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Exploring Addition

This warm-up problem explores the use of base 6 numbers and mental addition concepts. Practice addition strategies, mental arithmetic, estimation, and rounding techniques. Learn through manipulatives and word problems to enhance mathematical skills.

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Exploring Addition

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  1. Warm up problem: What is wrong with saying 372 base 6? What is a better way of writing this number in base 6?

  2. Exploring Addition Addition in Alphabitia Exploration 3.1, Part 1 Use manipulatives to help you

  3. Homework for Wednesday • Read Section 3.1 in the textbook • Exercises pp. 150-151: 5, 6, 24

  4. Important announcements • First exam: Wednesday, September 19th1.2, 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

  5. 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

  6. 0 2 4 6 8 10 a b c Ways to represent addition: • 1. Counters • 2. Number Line • 3. Part-Part Whole

  7. 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.

  8. Addition and Place Value • If we have 154 + 69

  9. 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

  10. No pencils! • 23 + 96 • 489 + 723

  11. Estimation • Get a QUICK answer that is close but not exact!

  12. 5 seconds to get a quick estimate • 382 - 147

  13. 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

  14. You try some • 45 + 87 • 391 + 1472

  15. 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

  16. 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.

  17. 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.

  18. Explain the math • 348+ 472 10 117__ • 820

  19. Explain the math • 471+ 299 10 160 600 • 770 • How is this different from the previous problem?

  20. 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.

  21. Subtraction • Take-away • Comparison

  22. Subtraction vocabulary • 89 Minuend - 24 Subtrahend 65 Difference

  23. Strategies • Break the number apart • Using negative numbers • Adding up

  24. The Standard Algorithm

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