Math // Addition & Subtraction

Adding within 100

Add within 100 using strategies based on place value, including adding a two-digit and one-digit number, and a two-digit and a multiple of 10

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

Quick check

Can the learner work out sums like '47 + 8' or '35 + 50' by thinking about the tens and ones separately rather than counting up one at a time?

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.
  • Calculate 46 + 7 using place value (46 + 4 + 3 = 53)
  • Calculate 38 + 40 = 78 using tens understanding
  • Relate the strategy to a written method and explain the reasoning

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

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Adding within 100

Ages 6 to 7 // Method

Leads to

2 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

Children aged 6-7 add within 100 using place-value strategies, not a column algorithm. They partition addends, use known number bonds to bridge a ten (46+7 as 46+4+3), and add tens to tens leaving the ones untouched (38+40=78). A concrete-pictorial-abstract progression (bead strings, base-ten blocks, number lines, then jottings) makes the tens boundary visible before it is recorded symbolically. The crossing-a-ten moment and the tens-onto-tens move are the two insights to build and check.

Common misconceptions

  • Treating a multiple of ten as ones: 38+40 done as 38+4=42
  • Not bridging the ten: 46+7 done as 6+7=13, keeping the 3 and losing the extra ten (answer 43), or concatenating to 413
  • Adding the added amount to the wrong part (ones added to the tens digit)
  • Persisting with count-all/count-on-in-ones instead of using place value

Useful representations

  • Bead string / 100-bead frame (bridging a ten made visible)
  • Base-ten blocks (tens rods and ones)
  • Number line with jumps (partition the added amount into a jump to the next ten, then the rest)
  • Part-whole model (partition the addend, e.g. 7 = 4 + 3)
  • Hundred square (move along for ones, down for tens)

Teaching practices

  • Extend within-20 'make ten' bonds to numbers within 100 — 46+7 uses the same partition of 7 into 4+3 that 6+7 does (NCETM Spine 1.13: known within-ten facts applied to a two-digit + single-digit number)
  • Keep tens and ones distinct: for 38+40, add the multiple of ten to the tens and leave the ones alone, so the child feels tens land on tens
  • Use multiple connected representations for the same calculation — bead string, part-whole diagram, number line, and symbolic jotting — so the strategy transfers
  • Secure fluent partitioning of numbers to ten first; it is the explicit prerequisite for independent bridging
  • Ask the child to relate the mental strategy to a written record and justify it, not just state the answer (curriculum: explain the reasoning)

Activities to try

  1. 1

    Watch a ten compose when you cross the boundary

    Why it works: Bridging a ten is not an arbitrary rule: the extra ten is physically composed from ten ones, and the make-ten partition (7 = 4 + 3) is the same move used within 20 applied at 46.

    1. Start with 46 shown on a bead string or in a base-ten workspace
    2. Add single ones one at a time, saying the running total aloud (47, 48, 49, 50, 51, 52, 53)
    3. When the added one makes ten loose ones, see that they complete a ten (on a bead string, the next block of ten beads is filled; with base-ten blocks, swap the ten ones for a ten-rod), so the count goes 49, then 50, then on to 53
    4. Re-tell what happened: 'I added 4 to reach 50, then 3 more to make 53', and link it to the partition 7 = 4 + 3
    5. Repeat for 53 + 9 (bridge to 60 by adding 7, then +2)
  2. 2

    Tens land on tens: add a multiple of ten

    Why it works: A multiple of ten joins the tens, not the ones; four tens combine with three tens to make seven tens, leaving the ones unchanged.

    1. Start with 38 shown with three ten-rods and eight ones
    2. Add four ten-rods, watching them join the tens while the eight ones stay untouched
    3. State the total as 70 + 8 = 78, and say why the ones did not change
    4. Check by a different order: add 30 + 40 = 70 first, then the 8 — confirm it gives the same 78
    5. Contrast with the wrong move: 'is 38 + 40 the same as 38 + 4? why not?' — notice 42 is only 4 more than 38, far too small after adding forty
  3. 3

    Partition the addend with a part-whole picture

    Why it works: Choosing the partition that lands exactly on the next ten is what makes bridging efficient; the structure of the strategy can be seen even before acting it out.

    1. Look at 46 + 7 with 7 shown in a part-whole model
    2. Split the 7 into 4 (the amount needed to reach the next ten) and 3 (the rest)
    3. Mark where the calculation crosses a ten (at 50) and label it 'this is where we cross a ten'
    4. Say the two jumps: 46 + 4 = 50, then 50 + 3 = 53

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
1.NBT.4

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