Doubles Plus One¶

Strategy · All strategies
Evidence · 3 claims (1 for, 1 mixed, 1 against) · 7 studies (3 review, 2 causal, 1 quant-synthesis, 1 theoretical), q1–q4 · 1 of 7 report an effect size

Description¶

Doubles Plus One is a mental-math strategy for addition facts in which a learner transforms an unfamiliar near-double fact into a known doubles fact plus one — for example, solving 6+7 by recalling 6+6=12 and adding 1 to get 13. It is typically taught after doubles facts are automatic, so the strategy recruits existing fluency rather than building new facts from counting. It belongs to a family of "derived fact" or "thinking strategies" (doubles plus two, make-ten, near-tens) that replace rote memorization of the full fact table with a small set of retrievable anchors plus generalizable transformations.

Design Implications¶

The strategy reduces the memory burden of fact mastery by leveraging retrieval of a small anchor set and a simple rule, consistent with evidence that chunking related facts reduces working-memory load Chunking reduces working memory load. [+M]. Derived-fact instruction is a hallmark of Cognitively Guided Instruction, which builds instruction on the informal strategies children already use. Effectiveness depends on doubles fluency first: if the anchor fact (6+6) is not retrieved automatically, the strategy adds steps rather than removing them Automatic word recognition frees resources for comprehension. [~M] — the same retrieval-automaticity principle applies to math facts.

Context¶

Requirements¶

• Automatic recall of doubles facts to at least 10+10 before introducing the strategy
• Explicit modeling of the decomposition (near-double → double → adjust) with concrete and visual supports (Ten-Frames, number racks, dot arrangements showing the extra one)
• Timed or spaced practice so the derived fact itself becomes directly retrievable over time

Constraints¶

• If doubles are not yet fluent, the strategy increases cognitive load instead of reducing it Cognitive overload degrades learning. [-M]
• Learners may over-rely on the derivation and never consolidate direct retrieval; without spaced practice the strategy becomes a permanent crutch that slows fact fluency [-M]
• Less useful for facts far from doubles (e.g., 3+8); forcing the strategy onto non-near-double facts produces errors and confusion [~W]

Implementation Variability¶

• Doubles Plus Two for facts like 6+8 (double 7, then ±1, or double 6 plus 2)
• Doubles Minus One for facts like 7+6 (7+7 minus 1), which some learners find easier
• Concrete → representational → abstract sequence: dot cards with the "extra one" highlighted, then ten-frames, then bare numerals
• Student-invented strategies: elicit learners' own near-double reasoning before naming the strategy (CGI orientation)

Target Learners¶

• Students in grades 1–3 building addition fluency within 20 [+M]
• Learners who already count-on accurately but have not consolidated most facts — the strategy gives them a bridge from counting to retrieval
• Students with weak rote memory for facts benefit especially, since the strategy reduces what must be memorized [~M]

Target Learning Goals¶

• Addition fact fluency within 20 (e.g., CCSS 2.OA.B.2: fluently add and subtract within 20 using mental strategies)
• Number sense: understanding relationships between facts rather than treating them as isolated items
• Early algebraic thinking: the transform-and-adjust structure previews properties like compensation

Instructions¶

1. Verify doubles fluency with a quick diagnostic; reteach doubles if retrieval is slow.
2. Demonstrate the strategy on a near-double fact using a dot card or ten-frame, making the "hidden double plus one" visible.
3. Have learners sort a set of fact cards into "doubles," "doubles plus one," and "neither" to build discrimination of when the strategy applies.
4. Practice with spaced retrieval — mixed decks of doubles and near-doubles — so derived facts consolidate into direct recall.
5. Ask learners to explain their thinking aloud (Think-Aloud) to surface when the strategy helps and when another strategy (make-ten) is faster.

Related Strategies¶

• Make Ten — the complementary restructuring strategy for facts with sums near 10
• Counting On — the earlier-emerging strategy Doubles Plus One is meant to replace
• Doubles Minus One — the mirror-image variant for facts just below a double

Examples¶

• DreamBox Learning — adaptive math platform that presents near-double facts with visual "double plus one" dot arrangements and adjusts based on whether learners use the strategy or fall back to counting.
• Investigations in Number, Data, and Space (TERC) — elementary curriculum that introduces doubles and near-doubles as "helper facts" within its number-combinations strand.
• Math Recovery — intervention program that assesses whether a child uses derived-fact strategies and targets near-doubles as a key transition from counting to retrieval.

Key Sources¶

• Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children's mathematics: Cognitively guided instruction. Heinemann.
• Baroody, A. J. (2006). Why children have difficulties mastering the basic number combinations and how to help them. Teaching Children Mathematics, 13(1), 22–31. doi:10.5951/TCM.13.1.0022
• National Research Council. (2001). Adding it up: Helping children learn mathematics. National Academy Press. doi:10.17226/9822
• Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Information Age Publishing.