Free Make Ten, Doubles, and Subtraction Strategy Games

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Research and classroom practice consistently show that using visual tools such as ten frames and counters helps students build strong mental images of number relationships and understand how numbers can be decomposed and recombined. Because our place value system is built around groups of ten, developing this understanding early supports later work with larger numbers, place value, and multi-digit addition.

Ten frames are especially powerful because they allow students to see and physically move quantities. Research on the Make Ten strategy confirms it is one of the most effective mental math approaches for building addition fluency within 20 — and that students who develop this strategy early are better equipped for the demands of multi-digit arithmetic later on.

The Make Ten strategy is one of the core addition strategies assessed in the Primary Numeracy Intervention Program, a free K–3 math intervention built on the same research foundation as this game. If this activity is revealing gaps in your students' addition strategy development, the program gives you a precise diagnostic tool to identify exactly where the breakdown occurs and leveled materials to address it systematically — all free after completing a two-hour training.

 Fuson (1986) was among the first to demonstrate that teaching first graders to subtract by counting up — starting at the smaller number and counting forward to the larger — produced considerable improvement on timed tests of difficult subtraction combinations. Rather than counting back from the minuend, students who learned to count up showed stronger accuracy and greater flexibility across problem types.

Building on that work, Fuson & Willis (1988) found that across ten classrooms, first- and second-grade students of all ability levels who were taught to count up while tracking hops with finger patterns showed improved performance on take-away, compare, and equalize word problems — and were able to accelerate their learning of subtraction topics by as much as three years. Crucially, the strategy did not interfere with students' understanding of take-away problems; it deepened it.

Decades of follow-up research have reinforced these findings. Verschaffel, Torbeyns, and colleagues reviewed the full body of literature on subtraction by addition and concluded there is recurrent and convincing evidence for its frequent, efficient, and flexible use — not only among young children, but among adults — across single-digit mental subtraction, multidigit subtraction, and word problems alike.

The number line is a key tool supporting this strategy. The What Works Clearinghouse Practice Guide on elementary mathematics intervention identifies use of the number line as a distinct evidence-based recommendation — one that facilitates the learning of mathematical concepts and procedures, builds grade-level understanding, and prepares students for advanced mathematics. 

Doubles facts are widely recognized in mathematics education research as one of the first sets of addition facts students should be taught to automaticity. Because both addends are identical, doubles are easier to visualize and remember than other addition facts — making them a natural starting point for building fact fluency.

The National Council of Teachers of Mathematics emphasizes that fact fluency should be built through strategic thinking and pattern recognition rather than rote memorization alone — and doubles facts are one of the clearest examples of a fact set where visual patterns and structural reasoning make memorization natural and meaningful.

Doubles facts and addition fact fluency are among the core skills assessed in the Primary Numeracy Intervention Program, a free K–3 math intervention built on the same research foundation as this game. If this activity is revealing gaps in your students' fact fluency development, the program gives you a precise diagnostic tool to identify exactly where the breakdown occurs and leveled materials to address it systematically — all free after completing a two-hour training.

Research on how children develop addition fact fluency consistently identifies derived fact strategies — strategies where students use a known fact to figure out an unknown one — as a critical bridge between counting strategies and full automaticity. The near-doubles strategy is one of the most well-documented examples of this, and it is widely recommended in mathematics education research as an explicit instructional target in Grades 1 through 3. 

Studies on arithmetic strategy development show that students who are explicitly taught derived fact strategies like near-doubles outperform students who rely on counting or rote memorization alone — both in speed and in their ability to transfer their knowledge to new and unfamiliar problems.

The National Council of Teachers of Mathematics emphasizes that building fact fluency through strategic reasoning — rather than drill alone — leads to deeper understanding and more durable learning. The near-doubles strategy is one of the clearest examples of how strategic thinking and fact knowledge reinforce each other.

Near-doubles and derived fact strategies are among the core addition strategies assessed in the Primary Numeracy Intervention Program, a free K–3 math intervention built on the same research foundation as this game. If this activity is revealing gaps in your students' strategy development or fact fluency, the program gives you a precise diagnostic tool to identify exactly where the breakdown occurs and leveled materials to address it systematically — all free after completing a two-hour training.