or one hundred. Another valid method pairs 26 with 34 to make 60 and pairs 18 with 22 to make 40. Then 60 + 40 = 100. Both methods preserve every shape and describe the same total. Show the tens and loose ones with drawings before comparing the two written methods.

Notice the reasoning

A student might record eight tens and twenty ones but then write 820. Ask them what twenty ones are worth and exchange each group of ten ones for a ten. Eight tens and twenty ones mean 80 + 20, not digits placed beside one another. A learner may also skip one tray after making a convenient pair; check that all four original amounts appear in the explanation. The addends are two-digit numbers even though their sum is three digits. Regrouping changes the representation of the total, not the number of shapes. Keep the unit “shapes” attached to the quantities.

Try a related task

Change the 22-shape tray to 23 shapes without rebuilding the entire calculation. The total becomes 101 because one shape was added. Explain why that adjustment is valid, then check using tens and ones. For a fresh example, choose four two-digit numbers and look for pairs whose ones make ten. Pairing is useful when it makes the calculation easier, but every pair need not end in zero. Retain a drawing and a written explanation so the teacher can tell whether a learner understands the exchange or is following a memorized digit rule.

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

Visit the Grade 2 math learning Online Center for broader support or choose a related task from the existing Grade 2 worksheet collection. This is a general collection, not a certification of complete Michigan alignment.

Grade 2 is below the M-STEP summative mathematics range. Use classroom observations, models, and explanations alongside the school’s early learning and assessment 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.

Michigan Grade 2 math: useful study questions