See the connection
6 + 7 = 6 + 6 + 1 = 13
Build two rows of 6 counters, then put one extra counter in the second row. The double makes 12; the extra counter makes 13.
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 |
|---|---|---|
| 5 + 6 | Smaller double + 1 | 5 + 5 + 1 = 11 Only one group has one extra item. |
| 8 + 9 | Larger double − 1 | 9 + 9 − 1 = 17 The group of 8 is one short of 9. |
1. Make the double visible first
A double adds a number to itself: 4 + 4, 6 + 6, or 8 + 8. Arrange counters in matching rows and connect the picture to the equation. If the child must count every counter, spend time establishing these doubles before asking for quick adjustments.
Try it together
Place 5 counters in each of two rows. Ask what is the same about the rows, then label the total 5 + 5 = 10.
2. Double the smaller number and add one
For adjacent addends, the larger addend has one more item. Keep the smaller double unchanged and add that extra item once. Point to the extra counter while writing the adjustment.
Try it together
For 7 + 8, start with 7 + 7 = 14. Add one counter to one row: 14 + 1 = 15. Ask why you did not add two.
3. Double the larger number and subtract one
The same fact can be derived from the larger double. This is useful if that double is more familiar. Compare both approaches with the same model; do not require a child to use both before either is secure.
Try it together
For 7 + 8, show 8 + 8 = 16. Remove one counter from one row: 16 − 1 = 15. Compare this with the previous example.
4. Choose the strategy that fits
Near doubles are a useful option, not a rule for all addition. A fact such as 8 + 5 may be easier by making ten. Ask which known fact helps, then revisit a few near doubles in a different order on another day.
Try it together
Compare 6 + 7 and 8 + 5. Ask the learner to choose a double or a ten and explain their choice. Both facts total 13, but different relationships may feel easier.
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 a double to solve 4 + 5.
Show answer & explanation
9
4 + 4 = 8. One extra counter gives 9.
Use 8 + 8 to solve 7 + 8.
Show answer & explanation
15
8 + 8 = 16. The 7 is one smaller than 8, so subtract one: 15.
A child says 6 + 7 = 15 because 7 + 7 = 14, then adds one. What needs to change?
Show answer & explanation
Subtract one from 14, giving 13.
The starting double uses two groups of 7. The original fact has a group of 6, so there is one fewer item.
A simple routine to try
Adapt the amount and pace to the learner. This is a suggested routine, not a fixed prescription.
- Build a familiar double with counters.
- Add one counter to one row and explain the new equation.
- Try two near doubles independently, with support available.
- Revisit the facts later without keeping them in a fixed order.
What to watch for
A common error is doubling the larger number and then adding one. Name the starting double explicitly. If you start from the smaller double, add one; if you start from the larger double, subtract one.
When to take the next step
Move to a varied addition set when the learner can explain the adjustment and answer accurately across sessions. Extend to addends two apart only after the one-more relationship is clear.
Common questions
Is 6 + 8 a near double?
Some materials use “near doubles” for addends two apart as well. Here we start with addends one apart. For 6 + 8, a related strategy is 6 + 6 + 2 = 14, or moving one from 8 to 6 to make 7 + 7.
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 →