Transcript Document
Warm up problem: What is wrong with saying 372 base 6? What is a better way of writing this number in base 6? Exploring Addition Addition in Alphabitia Exploration 3.1, Part 1 Use manipulatives to help you Homework for Wednesday • Read Section 3.1 in the textbook • Exercises pp. 150-151: 5, 6, 24 Important announcements • First exam: Wednesday, September 19th 1.2, 1.3, 1.4, 1.7; 2.3; 3.1, 3.2 and Explorations • Last day to drop without a W is 9/14 • Pick up 302A packet at the bookstore-need by Monday, September 17th Mental addition • • • • • • 39 + 57 Leading digit (30 + 50) + (9 + 7) Compensation (40 - 1) + 57 Compensation (40 + 57) - 1 Break and Bridge (39 + 50) + 7 Compatible Numbers (39 + 51) + 6 Ways to represent addition: • 1. Counters • 2. Number Line 0 • 3. Part-Part Whole 2 4 6 a c 8 10 b Vocabulary of addition • • • • A+B=C A and B are called Addends C is called the Sum Since A + B = B + A every time, we give it a special name: commutative property. • Since A + (B + C) = (A + B) + C every time, we give it a special name: associative property. Addition and Place Value • If we have 154 + 69 Mental Arithmetic • • • • • • 39 + 57 Leading digit (30 + 50) + (9 + 7) Compensation (40 - 1) + 57 Compensation (40 + 57) - 1 Break and Bridge (39 + 50) + 7 Compatible Numbers (39 + 51) + 6 No pencils! • 23 + 96 • 489 + 723 Estimation • Get a QUICK answer that is close but not exact! 5 seconds to get a quick estimate • 382 - 147 Estimation methods • • • • • • • • 382 - 147 Actual answer: 235 Ways to estimate: 380 - 150 = 230 400 - 150 - 20 = 230 375 - 150 = 225 385 - 145 = 240 390 - 140 = 250 You try some • 45 + 87 • 391 + 1472 Estimation vs. Exact Answer • Are the exact values of the addends given? • Is the exact value of the sum required? • In general: changing values (like population), measurement values (like distance), and predictions (like 35% chance of rain) are estimates Rounding • When you estimate, you are rounding to the nearest ten, hundred, million, etc. • If you round up, you are making an overestimation. • If you round down, you are making an underestimation. A problem: • I am thinking of 3 numbers whose sum is greater than 70. • Look at each statement below. Mark it as true or false. Be ready to explain why. • All three numbers are greater than 20. • If two of the number are less than 20, the other must be greater than 20. Explain the math • 348 + 472 10 11 7__ • 820 Explain the math • 471 + 299 10 160 600 • 770 • How is this different from the previous problem? Explain why the child made the mistake • 341 + 287 is the same as 340 + 290 + 7 + 3 • 749 + 684 is the same as 700 + 600 + 49 + 1 + 84 + 16 • 322 + 468 is the same as 320 + 460 • Would the mistake have been made if manipulatives had been used? Explain. Subtraction • Take-away • Comparison Subtraction vocabulary • 89 Minuend - 24 Subtrahend 65 Difference Strategies • Break the number apart • Using negative numbers • Adding up The Standard Algorithm