See the connection
8 + 5 = 10 + 3 = 13
Split 5 into 2 and 3. Move 2 to the 8 to make ten; 3 are left. The total stays the same.
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 |
|---|---|---|
| Add 0 or 1 | Keep the quantity, or take the next number | 8 + 0 = 8; 8 + 1 = 9 Zero adds no items. One adds one item. |
| Add 2 | Count on two when needed | 7 + 2: 8, 9 Begin with the known quantity of 7 instead of recounting it. |
| Doubles | Use two equal groups | 6 + 6 = 12 The same quantity appears twice. |
| Near doubles | Use a double, then adjust | 6 + 7 = 12 + 1 = 13 The second group has one extra item. |
| Add 9 | Add ten, then subtract one | 9 + 6 = 10 + 6 − 1 = 15 Nine is one less than ten. |
| Crossing ten | Make ten, then add the rest | 8 + 5 = 10 + 3 = 13 Split 5 into 2 and 3; moving the 2 keeps the total unchanged. |
1. Count on from a known quantity
When a learner can recognize and hold a quantity, show how to start there and count the extra items. Connect the action to the equation. This bridges counting every object and using relationships.
Try it together
Show 6 counters and add 2. Say “Six … seven, eight.” Then compare with 2 + 6: the total is unchanged.
2. Use doubles to find near doubles
Build two equal groups. Once 6 + 6 is understood and familiar, show that 6 + 7 contains one extra item. Have the child explain where the extra one appears.
Try it together
Build two rows of 6 counters. Add one counter to the second row: 6 + 7 = 6 + 6 + 1 = 13.
3. Make a ten
A ten-frame helps children see how much is needed to complete ten. Partition the second addend, move that amount, and name what remains. Do not teach moving counters as an unexplained trick.
Try it together
Place 8 counters in a ten-frame and 5 beside it. Move 2 into the empty spaces. Read the worked example above together.
4. Choose a strategy, then retrieve
Compare more than one sensible approach. A learner might solve 9 + 8 by making ten or by using 8 + 8 + 1. Practice a small set over time, asking for an explanation occasionally rather than after every fluent answer.
Try it together
Ask “Which fact do you already know that could help with 7 + 8?” Let the child choose a representation.
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.
Solve 7 + 8 using a double.
Show answer & explanation
15
7 + 7 = 14, then add one: 15. Or use 8 + 8 − 1.
Make ten to solve 8 + 6.
Show answer & explanation
14
Split 6 into 2 and 4. Then 8 + 2 + 4 = 10 + 4 = 14.
A simple routine to try
Adapt the amount and pace to the learner. This is a suggested routine, not a fixed prescription.
- Warm up with a familiar double.
- Model one near double or make-ten example.
- Try a few related facts, then mix in familiar ones.
- Return to those facts on another day.
What to watch for
Counting on is useful, but counting one by one forever limits efficiency. Offer relationships without shaming fingers or other tools. Check that the learner can partition numbers before introducing make-ten.
When to take the next step
Add less familiar combinations when the child accurately uses the current relationship across sessions. For a greater challenge, ask for two strategies or a missing-addend equation.
Common questions
Should children memorize addition facts first?
Build meaning and relationships alongside recall practice. Reciting answers without understanding can make unfamiliar problems harder to solve. Familiar facts can then serve as anchors for new ones.
What is the make-ten strategy?
Partition one addend to complete ten with the other, then add what remains. For 7 + 5, split 5 into 3 and 2: 7 + 3 + 2 = 12. A ten-frame makes the regrouping visible.
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 →