B. Number · Operations: Adding, Subtracting and Equal GroupsMental Math to 50
B2.3 B2.1About 35 minutes
Learning goals- I can add and subtract 10 or 20 from a number in my head.
- I can add tens first, then ones.
- I can jump to the next ten to add or subtract.
- I can explain the strategy I used.
Words to know
mental math
Doing math in your head, without paper. You can use a picture in your mind, like a number line.
tens
Groups of ten. In 34 there are 3 tens.
ones
Single units. In 34 there are 4 ones.
next ten
The closest ten after a number. The next ten after 27 is 30.
strategy
A plan or a way to solve a problem.
Let's start with a challenge
Can you solve 26 + 10 in your head? Most people can say 36 right away. Why is it so easy? Because only the tens change: 2 tens become 3 tens.
In this lesson you will add and subtract numbers that add up to 50 or less, in your head, using clever strategies. You might use paper to show your thinking, but the work happens in your brain.
Strategy 1: Add and subtract tens
When you add 10, the tens digit goes up by 1. The ones digit stays the same.
- 14 + 10 = 24
- 31 + 10 = 41
- 18 + 20 = 38 (2 more tens)
When you subtract 10, the tens digit goes down by 1.
Strategy 2: Tens first, then ones
To add a two-digit number, split it into tens and ones. Add the tens first, then the ones.
23 + 15: Split 15 into 10 and 5. 23 + 10 = 33. 33 + 5 = 38.
Worked exampleExample 1: Tens first
- Split 14 into 10 and 4.
- 32 + 10 = 42.
- 42 + 4 = 46.
Strategy 3: Jump to the next ten
Sometimes adding the ones takes you past a ten. Jump to the ten first.
28 + 6: The next ten after 28 is 30. 28 needs 2 to get there. Split 6 into 2 and 4. 28 + 2 = 30. 30 + 4 = 34.
This is just like make ten from Grade 1, but with bigger numbers!
Worked exampleExample 2: Jump to the next ten
Mira has 37 stickers. She gets 5 more. How many does she have now?
- The next ten after 37 is 40. 37 needs 3 to get there.
- Split 5 into 3 and 2.
- 37 + 3 = 40.
- 40 + 2 = 42.
Strategy 4: Jump back to a ten to subtract
33 − 5: Jump back to the ten first. 33 − 3 = 30. 5 is 3 and 2, so take away 2 more: 30 − 2 = 28.
Worked exampleExample 3: Subtract tens, then ones
- Split 23 into 20 and 3.
- Take away the tens: 48 − 20 = 28.
- Take away the ones: 28 − 3 = 25.
48 − 23 = 25. Check: 25 + 23 = 48.
Strategy 5: Use a fact you know
You know 6 + 3 = 9. That helps with bigger numbers too:
- 16 + 3 = 19
- 26 + 3 = 29
- 36 + 3 = 39
Only the tens are different. The ones work the same way!
Worked exampleExample 4: Adding 9
- Adding 9 is almost adding 10.
- 25 + 10 = 35.
- We added 1 too many, so take 1 away: 35 − 1 = 34.
Explain your strategy
Mathematicians share their thinking. After you solve a question, say how:
- "I added the tens first, then the ones."
- "I jumped to 30 first."
- "I added 10 and took 1 away."
There is often more than one good way. Try to find a way that is quick for you.
Just for funGood news: your brain has a built-in calculator. It's called mental math, and it never needs batteries!
Hands-on activityHundred chart (or 50 chart) jumps
You need: a number chart from 1 to 50 (draw 5 rows of 10 boxes and write 1 to 50, or print one) and a small toy to use as a game piece.
- Put the toy on any number, like 12.
- A grown-up calls out a move: "+ 10", "+ 20", "− 10", "+ 3".
- Move the toy. Moving down one row adds 10. Moving up one row subtracts 10. Moving right adds 1.
- Say the number sentence: 12 + 10 = 22.
- Now try to close your eyes and picture the chart before you move!
Math talk: "Why does moving down a row add 10?"
Your turn
44. The tens go up by one.
321 + 17 = ? Add tens first.
38. 21 + 10 = 31, then 31 + 7 = 38.
419 + 5 = ? Jump to the next ten.
24. 19 + 1 = 20, then 20 + 4 = 24.
38. 42 − 2 = 40, then 40 − 2 = 38.
25. 16 + 10 = 26, then take 1 away: 25.
7There are 39 kids in the gym. 15 go back to class. How many are still in the gym?
24 kids. 39 − 10 = 29, then 29 − 5 = 24.
More practice: on your own
126 + 18 = ? Explain how you did it.
44. 26 + 10 = 36. Then 36 + 8: jump 4 to 40, then 4 more to 44.
28. 35 − 5 = 30, then 30 − 2 = 28.
15. 47 − 30 = 17, then 17 − 2 = 15. Check: 15 + 32 = 47.
4A school bus has 28 children on it. At the next stop, 7 more get on. How many children are on the bus now?
35 children. 28 + 2 = 30, then 30 + 5 = 35.
42. 33 + 10 = 43, then 1 less is 42.
Challenge
1Show two different ways to solve 18 + 24.
42. Way 1: 18 + 20 = 38, then 38 + 4 = 42. Way 2: 18 + 2 = 20, then 20 + 22 = 42. (Other ways are fine too.)
2Fill in the blank: 27 + __ = 40
13. 27 + 3 = 30, then 30 + 10 = 40. 3 + 10 = 13.
3Noor solved 45 − 18 like this: 45 − 10 = 35, then 35 − 8 = 27. Ali solved it like this: 45 − 20 = 25, then he added 2 back. Who is right?
Both are right. The answer is 27. Ali took away 20, which is 2 too many, so he added 2 back: 25 + 2 = 27.
Quiz
3. For 27 + 5, what is the next ten after 27?
6. To add 9 in your head, you can...
Big idea: B2.3 asks Grade 2 children to use mental math strategies, including estimation, to add and subtract whole numbers that add up to no more than 50, and to explain the strategies they use. Mental math builds number sense: children think of numbers as tens and ones and use friendly numbers.
Common mistakes:
- Adding 10 to the ones (26 + 10 = 27 or 216). Use base-ten blocks or a hundred chart: adding 10 moves straight down one row.
- Losing track of the second jump (28 + 6: 28 + 2 = 30, then stopping or adding 6 again). Draw the jumps on an open number line.
- Thinking there is only one right way. Celebrate different strategies that give the same answer.
How to help: Use dimes, or bundles of 10 straws for adding tens. Ask "How did you figure that out?" and let your child explain. It is fine to jot an open number line on paper while learning; the goal is to do more in the head over time.