See the connection
13 − 8 = 5 because 8 + 5 = 13
Count up from 8 to 10 (2), then from 10 to 13 (3). The difference is 2 + 3 = 5.
Quick-reference strategies
Choose a relationship the learner understands. These are useful options, not a required sequence or a guarantee of instant recall.
| Fact or set | Try this | Example & explanation |
|---|---|---|
| Subtract 0 or the whole | Use whole-part meaning | 9 − 0 = 9; 9 − 9 = 0 Remove nothing, or remove all the items. |
| Subtract 1 or 2 | Count back a small amount | 8 − 2: 7, 6 Each step removes one. Keep track of the number of steps. |
| Numbers close together | Find the gap by counting up | 15 − 13 = 2 13 needs 2 more to reach 15. |
| Known addition fact | Find the missing addend | 12 − 7 = 5 because 7 + 5 = 12 The same whole has the same two parts. |
| Crossing ten | Subtract in parts through ten | 14 − 6 = 14 − 4 − 2 = 8 Split the 6 removed into 4 and 2. |
1. Show the whole and its parts
Use a collection of objects to represent the whole. Remove or cover one part and ask what remains. Link each number in the equation to the model.
Try it together
Show 9 counters. Cover 4. Ask “How many are hidden? How many can you see? What is the whole?” Write 9 − 4 = 5.
2. Think of a missing addend
Connect subtraction to addition explicitly. If 7 + 5 = 12, then 12 − 7 asks for that missing 5. Use a bar model to show the same whole and parts.
Try it together
Write 7 + □ = 12 beside 12 − 7 = □. Let the learner build the relationship with counters before filling the boxes.
3. Count up when the numbers are close
When subtracting nearby numbers, finding the gap may be simpler than counting backward many times. On a number line, label both the start and the end of each jump.
Try it together
For 15 − 12, jump from 12 to 15: 3. For 13 − 8, try the two jumps through ten shown above.
4. Use fact families thoughtfully
Write related addition and subtraction equations from one model. Ask how the equations describe the same quantities, then practice recalling them across days.
Try it together
With 6, 8, and 14, build 6 + 8 = 14, 8 + 6 = 14, 14 − 6 = 8, and 14 − 8 = 6. Explain why 6 − 14 is a different problem.
Try it: think, then check
Work it out before opening the answer. Use counters or a drawing if helpful. The explanation matters as much as the result.
Use addition to solve 13 − 6.
Show answer & explanation
7
6 + 7 = 13, so the missing part is 7.
Count up to solve 16 − 14.
Show answer & explanation
2
From 14 to 16 is a gap of 2. You do not need to count backward fourteen times.
A simple routine to try
Adapt the amount and pace to the learner. This is a suggested routine, not a fixed prescription.
- Build a whole and two parts.
- Connect one subtraction fact to an addition fact.
- Try a close-number example by counting up.
- Mix a few established and developing subtraction facts.
What to watch for
Do not teach “subtract the smaller digit from the larger digit” as a general rule. Preserve the order of the quantities. If a learner loses track counting backward, model a missing-addend or number-line approach.
When to take the next step
Move forward when the child can interpret the equation and select a workable strategy. Reduce the number range and use counters when the whole-part relationship is unclear.
Common questions
Is counting up really subtraction?
Yes. Counting from the smaller quantity to the larger one measures their difference. Connect the jumps to the subtraction equation so the strategy has a clear meaning.
Research behind the guidance
These sources support the teaching principles. The examples and routines are FluentFacts’ practical applications, not individually tested interventions or a promise of outcomes.
Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (2021)
What Works Clearinghouse · Institute of Education SciencesSupports systematic instruction, mathematical language, representations, number lines, and carefully used fluency activities in elementary intervention.
Put it into practice: Teach one relationship explicitly, connect a model to its equation, and give specific feedback before asking for independent recall.
Organizing Instruction and Study to Improve Student Learning (2007)
Institute of Education SciencesRecommends spacing learning over time, connecting concrete and abstract representations, and using retrieval to strengthen learning.
Put it into practice: Revisit a small fact set across days. Ask the learner to produce an answer before checking, then correct mistakes with a useful strategy.
Adding It Up: Helping Children Learn Mathematics (2001)
National Research CouncilDescribes mathematical proficiency as interwoven strands, including conceptual understanding, procedural fluency, strategic competence, reasoning, and productive disposition.
Put it into practice: Look for accurate answers, flexible strategies, and an explanation of why the fact works. Record progress beyond speed alone.
Put the idea into practice.
Choose an operation and a suitable fact range in FluentFacts. Begin with facts the learner understands.
Choose your practice Or create a worksheet →