The missing number does not always come last. It can be anywhere.
Step 1: Picture It
Start with something you already know.
A balance with blocks
- A balance has a pan on each side.
- Same weight on each side keeps it level.
- Swap the two sides, and it stays level.
The equal sign means level: both sides are worth the same.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
What the equal sign means
The equal sign does not mean "the answer comes next". It means both sides are worth the same.
Equal means both sides have exactly the same value.
So 15 = 7 + 8 is a perfectly good sentence. It says the same thing backwards.
Check by putting it back
Once you have an answer, put it in the sentence and see whether both sides match.
Step 3: Try It Yourself
Tap and try it out.
8 and 7 makes 15.
9 and 6 makes 15.
How many
8 and 7 make 15.
Step 4: In Real Life
A piggy bank
You had some coins. You added 7. Now there are 15. How many at the start? ? + 7 = 15. Eight.
Step 5: Watch an Example
One step at a time.
Watch Leo Find a Start
Leo is asked: ? + 6 = 14.
- Step 1
He sees the missing number is at the start.
Watch Maya Find a Middle
Maya is asked: 16 − ? = 9. She starts. You finish.
- Step 1
She sees the missing number is in the middle.
Step 6: Your Turn
Practice makes it stick.
The Jar
Problem 1 of 13
Ana put 7 more marbles in a jar. Now there are 16. How many were in it before?
marbles
The Bookshelf
Problem 2 of 13
Leo took 8 books off a shelf. 7 are left. How many books were there at the start?
books
Fill the Gap
Put each answer back in. Do both sides match?
Problem 3 of 13
9 + ? = 16
Problem 4 of 13
? + 5 = 13
Problem 5 of 13
17 − ? = 9
Problem 6 of 13
14 = 6 + ?
Find the Mistake
A friend found a missing number. Spot the slip, then fix it.
Problem 7 of 13
Ben solves ? + 5 = 12. He says 17. What did Ben do?
Ben's work for ? + 5 = 12
- 112 + 5 = 17
- Answer17
Problem 8 of 13
? + 5 = 12. What is the missing number?
Problem 9 of 13
Ana solves 14 − ? = 9. She says 6. What did Ana do?
Ana's work for 14 − ? = 9
- 19, 10, 11, 12, 13, 14
- Answer6
Problem 10 of 13
14 − ? = 9. What is the missing number?
Which Way?
Is a part missing, or the whole? Pick the way.
Problem 11 of 13
7 + ? = 15. Which way finds the missing number?
Problem 12 of 13
? − 6 = 9. Which way finds the missing number?
Build the Total
Build it, then check.
Problem 13 of 13
8 and 7 more. Fill that many boxes.
How many
Step 7: Quick Check
Show what you know.
Question 1 of 2
? + 8 = 15
Question 2 of 2
What does the equal sign mean?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 1
8 + 4 = ? + 5. What is the missing number?
What You Learned
- The missing number can be anywhere in the sentence.
- The equal sign means both sides are worth the same.
- Check an answer by putting it back in.
For the grown-up
This lesson is where the child solves equations within 20 with the unknown in any position, including start unknown. Fluency within twenty is not speed for its own sake. Facts that come without thinking free up the working memory that the next four years of mathematics need, and a child recomputing 8 + 6 every time has nothing left over for the problem it sits inside.
Watch for finger counting that has gone underground — a pause, a glance away, lips moving. The strategy has not gone; it has just got quieter.
Short and often beats long and rare. Two minutes of the facts they nearly know is worth more than twenty minutes of the ones they already do.
Where the unknown can hide — A missing number can sit in three places: at the start (? + 6 = 14), in the middle (7 + ? = 15), or at the end (9 + 4 = ?). Only the last one is ordinary addition. The other two look harder but are the same fact family seen from a different side.
Turn it into a subtraction — For 7 + ? = 15, ask what 15 - 7 is. The whole is 15, one part is 7, so the other part is 8. Whenever the whole is known and one part is missing, subtract. Whenever both parts are known, add. Deciding which case you are in is most of the work.
Always put your answer back in — Once you think ? is 8, write the sentence out with 8 in place of the question mark: 7 + 8 = 15. If it is true, you are done. This check costs almost nothing and catches the most common error, which is subtracting the wrong way round.
Ask what would balance it — ☐ + 8 = 15. What joins 8 to make 15? Count up: 7. 15 − ☐ = 8. What was taken to leave 8? Count up from 8 to 15: 7. 15 = 7 + ☐. The whole is on the left this time, and it changes nothing. Wherever the box sits, ask what makes both sides worth the same.