Mental Math
This is what I charted during one of our mental math Number Talks from last week. I thought you might like to know what it looks like.
This was the second day that I had given them a multiplication problem. We were previously working on subtraction and addition.
I gave them the problem, 14 x 4, and asked that they try to solve it mentally. I called on five students who showed me they were ready to share their solutions. This is what they said...
The first student said she pictured a bar diagram with 4 bars, each with the number 14. Then she took me through her thinking... she doubled 14 two times and then used place value to add 28 + 28. (20 + 20 = 40, 8 + 8 = 16, 40 + 16 = 56).
The second student started with 14 on a number line and then added 14 three times.
The third student also used a number line, but said he/she (I can't remember who it was!) pictured adding 10 four times and then 4 four times.
The fourth student rounded to 15, multiplied using place value (ones place and then the tens place), and then added.
The fifth student also rounded to 15, but he/she doubled 15 twice and added to get 60. Then, he/she subtracted 4 to compensate for the amount he/she added to round.
Pretty exciting stuff!
This was the second day that I had given them a multiplication problem. We were previously working on subtraction and addition.
I gave them the problem, 14 x 4, and asked that they try to solve it mentally. I called on five students who showed me they were ready to share their solutions. This is what they said...
The first student said she pictured a bar diagram with 4 bars, each with the number 14. Then she took me through her thinking... she doubled 14 two times and then used place value to add 28 + 28. (20 + 20 = 40, 8 + 8 = 16, 40 + 16 = 56).
The second student started with 14 on a number line and then added 14 three times.
The third student also used a number line, but said he/she (I can't remember who it was!) pictured adding 10 four times and then 4 four times.
The fourth student rounded to 15, multiplied using place value (ones place and then the tens place), and then added.
The fifth student also rounded to 15, but he/she doubled 15 twice and added to get 60. Then, he/she subtracted 4 to compensate for the amount he/she added to round.
Pretty exciting stuff!
Addition + Subtraction Strategies We've Learned So Far
Some of these still need to be reviewed, but students should be able to explain the basics of the strategies and will eventually feel comfortable using them in math class and in the real world. In class, I present students with a string of numbers that build on each other and highlight the strategy that we are focusing on for the day.
I will take a picture of an addition and subtraction chart and post it this week.
Strategy 1: Subtract the same amount from both numbers.
Taking 1 away from both numbers makes the numbers easier to work with and it doesn’t change the distance between the numbers.
Examples: 56 – 21 becomes 55-20
76 – 31 becomes 75 - 30
(This problem can be explained very clearly on a number line.)
Strategy 2: Near doubles - Add or subtract to make a double.
Example: 22+23 (Subtract 1 from 23 to make a double)
22 + 22 = 44, then add the one you subtracted… 44 + 1 = 45
Strategy 3: Round up and then add. Subtract what you rounded.
Example: 853 + 999
999 rounds to 1,000
1000 + 853 = 1,853
1853 – 1 = 1,852
(This problem can be explained very clearly on a number line.)
Strategy 4: When subtracting, round the smaller number and then add or subtract what you rounded.
Example: 9135 – 999
999 rounds to 1,000
9135 – 1000 = 8135
8135 + 1 = 8136
(This problem can be explained very clearly on a number line.)
I will take a picture of an addition and subtraction chart and post it this week.
Strategy 1: Subtract the same amount from both numbers.
Taking 1 away from both numbers makes the numbers easier to work with and it doesn’t change the distance between the numbers.
Examples: 56 – 21 becomes 55-20
76 – 31 becomes 75 - 30
(This problem can be explained very clearly on a number line.)
Strategy 2: Near doubles - Add or subtract to make a double.
Example: 22+23 (Subtract 1 from 23 to make a double)
22 + 22 = 44, then add the one you subtracted… 44 + 1 = 45
Strategy 3: Round up and then add. Subtract what you rounded.
Example: 853 + 999
999 rounds to 1,000
1000 + 853 = 1,853
1853 – 1 = 1,852
(This problem can be explained very clearly on a number line.)
Strategy 4: When subtracting, round the smaller number and then add or subtract what you rounded.
Example: 9135 – 999
999 rounds to 1,000
9135 – 1000 = 8135
8135 + 1 = 8136
(This problem can be explained very clearly on a number line.)
