Illinois Grade 2 Math

Regrouping changes how a quantity is represented, not its total value. A subtraction with a zero in the tens place makes that distinction especially useful. Students can follow each exchange with base-ten blocks or drawings before connecting the model to a written method.

Try the worked activity

A classroom has 402 paper squares and uses 178. How many remain? Represent the starting quantity in hundreds, tens, and ones, then explain each exchange needed to subtract.

Follow the reasoning

Start with four hundreds, zero tens, and two ones. Exchange one hundred for ten tens: three hundreds, ten tens, and two ones still represent 402. Exchange one of those tens for ten ones, leaving three hundreds, nine tens, and twelve ones. Remove one hundred, seven tens, and eight ones for 178. The remaining two hundreds, two tens, and four ones represent 224. Addition checks the result: 224 + 178 = 402.

Check the explanation

The zero tens do not become nine tens by themselves. That representation results from exchanging a hundred for ten tens and then exchanging one ten for ones. Each exchange preserves the total. Explain what the written changes mean rather than call them borrowing without showing the quantity. Subtracting the smaller digit from the larger digit in each column would ignore the direction of the subtraction and the relationship among the places.

Use the next session

1. Build or draw the starting 402.
2. Exchange place-value units while keeping the total unchanged.
3. Remove 178 and check the remaining amount by addition.

Change the used amount to 186. Use the same renamed start of three hundreds, nine tens, and twelve ones, then remove one hundred, eight tens, and six ones to leave 216. Explain why changing the amount removed does not change the original 402. Ask a partner to identify the value preserved at each exchange. Continue with a different subtraction that needs fewer exchanges so the student chooses a strategy based on the actual quantities. This example supports a selected place-value expectation, not a requirement to use one named algorithm for every Grade 2 problem.

Selected references from Illinois’s adopted mathematics document

The Illinois mathematics standards directory links the Illinois Learning Standards document incorporating Common Core. 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 Illinois alignment.

Grade 2 is below Illinois’s IAR mathematics testing range, which begins in Grade 3. Use classroom observations, models, and explanations to plan early learning. Read Illinois’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.

Illinois Grade 2 math: useful study questions