Addition and Subtraction Facts to 20
Warm-up
Number talk: 9 + 7. Students solve mentally (no paper). Collect strategies: making 10 (9+1+6=16), doubles-plus-one (8+8=16), decompose 7 (9+1+6). All give 16. Which strategy is fastest for you? Strategies are personal: the goal is having at least one reliable strategy for every fact.
Explore
Fact family exploration: each group receives a set of three numbers (e.g., 6, 9, 15). Write all four related facts. Then: is there a strategy connection between the addition facts and the subtraction facts? (Yes: 15 - 9 can be solved by thinking 9 + ? = 15.)
Formalize
Fluency assessment check-in: pose 10 addition facts to 20 in quick succession. Students record answers. Review: which facts were instant? Which needed a strategy? Target the slow ones: what strategy works best? Pair students to practice their personal weak spots.
Addition and Subtraction Facts to 20
Highlight the commutative property formally: show 6+8 and 8+6. Are these the same? (Same sum, different order.) How many of our 20x20 addition facts are duplicates? (Exactly half, since ab = ba.) So there are only 55 unique facts (including doubles), not 100. This makes the task feel manageable.
Practice
Students complete a timed (or untimed) set of 20 mixed addition and subtraction facts to 20, self-assessing which facts are instant vs. still need a strategy. Exit ticket: write the fact family for 6, 7, 13.
Exit ticket
Students complete a timed (or untimed) set of 20 mixed addition and subtraction facts to 20, self-assessing which facts are instant vs. still need a strategy. Exit ticket: write the fact family for 6, 7, 13.
Make ten: 8 needs 2; split 7 into 2 + 5; then 10 + 5 = 15.
Doubles plus one: 7 + 7 = 14 is known; 8 is one more than 7; so 14 + 1 = 15.
Doubles minus one: 8 + 8 = 16 is known; 7 is one less; 16 − 1 = 15.
Count on (the fallback): 8… 9, 10, 11, 12, 13, 14, 15 — seven counts. It works, but notice how much longer it takes than the other three.
The point of doing one fact four ways: strategies are CHOICES, and different facts have different best doors. 9 + 6 begs for make-ten; 7 + 8 begs for doubles. Fluency isn't speed alone — it's picking the door that opens easiest.
Step 1: Post a blank addition chart (0–9 across the top and side, 100 cells) and announce the goal: prove there's nothing to fear on it.
Step 2: Colour the easy structure first: +0 facts (a whole row and column — the number itself), +1 facts (just count one), and doubles (the diagonal: 6 + 6 = 12…). The chart is already half coloured.
Step 3: Colour strategy neighbourhoods: near-doubles hug the doubles diagonal (7 + 8 lives beside 7 + 7); make-ten facts cluster where addends push past ten (9 + anything: slide 1 over, so 9 + 6 becomes 10 + 5).
Step 4: Count what remains uncoloured — a handful of stragglers (like 3 + 6). Adopt each with whatever strategy fits.
The message of the sweep: 100 facts is not 100 memorizations; it's five ideas covering the whole board. Confidence comes from seeing the board conquered by structure.
Step 1: Reframe: 15 − 8 asks "8 plus WHAT is 15?" Every subtraction fact is an addition fact wearing a disguise.
Step 2: Answer through ten: 8 + 2 = 10, then 10 + 5 = 15. The jumps were 2 and 5, so the answer is 7.
Step 3: Tie it to the fact family triangle: 15 on top, 8 and 7 below. One triangle holds four facts — 8 + 7, 7 + 8, 15 − 8, 15 − 7 — and knowing any one unlocks the rest.
Step 4: Practice pattern for the week: every time a student answers an addition fact, ask for its two subtraction siblings on the spot ("6 + 9 = 15 — so 15 − 9 = ? and 15 − 6 = ?").
Watch for: students maintaining two separate mental filing cabinets, one for addition and one (shakier) for subtraction. The triangle merges the cabinets — that merge IS the learning.