MMati Learning Hub

TOPIC 2 · GRADE 3

Subtraction and Regrouping

Decompose place-value units to subtract and prove the difference with addition.

Grade 3 focus: Place value, decomposition, differences, comparison, and addition as an inverse operation.

BIG IDEA

Subtraction finds what remains or the distance between quantities. One larger place-value unit can be decomposed into 10 of the next smaller unit without changing the number.

INTERACTIVE MATH LAB

Build it. Change it. Explain it.

MODEL 1 OF 3

MATH LANGUAGE

minuend
the amount you start with
subtrahend
the amount taken away
difference
the result or distance between amounts
decompose
rename 1 larger unit as 10 smaller units

REPRESENT IT

  • base-ten blocks
  • open number line
  • comparison bars
  • vertical algorithm

STRATEGY STEPS

  1. 1Decide whether the situation asks what remains or how far apart two amounts are.
  2. 2Align equal place values and begin with the ones.
  3. 3When a place lacks enough units, decompose 1 unit from the place to its left.
  4. 4Check by adding the difference to the amount subtracted.

WATCH OUT

Decomposing does not add value. For example, 4 hundreds 0 tens 2 ones and 3 hundreds 9 tens 12 ones both equal 402.

TRY IT

Choose a starting number and amount to subtract, then watch each place-value exchange.

WORKED EXAMPLE

402 − 178

  1. Estimate: 400 − 180 is about 220.
  2. Decompose 1 hundred into 10 tens, then 1 ten into 10 ones: 402 becomes 3 hundreds, 9 tens, 12 ones.
  3. Ones: 12 − 8 = 4. Tens: 9 − 7 = 2.
  4. Hundreds: 3 − 1 = 2. The difference is 224.