a) Doubles Facts: 4 + 4, 40 + 40, 400 + 400, and 4000 + 4000 b) Plus One Facts: (next number) 5 + 1, 50 + 10, 500 + 100, 5000 + 1000 c) Plus Two Facts: (2-more-than facts) 7 + 2, 70 + 20, 700 + 200, 7000 + 2000 d) Plus Three Facts: 6 + 3, 60 + 30, 600 + 300, 6000 + 3000 e) Near Doubles: (1-apart facts) 3 + 4, 30 + 40, 300 + 400, 3000 + 4000 f) Plus Zero Facts: (no-change) 8 + 0, 80 + 0, 800 + 0, 8000 + 0 g) Doubles Plus 2 Facts: (double in-between or 2-apart facts) 5 + 3, 50 + 30, 500 + 300, 5000 + 3000 h) Make 10 Facts: 9 + 6, 90 + 60, 900 + 600; 8 + 4, 80 + 40, 800 + 400 I) Make 10 Extended: (with a 7) 7+ 4, 70 + 40, 700 + 400, 7000 + 4000
• Up Through 10: This strategy involves counting the difference between the two numbers by starting with the smaller number, keeping track of the distance to ten, and then adding this amount to the rest of the distance to the greater number. Examples a) For 12 – 7, think, “Starting at 7, it’s 3 to get to 10 and then 2 more to get to 12, so that’s 5 altogether” b) For 16 – 9, think, “It’s 1 from 9 to get to 10, and then 6 more to 16, so that’s 7 altogether”
• Back Down Through 10: With this strategy, you start with the larger number and subtract part of the subtrahend to get to 10, and then subtract the rest of the subtrahend. Examples a) For 15 – 8, think,“15 subtract 5 (one part of the 8) gets me to 10, and then 3 more (the rest of the 8) takes me to 7.” b) For 13 – 4, think, “13 subtract 3 is 10, and then 1 more takes me to 9”
Make 10s, 100s, or 1000s (Extension)
Make Ten is a thinking strategy introduced in grade 2 for addition facts which have an 8 or a 9 as one of the addends. It involves taking part of the other number and adding it to the 8 or 9 to make a 10 and then adding on the rest. For example: For 8 + 6, you take 2 from the 6 and give it to the 8 to make 10 + 4. Students should understand that the purpose of this strategy is to get a 10 which is easy to add. A common error occurs when students forget that the other addend has changed as well. This strategy should be compared to the compensation strategy. As well, the “make 10” strategy can be extended to facts involving 7. For 7 + 4, think: 7 and 3 (from the 4) is 10, and 10 + 1 (the other part of the 4 ) is 11. In Grade 3, students would have applied this same strategy to sums involving single-digit numbers added to 2-digit numbers as a “make 10s” strategy. In Grade 4, this strategy should be extended to “make 100s” and “make 1000s.” Examples For 58 + 6, think, “58 plus 2 (from the 6) is 60, and 60 plus 4 (the other part of 6)
Mental Computation – Subtraction •
Using Subtraction Facts for 10s, 100s, and 1000s (New) This strategy involves the subtraction of two numbers in the tens, hundreds, or thousands as if they were single-digit subtraction facts, and then applying the place value to the answer. Examples For 80 – 30, think,“8 tens subtract 3 tens is 5 tens, or 50.” For 500 – 200, think, “5 hundreds subtract 2 hundreds is 3 hundreds, or 300.” For 9000 – 4000, think, “9 thousands subtract 4 thousands is 5 thousands, or 5000.”