TL;DR: Both number bonds and fact families help children with ADHD learn basic math facts by highlighting relationships between numbers, but they do so in different ways. Number bonds use visual “part–whole” representations that build conceptual understanding and may reduce working memory load by creating mental schemas. Fact families group related addition/subtraction or multiplication/division facts, reducing the total facts to memorize and helping children retrieve answers through inverse relationships. Evidence suggests that in practice, a combination of both methods – conceptual learning with number bonds and structured practice with fact families – might offer the best of both worlds.

Introduction

Teaching math to children with ADHD requires careful attention to cognitive load and engagement. ADHD is associated with deficits in working memory and executive function, which often translate into difficulties in math. Children with ADHD can struggle to hold multiple numbers or steps in mind, leading to errors and frustration during calculations. Two common methods for building foundational math fact fluency are number bonds and fact families. This article compares these approaches through the lens of cognitive load theory and evidence-based research, focusing on how each method impacts working memory demands and student engagement for ADHD learners.

Understanding Number Bonds and Fact Families

Number Bonds: Number bonds are a visual representation of the “part–part–whole” relationship of numbers. A simple number bond shows how two (or more) parts combine to form a whole (e.g., 3 and 5 make 8). This concept, popularized by Singapore math, is introduced with concrete objects (like counters or beads) and then pictorial diagrams (circles connected by lines) before moving to abstract numbers. The goal is to build a deep understanding that numbers can be composed and decomposed in various ways. Educational research considers part–whole understanding one of the most fundamental milestones in early math development. In fact, mastery of part–whole relations in early childhood is a strong predictor of later math achievement. By internalizing number bonds, children learn to see connections (for example, knowing 8 can be 3+5 or 4+4) and develop what educators call “number sense”. For a learner with ADHD, number bonds offer a structured yet flexible framework: they can use tactile manipulatives and visuals, which leverages multiple senses and can keep them actively engaged while learning basic facts.

Fact Families: A fact family is a set of related math facts involving the same numbers. For instance, the numbers 3, 5, and 8 form a fact family yielding four facts: 3 + 5 = 8, 5 + 3 = 8, 8 – 5 = 3, and 8 – 3 = 5. In multiplication/division, 6, 8, and 48 would produce 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 6 = 8, and 48 ÷ 8 = 6. Teaching fact families emphasizes the inverse relationship between operations (addition vs. subtraction, multiplication vs. division). Instead of memorizing isolated facts, students learn a cluster of related facts together. This approach is considered more efficient because it exploits logical connections: if a student knows one fact in the family, they can derive the others. Importantly, learning facts as families effectively reduces the number of individual items a child needs to memorize, which can lessen the burden on working memory. Many math fluency programs (e.g., Reflex Math) are built around the fact family strategy because it develops automaticity (quick, effortless recall) while reinforcing understanding of operations. 

Number Bonds vs. Fact Families

For children with ADHD, fact families can provide clarity and structure – they see patterns in math facts rather than a random scatter of equations. However, drilling fact families can become tedious, so teachers often incorporate games, flashcards, or apps to keep practice engaging.

Cognitive Load and Working Memory

Why focus on working memory? Working memory is the “mental workspace” we use to hold and manipulate information, and it is notably limited in capacity. ADHD is strongly linked to working memory impairments, meaning that children with ADHD have a harder time juggling multiple pieces of information at once. 

In math, a student might need to recall basic facts while also following multi-step procedures; this can easily overwhelm a child with ADHD if the foundational facts are not automatic. Research shows a significant relationship between working memory and arithmetic skills – one meta-analysis found a medium correlation, with verbal working memory being especially important for arithmetic in primary children. In practice, this means that any instructional method which reduces the working memory load can benefit ADHD learners.

Cognitive load theory provides a useful framework here. It distinguishes between intrinsic load (the inherent complexity of the material) and extraneous load (avoidable distractions or inefficient instruction). For ADHD learners, minimizing extraneous cognitive load is critical – clear, uncluttered presentations and step-by-step guidance help prevent overload. 

