Questions: Number Bonds to 10

Question 1

Maria wants to add 8 + 5 in her head. She thinks: '8 needs 2 more to make 10, and 5 has a 2 to spare — so I'll make 10 and have 3 left over: 13.' What strategy is she using?

• A. She is counting on from 8
• B. She is using number bonds to 10 to break apart 5
• C. She is guessing because she doesn't know 8 + 5
• D. She is doubling 5 and subtracting 2

Answer: (B)

Maria is using the 'make a ten' strategy — a direct application of knowing number bonds to 10. She recognizes that 8 needs 2 to reach 10, then decomposes 5 into 2 + 3 using a bond. This shows that number bonds are tools for mental math, not just addition facts to memorize. Option A (counting on) would mean adding 1 at a time from 8; she's doing something more sophisticated.

Question 2

How many different ways can 10 be broken into two whole-number parts (counting 0 + 10 as one way)?

• A. 5 ways (only the symmetric pairs like 5+5, 4+6, 3+7)
• B. 9 ways
• C. 11 ways
• D. 10 ways (from 0+10 all the way to 9+1)

Answer: (D)

There are exactly 10 pairs: 0+10, 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, and 9+1. A common misconception is to count only one direction (e.g., 3+7 but not 7+3) and arrive at 5 or 6 pairs. But 3+7 and 7+3 are two different number bonds even though they use the same numbers — they represent different part-whole arrangements. The full set has 10 members.

Question 3

If you know that 7 + 3 = 10, you automatically know that 3 is the partner needed to complete 10 when you have 7.

• T. True
• F. False

Answer: True

This is exactly the part-whole relationship that number bonds teach. 10 is the whole, 7 and 3 are the parts. Knowing any two of the three values lets you figure out the third. If you have 7 and the whole is 10, then the missing part must be 3 — without any calculation beyond recognizing the bond.

Question 4

A child who has learned number bonds to 10 knows exactly 10 addition facts.

• T. True
• F. False

Answer: False

Number bonds are about understanding the part-whole relationship, not just memorizing facts. Knowing all bonds to 10 gives you far more than 10 facts: each bond (e.g., 6+4=10) immediately implies its reverse (4+6=10), two subtraction facts (10-6=4 and 10-4=6), and the 'make a ten' strategy for adding larger numbers. The value of number bonds comes from the relationships they encode, not from counting individual facts.

Question 5

Why does knowing your number bonds to 10 help you add numbers bigger than 10, like 8 + 7?

Model answer: Because you can use 'make a ten' — split 7 into 2 + 5, use the 2 to bring 8 up to 10, then add the remaining 5: 10 + 5 = 15. The bond 8 + 2 = 10 is the bridge.

This is the key payoff of knowing number bonds automatically. Instead of counting up from 8 to 15 (slow and error-prone), a student with fluent bonds decomposes one addend to create a friendly group of 10, then adds the remainder. This 'make a ten' strategy is one of the most powerful mental arithmetic techniques and relies entirely on instant recall of bonds to 10.