1. Week 4 Shopping: 1.You have a strict budget when you are shopping for groceries. If you know that you can’t spend more than $20, how do you keep track of “how much is in your cart” so that you don’t have to put anything back? 2.You need to spend at least $10 to get a discount on school supplies. How do you keep track of how much you’ve spent in order to get the discount?

3. Agenda Don’t forget to initial attendance sheet! Homework “key”: a = answer with work, j = justify, s = strategy, e = extend your thinking Homework comment Estimation and Rounding Subtraction

4. #6, 10 Section 3.1 in textbook Ask yourself… “Were students applying correct “rules” incorrectly or do they not seem to be using the algorithm at all?” Are the students not understanding place value or not understanding the algorithm? Is it something else? “Would students have made any of these mistakes if they were using base 10 blocks?”

5. Ask yourself… “If students thought of each number as more than a collection of digits, (e.g., 56 is 5 tens and 6 ones) would these mistakes be made?” “Do my explanations focus on rules or on the reason why, mathematically, these errors do not produce the correct answer?”

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

7. 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.

8. You will have 10 seconds 382 - 147

9. Estimation 382 - 147 Actual answer: 235 Ways to estimate: 380 - 150 = 230 400 - 150 - 20 = 230 375 - 150 = 225 385 - 145 = 240 390 - 140 = 250

10. You try: 45 + 87 391 + 1472

11. 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

12. 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.

13. Subtraction Vocabulary: A – B = C A is the minuend B is the subtrahend C is the difference

14. Try this: Is A - B = B - A? 6 - 4 = 4 - 6? What is true of 6 - 4 and 4 - 6? One of the worst things we can do is lie to kids: “You can’t take a bigger number away from a smaller number.” Or “You have to put the bigger number first (in the minuend).”

15. How do we illustrate 4-6?

16. Pictorial Models Take away Judy has 7 crosses and gives 2 to Jake. How many does Judy have left?

17. Pictorial Models Comparison Amy has 7 crosses and Andy has 2. How many more crosses than Andy does Amy have?

18. Homework Due Friday: Read Section 3.2 Due Wednesday: Section 3.2 p. 166-168 #1abc, 4, 7cdf, 20, 28ac