Moreover, building schemas in long-term memory (through practice and understanding) effectively expands usable working memory capacity for a task. Both number bonds and fact families aim to create such schemas: number bonds by internalizing part-whole relationships, and fact families by linking operations and inverses. Once a child commits a number bond (say 10 broken into 6 and 4) or a fact family (4+6=10, 10–6=4, etc.) to long-term memory, recalling it places almost no strain on working memory. Fluent retrieval of math facts has been shown to “free up” working memory for more complex problem-solving. In other words, when basic facts become automatic, a student with ADHD can devote their mental resources to understanding the problem at hand instead of calculating simple combinations.

Number Bonds: In terms of cognitive load, number bonds may initially introduce a new concept (part-whole representation) that children must grasp, which is an intrinsic load. However, this concept leverages children’s innate ability to recognize totals and subsets (e.g., seeing that six eggs can be two groups of three). By using concrete objects and visuals, number bonds offload some of the cognitive work to the environment – children literally see the two parts and the whole, rather than having to hold all numbers in mind. This concrete-to-abstract progression aligns with research-based practices for teaching math to students with learning difficulties. As a child practices number bonds, they begin forming mental “chunks” (for example, knowing all the pairs that make 10). These chunks are stored in long-term memory as schemas. Later on, when solving a problem like 10 + 4 – 6, an ADHD learner who knows 10’s number bonds can quickly recognize that 6 and 4 make 10, simplifying the mental calculation. Thus, number bonds can reduce working memory load by providing a strong conceptual scaffold and by fostering automatic recall of common combinations (e.g., bonds of 5, 10, 20).

Fact Families: Fact families similarly aim to reduce the cognitive load, but through a slightly different mechanism. By teaching facts in related groups, the method exploits the brain’s preference for patterns and connections. Instead of treating “8 + 5 = 13” as separate from “13 – 5 = 8,” the fact family approach links them, effectively turning two facts into one idea. This integration is valuable for a child with limited working memory – it’s easier to remember one coherent pattern (a set of three numbers interrelated) than to memorize dozens of isolated sums or differences. A report on math fact instruction for struggling learners noted that learning related facts together is often easier and more efficient than learning them separately. As students practice fact families, they also reinforce understanding of inverse operations, which adds meaning to the memorization. 

There is empirical support that focusing on the relationship between addition and subtraction (or multiplication and division) can improve retention of math facts and help students reach automaticity faster. For ADHD learners, fact families can thus lower intrinsic load (by simplifying the sheer quantity of facts to learn) and extraneous load (by providing a consistent structure to fact practice). However, one challenge is that some children may still attempt to rote-memorize even within families; teachers should encourage using the relationships (e.g., “If I know 3+4=7, I can figure out 7–4”) to fully capitalize on this strategy.

Engagement and Motivation

Children with ADHD often face motivational and engagement hurdles, especially for repetitive tasks like drilling math facts. High interest and interactive learning experiences can significantly improve their focus and persistence. Therefore, any math teaching method must consider not only cognitive efficiency but also how to keep the child engaged. Both number bonds and fact families can be taught in engaging ways, and research as well as educator reports suggest that multisensory and game-based activities are particularly beneficial for ADHD students.

Number Bonds and Engagement: By nature, number bonds lend themselves to hands-on exploration. Teachers commonly use manipulatives (such as blocks, counters, or even plastic toys) to represent the parts and whole. For example, a student might split a pile of 10 counters into two groups and see the different combinations that make 10. This kind of concrete activity can captivate children with ADHD by making abstract numbers tangible and fun. It also channels their excess energy into a focused task (moving objects, drawing bond diagrams) rather than solely worksheet-based drills. 

Educators have noted that incorporating physical objects or pictorial worksheets for number bonds helps maintain the interest of inattentive learners, turning math into a sort of puzzle or game. Number bond practice can also be differentiated easily: students progress at their own pace, and the open-ended nature of “finding all the ways to make a number” can feel like a discovery exercise rather than rote memorization. All of this supports engagement. While there is not yet a specific experimental study comparing ADHD students’ on-task behavior during number bond lessons versus other methods, the emphasis on visual and kinesthetic learning aligns with general recommendations for teaching ADHD learners. 

One caution is to avoid making even number bonds overly “busy” or flashy in a way that distracts; the presentation should be clear and goal-focused to avoid adding extraneous cognitive load (e.g., simple diagrams with limited elements are better than cluttered graphics).

