B2.1 How the operations connect
Adding the same number again and again is multiplying: 2 + 2 + 2 is 3 groups of 2. Taking away the same number again and again is dividing. Subtraction also undoes addition.
Example
Check 7 + 6 = 13 using subtraction.
- Start from the answer: 13 − 6 = 7. ✓
- Or: 13 − 7 = 6. ✓
- If the take-away gives you back a number you started with, the addition was right.
B2.2 Facts to 20
Facts to 20 build on facts to 10. Doubles (7 + 7), near doubles (7 + 8), and making ten (8 + 5 → 10 + 3) make them fast.
Example
7 + 6 = ? and its related subtraction facts.
- 7 + 6 = 13. Also 6 + 7 = 13.
- 13 − 6 = 7 and 13 − 7 = 6.
- Four facts, one family.
B2.3 Mental math to 50
To add in your head, jump to the next ten first, then add what is left. Estimate before you start so you know about where the answer lands.
Example
Add 33 + 9 in your head.
- Estimate: about 33 + 10 = 43, so a little less.
- 33 needs 7 to reach 40. Take 7 from 9: 2 left.
- 40 + 2 = 42.
B2.4 Adding and subtracting to 100
For numbers to 100, add the tens, add the ones, then join them. Sometimes the ones make a new ten — regroup it.
Example
A jar holds 38 crackers. 25 more go in. How many now?
- Number sentence: 38 + 25 = ?
- Tens and ones, then join: 63.
- Check: 63 − 25 = 38. ✓
- Read the story and picture it.
- Joining or taking away?
- Write the number sentence.
- Solve with tens and ones; regroup if needed.
- Check with the partner fact.
B2.5 Multiplying: equal groups
Example
3 groups of 2 crackers. How many altogether?
- Repeated addition: 2 + 2 + … (3 times) = 6.
- Multiplication says the same thing: 3 × 2 = 6.
- Groups can be parts too: 3 groups of one half make 1 and a half.
B2.6 Dividing: equal sharing
Example
Share 12 crackers equally among 4 friends.
- Deal them out one at a time until they are gone.
- Each friend gets 3.
- Check: 4 × 3 = 12. Division and multiplication are partners.
Summary
- Repeated adding is multiplying; repeated taking away is dividing.
- Facts to 20: doubles, near doubles, make ten.
- Jump to the next ten to add in your head.
- Equal groups multiply; equal sharing divides.