Addition Fact Strategies: Doubles, Near-Doubles and Making Ten
A doubles fact has two numbers the same, like 6 + 6. A near-double is a double plus one, like 6 + 7. To make ten for 8 + 5, take 2 from the 5 to make 10. Then add the 3 left. These worked examples are ours. We suggest one strategy at a time, alongside your child's math instruction.
TL;DR
- A doubles fact has two numbers the same, like 6 + 6. Near-doubles is another name for doubles plus one. For 6 + 7, think 6 + 6, then one more. That worked example is ours.
- To make ten for 8 + 5, take 2 from the 5 to make 10. Then add the 3 left. That worked example is ours.
- A 2021 federal guide on extra math help lists strategies a child can fall back on. They are counting on, doubles, doubles plus one, and pairs that make ten.
- A 2021 federal guide on extra math help rates the evidence for short timed practice as strong. Teaching a strategy first is one of its steps. Strong means its studies kept finding gains, across different groups of children. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success.
- The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.
An addition fact is a sum of two single-digit numbers, like 6 + 7.
”Addition factWhat does the federal guide say about addition strategies?
A US federal guide on extra math help came out in 2021 (Fuchs and colleagues). It covers children who struggle with math, from kindergarten to sixth grade. It is about help in small groups or one to one, at school. It is not a guide to dyscalculia. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success.
The guide lists strategies a child can fall back on. They are counting on, doubles, doubles plus one, and pairs that make ten. The guide puts them before timed practice. It rates the evidence for short timed practice as strong. Teaching a strategy first is one of its steps. Strong means its studies kept finding gains, across different groups of children. In 19 of its 27 studies of timed practice, children were taught a strategy first.
Each study tested a whole package of help. So the guide cannot say what one step adds on its own.
The four strategies, one at a time
The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it. The worked examples below are ours too.
Counting on. For 8 + 3, start at 8. Count up three: 9, 10, 11. In our view, start from the bigger number. It means fewer counts.
Doubles. Both numbers are the same: 3 + 3, 5 + 5, 6 + 6. To us, a double is easy to picture. An egg box holds two rows of six. So 6 + 6 is 12.
Doubles plus one. Near-doubles is another name for doubles plus one. For 6 + 7, think 6 + 6 is 12. Then add one more to get 13. Your child uses a fact they know to reach a new one.
Making ten. The guide calls these pairs combinations of ten. Some are 1 + 9, 2 + 8 and 3 + 7. For 8 + 5, take 2 from the 5 to make 10. Then add the 3 left. That worked example is ours.
Our suggestion is to teach one strategy at a time. Stay with it until your child picks it on their own. Then mix it with the ones before.
Objects, then a drawing, then the numbers
The guide rates the evidence for hands-on and drawn models, linked to the numbers, as strong. The guide shows the model and the numbers together. Objects, then a drawing, then the numbers is our own working order. Which model suits which topic is the panel's advice.
Here is how we would do it for 8 + 5. Draw a box with two rows of five spaces. That is a ten frame. Put 8 buttons in it. Two spaces are empty. Move 2 of the 5 new buttons in. Now there is a full ten, and 3 left over. Next, draw the same thing with dots. Last, write 8 + 5 = 10 + 3 = 13.
The guide says to fade out objects and drawings only as a child becomes accurate without them. In our view, go back to the buttons whenever a sum gets hard.
Making ten on a number line
The guide also uses a number line for adding, as a distance along the line. It rates the evidence for number lines as strong. That grade is for the advice as a whole, not for each step in it. Only two of the guide's number-line studies used the line for adding and subtracting.
Our version: for 8 + 5, start on 8. Jump 2 to land on 10. Then jump 3 more to land on 13. Say each jump out loud as it happens. Our page Number Line Activities to Try at Home has more.
Where timed practice fits
The guide recommends short timed practice, 1 to 5 minutes, on facts already taught. It rates the evidence for short timed practice as strong. It says not to use timed work to teach a new idea. In the panel's opinion, timed worksheets alone do not build fluency. The goal is right answers, not how many are tried. Progress charts are kept private.
For timed addition practice, the guide starts with easier facts, like plus-one facts and doubles. Earlier sets are then mixed back in. The order is the panel's advice.