Number bond activity


Fact Families and Engagement: Fact families, if taught through traditional flashcards or drill worksheets alone, might not inherently excite a child with ADHD. The key is how the practice is structured. One effective approach is using gamified learning. For instance, Monster Math (an online program) combines Number bond and fact-family approach delivered via adaptive video games, with points and rewards, to sustain student motivation. 

In a classroom, teachers might turn fact family practice into a game (like a memory match or a timed challenge to find all four facts in a family). There is growing evidence that game-based learning can significantly increase engagement and interest in math for students with ADHD. 

Additionally, immediate feedback – a common feature in both digital math games and teacher-led activities like oral fact family quizzes – taps into the reward sensitivity in ADHD brains, providing the instant stimulation that helps keep them focused. Importantly, fact families lend themselves well to brief, frequent practice sessions (since each “family” is a small set of facts). Teachers can introduce a “fact family of the day” and revisit it repeatedly in quick bursts, which capitalizes on spaced repetition while preventing boredom. Over time, as students see their speed and accuracy improve, their confidence grows – and confidence itself is a powerful motivator, particularly for ADHD learners who may have experienced repeated frustrations in math. To summarize, while the content of fact families is inherently structured, making the practice interactive and rewarding is crucial. Combining the fact family approach with engaging techniques (like competitive team quizzes, digital apps, or hands-on card games) appears to yield the best outcomes in terms of attention and enthusiasm for ADHD students.

Evidence from Research

Direct research comparing number bonds and fact families specifically for ADHD populations is limited, as most studies focus on broader math intervention strategies or cognitive training. However, existing peer-reviewed studies and reviews shed light on elements of each approach:

  • Working Memory as a Bottleneck: A recent study by Gaye et al. (2024) found that working memory (across its visual and verbal components) accounts for over half the variance in children’s math achievement. Inattentive ADHD symptoms also had an additional, smaller effect on math performance. This underscores that any method which alleviates working memory demand – e.g., by making math facts automatic or externally supported – can directly improve math outcomes for ADHD learners. Both number bonds and fact families aim to build such automaticity and support, though via different routes.
  • Fluency and Cognitive Load: An evidence-informed review on math fact fluency for students with learning disabilities (many of whom had co-occurring ADHD) emphasizes that developing fluency is critical to reducing cognitive load. It recommends strategies like grouping related facts and using consistent, structured practice to help transfer knowledge to long-term memory. This aligns well with the fact family approach (grouping facts) and also supports number bonds (which give structure and meaning to basic combinations).
  • Intervention Studies on Math Facts: In a study of math fact interventions for students with ADHD, Brady and Kubina (2010) examined the “endurance” of multiplication fact fluency using intensive practice techniques. They found that with consistent practice, students with ADHD could achieve fluency and maintain it over time (endurance), especially when interventions were carefully designed to provide sufficient opportunities for response. While this study did not pit number bonds against fact families, it demonstrates that ADHD students can successfully reach automatic recall with evidence-based practice, highlighting the importance of frequent, focused drills (which could be structured around fact families) paired with strategies to maintain engagement. The success of such interventions likely comes from reinforcing memory (benefiting working memory limits) and using high-interest formats (benefiting attention).
  • Part-Whole Reasoning Benefits: Separate from ADHD-specific research, mathematics education research validates the importance of part-whole reasoning (the principle behind number bonds). Marx et al. (2025) note that part-whole understanding is “probably the major conceptual achievement of the early school years” and a key predictor of later success. Although this is a general finding, it suggests that investing time in number bonds can pay dividends for all students, including those with ADHD, by giving them a strong conceptual foothold that makes learning higher-level math easier down the line. A child who grasps part-whole relations early may find multi-step arithmetic problems less intimidating because they see the logical substructure of those problems.

In summary, the literature supports key pieces of both approaches. Building a robust schema for math facts (whether through part-whole insights or fact relationships) is beneficial for reducing cognitive load in ADHD learners. Likewise, maintaining student engagement through interactive, multisensory practice is crucial. However, no study to date appears to directly compare number bonds and fact families head-to-head for ADHD populations. In practice, these methods are not mutually exclusive but complementary. Number bonds might be introduced first to ground understanding, and fact families used to drill and extend that knowledge. 

