Addition & Subtraction
Elementary (K-2) · Mathematics
Addition and subtraction in K-2 move from counting every object to knowing sums and differences within 20 without counting. This topic covers the strategies that make that shift happen: counting on from the larger number, doubles and near-doubles, making ten, and using a known addition fact to answer a subtraction question. Sessions are spoken, so a child explains how they got an answer rather than just filling in a box, which is where gaps in strategy usually show up.
Start a session on Addition & SubtractionWhat this covers
- Counting on and counting back from a number instead of restarting at one (7 + 3 by saying eight, nine, ten)
- Part-part-whole thinking: seeing that 4 and 6 make 10, so 10 - 6 must be 4
- Making ten to add within 20, such as 8 + 5 becoming 10 + 3
- Doubles and near-doubles facts (6 + 6, then 6 + 7) as anchors for recall
- Reading one- and two-step word problems and deciding whether to join, separate, or compare
- Finding the missing number in equations like 5 + __ = 12 and __ - 3 = 9
- Adding and subtracting within 100 using tens and ones jumps, for children ready in Grade 2
Where learners get stuck
- Counting the first number again on fingers, so 9 + 2 takes eleven counts instead of two
- Children learn addition first as 'count everything,' and nothing in the written problem tells them the first number can be held in their head. Counting on has to be taught and rehearsed out loud.
- Believing subtraction always means the answer gets smaller and that you can only take the little number from the big one, so 4 - 9 is 'just 5'
- Every early example follows that pattern, so children generalise a rule that works until it doesn't. It also causes them to flip digits when subtracting two-digit numbers later.
- Reading the equals sign as 'write the answer here,' so 3 + 4 = __ + 2 gets answered with 7
- Almost every worksheet puts the blank on the right, which trains a procedure instead of the idea that both sides balance. Missing-addend problems expose this immediately.
- Choosing an operation from keywords like 'more' or 'left' rather than the situation
- Keyword shortcuts work on simple problems, then fail on comparison problems such as 'Sam has 3 more than Ana; Sam has 11' where 'more' signals subtraction.
What a session looks like
A session runs about 20-25 minutes of talking back and forth. Evelyn poses a small number of problems, asks the child to say the answer and then explain the strategy, and adjusts the numbers up or down based on what they hear. Word problems are read aloud and acted out with objects the child names from their own room. When a fact is answered by slow finger counting, Evelyn slows down and rebuilds it with a ten-frame or doubles picture instead of moving on. Parents get a short note on which facts were fluent and which needed counting.
Helpful to know first
- Counting forward to at least 20 and recognising written numerals
- Understanding that the last number counted tells how many are in the group
- Comfort saying answers out loud to an adult, with a parent nearby for the first sessions
Questions
- My child can add but still uses fingers for everything. Is that a problem?
- Fingers are fine as a stage. The concern is when a child counts one by one for facts like 8 + 2 in second grade, since that slows every later problem. Sessions target the specific facts that still need counting and replace them with making-ten and doubles strategies.
- Should my kindergartener be doing subtraction yet?
- Kindergarten work usually stays within 5 or 10 and focuses on taking away objects and telling how many are left. Formal written subtraction can wait; the spoken part-whole work here builds the foundation for it.
- Does this cover carrying and borrowing?
- Two-digit addition and subtraction with regrouping is introduced for Grade 2 learners who are fluent within 20. The place value ideas behind it are handled in the Place Value topic, and the two work well together.
- How do I know whether to start here or with counting?
- If your child cannot yet count reliably to 20 or loses track when counting a set of objects, start with Counting and Number Sense. The first session includes a few short questions that show which is the better fit.