For a child who gets anxious, the guide suggests saying that finishing is not expected. If worry or mood is the thing, talk to someone who works with children's mental health.
Keep the practice going, and check what the fact means alongside it.
When to ask for help
Each of these is a reason to ask for help on its own.
- Little change, even with steady practice and good teaching.
- Math well below your child's other schoolwork.
- A teacher who raises a concern about math.
- Extreme upset about math.
- Complete avoidance of math.
- Worry about math that spreads into the rest of learning.
- Sadness or worry that lasts.
- A skill that was there and has gone. Our position is that a lost skill goes to a doctor first, not a tutor.
If no skill has gone, start with the teacher. Say what you are seeing at home, and what you have tried. Beyond the teacher, the right person depends on what it turns out to be about. If the work is too hard, someone who works on that school skill. If worry or mood is the thing, someone who works with children's mental health. In our view, if you are worried enough to ask, a professional evaluation is worth asking about.
Any talk of hurting themselves is a same-day call to your doctor or a crisis line.
In the classroom
In our view, note which strategy a child reaches for on each fact.
One sentence for an email home: "She did 7 + 8 as 7 + 7 and one more today. What do you see at home?"
Key Takeaways
Near-doubles is another name for doubles plus one.
In our view, teach one strategy at a time. Show it with objects first, then a drawing, then the numbers.
A 2021 federal guide on extra math help rates the evidence for short timed practice as strong. Teaching a strategy first is one of its steps. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success.
Keep the practice going, and check what the fact means alongside it.
The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.
Our position is that a lost skill goes to a doctor first, not a tutor.
Put six buttons in a row. Put six more below them. Ask your child how many. Then add one more button and ask again. You are not testing anything. You are watching how they get there. Do they count from one, or use the 12? This routine is ours. It is one thing to notice, not an answer on its own.
”What to do tonightWhat to use next
A set of questions you answer about what you see at home. A screener is a starting point, not a diagnosis. If your child might need formal accommodations (an IEP or 504 plan), or you suspect a vision, hearing, or medical cause, pursue a professional evaluation too — that's the only route to those supports.
What sits underneath arithmetic, one skill at a time, worked alongside math instruction, not in place of it.
Common questions from parents
What is the make ten strategy?
A child breaks one number so the other becomes 10. For 8 + 5, take 2 from the 5 to make 10. Then add the 3 left. That worked example is ours. A 2021 federal guide on extra math help names combinations of ten as a fall-back strategy. The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.
What is doubles plus one?
Doubles plus one uses a double to find the fact next to it. Near-doubles is another name for it. For 6 + 7, think 6 + 6 is 12. Then add one more to get 13. That worked example is ours. A 2021 federal guide on extra math help lists doubles plus one as a fall-back strategy. The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.
In what order should I teach addition facts?
A 2021 federal guide on extra math help gives an order for timed practice. It starts with easier facts, like plus-one facts and doubles. Earlier sets are then mixed back in. The order is the panel's advice. Our suggestion is one strategy at a time, with objects first. The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.
Should my child do timed addition practice?
Timed practice has its place. A 2021 federal guide on extra math help covers timed practice. The guide recommends short timed practice, 1 to 5 minutes, on facts already taught. It says not to use timed work to teach a new idea. In the panel's opinion, timed worksheets alone do not build fluency. The guide rates the evidence for short timed practice as strong. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success. The goal is right answers, not how many are tried. Progress charts are kept private.
What about subtraction?
A 2021 federal guide on extra math help lists the same fall-back strategies for subtracting as for adding. They are counting on, doubles, doubles plus one, and pairs that make ten. The guide also shows subtracting as a distance on a number line. It rates the evidence for number lines as strong. That grade is for the advice as a whole, not for each step in it. Only two of the guide's number-line studies used the line for adding and subtracting. Its studies were of help given in school, not at home. Nothing in the guide tests Learning Success. In our view, start from an addition fact your child knows. For 13 − 5, ask what goes with 5 to make 13. That worked example is ours. The home routines on this page are ours. We hold no study that tests them at home. Do them alongside your child's math instruction, not in place of it.