Adding and subtracting are not two skills. They are one relationship read in different directions.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Four sentences from one bond
Parts of 8 and 7 make 15. That gives 8 + 7, 7 + 8, 15 − 8, and 15 − 7.
Why this saves work
If you know 8 + 7 = 15, you already know 15 − 8. You do not have to work it out again.
Step 2: Try It Yourself
Tap and try it out.
15
8
7
- 8 + 7 = 15
How many
15 and 5 make 20. There are 5 empty spaces.
8 and 7 make 15.
Step 3: In Real Life
A parking lot
A lot holds 15 cars. 9 are parked. 6 spaces are free. 9 + 6, 6 + 9, 15 − 9, 15 − 6. One lot, four facts.
Step 4: Watch an Example
One step at a time.
Watch Ana Reuse a Fact
Ana is asked for 16 − 9, and she already knows 9 + 7 = 16.
- Step 1
She reads the question as a missing part, not a take-away.
Step 5: Your Turn
Practice makes it stick.
The Coat Rack
Problem 1 of 2
14 coats hang on a rack. 6 are red. How many coats are not red?
coats
Lost Marbles
Problem 2 of 2
Leo had 17 marbles. Now he has 9. How many did he lose?
marbles
Use the Family
Each question can be answered with a fact you already know.
1 of 4
You know 7 + 6 = 13. What is 13 − 7?
2 of 4
You know 9 + 8 = 17. What is 17 − 8?
3 of 4
Parts of 5 and 9. What is the whole?
4 of 4
Whole 18, one part 9. What is the other part?
Show the Missing Part
Build it, then check.
15 is 8 and how many? Show that part.
How many
Step 6: Quick Check
Show what you know.
Question 1 of 2
You know 8 + 5 = 13. What is 13 − 5?
Question 2 of 2
How many number sentences come from parts of 6 and 9?
What You Learned
- Two parts and a whole make four number sentences.
- A subtraction question is asking for the missing part.
- Knowing one fact hands you the other three.
For the grown-up
This lesson is where the child writes the four related equations for a part-part-whole relationship within 20. 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.
Why the four sentences belong together — A fact family is built from three numbers where two of them combine to make the third, like 5, 8 and 13. Those three numbers can be arranged into two additions and two subtractions. They are not four separate facts to memorize — they are one relationship described from four directions.
The four sentences in full — From 5, 8 and 13: 5 + 8 = 13, 8 + 5 = 13, 13 - 5 = 8, and 13 - 8 = 5. The biggest number, 13, is the whole. It sits alone after the equals sign in the additions, and it starts both subtractions. Spotting which number is the whole is the key to writing the family correctly.
What this buys you — If you know 5 + 8 = 13, you already know 13 - 8 without doing any subtracting. Children who see fact families stop treating subtraction as a separate skill to be dreaded. Subtraction becomes a question about addition: what do I add to 8 to reach 13?
One relationship, four sentences — Parts 6 and 7. Whole 13. 6 + 7 = 13 7 + 6 = 13 13 − 6 = 7 13 − 7 = 6 The three numbers never changed. Only which one you were hunting for.