Math // Addition & Subtraction

Addition and subtraction within 1000

Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds

Ages
7 to 8
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
1 code

Quick check

Can the learner add or subtract numbers in the hundreds — like '347 + 256' — by thinking about hundreds, tens, and ones separately, or drawing a diagram to help?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Add two three-digit numbers using base-ten blocks or drawings, composing a ten or hundred when necessary
  • Subtract three-digit numbers, decomposing a ten or hundred when necessary
  • Relate the concrete/drawn strategy to a written method and explain why it works

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics

You are here

Addition and subtraction within 1000

Ages 7 to 8 // Method

Leads to

3 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Year 3 learners add and subtract within 1000 by extending the compose/decompose-a-ten idea to a second boundary: ten tens make a hundred, and a hundred can be broken back into ten tens. Taught concretely then pictorially then in writing for the SAME calculation, so 'carrying' and 'borrowing' across two columns are understood as exchange, not digit rituals. Across-a-zero subtraction (e.g. 402−137) is the hardest, most error-prone case and deserves deliberate attention.

Common misconceptions

  • Smaller-from-larger subtraction across any column (e.g. ones done as larger-minus-smaller)
  • Failing to compose a hundred: ten or more tens left in the tens place (170+80 recorded with 15 in the tens column)
  • Borrow-across-zero errors: decomposing when the adjacent column is 0 (402−137) done incorrectly
  • Treating each column independently with no exchange, so carried/borrowed units vanish

Useful representations

  • Base-ten blocks (ones, ten-rods, hundred-flats) on a place-value mat
  • Place-value counters on a H-T-O grid
  • Part-whole / partitioning drawings (256 = 200+50+6)
  • Number line for count-up subtraction across hundreds
  • Expanded written layout bridging to compact columns

Teaching practices

  • Work concrete→pictorial→written for the SAME calculation so the recording mirrors the exchange (NCETM Spine 1.17: strategies across the hundreds boundary combine bridging-ten with unitising)
  • Make both boundaries explicit: ten ones → one ten, and ten tens → one hundred; and the reverse for subtraction
  • Use place-value counters or base-ten on a H-T-O mat so an exchanged unit physically moves one column left/right
  • Deliberately include 'exchange across a zero' cases (e.g. 402−137) since these are the hardest and most error-prone
  • Check with estimation and the inverse operation (DfE Year 3)

Activities to try

  1. 1

    Double exchange on a place-value mat: 256 + 167

    Why it works: Carrying across two columns is the same exchange move repeated at a second boundary: ten ones become one ten, and ten tens become one hundred.

    1. Lay out 256 and 167 with base-ten blocks (or place-value counters) on a H-T-O mat.
    2. Combine the ones: 6+7=13. Exchange ten ones for one ten and move that ten into the tens column (leave 3 ones).
    3. Combine the tens: 5+6+1(carried)=12 tens. Exchange ten tens for one hundred and move it into the hundreds column (leave 2 tens).
    4. Combine the hundreds: 2+1+1(carried)=4. Read the result: 423.
    5. Record the matching written steps beside the blocks — first in an expanded layout, then in compact columns — so each written mark names a physical exchange.
  2. 2

    Cascade across a zero: 402 − 137

    Why it works: When a column is empty you cannot borrow directly; you must first decompose the next higher unit to fill it, then decompose again — a cascade, not a one-step borrow.

    1. Build 402 with blocks on the mat (4 hundreds, 0 tens, 2 ones).
    2. Try to subtract the ones (2−7): there aren't enough, and there are no tens to borrow — notice the empty tens column.
    3. Break one hundred into ten tens (now 3 hundreds, 10 tens, 2 ones).
    4. Break one of those tens into ten ones (now 3 hundreds, 9 tens, 12 ones). This is 402 written as 300+90+12.
    5. Subtract: 12−7=5, 90−30=60, 300−100=200 → 265.
  3. 3

    Annotated worked example: reveal each exchange step

    Why it works: Each written exchange step corresponds to a specific regrouping of units; a step-by-step reference makes the structure of the double regroup visible.

    1. Study a worked addition and a worked across-zero subtraction with each exchange step hidden until requested.
    2. Before revealing, predict what happens to a pile of ten tens, or where a borrowed ten in an empty column comes from.
    3. Reveal the step (e.g. the tens pile becoming one hundred and some tens; the zero column being fed from a decomposed hundred) and compare it with your prediction.
    4. Explain in your own words why the unit moved one column over.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
2.NBT.7

Math // Addition & Subtraction

More in Addition & Subtraction

All 52 topics