Make Ten¶

Strategy · All strategies
Evidence · no claims cited

Description¶

Make Ten (also called "bridging through ten" or the "ten-structure" strategy) is a mental computation strategy for single-digit addition with sums above ten. Learners decompose one addend so that the other addend is completed to a full ten, then add the remainder to the ten (8 + 5 becomes 8 + 2 + 3, then 10 + 3 = 13). It is typically taught with ten-frames, number bonds, and Cuisenaire rods so the decomposition is grounded in a visual quantity structure rather than a memorized procedure.

Design Implications¶

Make Ten converts an unsolved fact into a solved one: instead of retrieving 8 + 5 directly, learners restructure the problem around the anchor of ten, which is a highly practiced, automatic quantity [chunking-reduces-working-memory-load]. This reduces the working-memory demand of the computation Cognitive Load Management [+M] and builds place-value understanding that later supports multi-digit addition and regrouping [+M]. The strategy is most effective when learners first have fluency with the complements of ten (number bonds to 10) and with decomposing numbers; without those prerequisites, the decomposition step itself becomes a new burden [~M].

Context¶

Requirements¶

• Automatic recall of number bonds to ten (1+9, 2+8, 3+7, …) before the strategy is introduced
• Concrete or visual models — ten-frames, rekenreks, Cuisenaire rods — that make the "completing the ten" action visible
• Explicit Demonstration of the decomposition step, including why one addend is split rather than the other
• Distributed Practice with varied fact pairs so the strategy generalizes rather than attaching to a few memorized examples

Constraints¶

• Ineffective if learners have not automatized complements of ten; the strategy then adds load instead of reducing it [-M]
• Can be over-applied: learners may decompose even when direct retrieval is faster, slowing performance; instruction should eventually support flexible strategy choice [~S] — strategy flexibility, not strategy use per se, predicts fluency
• Rote teaching of the steps without ten-structured models produces a procedure disconnected from quantity, which does not transfer to subtraction or multi-digit contexts [-M]
• Less relevant for learners who already retrieve single-digit facts automatically; forcing the strategy on them is redundant [~M]

Implementation Variability¶

• Ten-frame first: learners physically move counters to fill a ten-frame, then record the decomposition symbolically
• Number-bond notation: the split addend is recorded as a part-whole diagram before the equation
• Open number line: bridging through ten is represented as jumps (8 → 10 → 13), which later extends to bridging through decades (e.g., 47 + 8 → 47 + 3 + 5)
• Comparison format: learners compare Make Ten with counting-on or retrieval on the same facts, which supports strategy selection [comparing-contrasting-cases-improves-learning]

Target Learners¶

• Students in grades 1–2 who have mastered combinations to ten but not yet automatized facts with sums 11–18 [+M]
• Students relying on inefficient count-all strategies; Make Ten gives a structured replacement for counting [+M]
• Less appropriate for learners who already retrieve these facts automatically, for whom it adds steps without benefit [~M]

Target Learning Goals¶

• Procedural fluency with addition facts within 20
• Conceptual understanding of the base-ten structure and part-whole decomposition
• Foundation for regrouping in multi-digit addition and subtraction

Instructions¶

1. Activate complements of ten. Quick oral or ten-frame routines until number bonds to ten are automatic (Activation).
2. Model with a ten-frame. Demonstrate 8 + 5: place 8 counters, add 2 to complete the ten, then add the remaining 3; narrate the decomposition aloud (Demonstration).
3. Record symbolically. Write 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13, connecting each step to the physical action.
4. Practice with varied facts. Work through fact pairs (8+5, 9+4, 7+6) with ten-frames, then fade the frames to mental execution (Fading).
5. Compare and choose. Contrast Make Ten with counting-on and retrieval across several facts so learners select the efficient strategy per problem [comparing-contrasting-cases-improves-learning] [+M].

Related Strategies¶

• Counting On — the less efficient precursor strategy Make Ten typically replaces
• Doubles Plus/Minus One — a companion decomposition strategy for facts near doubles; both teach that facts can be restructured rather than only memorized
• Bridging Through Decades — the multi-digit extension of the same structure (47 + 8)

Examples¶

• Singapore Math / Math in Focus — introduces Make Ten via number bonds and ten-frames in Grade 1 before multi-digit addition (Math in Focus)
• Japanese elementary textbooks (e.g., Tokyo Shoseki Mathematics) — build "ten-structured" teen-sum understanding through explicit lesson sequences on completing ten (Murata 2004)
• Number Talks (Parrish, 2010) — classroom routines in which students share Make Ten decompositions aloud, exposing multiple solution paths
• DreamBox Learning — adaptive digital ten-frame activities that require completing the ten before accepting an answer (DreamBox)

Key Sources¶

• Murata, A. (2004). Paths to learning ten-structured understandings of teen sums: Addition solution methods of Japanese Grade 1 students. Cognition and Instruction, 22(2), 185–218. doi:10.1207/s1532690xci2202_2
• 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.
• Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grades one through three. Journal for Research in Mathematics Education, 15(3), 179–202. doi:10.2307/748348
• Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2004). Strategic aspects of simple addition and subtraction: The influence of mathematical ability. Learning and Instruction, 14(2), 177–195. doi:10.1016/j.learninstruc.2004.01.003