Doubles Minus One¶

Strategy · All strategies
Evidence · 3 claims (3 for) · 8 studies (4 causal, 2 quant-synthesis, 2 review), q2–q4 · 2 of 8 report an effect size

Description¶

Doubles Minus One (also called "near doubles" or "doubles −1") is a mental computation strategy for addition facts such as 7+6 or 8+7. Learners anchor on a memorized doubles fact (7+7=14), then adjust: because 6 is one less than 7, the sum is one less than 14, so 7+6=13. The strategy converts roughly a dozen hard-to-memorize facts into applications of facts already known, using the structural relationship between addends.

Design Implications¶

Doubles Minus One is a form of derived-fact instruction: rather than rote memorization of every fact, learners reuse known facts and apply a relational rule, which builds number sense and supports transfer to the full addition table Analogical reasoning improves transfer. [+M]. It reduces the memory burden of fact learning by chunking related facts around a single anchor Chunking reduces working memory load. [+M]. The strategy works only when the doubles themselves are automatic; if learners must compute 7+7, the adjustment step overloads working memory Cognitive overload degrades learning. [+M].

Context¶

Requirements¶

• Fluency with doubles facts (1+1 through 10+10) as a prerequisite — assess before introducing
• Explicit modeling of the adjustment reasoning, ideally with ten-frames, dot cards, or number lines that show the "one less" visually
• Sequenced practice moving from concrete representations to mental application (Direct Instruction followed by distributed practice)

Constraints¶

• Ineffective if doubles are not yet automatic — the strategy adds a step, so it slows down learners who must reconstruct the anchor fact [~M]
• Some learners overgeneralize and apply "minus one" to facts that are not near-doubles (e.g., 7+3); instruction must include non-near-double contrasts Comparing contrasting cases improves learning. [+M]
• If taught as a rote procedure ("when numbers are next to each other, subtract one") without the underlying why, it becomes one more fact to memorize rather than a relational tool [~W]
• Less efficient than direct recall for learners who have already automatized the target facts; continued strategy use can interfere with automaticity goals [~M]

Implementation Variability¶

• Doubles Plus One: the mirror strategy for facts like 6+7 (6+6 plus one); typically taught alongside or immediately after
• Concrete → pictorial → mental: ten-frames and dot arrangements first, then visualized doubles, then purely mental application
• Student-generated sorting: learners sort fact cards into "doubles," "doubles minus one," "doubles plus one," and "neither" before practicing, forcing relational analysis
• Game-based practice: games where near-double cards must be matched to their double anchor (e.g., "Salute," "Near Doubles Concentration")

Target Learners¶

• Students in grades 1–3 building addition fact fluency, after doubles are secure
• Learners who struggle with rote memorization but can reason relationally — the strategy gives them a generative route to facts they cannot yet recall [~M]
• Less appropriate for learners who already recall near-double facts automatically; for them the strategy is redundant and may slow retrieval [~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")
• Relational/structural understanding of the number system: how facts relate to one another
• Foundation for later compensation strategies in multi-digit arithmetic and algebra (e.g., 49+27 as 50+27−1)

Instructions¶

1. Verify prerequisite fluency. Quick-check doubles facts; reteach with ten-frames if any doubles exceed a 2-second recall.
2. Model with representation. Show 6+6 on a ten-frame, then move one counter to make 7+5; narrate: "One counter moved away, so the total is one less than 12." (Direct Instruction)
3. Contrast cases. Present 6+5 next to 6+3 and ask which is a near-double and why, so learners learn the conditions of the strategy, not just the steps Comparing contrasting cases improves learning. [+M]
4. Fade the representation. Move from visible ten-frames to imagined doubles to purely mental application, shrinking support as competence grows.
5. Distribute practice. Short, spaced practice sessions mixing doubles, doubles minus one, and doubles plus one, with feedback on both accuracy and strategy use.
6. Connect forward. Extend the same compensation logic to two-digit addition (38+25 → 40+25−2) to show the strategy is an instance of a general idea.

Related Strategies¶

• Counting On — a less efficient earlier strategy that Doubles Minus One typically replaces
• Make Ten — the other core mental strategy for facts within 20; often taught in the same sequence
• Doubles Plus One — the complementary near-double strategy for addends one greater

Examples¶

• Investigations in Number, Data, and Space (TERC) — the "Making Sense of number facts" units explicitly develop near-double strategies with ten-frame models before fluency practice.
• Number Talks (Parrish, 2010) — classroom routines in which teachers pose a fact like 8+7 and elicit multiple strategies, with Doubles Minus One as one expected student explanation.
• Math Recovery — one-to-one intervention assessments specifically probe whether a child can derive near-double facts, using it as a diagnostic marker of strategy sophistication.

Key Sources¶

• Parrish, S. D. (2010). Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K–5. Math Solutions.
• 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
• 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.
• National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. NCTM.
• Thornton, C. A. (1978). Emphasizing thinking strategies in basic fact instruction. Journal for Research in Mathematics Education, 9(3), 214–227. doi:10.2307/748999