The decision may also depend on individual learner preferences – some children with ADHD might latch onto the visual nature of number bonds, while others might enjoy the pattern-finding aspect of fact families. 

Conclusion

Evidence-based insights suggest that both approaches have merit: research in cognitive science and math education validates the importance of reducing working memory demands (through fluency and schema-building) and keeping learning motivating for students with attention challenges. Rather than choosing one method over the other, educators and parents might consider using them in tandem. 

For example, start with number bonds using hands-on materials to build understanding, then reinforce those connections with fact family exercises and games to achieve automatic recall. Ultimately, the goal is to enable the ADHD learner to recall basic math facts with little mental effort – this paves the way for tackling more complex math with confidence. As they become fluent, children experience fewer frustrating bottlenecks in working memory and more success in math overall. By combining the strengths of number bonds and fact families, and grounding our approach in research on cognitive load and engagement, we can better support ADHD learners on their journey to math proficiency.

FAQ

Q1: Which is better for a child with ADHD, number bonds or fact families?

​There is no one-size-fits-all answer – both techniques have advantages, and the best approach may be to use both in complement. Number bonds excel at building conceptual understanding of how numbers work, which can be very helpful for an ADHD child who needs that strong foundation. Fact families excel at structuring practice and reducing the sheer volume of facts to memorize, which can lighten the memory load. 

Q2: How do number bonds reduce cognitive load for ADHD learners?

Number bonds reduce cognitive load by externalizing and simplifying the information a child needs to process. Instead of mentally keeping track of three numbers and their relationships, the number bond diagram (or manipulatives) lays it out visually. This helps because children with ADHD often benefit from seeing and touching the math, not just hearing it or trying to recall it abstractly. The part-whole schema also creates a mental shortcut: once a child knows, for example, that 7 is 3 + 4, they don’t have to re-calculate 3 + 4 every time – it becomes a known “chunk” stored in long-term memory. 

Q3: My child finds drilling math facts boring. How can I make practice more engaging for an ADHD learner?

Engagement is crucial, and fortunately there are many ways to make math fact practice more fun. Here are a few evidence-backed strategies:

  • Use games and technology: Incorporate math fact games – these could be digital apps such as Monster Math that use a fact family approach in a game format, or physical games like bingo, card games, or timed challenges. Studies show that game-based learning can significantly boost attention and motivation in students with ADHD. 
  • Keep sessions short and frequent: Short bursts of practice (5–10 minutes at a time) are often more effective for ADHD learners than a single long session. During these short sessions, maintain a high level of interaction – for instance, rapid-fire Q&A or a quick race to write down a fact family. Frequent breaks and variety prevent burnout and boredom.
  • Multisensory approaches: Don’t limit practice to pen-and-paper. Let your child use magnetic numbers, write on a mini whiteboard, or even jump or toss a ball while reciting facts (physical activity can help some kids with ADHD focus better). Using visual aids and hands-on materials, like number bond circles or fact family triangle cards, can also sustain interest. Bringing numbers into the kitchen could be another strong way to engage the senses. 
  • Incorporate immediate feedback and positive reinforcement: Children with ADHD respond well to immediate feedback. When practicing, let them know right away if they got it correct. Celebrate progress – for example, use a sticker chart or a leveling-up system for mastered facts. Positive reinforcement (praise, rewards, or just the child seeing their own improvement) increases engagement and builds confidence. 

References

  1. Gaye, F., Groves, N. B., Chan, E. S. M., Cole, A. M., Jaisle, E. M., Soto, E. F., & Kofler, M. J. (2024). Working Memory and Math Skills in Children with and without ADHD. Neuropsychology, 38(1), 1–16. DOI: 10.1037/neu0000920
  2. Brady, K. K., & Kubina, R. M. (2010). Endurance of multiplication fact fluency for students with attention deficit hyperactivity disorder. Behavior Modification, 34(2), 79–93. DOI: 10.1177/0145445510361331
  3. Marx, C., Roesch, S., Moeller, K., & Benz, C. (2025). From the whole to its parts – A systematic analysis of affordances for learning part–whole relations in digital apps. International Electronic Journal of Mathematics Education, 20(1), em0802. DOI: 10.29333/iejme/15677